CN103675005A - Soft industrial melt index measurement instrument and method for optimal fuzzy network - Google Patents

Abstract

Translated fromChinese

本发明公开了一种最优模糊网络的工业熔融指数软测量仪表及方法。该方法通过引入支持向量机对原有的模糊神经网络进行优化，解决了模糊神经网络构建过程中参数难设定的问题。在本发明中，现场智能仪表、控制站与DCS数据库连接，软测量值显示仪包括最优模糊网络的工业熔融指数软测量模型，DCS数据库与软测量模型的输入端连接，所述最优模糊网络的工业熔融指数软测量模型的输出端与熔融指数软测量值显示仪连接。最后，本发明具有在线测量、计算速度快、抗噪声能力强、推广性能好的特点。

The invention discloses an optimal fuzzy network industrial melting index soft measuring instrument and method. This method optimizes the original fuzzy neural network by introducing support vector machine, and solves the problem of difficult parameter setting in the process of fuzzy neural network construction. In the present invention, the on-site intelligent instrument, the control station are connected with the DCS database, the soft measurement value display instrument includes the industrial melt index soft measurement model of the optimal fuzzy network, the DCS database is connected with the input end of the soft measurement model, and the optimal fuzzy The output end of the industrial melt index soft sensor model of the network is connected with the melt index soft sensor value display instrument. Finally, the present invention has the characteristics of on-line measurement, fast calculation speed, strong anti-noise ability and good generalization performance.

Description

Translated fromChinese

最优模糊网络的工业熔融指数软测量仪表及方法Industrial melt index soft sensor instrument and method based on optimal fuzzy network

技术领域technical field

本发明涉及软测量仪表及方法，尤其涉及一种最优模糊网络的工业熔融指数软测量仪表及方法。 The invention relates to a soft measuring instrument and a method, in particular to an industrial melting index soft measuring instrument and a method of an optimal fuzzy network. the

背景技术Background technique

聚丙烯是一种由丙烯聚合而成的半结晶的热塑性塑料，具有较高的耐冲击性，机械性质强韧，抗多种有机溶剂和酸碱腐蚀，在工业界有广泛的应用，是平常最常见的高分子材料之一。熔融指数（MI）是聚丙烯生产中确定最终产品牌号的重要质量指标之一，它决定了产品的不同用途。熔融指数的精确、及时的测量，对生产和科研，都有非常重要的作用和指导意义。然而，熔融指数的在线分析测量目前仍然很难做到，缺乏熔融指数的在线分析仪是制约聚丙烯产品质量的一个主要问题。MI只能通过人工取样、离线化验分析获得，而且一般每2-4小时分析一次，时间滞后大，难以满足生产实时控制的要求。 Polypropylene is a semi-crystalline thermoplastic polymerized from propylene. It has high impact resistance, strong mechanical properties, and resistance to various organic solvents and acid and alkali corrosion. It is widely used in the industry and is common. One of the most common polymer materials. Melt index (MI) is one of the important quality indicators to determine the grade of the final product in the production of polypropylene, which determines the different uses of the product. Accurate and timely measurement of melt index plays a very important and guiding role in production and scientific research. However, the on-line analysis and measurement of melt index is still difficult to achieve, and the lack of on-line analyzer for melt index is a major problem restricting the quality of polypropylene products. MI can only be obtained through manual sampling and off-line assay analysis, and is generally analyzed every 2-4 hours, with a large time lag and difficult to meet the requirements of real-time production control. the

近年来关于MI的在线预报的研究工作大部分都集中在人工神经网络上面，取得了不错的效果。但是人工神经网络也有其自身的缺点，例如过拟合、隐含层的节点数目和参数不好确定。其次，工业现场采集到的DCS数据也因为噪音、人工操作误差等带有一定的不确定误差，所以使用确定性强的人工神经网络的预报模型一般推广能力不强。 In recent years, most of the research work on MI online forecasting has been concentrated on the artificial neural network, and good results have been achieved. But the artificial neural network also has its own shortcomings, such as overfitting, the number of nodes and parameters of the hidden layer are not easy to determine. Secondly, the DCS data collected at the industrial site also has certain uncertain errors due to noise, manual operation errors, etc., so the prediction model using a highly deterministic artificial neural network is generally not strong in generalization. the

1965年美国数学家L.Zadeh首先提出了Fuzzy集合的概念。随后模糊逻辑以其更接近于日常人们的问题和语意陈述的方式，开始代替坚持所有事物都可以用二元项表示的经典逻辑。1987年，Bart Kosko率先将模糊理论与神经网络有机结合进行了较为系统的研究。在这之后的时间里，模糊神经网络的理论及其应用获得了飞速的发展，各种新的模糊神经网络模型的提出及其相适应的学习算法的研究不仅加速了模糊神经理论的完善，而且在实践中也得到了非常广泛的应用。 In 1965, American mathematician L. Zadeh first proposed the concept of fuzzy set. Fuzzy logic then began to replace classical logic, which insisted that everything can be represented by binary terms, in the way that it was closer to everyday people's problems and semantic statements. In 1987, Bart Kosko took the lead in organically combining fuzzy theory with neural networks for a more systematic research. In the following time, the theory of fuzzy neural network and its application have been developed rapidly. The introduction of various new fuzzy neural network models and the study of their corresponding learning algorithms not only accelerated the perfection of fuzzy neural network theory, but also It has also been widely used in practice. the

支持向量机，由Vapnik在1998年引入，通过使用统计理论学习中结构风险最小化而非一般的经验结构最小化方法，把原有的最优分类面问题转化为其对偶的优化问题，因而具有良好的推广能力，被广泛应用在模式识别、拟合和分类问题中。在本方案中，支持向量机被用来优化模糊神经网络模型中的线性参数。 Support vector machine, introduced by Vapnik in 1998, converts the original optimal classification surface problem into its dual optimization problem by using the structural risk minimization in statistical theory learning instead of the general empirical structure minimization method, so it has Good generalization ability, widely used in pattern recognition, fitting and classification problems. In this scheme, SVM is used to optimize the linear parameters in the fuzzy neural network model. the

发明内容Contents of the invention

为了克服已有的丙烯聚合生产过程的测量精度不高、对噪声敏感度低、推广性能差的不足，本发明提供一种在线测量、计算速度快、模型自动更新、抗噪声能力强、推广性能好的 最优模糊网络的工业熔融指数软测量仪表及方法。 In order to overcome the shortcomings of the existing propylene polymerization production process, such as low measurement accuracy, low sensitivity to noise, and poor generalization performance, the present invention provides an online measurement, fast calculation speed, automatic model update, strong anti-noise ability, and good generalization performance. Good Optimal Fuzzy Network Industrial Melt Index Soft Sensing Instrument and Method. the

一种最优模糊网络的工业熔融指数软测量仪表，包括丙烯聚合生产过程、用于测量易测变量的现场智能仪表、用于测量操作变量的控制站、存放数据的DCS数据库以及熔融指数软测量值显示仪，所述现场智能仪表、控制站与丙烯聚合生产过程连接，所述现场智能仪表、控制站与DCS数据库连接，所述软测量仪表还包括最优模糊网络的工业熔融指数软测量模型，所述DCS数据库与所述最优模糊网络的工业熔融指数软测量模型的输入端连接，所述最优模糊网络的工业熔融指数软测量模型的输出端与熔融指数软测量值显示仪连接，所述最优模糊网络的工业熔融指数软测量模型包括： An industrial melt index soft measurement instrument with optimal fuzzy network, including propylene polymerization production process, on-site intelligent instrument for measuring easily measurable variables, control station for measuring operating variables, DCS database for storing data, and melt index soft measurement Value display instrument, the on-site intelligent instrument, the control station are connected with the propylene polymerization production process, the on-site intelligent instrument, the control station are connected with the DCS database, and the soft sensor instrument also includes the industrial melt index soft sensor model of the optimal fuzzy network , the DCS database is connected to the input end of the industrial melt index soft sensor model of the optimal fuzzy network, and the output end of the industrial melt index soft sensor model of the optimal fuzzy network is connected to the melt index soft sensor value display instrument, The industrial melting index soft sensor model of described optimal fuzzy network comprises:

数据预处理模块，用于将从DCS数据库输入的模型训练样本进行预处理，使得训练样本的均值为0，方差为1，该处理采用以下算式过程来完成： The data preprocessing module is used to preprocess the model training samples input from the DCS database, so that the mean value of the training samples is 0 and the variance is 1. This processing is completed by the following calculation process:

计算均值：$\stackrel{\‾}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{TX}}_i---\left(1\right)$Calculate the mean:$\stackrel{\‾}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{TX}}_i---\left(1\right)$

计算方差：${\mathrm{\σ}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}({\mathrm{TX}}_i-\stackrel{\‾}{\mathrm{TX}})---\left(2\right)$Calculate the variance:${\mathrm{\σ}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}({\mathrm{TX}}_i-\stackrel{\‾}{\mathrm{TX}})---\left(2\right)$

标准化：$X=\frac{\mathrm{TX}-\stackrel{\‾}{\mathrm{TX}}}{{\mathrm{\σ}}_x}---\left(3\right)$standardization:$x=\frac{\mathrm{TX}-\stackrel{\‾}{\mathrm{TX}}}{{\mathrm{\σ}}_x}---\left(3\right)$

其中，TX_i为第i个训练样本，N为训练样本数，

为训练样本的均值，X为标准化后的训练样本。σ_x表示训练样本的标准差，σ²_x表示训练样本的方差。 Among them, TX_i is the i-th training sample, N is the number of training samples,

is the mean of the training samples, and X is the standardized training samples. σ_x represents the standard deviation of the training samples, and σ²_x represents the variance of the training samples.

模糊神经网络模块，对从数据预处理模块传过来的输入变量，进行模糊推理和建立模糊规则。对从数据预处理模块传过来的经过预处理过的训练样本X进行模糊分类，得到模糊规则库中每个模糊聚类的中心和宽度。设第p个标准化后的训练样本X_p=[X_p1,…,X_pn]，其中n是输入变量的个数。 The fuzzy neural network module performs fuzzy reasoning and establishes fuzzy rules for the input variables passed from the data preprocessing module. Perform fuzzy classification on the preprocessed training sample X passed from the data preprocessing module, and obtain the center and width of each fuzzy cluster in the fuzzy rule base. Let the p-th normalized training sample X_p =[X_p1 ,…,X_pn ], where n is the number of input variables.

设模糊神经网络有R个模糊规则，为了求得每个模糊规则对于训练样本X_p的每个输入变量X_pj,j=1,…,n，下面的模糊化方程将求出其对第i个模糊规则的隶属度： Assuming that the fuzzy neural network has R fuzzy rules, in order to obtain each fuzzy rule for each input variable X_pj , j=1,...,n of the training sample X_p , the following fuzzy equation will find its i-th The degree of membership of a fuzzy rule:

${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

其中m_ij和σ_ij分别表示第i个模糊规则的第j个高斯成员函数的中心和宽度，由模糊聚类求得。 Among them, m_ij and σ_ij represent the center and width of the jth Gaussian membership function of the i-th fuzzy rule respectively, which are obtained by fuzzy clustering.

设标准化后的训练样本X_p对模糊规则i的适应度为μ⁽ⁱ⁾(X_p)，则μ⁽ⁱ⁾(X_p)的大小可由下 式决定： Suppose the fitness of the standardized training sample X_p to the fuzzy rule i is μ⁽ⁱ⁾ (X_p ), then the size of μ⁽ⁱ⁾ (X_p ) can be determined by the following formula:

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Pi;</span>\&Pi;</span>}}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

求得输入训练样本对于每个规则的适应度之后，模糊神经网络对模糊规则输出进行推导以得到最后的解析解。在常用的模糊神经网络结构中，每个模糊规则推导的过程都可以表示为如下：首先求得训练样本中所有输入变量的线性乘积和，然后用此线性乘积和与规则的适用度μ⁽ⁱ⁾(X_p)相乘，得到最终的每条模糊规则的输出。模糊规则i的推导输出可以表示如下： After obtaining the fitness of the input training samples for each rule, the fuzzy neural network deduces the output of the fuzzy rules to obtain the final analytical solution. In the commonly used fuzzy neural network structure, the derivation process of each fuzzy rule can be expressed as follows: first obtain the linear product sum of all input variables in the training sample, and then use this linear product sum and the rule’s applicability μ^{(i )} (X_p ) to get the final output of each fuzzy rule. The derivation output of fuzzy rule i can be expressed as follows:

${\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

${\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>7</span>7</span>}<span><span>)</span>)</span>$

式中，f⁽ⁱ⁾为第i条模糊规则的输出，

是模糊神经网络模型对第p个训练样本的预测输出，a_ij,j=1,…,n是第i条模糊规则中第j个变量的线性系数，a_i0是第i条模糊规则中输入变量线性乘积和的常数项，b是输出偏置量。 In the formula, f⁽ⁱ⁾ is the output of the i-th fuzzy rule,

is the predicted output of the fuzzy neural network model for the p-th training sample, a_ij ,j=1,...,n is the linear coefficient of the j-th variable in the i-th fuzzy rule, and a_i0 is the input in the i-th fuzzy rule The constant term of the variable linear product sum, b is the output bias.

支持向量机优化模块，在式（7）中，输入变量线性乘积和中的参数的确定是模糊神经网络使用中用到的一个主要问题，这里我们采用把原有的模糊规则推导输出形式转换为支持向量机优化问题，再使用支持向量机进行线性优化，转换过程如下： Support vector machine optimization module, in formula (7), the determination of the parameters in the linear product sum of input variables is a main problem used in the use of fuzzy neural network, here we use the original fuzzy rule to derive the output form into Support vector machine optimization problem, and then use support vector machine for linear optimization, the conversion process is as follows:

$\begin{array}{c}{\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

其中X_p0为常数项且恒等于1。令 Among them, X_p0 is a constant term and is always equal to 1. make

其中，

表示原训练样本的转化形式，即把原来的训练样本转换为如上式形式，作为支持向量机的训练样本： in,

Indicates the transformation form of the original training sample, that is, convert the original training sample into the above formula, and use it as the training sample of the support vector machine:

其中y₁,…,y_N是训练样本的目标输出，取S作为新的输入训练样本集合，那么原有问题可以转化为如下的支持向量机对偶优化问题： Among them, y₁ ,...,y_N are the target output of the training samples, and S is taken as the new input training sample set, then the original problem can be transformed into the following support vector machine dual optimization problem:

$\mathrm{<span><span>R</span>R</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>,</span>,</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>,</span>,</span>\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>)</span>)</span><span><span>+</span>+</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

其中y_p是输入训练样本X_p的目标输出，ω是支持向量机超平面的法向量，f(X_p)是对应于X_p的模型输出，γ是支持向量机的惩罚因子，R(ω,b)是优化问题的目标函数，N是训练样本数，L_ε(y_p,f(X_p))表达式如下： where y_p is the target output of the input training sample X_p , ω is the normal vector of the support vector machine hyperplane, f(X_p ) is the model output corresponding to X_p , γ is the penalty factor of the support vector machine, R(ω ,b) is the objective function of the optimization problem, N is the number of training samples, and the expression of L_ε (y_p ,f(X_p )) is as follows:

其中ε是优化问题的误差容限，接下来使用支持向量机求得模糊神经网络的模糊规则最优推导线性参数和对偶优化问题的预报输出： Where ε is the error tolerance of the optimization problem, and then use the support vector machine to obtain the fuzzy rules of the fuzzy neural network to optimally derive the linear parameters and the forecast output of the dual optimization problem:

${\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>\&Element;</span>\&Element;</span>\mathrm{<span><span>SV</span>SV</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>R</span>R</span>}<span><span>;</span>;</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

其中α_k，

分别是y_p-f(X_p)大于0和小于0时对应的拉格朗日乘子,

即为对应于第p个标准化后的训练样本X_p的MI预报值。 where α_k ,

are the corresponding Lagrangian multipliers when y_p -f(X_p ) is greater than 0 and less than 0,

That is, the predicted value of MI corresponding to the pth normalized training sample X_p .

作为优选的一种方案，所述最优模糊网络的工业熔融指数软测量模型还包括：模型更新模块，用于模型的在线更新，定期将离线化验数据输入到训练集中，更新模糊神经网络模型。 As a preferred solution, the industrial melt index soft sensor model of the optimal fuzzy network further includes: a model updating module, which is used for online updating of the model, regularly inputs offline test data into the training set, and updates the fuzzy neural network model. the

一种最优模糊网络的工业熔融指数软测量方法，所述软测量方法具体实现步骤如下： An industrial melting index soft sensor method of an optimal fuzzy network, the specific implementation steps of the soft sensor method are as follows:

1）、对丙烯聚合生产过程对象，根据工艺分析和操作分析，选择操作变量和易测变量作为模型的输入，操作变量和易测变量由DCS数据库获得； 1) For the propylene polymerization production process object, according to the process analysis and operation analysis, the operational variables and easily measurable variables are selected as the input of the model, and the operational variables and easily measurable variables are obtained from the DCS database;

2）、用于将从DCS数据库输入的模型训练样本进行预处理，使得训练样本的均值为0，方差为1，该处理采用以下算式过程来完成： 2) It is used to preprocess the model training samples input from the DCS database, so that the mean value of the training samples is 0 and the variance is 1. This processing is completed by the following calculation process:

计算均值：$\stackrel{\&OverBar;}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{TX}}_i---\left(1\right)$Calculate the mean:$\stackrel{\&OverBar;}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{TX}}_i---\left(1\right)$

计算方差：${\mathrm{\&sigma;}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{TX}}_i-\stackrel{\&OverBar;}{\mathrm{TX}})---\left(2\right)$Calculate the variance:${\mathrm{\&sigma;}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{TX}}_i-\stackrel{\&OverBar;}{\mathrm{TX}})---\left(2\right)$

标准化：$X=\frac{\mathrm{TX}-\stackrel{\&OverBar;}{\mathrm{TX}}}{{\mathrm{\&sigma;}}_x}---\left(3\right)$standardization:$x=\frac{\mathrm{TX}-\stackrel{\&OverBar;}{\mathrm{TX}}}{{\mathrm{\&sigma;}}_x}---\left(3\right)$

其中，TX_i为第i个训练样本，N为训练样本数，

为训练样本的均值，X为标准化后的训练样本。σ_x表示训练样本的标准差，σ²_x表示训练样本的方差。 Among them, TX_i is the i-th training sample, N is the number of training samples,

is the mean of the training samples, and X is the standardized training samples. σ_x represents the standard deviation of the training samples, and σ²_x represents the variance of the training samples.

3）、对从数据预处理模块传过来的输入变量，进行模糊推理和建立模糊规则。对从数据预处理模块传过来的经过预处理过的训练样本X进行模糊分类，得到模糊规则库中每个模糊聚类的中心和宽度。设第p个标准化后的训练样本X_p=[X_p1,…,X_pn]，其中n是输入变量的个数。 3) Carry out fuzzy reasoning and establish fuzzy rules for the input variables passed from the data preprocessing module. Perform fuzzy classification on the preprocessed training sample X passed from the data preprocessing module, and obtain the center and width of each fuzzy cluster in the fuzzy rule base. Let the p-th normalized training sample X_p =[X_p1 ,…,X_pn ], where n is the number of input variables.

设模糊神经网络有R个模糊规则，为了求得每个模糊规则对于训练样本X_p的每个输入变量X_pj,j=1,…,n，下面的模糊化方程将求出其对第i个模糊规则的隶属度： Assuming that the fuzzy neural network has R fuzzy rules, in order to obtain each fuzzy rule for each input variable X_pj , j=1,...,n of the training sample X_p , the following fuzzy equation will find its i-th The degree of membership of a fuzzy rule:

${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

其中m_ij和σ_ij分别表示第i个模糊规则的第j个高斯成员函数的中心和宽度，由模糊聚类求得。 Among them, m_ij and σ_ij represent the center and width of the jth Gaussian membership function of the i-th fuzzy rule respectively, which are obtained by fuzzy clustering.

设标准化后的训练样本X_p对模糊规则i的适应度为μ⁽ⁱ⁾(X_p)，则μ⁽ⁱ⁾(X_p)的大小可由下式决定： Suppose the fitness of the standardized training sample X_p to the fuzzy rule i is μ⁽ⁱ⁾ (X_p ), then the size of μ⁽ⁱ⁾ (X_p ) can be determined by the following formula:

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Pi;</span>\&Pi;</span>}}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

求得输入训练样本对于每个规则的适应度之后，模糊神经网络对模糊规则输出进行推导以得到最后的解析解。在常用的模糊神经网络结构中，每个模糊规则推导的过程都可以表示为如下：首先求得训练样本中所有输入变量的线性乘积和，然后用此线性乘积和与规则的适用度μⁱ(X_p)相乘，得到最终的每条模糊规则的输出。模糊规则i的推导输出可以表示如下： After obtaining the fitness of the input training samples for each rule, the fuzzy neural network deduces the output of the fuzzy rules to obtain the final analytical solution. In the commonly used fuzzy neural network structure, the derivation process of each fuzzy rule can be expressed as follows: first obtain the linear product sum of all input variables in the training sample, and then use this linear product sum and the rule applicability μⁱ ( X_p ) to get the final output of each fuzzy rule. The derivation output of fuzzy rule i can be expressed as follows:

${\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

${\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>7</span>7</span>}<span><span>)</span>)</span>$

式中，f⁽ⁱ⁾为第i条模糊规则的输出，

是模糊神经网络模型对第p个训练样本的预测输出，a_ij,j=1,…,n是第i条模糊规则中第j个变量的线性系数，a_i0是第i条模糊规则中输入变量线 性乘积和的常数项，b是输出偏置量。 In the formula, f⁽ⁱ⁾ is the output of the i-th fuzzy rule,

is the predicted output of the fuzzy neural network model for the p-th training sample, a_ij ,j=1,...,n is the linear coefficient of the j-th variable in the i-th fuzzy rule, and a_i0 is the input in the i-th fuzzy rule The constant term of the variable linear product sum, b is the output bias.

4）、在式（7）中，输入变量线性乘积和中的参数的确定是模糊神经网络使用中用到的一个主要问题，这里我们采用把原有的模糊规则推导输出形式转换为支持向量机优化问题，再使用支持向量机进行线性优化，转换过程如下： 4) In formula (7), the determination of the parameters in the linear product sum of input variables is a major problem used in the use of fuzzy neural networks. Here we adopt the method of converting the original fuzzy rule derivation output form into a support vector machine Optimization problem, and then use the support vector machine for linear optimization, the conversion process is as follows:

$\begin{array}{c}{\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

其中X_p0为常数项且恒等于1。令 Among them, X_p0 is a constant term and is always equal to 1. make

其中，

表示原训练样本的转化形式，即把原来的训练样本转换为如上式形式，作为支持向量机的训练样本： in,

Indicates the transformation form of the original training sample, that is, convert the original training sample into the above formula, and use it as the training sample of the support vector machine:

其中y₁,…,y_N是训练样本的目标输出，取S作为新的输入训练样本集合，那么原有问题可以转化为如下的支持向量机对偶优化问题： Among them, y₁ ,...,y_N are the target output of the training samples, and S is taken as the new input training sample set, then the original problem can be transformed into the following support vector machine dual optimization problem:

$\mathrm{<span><span>R</span>R</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>,</span>,</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>,</span>,</span>\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>)</span>)</span><span><span>+</span>+</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

其中y_p是输入训练样本X_p的目标输出，ω是支持向量机超平面的法向量，f(X_p)是对应于X_p的模型输出，γ是支持向量机的惩罚因子，R(ω,b)是优化问题的目标函数，N是训练样本数，L_ε(y_p,f(X_p))表达式如下： where y_p is the target output of the input training sample X_p , ω is the normal vector of the support vector machine hyperplane, f(X_p ) is the model output corresponding to X_p , γ is the penalty factor of the support vector machine, R(ω ,b) is the objective function of the optimization problem, N is the number of training samples, and the expression of L_ε (y_p ,f(X_p )) is as follows:

其中ε是优化问题的误差容限，接下来使用支持向量机求得模糊神经网络的模糊规则最优推导线性参数和对偶优化问题的预报输出： Where ε is the error tolerance of the optimization problem, and then use the support vector machine to obtain the fuzzy rules of the fuzzy neural network to optimally derive the linear parameters and the forecast output of the dual optimization problem:

${\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>\&Element;</span>\&Element;</span>\mathrm{<span><span>SV</span>SV</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>R</span>R</span>}<span><span>;</span>;</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

其中α_k，

分别是y_p-f(X_p)大于0和小于0时对应的拉格朗日乘子,

即为对应于第p个标准化后的训练样本X_p的MI预报值。 where α_k ,

are the corresponding Lagrangian multipliers when y_p -f(X_p ) is greater than 0 and less than 0,

That is, the predicted value of MI corresponding to the pth normalized training sample X_p .

作为优选的一种方案：所述软测量方法还包括以下步骤：5）、定期将离线化验数据输入到训练样本集中，更新模糊神经网络模型。 As a preferred solution: the soft sensor method further includes the following steps: 5) Regularly input offline test data into the training sample set, and update the fuzzy neural network model. the

本发明的技术构思为：对丙烯聚合生产过程的重要质量指标熔融指数进行在线软测量，克服已有的聚丙稀熔融指数测量仪表测量精度不高、容噪能力差、模型参数设定难度大的不足，引入支持向量机对模糊神经网络模型进行自动优化。此模型相对于已有的熔融指数软测量模型有以下优点：（1）减小了噪声和人工操作误差对模型预报精度的影响；（2）增强了模型的推广性能，对已有模型的过拟合现象进行有效的抑制；（3）提高了模型的稳定性，降低了模型过发生过拟合的可能性。 The technical concept of the present invention is to conduct online soft measurement of the melt index, an important quality index in the production process of propylene polymerization, to overcome the problems of low measurement accuracy, poor noise tolerance and difficult model parameter setting of existing polypropylene melt index measuring instruments Insufficient, the introduction of support vector machine to automatically optimize the fuzzy neural network model. Compared with the existing melt index soft sensor model, this model has the following advantages: (1) It reduces the impact of noise and manual operation errors on the model prediction accuracy; (3) The stability of the model is improved, and the possibility of over-fitting of the model is reduced. the

本发明的有益效果主要表现在：1、在线测量；2、模型自动更新；3、抗噪声干扰能力强、4、精度高；5、推广能力强。 The beneficial effects of the present invention are mainly manifested in: 1. online measurement; 2. automatic update of the model; 3. strong anti-noise interference ability; 4. high precision; 5. strong popularization ability. the

附图说明Description of drawings

图1是最优模糊网络的工业熔融指数软测量仪表及方法的基本结构示意图； Fig. 1 is the basic structure schematic diagram of the industrial melting index soft measuring instrument and method of optimal fuzzy network;

图2是最优模糊网络的工业熔融指数软测量模型结构示意图。 Figure 2 is a schematic diagram of the structure of the industrial melt index soft sensor model of the optimal fuzzy network. the

具体实施方式Detailed ways

下面结合附图对本发明作进一步描述。本发明实施例用来解释说明本发明，而不是对本发明进行限制，在本发明的精神和权利要求的保护范围内，对本发明作出的任何修改和改变，都落入本发明的保护范围。 The present invention will be further described below in conjunction with the accompanying drawings. The embodiments of the present invention are used to explain the present invention, rather than to limit the present invention. Within the spirit of the present invention and the protection scope of the claims, any modification and change made to the present invention will fall into the protection scope of the present invention. the

实施例1 Example 1

参照图1、图2，一种基于支持向量机优化模糊神经网络的丙烯聚合生产过程软测量仪表，包括丙烯聚合生产过程1、用于测量易测变量的现场智能仪表2、用于测量操作变量的控制站3、存放数据的DCS数据库4以及熔融指数软测量值显示仪6，所述现场智能仪表2、控制站3与丙烯聚合生产过程1连接，所述现场智能仪表2、控制站3与DCS数据库4连接，所述软测量仪表还包括支持向量机优化模糊神经网络的软测量模型5，所述DCS数据库4与所述最优模糊网络的工业熔融指数软测量模型5的输入端连接，所述最优模糊网络的工业熔融指数软测量模型5的输出端与熔融指数软测量值显示仪6连接，所述最优模糊网络的工业熔融指数软测量模型包括： Referring to Fig. 1 and Fig. 2, a soft measuring instrument for propylene polymerization production process based on support vector machine optimized fuzzy neural network, including propylene polymerization production process 1, on-site intelligent instrument 2 for measuring easy-to-measure variables, and for measuring operational variables The control station 3, the DCS database 4 for storing data, and the melt index soft measurement value display instrument 6, the on-site intelligent instrument 2, the control station 3 are connected to the propylene polymerization production process 1, the on-site intelligent instrument 2, the control station 3 and The DCS database 4 is connected, and the soft sensor instrument also includes the soft sensor model 5 of the support vector machine optimization fuzzy neural network, and the DCS database 4 is connected with the input end of the industrial melting index soft sensor model 5 of the optimal fuzzy network, The output end of the industrial melt index soft sensor model 5 of the optimal fuzzy network is connected with the melt index soft sensor value display instrument 6, and the industrial melt index soft sensor model of the optimal fuzzy network includes:

数据预处理模块：用于将从DCS数据库输入的模型训练样本进行预处理，使得训练样本的均值为0，方差为1，该处理采用以下算式过程来完成： Data preprocessing module: used to preprocess the model training samples input from the DCS database, so that the mean value of the training samples is 0, and the variance is 1. The processing is completed by the following calculation process:

计算均值：$\stackrel{\&OverBar;}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{TX}}_i---\left(1\right)$Calculate the mean:$\stackrel{\&OverBar;}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{TX}}_i---\left(1\right)$

计算方差：${\mathrm{\&sigma;}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{TX}}_i-\stackrel{\&OverBar;}{\mathrm{TX}})---\left(2\right)$Calculate the variance:${\mathrm{\&sigma;}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{TX}}_i-\stackrel{\&OverBar;}{\mathrm{TX}})---\left(2\right)$

标准化：$X=\frac{\mathrm{TX}-\stackrel{\&OverBar;}{\mathrm{TX}}}{{\mathrm{\&sigma;}}_x}---\left(3\right)$standardization:$x=\frac{\mathrm{TX}-\stackrel{\&OverBar;}{\mathrm{TX}}}{{\mathrm{\&sigma;}}_x}---\left(3\right)$

其中，TX_i为第i个训练样本，N为训练样本数，

为训练样本的均值，X为标准化后的训练样本。σ_x表示训练样本的标准差，σ²_x表示训练样本的方差。 Among them, TX_i is the i-th training sample, N is the number of training samples,

is the mean of the training samples, and X is the standardized training samples. σ_x represents the standard deviation of the training samples, and σ²_x represents the variance of the training samples.

模糊神经网络模块，对从数据预处理模块传过来的输入变量，进行模糊推理和建立模糊规则。对从数据预处理模块传过来的经过预处理过的训练样本X进行模糊分类，得到模糊规则库中每个模糊聚类的中心和宽度。设第p个标准化后的训练样本X_p=[X_p1,…,X_pn]，其中n是输入变量的个数。 The fuzzy neural network module performs fuzzy reasoning and establishes fuzzy rules for the input variables passed from the data preprocessing module. Perform fuzzy classification on the preprocessed training sample X passed from the data preprocessing module, and obtain the center and width of each fuzzy cluster in the fuzzy rule base. Let the p-th normalized training sample X_p =[X_p1 ,…,X_pn ], where n is the number of input variables.

设模糊神经网络有R个模糊规则，为了求得每个模糊规则对于训练样本X_p的每个输入变量X_pj,j=1,…,n，下面的模糊化方程将求出其对第i个模糊规则的隶属度： Assuming that the fuzzy neural network has R fuzzy rules, in order to obtain each fuzzy rule for each input variable X_pj , j=1,...,n of the training sample X_p , the following fuzzy equation will find its i-th The degree of membership of a fuzzy rule:

${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

其中m_ij和σ_ij分别表示第i个模糊规则的第j个高斯成员函数的中心和宽度，由模糊聚类求得。 Among them, m_ij and σ_ij represent the center and width of the jth Gaussian membership function of the i-th fuzzy rule respectively, which are obtained by fuzzy clustering.

设标准化后的训练样本X_p对模糊规则i的适应度为μ⁽ⁱ⁾(X_p)，则μ⁽ⁱ⁾(X_p)的大小可由下式决定： Suppose the fitness of the standardized training sample X_p to the fuzzy rule i is μ⁽ⁱ⁾ (X_p ), then the size of μ⁽ⁱ⁾ (X_p ) can be determined by the following formula:

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Pi;</span>\&Pi;</span>}}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

求得输入训练样本对于每个规则的适应度之后，模糊神经网络对模糊规则输出进行推导以得到最后的解析解。在常用的模糊神经网络结构中，每个模糊规则推导的过程都可以表示为如下：首先求得训练样本中所有输入变量的线性乘积和，然后用此线性乘积和与规则的适用度μ⁽ⁱ⁾(X_p)相乘，得到最终的每条模糊规则的输出。模糊规则i的推导输出可以表示如下： After obtaining the fitness of the input training samples for each rule, the fuzzy neural network deduces the output of the fuzzy rules to obtain the final analytical solution. In the commonly used fuzzy neural network structure, the derivation process of each fuzzy rule can be expressed as follows: first obtain the linear product sum of all input variables in the training sample, and then use this linear product sum and the rule’s applicability μ^{(i )} (X_p ) to get the final output of each fuzzy rule. The derivation output of fuzzy rule i can be expressed as follows:

${\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

${\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>7</span>7</span>}<span><span>)</span>)</span>$

式中，f⁽ⁱ⁾为第i条模糊规则的输出，是模糊神经网络模型对第p个训练样本的预测输出，a_ij,j=1,…,n是第i条模糊规则中第j个变量的线性系数，a_i0是第i条模糊规则中输入变量线性乘积和的常数项，b是输出偏置量。 In the formula, f⁽ⁱ⁾ is the output of the i-th fuzzy rule, is the predicted output of the fuzzy neural network model for the p-th training sample, a_ij ,j=1,...,n is the linear coefficient of the j-th variable in the i-th fuzzy rule, and a_i0 is the input in the i-th fuzzy rule The constant term of the variable linear product sum, b is the output bias.

支持向量机优化模块，在式（7）中，输入变量线性乘积和中的参数的确定是模糊神经网络使用中用到的一个主要问题，这里我们采用把原有的模糊规则推导输出形式转换为支持向量机优化问题，再使用支持向量机进行线性优化，转换过程如下： In the support vector machine optimization module, in formula (7), the determination of the parameters in the linear product sum of input variables is a main problem used in the use of fuzzy neural networks. Here we use the method of converting the original fuzzy rule derivation output form into Support vector machine optimization problem, and then use support vector machine for linear optimization, the conversion process is as follows:

$\begin{array}{c}{\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

其中X_p0为常数项且恒等于1。令 Among them, X_p0 is a constant term and is always equal to 1. make

其中，表示原训练样本的转化形式，即把原来的训练样本转换为如上式形式，作为支持向量机的训练样本： in, Indicates the transformation form of the original training sample, that is, convert the original training sample into the above formula, and use it as the training sample of the support vector machine:

其中y₁,…,y_N是训练样本的目标输出，取S作为新的输入训练样本集合，那么原有问题可以转化为如下的支持向量机对偶优化问题： Among them, y₁ ,...,y_N are the target output of the training samples, and S is taken as the new input training sample set, then the original problem can be transformed into the following support vector machine dual optimization problem:

$\mathrm{<span><span>R</span>R</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>,</span>,</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>,</span>,</span>\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>)</span>)</span><span><span>+</span>+</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

其中y_p是输入训练样本X_p的目标输出，ω是支持向量机超平面的法向量，f(X_p)是对应于X_p的模型输出，γ是支持向量机的惩罚因子，R(ω,b)是优化问题的目标函数，N是训练样本数，L_ε(y_p,f(X_p))表达式如下： where y_p is the target output of the input training sample X_p , ω is the normal vector of the support vector machine hyperplane, f(X_p ) is the model output corresponding to X_p , γ is the penalty factor of the support vector machine, R(ω ,b) is the objective function of the optimization problem, N is the number of training samples, and the expression of L_ε (y_p ,f(X_p )) is as follows:

其中ε是优化问题的误差容限，接下来使用支持向量机求得模糊神经网络的模糊规则最优推导线性参数和对偶优化问题的预报输出： Where ε is the error tolerance of the optimization problem, and then use the support vector machine to obtain the fuzzy rules of the fuzzy neural network to optimally derive the linear parameters and the forecast output of the dual optimization problem:

${\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>\&Element;</span>\&Element;</span>\mathrm{<span><span>SV</span>SV</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>R</span>R</span>}<span><span>;</span>;</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

其中α_k，

分别是y_p-f(X_p)大于0和小于0时对应的拉格朗日乘子,即为对应于第p个标准化后的训练样本X_p的MI预报值。 where α_k ,

are the corresponding Lagrangian multipliers when y_p -f(X_p ) is greater than 0 and less than 0, That is, the predicted value of MI corresponding to the pth normalized training sample X_p .

所述最优模糊网络的工业熔融指数软测量模型还包括：模型更新模块，用于模型的在线更新，定期将离线化验数据输入到训练集中，更新模糊神经网络模型。 The industrial melting index soft sensor model of the optimal fuzzy network also includes: a model update module, which is used for online update of the model, regularly inputs offline test data into the training set, and updates the fuzzy neural network model. the

根据反应机理以及流程工艺分析，考虑到聚丙烯生产过程中对熔融指数产生影响的各种因素，取实际生产过程中常用的九个操作变量和易测变量作为建模变量，有：三股丙稀进料流率，主催化剂流率，辅催化剂流率，釜内温度、压强、液位，釜内氢气体积浓度。表1列出了作为软测量模型5输入的9个建模变量，分别为釜内温度（T）、釜内压力（P）、釜内液位（L）、釜内氢气体积浓度（X_v）、3股丙烯进料流率（第一股丙稀进料流率f1，第二股丙稀进料流率f2，第三股丙稀进料流率f3）、2股催化剂进料流率(主催化剂流率f4，辅催化剂流率f5)。反应釜中的聚合反应是反应物料反复混合后参与反应的，因此模型输入变量涉及物料的过程变量采用前若干时刻的平均值。此例中数据采用前一小时的平均值。熔融指数离线化验值作为软测量模型5的输出变量。通过人工取样、离线化验分析获得，每4小时分析采集一次。 According to the analysis of reaction mechanism and process technology, taking into account various factors that affect the melt index in the production process of polypropylene, nine commonly used operating variables and easy-to-measure variables in the actual production process are used as modeling variables, including: three-strand propylene Feed flow rate, main catalyst flow rate, auxiliary catalyst flow rate, temperature, pressure, liquid level in the kettle, hydrogen volume concentration in the kettle. Table 1 lists the nine modeling variables used as the input of the soft sensor model 5, which are the temperature in the tank (T), the pressure in the tank (P), the liquid level in the tank (L), and the volume concentration of hydrogen in the tank (X_v ), 3 propylene feed flow rates (the first propylene feed flow rate f1, the second propylene feed flow rate f2, the third propylene feed flow rate f3), 2 catalyst feed streams Rate (main catalyst flow rate f4, auxiliary catalyst flow rate f5). In the polymerization reaction in the reactor, the reaction materials participate in the reaction after repeated mixing, so the model input variables related to the process variables of the materials adopt the average value of the previous several moments. In this example the data is averaged over the previous hour. The off-line test value of melt index is used as the output variable of the soft sensor model 5. It is obtained through manual sampling and offline assay analysis, and is analyzed and collected every 4 hours.

现场智能仪表2及控制站3与丙烯聚合生产过程1相连，与DCS数据库4相连；软测量模型5与DCS数据库及软测量值显示仪6相连。现场智能仪表2测量丙烯聚合生产对象的易测变量，将易测变量传输到DCS数据库4；控制站3控制丙烯聚合生产对象的操作变量，将操作变量传输到DCS数据库4。DCS数据库4中记录的变量数据作为基于粒子群算法优化加权最小二乘支持向量机模糊方程的软测量模型5的输入，软测量值显示仪6用于显示最优模糊网络的工业熔融指数软测量模型5的输出，即软测量值。 The on-site intelligent instrument 2 and the control station 3 are connected with the propylene polymerization production process 1 and with the DCS database 4; the soft measurement model 5 is connected with the DCS database and the soft measurement value display instrument 6. The on-site intelligent instrument 2 measures the easily measurable variables of the propylene polymerization production object, and transmits the easily measurable variables to the DCS database 4; the control station 3 controls the operational variables of the propylene polymerization production objects, and transmits the operational variables to the DCS database 4. The variable data recorded in the DCS database 4 is used as the input of the soft sensor model 5 based on particle swarm optimization weighted least squares support vector machine fuzzy equation, and the soft sensor value display device 6 is used to display the industrial melting index soft sensor of the optimal fuzzy network The output of model 5, namely the soft measurement value. the

表1：最优模糊网络的工业熔融指数软测量模型所需建模变量 Table 1: Modeling variables required for the industrial melt index soft sensor model of the optimal fuzzy network

变量符号variable symbol变量含义variable meaning变量符号variable symbol变量含义variable meaningTT釜内温度Kettle temperaturef1f1第一股丙稀进料流率The first propylene feed flow ratePP釜内压强pressure in kettlef2f2第二股丙稀进料流率The second propylene feed flow rateLL釜内液位Liquid level in kettlef3f3第三股丙稀进料流率The third propylene feed flow rateX_vx_v釜内氢气体积浓度Hydrogen volume concentration in the kettlef4f4主催化剂流率main catalyst flow rate the thef5f5辅催化剂流率cocatalyst flow rate

最优模糊网络的工业熔融指数软测量模型5，包括以下3个部分： The industrial melting index soft sensor model 5 of the optimal fuzzy network includes the following three parts:

数据预处理模块7用于将从DCS数据库输入的模型训练样本进行预处理，使得训练样本的均值为0，方差为1，该处理采用以下算式过程来完成： The data preprocessing module 7 is used to preprocess the model training samples imported from the DCS database, so that the mean value of the training samples is 0, and the variance is 1. This processing is completed by the following calculation process:

计算均值：$\stackrel{\&OverBar;}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{TX}}_i---\left(1\right)$Calculate the mean:$\stackrel{\&OverBar;}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{TX}}_i---\left(1\right)$

计算方差：${\mathrm{\&sigma;}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{TX}}_i-\stackrel{\&OverBar;}{\mathrm{TX}})---\left(2\right)$Calculate the variance:${\mathrm{\&sigma;}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{TX}}_i-\stackrel{\&OverBar;}{\mathrm{TX}})---\left(2\right)$

标准化：$X=\frac{\mathrm{TX}-\stackrel{\&OverBar;}{\mathrm{TX}}}{{\mathrm{\&sigma;}}_x}---\left(3\right)$standardization:$x=\frac{\mathrm{TX}-\stackrel{\&OverBar;}{\mathrm{TX}}}{{\mathrm{\&sigma;}}_x}---\left(3\right)$

其中，TX_i为第i个训练样本，N为训练样本数，

为训练样本的均值，X为标准化后的训练样本。σ_x表示训练样本的标准差，σ²_x表示训练样本的方差。 Among them, TX_i is the i-th training sample, N is the number of training samples,

is the mean of the training samples, and X is the standardized training samples. σ_x represents the standard deviation of the training samples, and σ²_x represents the variance of the training samples.

模糊神经网络模块8，对从数据预处理模块传过来的输入变量，进行模糊推理和建立模糊规则。对从数据预处理模块传过来的经过预处理过的训练样本X进行模糊分类，得到模糊规则库中每个模糊聚类的中心和宽度。设第p个标准化后的训练样本X_p=[X_p1,…,X_pn]，其中n是输入变量的个数。 The fuzzy neural network module 8 performs fuzzy reasoning and establishes fuzzy rules on the input variables passed from the data preprocessing module. Perform fuzzy classification on the preprocessed training sample X passed from the data preprocessing module, and obtain the center and width of each fuzzy cluster in the fuzzy rule base. Let the p-th normalized training sample X_p =[X_p1 ,…,X_pn ], where n is the number of input variables.

设模糊神经网络有R个模糊规则，为了求得每个模糊规则对于训练样本X_p的每个输入变量X_pj,j=1,…,n，下面的模糊化方程将求出其对第i个模糊规则的隶属度： Assuming that the fuzzy neural network has R fuzzy rules, in order to obtain each fuzzy rule for each input variable X_pj , j=1,...,n of the training sample X_p , the following fuzzy equation will find its i-th The degree of membership of a fuzzy rule:

${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

其中m_ij和σ_ij分别表示第i个模糊规则的第j个高斯成员函数的中心和宽度，由模糊聚类求得。 Among them, m_ij and σ_ij represent the center and width of the jth Gaussian membership function of the ith fuzzy rule respectively, which are obtained by fuzzy clustering.

设标准化后的训练样本X_p对模糊规则i的适应度为μ⁽ⁱ⁾(X_p)，则μ⁽ⁱ⁾(X_p)的大小可由下式决定： Suppose the fitness of the standardized training sample X_p to the fuzzy rule i is μ⁽ⁱ⁾ (X_p ), then the size of μ⁽ⁱ⁾ (X_p ) can be determined by the following formula:

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Pi;</span>\&Pi;</span>}}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

求得输入训练样本对于每个规则的适应度之后，模糊神经网络对模糊规则输出进行推导以得到最后的解析解。在常用的模糊神经网络结构中，每个模糊规则推导的过程都可以表示为如下：首先求得训练样本中所有输入变量的线性乘积和，然后用此线性乘积和与规则的适用度μ⁽ⁱ⁾(X_p)相乘，得到最终的每条模糊规则的输出。模糊规则i的推导输出可以表示如下： After obtaining the fitness of the input training samples for each rule, the fuzzy neural network deduces the output of the fuzzy rules to obtain the final analytical solution. In the commonly used fuzzy neural network structure, the derivation process of each fuzzy rule can be expressed as follows: first obtain the linear product sum of all input variables in the training sample, and then use this linear product sum and the rule’s applicability μ^{(i )} (X_p ) to get the final output of each fuzzy rule. The derivation output of fuzzy rule i can be expressed as follows:

${\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

${\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>7</span>7</span>}<span><span>)</span>)</span>$

式中，f⁽ⁱ⁾为第i条模糊规则的输出，

是模糊神经网络模型对第p个训练样本的预测输出，a_ij,j=1,…,n是第i条模糊规则中第j个变量的线性系数，a_i0是第i条模糊规则中输入变量线性乘积和的常数项，b是输出偏置量。 In the formula, f⁽ⁱ⁾ is the output of the i-th fuzzy rule,

is the predicted output of the fuzzy neural network model for the p-th training sample, a_ij ,j=1,...,n is the linear coefficient of the j-th variable in the i-th fuzzy rule, and a_i0 is the input in the i-th fuzzy rule The constant term of the variable linear product sum, b is the output bias.

支持向量机优化模块9，在式（7）中，输入变量线性乘积和中的参数的确定是模糊神经网络使用中用到的一个主要问题，这里我们采用把原有的模糊规则推导输出形式转换为支持向量机优化问题，再使用支持向量机进行线性优化，转换过程如下： Support vector machine optimization module 9, in formula (7), the determination of the parameters in the linear product sum of input variables is a main problem used in the use of fuzzy neural networks, here we use the original fuzzy rule derivation output form conversion To optimize the problem for the support vector machine, and then use the support vector machine for linear optimization, the conversion process is as follows:

$\begin{array}{c}{\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

其中X_p0为常数项且恒等于1。令 Among them, X_p0 is a constant term and is always equal to 1. make

其中，

表示原训练样本的转化形式，即把原来的训练样本转换为如上式形式，作为支持向量机的训练样本： in,

Indicates the transformation form of the original training sample, that is, convert the original training sample into the above formula, and use it as the training sample of the support vector machine:

其中y₁,…,y_N是训练样本的目标输出，取S作为新的输入训练样本集合，那么原有问题可以 转化为如下的支持向量机对偶优化问题： Among them, y₁ ,...,y_N are the target output of training samples, and S is taken as the new input training sample set, then the original problem can be transformed into the following support vector machine dual optimization problem:

$\mathrm{<span><span>R</span>R</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>,</span>,</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>,</span>,</span>\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>)</span>)</span><span><span>+</span>+</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

其中y_p是输入训练样本X_p的目标输出，ω是支持向量机超平面的法向量，f(X_p)是对应于X_p的模型输出，γ是支持向量机的惩罚因子，R(ω,b)是优化问题的目标函数，N是训练样本数，L_ε(y_p,f(X_p))表达式如下： where y_p is the target output of the input training sample X_p , ω is the normal vector of the support vector machine hyperplane, f(X_p ) is the model output corresponding to X_p , γ is the penalty factor of the support vector machine, R(ω ,b) is the objective function of the optimization problem, N is the number of training samples, and the expression of L_ε (y_p ,f(X_p )) is as follows:

其中ε是优化问题的误差容限，接下来使用支持向量机求得模糊神经网络的模糊规则最优推导线性参数和对偶优化问题的预报输出： Where ε is the error tolerance of the optimization problem, and then use the support vector machine to obtain the fuzzy rules of the fuzzy neural network to optimally derive the linear parameters and the forecast output of the dual optimization problem:

${\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>\&Element;</span>\&Element;</span>\mathrm{<span><span>SV</span>SV</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>R</span>R</span>}<span><span>;</span>;</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

其中α_k，

分别是y_p-f(X_p)大于0和小于0时对应的拉格朗日乘子,

即为对应于第p个标准化后的训练样本X_p的MI预报值。 where α_k ,

are the corresponding Lagrangian multipliers when y_p -f(X_p ) is greater than 0 and less than 0,

That is, the predicted value of MI corresponding to the pth normalized training sample X_p .

模型更新模块10，用于模型的在线更新，定期将离线化验数据输入到训练集中，更新模糊神经网络模型。 The model update module 10 is used for online update of the model, regularly inputs the offline test data into the training set, and updates the fuzzy neural network model. the

实施例2 Example 2

参照图1、图2，一种最优模糊网络的工业熔融指数软测量方法，所述软测量方法具体实现步骤如下： With reference to Fig. 1, Fig. 2, a kind of industrial melting index soft-sensing method of optimal fuzzy network, described soft-sensing method concrete realization steps are as follows:

1）、对丙烯聚合生产过程对象，根据工艺分析和操作分析，选择操作变量和易测变量作为模型的输入，操作变量和易测变量由DCS数据库获得； 1) For the propylene polymerization production process object, according to the process analysis and operation analysis, the operational variables and easily measurable variables are selected as the input of the model, and the operational variables and easily measurable variables are obtained from the DCS database;

2）、用于将从DCS数据库输入的模型训练样本进行预处理，使得训练样本的均值为0，方差为1，该处理采用以下算式过程来完成： 2) It is used to preprocess the model training samples input from the DCS database, so that the mean value of the training samples is 0 and the variance is 1. This processing is completed by the following calculation process:

计算均值：$\stackrel{\&OverBar;}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{TX}}_i---\left(1\right)$Calculate the mean:$\stackrel{\&OverBar;}{\mathrm{TX}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{TX}}_i---\left(1\right)$

计算方差：${\mathrm{\&sigma;}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{TX}}_i-\stackrel{\&OverBar;}{\mathrm{TX}})---\left(2\right)$Calculate the variance:${\mathrm{\&sigma;}}_x^2=\frac{1}{N-1}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{TX}}_i-\stackrel{\&OverBar;}{\mathrm{TX}})---\left(2\right)$

标准化：$X=\frac{\mathrm{TX}-\stackrel{\&OverBar;}{\mathrm{TX}}}{{\mathrm{\&sigma;}}_x}---\left(3\right)$standardization:$x=\frac{\mathrm{TX}-\stackrel{\&OverBar;}{\mathrm{TX}}}{{\mathrm{\&sigma;}}_x}---\left(3\right)$

其中，TX_i为第i个训练样本，N为训练样本数，

为训练样本的均值，X为标准化后的训练样本。σ_x表示训练样本的标准差，σ²_x表示训练样本的方差。 Among them, TX_i is the i-th training sample, N is the number of training samples,

is the mean of the training samples, and X is the standardized training samples. σ_x represents the standard deviation of the training samples, and σ²_x represents the variance of the training samples.

3）、对从数据预处理模块传过来的输入变量，进行模糊推理和建立模糊规则。对从数据预处理模块传过来的经过预处理过的训练样本X进行模糊分类，得到模糊规则库中每个模糊聚类的中心和宽度。设第p个标准化后的训练样本X_p=[X_p1,…,X_pn]，其中n是输入变量的个数。 3) Carry out fuzzy reasoning and establish fuzzy rules for the input variables passed from the data preprocessing module. Perform fuzzy classification on the preprocessed training sample X passed from the data preprocessing module, and obtain the center and width of each fuzzy cluster in the fuzzy rule base. Let the p-th normalized training sample X_p =[X_p1 ,…,X_pn ], where n is the number of input variables.

设模糊神经网络有R个模糊规则，为了求得每个模糊规则对于训练样本X_p的每个输入变量X_pj,j=1,…,n，下面的模糊化方程将求出其对第i个模糊规则的隶属度： Assuming that the fuzzy neural network has R fuzzy rules, in order to obtain each fuzzy rule for each input variable X_pj , j=1,...,n of the training sample X_p , the following fuzzy equation will find its i-th The degree of membership of a fuzzy rule:

${\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

其中m_ij和σ_ij分别表示第i个模糊规则的第j个高斯成员函数的中心和宽度，由模糊聚类求得。 Among them, m_ij and σ_ij represent the center and width of the jth Gaussian membership function of the i-th fuzzy rule respectively, which are obtained by fuzzy clustering.

设标准化后的训练样本X_p对模糊规则i的适应度为μ⁽ⁱ⁾(X_p)，则μ⁽ⁱ⁾(X_p)的大小可由下式决定： Suppose the fitness of the standardized training sample X_p to the fuzzy rule i is μ⁽ⁱ⁾ (X_p ), then the size of μ⁽ⁱ⁾ (X_p ) can be determined by the following formula:

${\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Pi;</span>\&Pi;</span>}}}{\mathrm{<span><span>M</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>\{</span>\{</span><span><span>-</span>-</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>m</span>m</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\}</span>\}</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

求得输入训练样本对于每个规则的适应度之后，模糊神经网络对模糊规则输出进行推导以得到最后的解析解。在常用的模糊神经网络结构中，每个模糊规则推导的过程都可以表示为如下：首先求得训练样本中所有输入变量的线性乘积和，然后用此线性乘积和与规则的适用度μ⁽ⁱ⁾(X_p)相乘，得到最终的每条模糊规则的输出。模糊规则i的推导输出可以表示如下： After obtaining the fitness of the input training samples for each rule, the fuzzy neural network deduces the output of the fuzzy rules to obtain the final analytical solution. In the commonly used fuzzy neural network structure, the derivation process of each fuzzy rule can be expressed as follows: first obtain the linear product sum of all input variables in the training sample, and then use this linear product sum and the rule’s applicability μ^{(i )} (X_p ) to get the final output of each fuzzy rule. The derivation output of fuzzy rule i can be expressed as follows:

${\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

${\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>7</span>7</span>}<span><span>)</span>)</span>$

式中，f⁽ⁱ⁾为第i条模糊规则的输出，

是模糊神经网络模型对第p个训练样本的预测输出，a_ij,j=1,…,n是第i条模糊规则中第j个变量的线性系数，a_i0是第i条模糊规则中输入变量线 性乘积和的常数项，b是输出偏置量。 In the formula, f⁽ⁱ⁾ is the output of the i-th fuzzy rule,

is the predicted output of the fuzzy neural network model for the p-th training sample, a_ij ,j=1,...,n is the linear coefficient of the j-th variable in the i-th fuzzy rule, and a_i0 is the input in the i-th fuzzy rule The constant term of the variable linear product sum, b is the output bias.

4）、在式（7）中，输入变量线性乘积和中的参数的确定是模糊神经网络使用中用到的一个主要问题，这里我们采用把原有的模糊规则推导输出形式转换为支持向量机优化问题，再使用支持向量机进行线性优化，转换过程如下： 4) In formula (7), the determination of the parameters in the linear product sum of input variables is a major problem used in the use of fuzzy neural networks. Here we adopt the method of converting the original fuzzy rule derivation output form into a support vector machine Optimization problem, and then use the support vector machine for linear optimization, the conversion process is as follows:

$\begin{array}{c}{\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>f</span>f</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span><span><span>(</span>(</span>\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>0</span>0</span>}}<span><span>)</span>)</span><span><span>]</span>]</span><span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\\ <span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>R</span>R</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>\&times;</span>\&times;</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>pj</span>pj</span>}}<span><span>+</span>+</span>\mathrm{<span><span>b</span>b</span>}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

其中X_p0为常数项且恒等于1。令 Among them, X_p0 is a constant term and is always equal to 1. make

其中，

表示原训练样本的转化形式，即把原来的训练样本转换为如上式形式，作为支持向量机的训练样本： in,

Indicates the transformation form of the original training sample, that is, convert the original training sample into the above formula, and use it as the training sample of the support vector machine:

其中y₁,…,y_N是训练样本的目标输出，取S作为新的输入训练样本集合，那么原有问题可以转化为如下的支持向量机对偶优化问题： Among them, y₁ ,...,y_N are the target output of the training samples, and S is taken as the new input training sample set, then the original problem can be transformed into the following support vector machine dual optimization problem:

$\mathrm{<span><span>R</span>R</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>,</span>,</span>\mathrm{<span><span>b</span>b</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>,</span>,</span>\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>p</span>p</span>}}<span><span>)</span>)</span><span><span>)</span>)</span><span><span>+</span>+</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

其中y_p是输入训练样本X_p的目标输出，ω是支持向量机超平面的法向量，f(X_p)是对应于X_p的模型输出，γ是支持向量机的惩罚因子，R(ω,b)是优化问题的目标函数，N是训练样本数，L_ε(y_p,f(X_p))表达式如下： where y_p is the target output of the input training sample X_p , ω is the normal vector of the support vector machine hyperplane, f(X_p ) is the model output corresponding to X_p , γ is the penalty factor of the support vector machine, R(ω ,b) is the objective function of the optimization problem, N is the number of training samples, and the expression of L_ε (y_p ,f(X_p )) is as follows:

其中ε是优化问题的误差容限，接下来使用支持向量机求得模糊神经网络的模糊规则最优推导线性参数和对偶优化问题的预报输出： Where ε is the error tolerance of the optimization problem, and then use the support vector machine to obtain the fuzzy rules of the fuzzy neural network to optimally derive the linear parameters and the forecast output of the dual optimization problem:

${\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>\&Element;</span>\&Element;</span>\mathrm{<span><span>SV</span>SV</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}^{<span><span>*</span>*</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&mu;</span>\&mu;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>kj</span>kj</span>}}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>R</span>R</span>}<span><span>;</span>;</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

其中α_k，

分别是y_p-f(X_p)大于0和小于0时对应的拉格朗日乘子,

即为对应于第p个标准化后的训练样本X_p的MI预报值。 where α_k ,

are the corresponding Lagrangian multipliers when y_p -f(X_p ) is greater than 0 and less than 0,

That is, the predicted value of MI corresponding to the pth normalized training sample X_p .

作为优选的一种方案：所述软测量方法还包括以下步骤：5）、定期将离线化验数据输入到训练样本集中，更新模糊方程模型。 As a preferred solution: the soft-sensing method further includes the following steps: 5) Regularly input offline test data into the training sample set, and update the fuzzy equation model. the

本实施例的方法具体实现步骤如下： The specific implementation steps of the method of this embodiment are as follows:

步骤1：对丙烯聚合生产过程对象1，根据工艺分析和操作分析，选择操作变量和易测变量作为模型的输入。操作变量和易测变量由DCS数据库4获得。 Step 1: For the propylene polymerization production process object 1, according to the process analysis and operation analysis, select the operation variables and easily measurable variables as the input of the model. Manipulated variables and measurable variables were obtained from the DCS database4. the

步骤2：对训练样本进行预处理，由数据预处理模块7完成。 Step 2: preprocessing the training samples, which is completed by the data preprocessing module 7 . the

步骤3：基于预处理过的训练样本数据建立初始模糊神经网络模型8。输入数据如步骤2所述获得，输出数据由离线化验获得。 Step 3: Establish an initial fuzzy neural network model 8 based on the preprocessed training sample data. Input data were obtained as described in step 2, and output data were obtained from off-line assays. the

步骤4：由支持向量机优化模块9优化初始模糊神经网络模型8的反模糊输出参数。 Step 4: Optimizing the defuzzification output parameters of the initial fuzzy neural network model 8 by the support vector machine optimization module 9 . the

步骤5：模型更新模块10定期将离线化验数据输入到训练集中，更新模糊神经网络模型，最优模糊网络的工业熔融指数软测量模型5建立完成。 Step 5: The model update module 10 regularly inputs the offline test data into the training set to update the fuzzy neural network model, and the industrial melt index soft sensor model 5 of the optimal fuzzy network is established. the

步骤6：熔融指数软测量值显示仪6显示最优模糊网络的工业熔融指数软测量模型5的输出，完成对工业聚丙烯生产熔融指数软测量的显示。 Step 6: The melt index soft measurement value display instrument 6 displays the output of the industrial melt index soft measurement model 5 of the optimal fuzzy network, and completes the display of the melt index soft measurement for industrial polypropylene production. the

Claims (2)

1. The utility model provides an industry melt index soft measurement instrument of optimum fuzzy network, is including the on-the-spot intelligent instrument that is used for measuring easy measurability variable, the control station that is used for measuring the operating variable, the DCS database of depositing data and the soft measurement value display instrument of melt index, on-the-spot intelligent instrument, control station and DCS database are connected, its characterized in that: the soft measuring instrument further comprises an industrial melt index soft measuring model of an optimal fuzzy network, the DCS database is connected with the input end of the industrial melt index soft measuring model of the optimal fuzzy network, the output end of the industrial melt index soft measuring model of the optimal fuzzy network is connected with a melt index soft measuring value display instrument, and the industrial melt index soft measuring model of the optimal fuzzy network comprises:

the data preprocessing module is used for preprocessing the model training samples input from the DCS database, so that the mean value of the training samples is 0, and the variance of the training samples is 1, and the processing is completed by adopting the following formula:

calculating an average value: <math> <mrow> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>TX</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow></math>

calculating the variance: <math> <mrow> <msubsup> <mi>&sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>TX</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow></math>

and (3) standardization: <math> <mrow> <mi>X</mi> <mo>=</mo> <mfrac> <mrow> <mi>TX</mi> <mo>-</mo> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> </mrow> <msub> <mi>&sigma;</mi> <mi>x</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow></math>

wherein, TX_iIs the ith training sample, N is the number of training samples,

is the mean of the training samples, and X is the normalized training sample. Sigma_xRepresenting the standard deviation, σ, of the training samples²_xRepresenting the variance of the training samples.

And the fuzzy neural network module is used for carrying out fuzzy reasoning and establishing a fuzzy rule on the input variable transmitted from the data preprocessing module. And carrying out fuzzy classification on the preprocessed training sample X transmitted from the data preprocessing module to obtain the center and the width of each fuzzy cluster in the fuzzy rule base. Let the p-th normalized training sample X_p=[X_p1,…,X_pn]Where n is the number of input variables.

Let the fuzzy neural network have R fuzzy rules, for obtaining each fuzzy rule for training sample X_pEach input variable X of_pjJ =1, …, n, whose membership to the i-th fuzzy rule is to be found by the following fuzzy equation:

<math> <mrow> <msub> <mi>M</mi> <mi>ij</mi> </msub> <mo>=</mo> <mi>exp</mi> <mo>{</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>-</mo> <msub> <mi>m</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mi>&sigma;</mi> <mi>ij</mi> <mn>2</mn> </msubsup> </mfrac> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow></math>

wherein m is_ijAnd σ_ijAnd respectively representing the center and the width of the jth Gaussian member function of the ith fuzzy rule, and obtaining the center and the width by fuzzy clustering.

Normalized training sample X_pFitness to fuzzy rule i is mu⁽ⁱ⁾(X_p) Then μ⁽ⁱ⁾(X_p) Can be determined by the following formula:

<math> <mrow> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Pi;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>M</mi> <mi>ij</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mo>{</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>-</mo> <msub> <mi>m</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mi>&sigma;</mi> <mi>ij</mi> <mn>2</mn> </msubsup> </mfrac> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow></math>

after the fitness of the input training sample to each rule is obtained, the fuzzy neural network deduces the output of the fuzzy rule to obtain the final analytic solution. In a commonly used fuzzy neural network structure, the process of deriving each fuzzy rule can be expressed as follows: firstly, the linear product sum of all input variables in the training sample is obtained, and then the linear product sum is used to match the fitness mu of the ruleⁱ(X_p) And multiplying to obtain the final output of each fuzzy rule. The derived output of the fuzzy rule i can be expressed as follows:

<math> <mrow> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&times;</mo> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow></math>

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <mo>[</mo> <msup> <mi>&mu;</mi> <mi>i</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&times;</mo> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <mi>b</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow></math>

in the formula (f)⁽ⁱ⁾For the output of the ith fuzzy rule,

is the predicted output of the fuzzy neural network model to the p-th training sample, a_ijJ =1, …, n is the linear coefficient of the jth variable in the ith fuzzy rule, a_i0Is a constant term of the linear product sum of the input variables in the ith fuzzy rule, and b is an output offset.

In formula (7), the determination of parameters in the input variable linear product sum is a main problem used in the use of the fuzzy neural network, here, the original fuzzy rule derivation output form is converted into the support vector machine optimization problem, and then the support vector machine is used for linear optimization, wherein the conversion process is as follows:

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mi>b</mi> </mrow></math>

<math> <mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <mo>[</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&times;</mo> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <mi>b</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow></math>

<math> <mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>&times;</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>+</mo> <mi>b</mi> </mrow></math>

wherein X_p0Is a constant term and is constant equal to 1. Order to

<math> <mrow> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>[</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>&times;</mo> <msub> <mi>X</mi> <mrow> <mi>p</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pn</mi> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </msup> <mo>&times;</mo> <msub> <mi>X</mi> <mrow> <mi>p</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </msup> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pn</mi> </msub> <mo>]</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow></math>

Wherein,

the conversion form of the original training sample is represented, namely, the original training sample is converted into the form of the formula as above, and the form is used as the training sample of the support vector machine:

<math> <mrow> <mi>S</mi> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mo>(</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> </mrow> <mrow> <mo>(</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>y</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow></math>

wherein y is₁,…,y_NThe target output of the training sample is taken, S is taken as a new input training sample set, and then the original problem can be converted into the following dual optimization problem of the support vector machine:

<math> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&gamma;</mi> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msub> <mi>L</mi> <mi>&epsiv;</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>p</mi> </msub> <mo>,</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>&omega;</mi> <mi>T</mi> </msup> <mi>&omega;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow></math>

wherein y is_pIs inputting a training sample X_pω is the normal vector of the hyperplane of the support vector machine, f (X)_p) Is corresponding to X_pγ is the penalty factor of the support vector machine, R (ω, b) is the objective function of the optimization problem, N is the number of training samples, L_ε(y_p,f(X_p) Expression) as follows:

wherein epsilon is the error tolerance of the optimization problem, then the support vector machine is used for obtaining the optimal derivation linear parameters of the fuzzy rule of the fuzzy neural network and the forecast output of the dual optimization problem:

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <msub> <mi>X</mi> <mi>kj</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>&Element;</mo> <mi>SV</mi> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <msub> <mi>X</mi> <mi>kj</mi> </msub> </mtd> <mtd> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>R</mi> <mo>;</mo> <mi>j</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced></math>

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>&lt;</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>,</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>></mo> <mo>+</mo> <mi>b</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow></math>

wherein alpha is_k，

(k =1, …, N) is y_p-f(X_p) Lagrange multipliers corresponding to greater than 0 and less than 0,

i.e. corresponding to the p-th normalized training sample X_pPredicted value of MI of (1).

The industrial melt index soft measurement model of the optimal fuzzy network further comprises:

and the model updating module is used for updating the model on line, inputting offline verification data into a training set regularly and updating the fuzzy neural network model.

2. A soft measurement method implemented by the soft measurement instrument for propylene polymerization production process based on support vector machine optimization fuzzy neural network as claimed in claim 1, characterized in that: the soft measurement method comprises the following concrete implementation steps:

1) selecting an operation variable and an easily-measured variable as input of a model for a propylene polymerization production process object according to process analysis and operation analysis, wherein the operation variable and the easily-measured variable are obtained by a DCS (distributed control system) database;

2) the method is used for preprocessing the model training samples input from the DCS database, so that the mean value of the training samples is 0, the variance is 1, and the processing is completed by adopting the following formula process:

calculating an average value: <math> <mrow> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>TX</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow></math>

calculating the variance: <math> <mrow> <msubsup> <mi>&sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>TX</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow></math>

and (3) standardization: <math> <mrow> <mi>X</mi> <mo>=</mo> <mfrac> <mrow> <mi>TX</mi> <mo>-</mo> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> </mrow> <msub> <mi>&sigma;</mi> <mi>x</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow></math>

wherein, TX_iIs the ith training sample, N is the number of training samples,is the mean of the training samples, and X is the normalized training sample. Sigma_xRepresenting the standard deviation, σ, of the training samples²_xRepresenting the variance of the training samples.

3) And carrying out fuzzy reasoning and establishing a fuzzy rule on the input variable transmitted from the data preprocessing module. And carrying out fuzzy classification on the preprocessed training sample X transmitted from the data preprocessing module to obtain the center and the width of each fuzzy cluster in the fuzzy rule base. Let the p-th normalized training sample X_p=[X_p1,…,X_pn]Where n is the number of input variables.

Let the fuzzy neural network have R fuzzy rules, for obtaining each fuzzy rule for training sample X_pEach input variable X of_pjJ =1, …, n, whose membership to the i-th fuzzy rule is to be found by the following fuzzy equation:

<math> <mrow> <msub> <mi>M</mi> <mi>ij</mi> </msub> <mo>=</mo> <mi>exp</mi> <mo>{</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>-</mo> <msub> <mi>m</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mi>&sigma;</mi> <mi>ij</mi> <mn>2</mn> </msubsup> </mfrac> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow></math>

wherein m is_ijAnd σ_ijAnd respectively representing the center and the width of the jth Gaussian member function of the ith fuzzy rule, and obtaining the center and the width by fuzzy clustering.

Normalized training sample X_pFitness to fuzzy rule i is mu⁽ⁱ⁾(X_p) Then μ⁽ⁱ⁾(X_p) Can be determined by the following formula:

<math> <mrow> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Pi;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>M</mi> <mi>ij</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mo>{</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>-</mo> <msub> <mi>M</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mi>&sigma;</mi> <mi>ij</mi> <mn>2</mn> </msubsup> </mfrac> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow></math>

after the fitness of the input training sample to each rule is obtained, the fuzzy neural network pair is fuzzyThe rule output is derived to obtain the final analytic solution. In a commonly used fuzzy neural network structure, the process of deriving each fuzzy rule can be expressed as follows: firstly, the linear product sum of all input variables in the training sample is obtained, and then the linear product sum is used to match the fitness mu of the rule⁽ⁱ⁾(X_p) And multiplying to obtain the final output of each fuzzy rule. The derived output of the fuzzy rule i can be expressed as follows:

<math> <mrow> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&times;</mo> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow></math>

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <mo>[</mo> <msup> <mi>&mu;</mi> <mi>i</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&times;</mo> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <mi>b</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow></math>

in the formula (f)⁽ⁱ⁾For the output of the ith fuzzy rule,is the predicted output of the fuzzy neural network model to the p-th training sample, a_ijJ =1, …, n is the linear coefficient of the jth variable in the ith fuzzy rule, a_i0Is a constant term of the linear product sum of the input variables in the ith fuzzy rule, and b is an output offset.

4) In the formula (7), the determination of the parameters in the linear product sum of the input variables is a main problem used in the use of the fuzzy neural network, here, the original fuzzy rule derivation output form is converted into the optimization problem of the support vector machine, and then the linear optimization is performed by using the support vector machine, wherein the conversion process is as follows:

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mi>b</mi> </mrow></math>

<math> <mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <mo>[</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&times;</mo> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <mi>b</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow></math>

<math> <mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>&times;</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pj</mi> </msub> <mo>+</mo> <mi>b</mi> </mrow></math>

wherein X_p0Is a constant term and is constant equal to 1. Order to

<math> <mrow> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>[</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>&times;</mo> <msub> <mi>X</mi> <mrow> <mi>p</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pn</mi> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </msup> <mo>&times;</mo> <msub> <mi>X</mi> <mrow> <mi>p</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> </msup> <mo>&times;</mo> <msub> <mi>X</mi> <mi>pn</mi> </msub> <mo>]</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow></math>

Wherein,

the conversion form of the original training sample is represented, namely, the original training sample is converted into the form of the formula as above, and the form is used as the training sample of the support vector machine:

<math> <mrow> <mi>S</mi> <mo>=</mo> <mo>{</mo> <mrow> <mo>(</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mrow> <mo>(</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>y</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow></math>

wherein y is₁,…,y_NThe target output of the training sample is taken, S is taken as a new input training sample set, and then the original problem can be converted into the following dual optimization problem of the support vector machine:

<math> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&gamma;</mi> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msub> <mi>L</mi> <mi>&epsiv;</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>p</mi> </msub> <mo>,</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>&omega;</mi> <mi>T</mi> </msup> <mi>&omega;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow></math>

wherein y is_pIs inputting a training sample X_pω is the normal vector of the hyperplane of the support vector machine, f (X)_p) Is corresponding to X_pModel output of (2)Gamma is the penalty factor of the support vector machine, R (omega, b) is the objective function of the optimization problem, N is the number of training samples, L_ε(y_p,f(X_p) Expression) as follows:

wherein epsilon is the error tolerance of the optimization problem, then the support vector machine is used for obtaining the optimal derivation linear parameters of the fuzzy rule of the fuzzy neural network and the forecast output of the dual optimization problem:

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mi>ij</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <msub> <mi>X</mi> <mi>kj</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>&Element;</mo> <mi>SV</mi> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <msub> <mi>X</mi> <mi>kj</mi> </msub> </mtd> <mtd> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>R</mi> <mo>;</mo> <mi>j</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced></math>

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>&alpha;</mi> <mi>k</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>&lt;</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>,</mo> <mover> <mi>&phi;</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>></mo> <mo>+</mo> <mi>b</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow></math>

wherein alpha is_k，

(k =1, …, N) is y_p-f(X_p) Lagrange multipliers corresponding to greater than 0 and less than 0,

i.e. corresponding to the p-th normalized training sample X_pPredicted value of MI of (1).

The soft measurement method further comprises the following steps: 5) and inputting the offline experimental data into a training sample set regularly, and updating the fuzzy neural network model.

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