技术领域technical field
本发明属于控制系统故障诊断技术领域，具体涉及一种化工生产过程故障监测方法，用于提高复杂化工生产过程故障监测的准确率。The invention belongs to the technical field of fault diagnosis of control systems, and in particular relates to a method for monitoring faults in chemical production processes, which is used for improving the accuracy of fault monitoring in complex chemical production processes.
背景技术Background technique
随着现代工业过程变得越来越复杂，许多工业过程(如化工过程)通常由高维且相互关联的海量数据组成。多变量统计过程监控(MSPM)是一种基于数据驱动的故障诊断技术，其本质是将高维数据转换为低维数据，并在低维数据中获取重要信息。典型的MSPM技术包含主成分分析(PCA)，偏最小二乘法(PLS)，独立成分分析(ICA)等。As modern industrial processes become more complex, many industrial processes, such as chemical processes, typically consist of high-dimensional and interrelated massive data. Multivariate Statistical Process Monitoring (MSPM) is a data-driven fault diagnosis technology whose essence is to convert high-dimensional data into low-dimensional data, and obtain important information in the low-dimensional data. Typical MSPM techniques include Principal Component Analysis (PCA), Partial Least Squares (PLS), Independent Component Analysis (ICA), etc.
PCA是一种广泛使用的降维技术，近几年来已经成功地应用于工业过程的在线监测，尤其是在化工过程中。很多文献在使用PCA进行故障监控时，都要求被监控的过程变量必须遵循高斯分布。然而在实际的复杂工业生产中，大多数过程变量不满足高斯分布。如果PCA方法用于非高斯过程的故障监测，则过程的统计特性将被削弱，导致过程故障监控不准确。为了解决过程数据非高斯问题，很多学者提出了ICA算法，ICA虽然提取了非高斯且相互独立的潜在独力分量，但处理的结果不够准确。为此，Lee等人提出一种基于非负矩阵(NMF)降维方法(D.D.Lee,and H.S.Seung,“Algorithms for non-negative matrixfactorization,”Advances in Neural Information Processing Systems,vol.13,no.6,pp.556-562,2000.)。与传统的MSPM监测方法相比，NMF算法对测量数据除了为非负外没有其他限制，具有更广泛的应用。此外，NMF算法可以从海量数据中捕获数据的局部特征，并且具有比传统MSPM方法更好的解释能力。PCA is a widely used dimensionality reduction technique that has been successfully applied to online monitoring of industrial processes in recent years, especially in chemical processes. Many literatures require that the monitored process variable must follow a Gaussian distribution when using PCA for fault monitoring. However, in actual complex industrial production, most process variables do not satisfy the Gaussian distribution. If the PCA method is used for fault monitoring of non-Gaussian processes, the statistical properties of the process will be weakened, resulting in inaccurate process fault monitoring. In order to solve the non-Gaussian problem of process data, many scholars have proposed the ICA algorithm. Although ICA extracts non-Gaussian and independent potential independent components, the processing results are not accurate enough. To this end, Lee et al. proposed a dimensionality reduction method based on non-negative matrix (NMF) (D.D.Lee, and H.S.Seung, "Algorithms for non-negative matrixfactorization," Advances in Neural Information Processing Systems, vol.13, no.6 , pp.556-562, 2000.). Compared with the traditional MSPM monitoring method, the NMF algorithm has no other restrictions on the measurement data except that it is non-negative, and has a wider application. In addition, NMF algorithms can capture local features of data from massive data and have better explanatory power than traditional MSPM methods.
然而，很多基于NMF的故障监测方法中，都采用了固定的NMF模型通常故障过程是缓慢变化的，基于固定模型的故障监测算法可能会降低故障监测的准确性。However, many NMF-based fault monitoring methods use a fixed NMF model. Usually, the fault process changes slowly, and the fixed model-based fault monitoring algorithm may reduce the accuracy of fault monitoring.
发明内容SUMMARY OF THE INVENTION
本发明的发明目的是提供一种化工生产过程故障监测方法，用于解决现有的化工生产过程故障诊断准确率低的问题。The purpose of the present invention is to provide a fault monitoring method in a chemical production process, which is used to solve the problem of low accuracy of fault diagnosis in the existing chemical production process.
为实现发明目的，可以采用如下的技术方案。To achieve the purpose of the invention, the following technical solutions can be adopted.
一种基于自适应分块非负矩阵分解(APNMF)的化工生产过程故障监测方法，用于处理化工生产过程中多个采集点监测的变量数据以识别出与已知故障相对应的数据，便于生产维护人员及早发现生产中的问题并做出相应处理，所述变量包括温度、压力、液位、流体速度和流量中的至少一种，包括以下步骤：A fault monitoring method for chemical production process based on adaptive block non-negative matrix factorization (APNMF), which is used to process variable data monitored by multiple collection points in the chemical production process to identify data corresponding to known faults, which is convenient for Production maintenance personnel find problems in production early and deal with them accordingly. The variables include at least one of temperature, pressure, liquid level, fluid velocity and flow, including the following steps:
步骤一，基于非负矩阵的全局故障监测；Step 1, global fault monitoring based on non-negative matrix;
离线采集化工生产过程中d个采集点的所述变量的Mn个历史正常样本，并构建历史矩阵对矩阵Xn′进行预处理得到矩阵Xn，以使其能够应用基于NMF的故障监测方法，然后利用NMF模型获取监测统计量Nn2和SPEn的控制限Nlim2和SPElim；Collect Mn historical normal samples of the variable at d collection points in the chemical production process offline, and construct a historical matrix Preprocess the matrix Xn ′ to obtain the matrix Xn , so that it can apply the NMF-based fault monitoring method, and then use the NMF model to obtain the monitoring statistics Nn2 and the control limits Nlim2 and SPElim of SPEn ;
在线采集化工生产过程中d个采集点的所述变量的M个测量样本，并构建测量矩阵Xg′＝[x1,x2,...,xM]∈Rd×M，对测量矩阵Xg′进行预处理，得到矩阵Xg，然后利用NMF模型获取第t个样本的统计量Ng2(t)和SPEg(t)，将其与控制限和SPElim进行比较，如果统计量Ng2(t)或SPEg(t)超过相应的控制限或SPElim，则将检测到的第t个样本认为故障样本，获取故障矩阵Mf为故障样本个数；M measurement samples of the variable at d collection points in the chemical production process are collected online, and a measurement matrix Xg ′=[x1 ,x2 ,...,xM ]∈Rd×M is constructed to measure the The matrix Xg ′ is preprocessed to obtain the matrix Xg , and then the NMF model is used to obtain the statistics Ng2 (t) and SPEg (t) of the t-th sample, and compare them with the control limit Compare with SPElim if the statistic Ng2 (t) or SPEg (t) exceeds the corresponding control limit or SPElim , then the detected t-th sample is regarded as a fault sample, and the fault matrix is obtained Mf is the number of fault samples;
步骤二，全局变量自适应分块；Step 2, global variables are adaptively divided into blocks;
根据步骤一得到的故障矩阵构建故障样本的残差矩阵：The fault matrix obtained according to step 1 Construct the residual matrix of the faulty samples:
Ef＝Xf-Wn(WnTWn)-1WnTXf (1)Ef =Xf -Wn (WnT Wn )-1 WnT Xf (1)
计算Pearson相关系数，表示为:Calculate the Pearson correlation coefficient, expressed as:
这里，Ef,i和Ef,j分别表示第i和第j个变量的残差，是Ef,i的平均值，是Ef,j的平均值；Here, Ef,i and Ef,j represent the residuals of the i-th and j-th variables, respectively, is the mean value of Ef,i , is the mean value of Ef,j ;
对Rf进行t检验，得到显著水平矩阵Sf；Perform a t test on Rf to obtain a significant level matrix Sf ;
对矩阵Sf使用完整的链接算法将变量划分为b个子块Ci(i＝1,2,...，b)，其中，子块数据由子块Ci(i＝1,2,...，b)的变量构成，且满足d1+d2+...,+db＝d；Divide the variable into b subblocks Ci (i=1,2,...,b) using a full chaining algorithm on the matrix Sf, where the subblock data Consists of variables of sub-block Ci (i=1,2,...,b), and satisfies d1 +d2 +...,+db =d;
步骤三，分块故障监测；Step 3, block fault monitoring;
根据子块Ci(i＝1,2,...，b)构造每个子块的历史正常数据矩阵然后利用基于NMF模型的故障监测方法获得每个子块Xi的监测统计量的控制限和监测统计量SPEi的控制限SPEi,lim；Construct the historical normal data matrix of each sub-block according to the sub-blocks Ci (i=1,2,...,b) Then use the fault monitoring method based onNMF model to obtain the monitoring statistics of each sub-block Xi the control limit of and the control limit SPEi,lim of the monitoring statistic SPEi ;
计算第t个样本的b+1组统计量N2(t)和SPE(t)，并将它们与相应的控制限进行比较:Compute the b+1 set of statisticsN2 (t) and SPE(t) for the t-th sample and compare them to the corresponding control limits:
如果b+1个统计量N2(t)或SPE(t)均没有超过相应的控制限，则将检测到的第t个样本认为正常样本，否则为故障样本。If neither of the b+1 statistics N2 (t) nor SPE (t) exceeds the corresponding control limit, the detected t-th sample is regarded as a normal sample, otherwise it is a fault sample.
优选的，在所述步骤一中，利用NMF模型获取监控统计量Nn2与SPEn的控制限的方法包括以下步骤：Preferably, in the step 1, the method for obtaining the control limits of the monitoring statistics Nn2 and SPEn by using the NMF model includes the following steps:
利用NMF算法，把Xn矩阵分解为非负矩阵Wn∈Rd×k和的乘积，其中,Wn为基矩阵，Hn为系数矩阵，k为降维的阶次，且满足不等式(d+Mn)k≤dMn；Using the NMF algorithm, the Xn matrix is decomposed into non-negative matrices Wn ∈ Rd×k and The product of , where Wn is the basis matrix, Hn is the coefficient matrix, k is the order of dimensionality reduction, and satisfies the inequality (d+Mn )k≤dMn ;
确定Wn和Hn的最优值：由给定的Wn、Hn初值，利用迭代法则进行更新迭代，直到这两个矩阵不在变化时，结束迭代；Determine the optimal values of Wn and Hn : From the given initial values of Wn and Hn , use the iterative rule to update and iterate until the two matrices are not changing, and end the iteration;
确定每个样本t的监控指标Nn2(t)和SPEn(t)在过程控制的监控中，监控模型如下Determine the monitoring indicators Nn2 (t) and SPEn (t) of each sample t In the monitoring of process control, the monitoring model is as follows
其中，为低阶重构矩阵，En为残差矩阵；in, is the low-order reconstruction matrix, andEn is the residual matrix;
在该监控模型中，监控指标Nn2和SPEn的计算公式如下In this monitoring model, the calculation formulas of monitoring indicators Nn2 and SPEn are as follows
这里,和分别为矩阵和Xn的行向量；here, and are matrices and the row vector of Xn ;
利用核密度估计(KDE)获取监控指标Nn2和SPEn的控制限和SPEn,lim。Using Kernel Density Estimation (KDE) to Obtain Control Limits for Monitoring Metrics Nn2 and SPEn and SPEn,lim .
应当明白，在所述步骤一中利用NMF模型获取监测统计量Ng2与SPEg的方法、所述步骤三中利用NMF模型获取每个子块Xi的监测统计量Ni2和SPEi的控制限的方法均与所述步骤一中利用NMF模型获取监控指标Nn2与SPEn的控制限的方法是类同的，其仅通过将Xn矩阵替换为测量矩阵Xg或子块Xi矩阵，属实质相同的方法。It should be understood that in the step 1, the method for obtaining the monitoring statistics Ng2 and SPEg by using the NMF model, and in the third step, the NMF model is used to obtain the monitoring statistics Ni2 and SPEi of each sub-block Xi . The method of control limits is similar to the method of obtaining the control limits of monitoring indicators Nn2 and SPEn by using the NMF model in the first step, only by replacing the Xn matrix with the measurement matrix Xg or the sub-block Xi matrix, which is essentially the same method.
进一步的，确定Wn和Hn的初值的方法是：Further, the method for determining the initial values of Wn and Hn is:
构造测量矩阵计算其协方差Construct the measurement matrix Calculate its covariance
对协方差S进行特征值分解，然后按照特征值的大小进行降序排列，S的特征值为λ1≥λ2≥...≥λd≥0，S的特征向量为p1,p2,...,pd；The eigenvaluesof thecovariance S are decomposed, and then sorted in descending order according to the sizeof theeigenvalues . ...,pd ;
PCA模型对XnT的分解如下The decomposition of XnT by the PCA model is as follows
其中，由S的前A个特征向量组成的P＝[p1,p2,...,pA]∈Rd×A为负载矩阵，为得分矩阵，T的每一列都是主元变量，A是主元个数，采用累计方差准则确定主元个数，累计方差准则为Among them, P=[p1 ,p2 ,...,pA ]∈Rd×A composed of the first A eigenvectors of S is the load matrix, is a score matrix, each column of T is a pivot variable, A is the number of pivots, and the cumulative variance criterion is used to determine the number of pivots. The cumulative variance criterion is
当前A个主元的累积贡献率超过85％时，主元模型包含了足够多的原数据信息，When the cumulative contribution rate of the current A pivots exceeds 85%, the pivot model contains enough original data information,
令k＝A，则Wn、Hn初值为Wn＝abs(P)∈Rd×k，其中abs(.)是求取矩阵每一个元素的绝对值。Let k=A, then the initial values of Wn and Hn are Wn =abs(P)∈Rd×k , Where abs(.) is to find the absolute value of each element of the matrix.
进一步的，在所述步骤一中，对矩阵Xn′进行预处理的方法是：将Xn′的每一行减去这一行所有样本数据的均值，然后除以这一行所有样本数据的标准差，最后对矩阵里面的每个数据取其绝对值。Further, in the first step, the method of preprocessing the matrix Xn ' is: subtract the mean value of all sample data in this row from each row of Xn ', and then divide by the standard deviation of all sample data in this row , and finally take its absolute value for each data in the matrix.
进一步的，对矩阵Xg′进行预处理的方法是：将Xg′的每一行减去对应的Xn′行所有样本数据的均值，然后除以对应Xn′行所有样本数据的标准差，最后对矩阵里面的每个数据取其绝对值。Further, the method of preprocessing the matrix Xg ' is: subtract the mean value of all sample data corresponding to Xn ' row from each row of Xg ', and then divide by the standard deviation of all sample data corresponding to Xn ' row , and finally take its absolute value for each data in the matrix.
本发明的有益效果是：本发明所采用的基于APNMF模型的故障诊断与传统的基于NMF模型的故障诊断相比，系统在不同运行条件下的过程变量能够自适应的分成多个子变量模块，全局变量空间和每个子变量空间由NMF方法建模。然后，采用核密度估计(KDE)方法计算定义的统计指标的控制限，之后进行故障的监测。该方法充分利用了块内局部信息和整体全局信息，提高故障监测的准确率。The beneficial effects of the present invention are: compared with the traditional fault diagnosis based on the NMF model, the fault diagnosis based on the APNMF model adopted by the present invention can adaptively divide the process variables of the system under different operating conditions into a plurality of sub-variable modules, and the global The variable space and each subvariable space are modeled by the NMF method. Then, the Kernel Density Estimation (KDE) method is used to calculate the control limits of the defined statistical indicators, and then the fault monitoring is carried out. The method makes full use of the local information in the block and the overall global information to improve the accuracy of fault monitoring.
附图说明Description of drawings
图1为本发明的流程图。FIG. 1 is a flow chart of the present invention.
图2为TE生产过程的原理图。Figure 2 is a schematic diagram of the TE production process.
图3为故障5的全局监测图，图中横坐标为样本(samples)。FIG. 3 is a global monitoring diagram of fault 5, and the abscissa in the diagram is samples.
图4为故障5的子块C1监测图。FIG. 4 is a monitoring diagram of sub-block C1 of fault 5 .
图5为故障5的子块C2监测图。FIG.5 is a monitoring diagram of sub-block C2 for fault 5. FIG.
图6为故障5的子块C3监测图。FIG.6 is a monitoring diagram of sub-block C3 of fault 5. FIG.
图7为故障5的子块C4监测图。FIG. 7 is a monitoring diagram of sub-blockC4 of fault 5. FIG.
图8为故障5的子块C5监测图。FIG. 8 is a monitoring diagram of sub-blockC5 of fault 5. FIG.
图9为故障5的子块C6监测图。FIG. 9 is a monitoring diagram of sub-blockC6 of fault 5. FIG.
图10为故障5的子块C7监测图。FIG.10 is a monitoring diagram of sub-block C7 of fault 5. FIG.
具体实施方式Detailed ways
下面结合附图和实施例来说明本发明的具体实施方式，但以下实施例只是用来详细说明本发明，并不以任何方式限制本发明的范围。The specific embodiments of the present invention will be described below with reference to the accompanying drawings and examples, but the following examples are only used to describe the present invention in detail, and do not limit the scope of the present invention in any way.
TE过程是由美国Eastman化学公司的Downs和Vogel提出的化工过程模型，该过程仿真是基于数据驱动的，是过程故障诊断监测的有效工具。因此，本发明选用TE仿真例子进行验证。在实施例1中以故障5冷凝器冷却水入口温度的阶跃变化为例进行说明。TE process is a chemical process model proposed by Downs and Vogel of Eastman Chemical Company in the United States. The process simulation is based on data-driven and is an effective tool for process fault diagnosis and monitoring. Therefore, the present invention selects a TE simulation example for verification. In Example 1, the step change of the cooling water inlet temperature of the condenser in fault 5 is taken as an example for description.
实施例1：本发明提出的一种基于自适应分块非负矩阵分解(APNMF)的化工生产过程故障监测方法，用于处理化工生产过程中多个采集点监测的变量数据以识别出与已知故障相对应的数据，所述变量包括温度、压力、液位、流体速度和流量中的至少一种，参见图1-3，包括以下步骤：Embodiment 1: A fault monitoring method for chemical production process based on adaptive block non-negative matrix factorization (APNMF) proposed by the present invention is used to process variable data monitored by multiple collection points in the chemical production process to identify The data corresponding to the known fault, the variables include at least one of temperature, pressure, liquid level, fluid velocity and flow rate, see Figure 1-3, including the following steps:
步骤一、基于非负矩阵的全局故障监测。Step 1. Global fault monitoring based on non-negative matrix.
1)运行TE过程仿真，离线采集d个监测点的所述变量的Mn个历史正常样本(即获取采集点记录的离线数据)，并构建历史矩阵对矩阵Xn′进行预处理，预处理方法是将Xn′的每一行减去这一行全部样本的均值(可以利用Matlab软件的mean函数)且除以相应的这一行所有样本的标准差(可以利用Matlab软件的std函数)，然后对矩阵里面的每个数据取其绝对值(可以利用Matlab软件的abs函数)，得到预处理后的矩阵Xn。这里，d＝33，Mn＝500。1) Run the TE process simulation, collect Mn historical normal samples of the variables of the d monitoring points offline (that is, obtain offline data recorded at the collection points), and construct a historical matrix The matrix Xn ' is preprocessed. The preprocessing method is to subtract the mean value of all samples in this row from each row of Xn ' (the mean function of Matlab software can be used) and divide by the corresponding standard deviation of all samples in this row ( You can use the std function of Matlab software), and then take the absolute value of each data in the matrix (you can use the abs function of Matlab software) to obtain the preprocessed matrix Xn . Here, d=33 andMn =500.
2)利用NMF算法，把矩阵Xn分解为非负矩阵Wn∈Rd×k和的乘积，可以表达为Xn≈WnHn。其中Wn为基矩阵，Hn为系数矩阵，k为降维的阶次，且满足不等式(d+Mn)k≤dMn。2) Using the NMF algorithm, decompose the matrix Xn into non-negative matrices Wn ∈ Rd×k and The product of , can be expressed as Xn ≈ Wn Hn . Wherein Wn is the basis matrix, Hn is the coefficient matrix, k is the order of dimension reduction, and satisfies the inequality (d+Mn )k≤dMn .
3)确定Wn和Hn的最优值。首先，利用PCA分解获取k值以及Wn、Hn的初值，具体方法如下，3) Determine the optimal values of Wn and Hn . First, use PCA decomposition to obtain the k value and the initial values of Wn , Hn , the specific method is as follows:
构造测量矩阵计算其协方差Construct the measurement matrix Calculate its covariance
对协方差S进行特征值分解，然后按照特征值的大小进行降序排列(可以利用Matlab软件中的eig函数)。S的特征值为λ1≥λ2≥...≥λd≥0，S的特征向量为p1,p2,...,pd。The eigenvalues of the covariance S are decomposed, and then sorted in descending order according to the size of the eigenvalues (the eig function in Matlab software can be used). The eigenvalues of S are λ1 ≥λ2 ≥...≥λd ≥0, and the eigenvectors of S are p1 , p2 ,...,pd .
PCA模型对XnT的分解如下The decomposition of XnT by the PCA model is as follows
其中，由S的前A个特征向量组成的P＝[p1,p2,...,pA]∈Rd×A为负载矩阵，为得分矩阵，T的每一列都是主元变量，A是主元个数，采用累计方差准则确定主元个数，累计方差准则为Among them, P=[p1 ,p2 ,...,pA ]∈Rd×A composed of the first A eigenvectors of S is the load matrix, is a score matrix, each column of T is a pivot variable, A is the number of pivots, and the cumulative variance criterion is used to determine the number of pivots. The cumulative variance criterion is
当前A＝17个主元的累积贡献率超过85％时，主元模型包含了足够多的原数据信息，When the cumulative contribution rate of the current A=17 pivots exceeds 85%, the pivot model contains enough original data information,
令k＝A，则Wn、Hn初值为Wn＝abs(P)∈Rd×k，其中abs(.)是求取矩阵每一个元素的绝对值。Let k=A, then the initial values of Wn and Hn are Wn =abs(P)∈Rd×k , Where abs(.) is to find the absolute value of each element of the matrix.
然后，基于利用PCA分解获取Wn、Hn初值，通过迭代法则，进行一定次数的更新迭代，直到这两个数变化较小时或者不在变化时，结束迭代。这里，迭代次数为1000次。迭代法则如下，Then, based on the PCA decomposition to obtain the initial values of Wn and Hn , through the iterative rule, a certain number of update iterations are performed, until the two numbers change little or do not change, the iteration ends. Here, the number of iterations is 1000. The iterative rule is as follows,
4)确定每个样本t的监控指标Nn2(t)和SPEn(t)。4) Determine the monitoring indicators Nn2 (t) and SPEn (t) of each sample t.
在过程控制的监控中，监控模型如下：In the monitoring of process control, the monitoring model is as follows:
其中，为低阶重构矩阵，En为残差矩阵；in, is the low-order reconstruction matrix, andEn is the residual matrix;
在该监控模型中，监控指标Nn2和SPEn的计算公式如下In this monitoring model, the calculation formulas of monitoring indicators Nn2 and SPEn are as follows
这里,和分别为矩阵和Xn的行向量；here, and are matrices and the row vector of Xn ;
5)计算监控统计量Nn2和SPEn的控制限。由于Nn2和SPEn都是单变量，此时适合选用核密度估计(KDE)求取控制限和SPElim(可以利用matlab软件中计算KDE的fitdist和icdf函数)。5) Calculate the control limits for monitoring statistics Nn2 and SPEn . Since Nn2 and SPEn are both univariate, it is suitable to use Kernel Density Estimation (KDE) to obtain the control limit. and SPElim (you can use the fitdist and icdf functions of KDE in matlab software).
6)在线采集化工生产过程中d个采集点的所述变量的M个测量样本，并构建测量矩阵Xg′＝[x1,x2,...,xM]∈Rd×M，对测量矩阵Xg′进行预处理，即将Xg′的每一行减去对应的Xn′行所有样本数据的均值，然后除以对应Xn′行所有样本数据的标准差，最后对矩阵里面的每个数据取其绝对值，得到预处理后的矩阵Xg。计算系数矩阵Hg＝WnTXg。这里，d＝33，M＝960。其中，在进行数据监测时，前160个数据为正常数据，后800个数据为故障数据。6) Collect online M measurement samples of the variable at d collection points in the chemical production process, and construct a measurement matrix Xg ′=[x1 ,x2 ,...,xM ]∈Rd×M , The measurement matrix Xg ′ is preprocessed, that is, each row of Xg ′ is subtracted from the mean of all sample data in the corresponding Xn ′ row, and then divided by the standard deviation of all the sample data in the corresponding Xn ′ row, and finally the matrix Take its absolute value for each data of , and get the preprocessed matrix Xg . Calculate the coefficient matrix Hg =WnT Xg . Here, d=33 and M=960. Among them, during data monitoring, the first 160 data are normal data, and the last 800 data are fault data.
7)使用公式(14)和(15)计算并得出第t(1≤t≤M)个样本的统计量Ng2(t)和SPEg(t)，将其与控制限和SPElim进行比较，如果统计量Ng2(t)或SPEg(t)超过相应的控制限或SPElim，则将检测到的第t个样本认为故障样本，获取故障矩阵Mf为故障样本个数；7) Calculate and obtain the statistics Ng2 (t) and SPEg (t) of the t (1≤t≤M) th sample using formulas (14) and (15), and compare them with the control limit Compare with SPElim if the statistic Ng2 (t) or SPEg (t) exceeds the corresponding control limit or SPElim , then the detected t-th sample is regarded as a fault sample, and the fault matrix is obtained Mf is the number of fault samples;
步骤二、全局变量自适应分块。Step 2: Global variable adaptive block.
8)根据步骤一得到的故障矩阵Mf为数据个数(Mf＝307)构建故障样本的残差矩阵：8) The fault matrix obtained according to step 1 Mf is the number of data (Mf =307) to construct the residual matrix of fault samples:
Ef＝Xf-Wn(WnTWn)-1WnTXf (16)Ef =Xf -Wn (WnT Wn )-1 WnT Xf (16)
9)计算Pearson相关系数，表示为:9) Calculate the Pearson correlation coefficient, which is expressed as:
这里，Ef,i和Ef,j分别表示第i和第j个变量的残差，是Ef,i的平均值，是Ef,j的平均值；Here, Ef,i and Ef,j represent the residuals of the i-th and j-th variables, respectively, is the mean value of Ef,i , is the mean value of Ef,j ;
10)对Rf进行t检验(可以利用Matlab软件的ttest函数)，得到显著水平矩阵Sf。Sf为变量之间的相关程度，范围为0到1。其中，Sf越小则两个变量之间的相关性越强。例如，如果Sf≤0.05，则两个变量的相关性是显著的。10) Perform a t test on Rf (the ttest function of Matlab software can be used) to obtain a significant level matrix Sf . Sf is the degree of correlation between variables, ranging from 0 to 1. Among them, the smaller the Sf is, the stronger the correlation between the two variables is. For example, the correlation of two variables is significant if Sf ≤ 0.05.
11)将矩阵Sf定义为距离矩阵，并使用完整的链接算法(可以利用Matlab软件的linkage函数)将变量划分为若干子块Ci(i＝1,2,...，b)。子块数据由子块Ci(i＝1,2,...，b)的变量构成，且满足d1+d2+...,+db＝d。这里共分为C1(1 2 2 9)2，C2(2 21 9 32)，C3(3 5 8 6 14)，C4(1 25 4 16 27 7 1320),C5(18 31 19 26),C6(17 33)和C7(10 28 11 24 22)七个子块。11) Define the matrix Sf as a distance matrix, and use a complete linkage algorithm (the linkage function of Matlab software can be used) to divide the variable into several sub-blocks Ci (i=1,2,...,b). subblock data It consists of variables of sub-blocks Ci (i=1, 2, . . . ,b ) and satisfies d1 +d2 + . It is divided into C1 (1 2 2 9) 2, C2 (2 21 9 32), C3 (3 5 8 6 14), C4 (1 25 4 16 27 7 1320), C5 (18 31 19 26), C6 (17 33) and C7 (10 28 11 24 22) seven sub-blocks.
步骤三、分块故障监测。Step 3: Block fault monitoring.
12)根据子块Ci(i＝1,2,...，b＝7)构造每个子块的历史正常数据矩阵并根据步骤一中的2)、3)步骤得到每个子块的基矩阵Wni和系数矩阵Hni。12) Construct the historical normal data matrix of each sub-block according to the sub-blocks Ci (i=1,2,...,b=7) And obtain the basis matrix Wni and coefficient matrix Hni of each sub-block according to steps 2) and 3) in step 1.
13)根据公式(14)、(15)构建每个子块的监测统计量Nn,i2和SPEn,i，并用KDE算法计算控制限和SPEi,lim。13) Construct the monitoring statistics Nn,i2 and SPEn,i of each sub-block according to formulas (14) and (15), and use the KDE algorithm to calculate the control limit and SPEi,lim .
14)构造子块测量数据矩阵并利用公式(14)、(15)计算每个子块Xi的监测统计量Ni2和SPEi。14) Construct sub-block measurement data matrix And use formulas (14) and (15) to calculate the monitoring statistics Ni2 and SPEi of each sub-block Xi.
15)计算第t个样本的b+1组统计量N2(t)和SPE(t)，并将它们与相应的控制限进行比较:15) Calculate the b+1 set of statisticsN2 (t) and SPE(t) for the t-th sample and compare them to the corresponding control limits:
如果b+1个统计量N2(t)或SPE(t)均没有超过相应的控制限，则将检测到的第t个样本认为正常样本，否则为故障样本。正常样本意味着判断结果是正常，故障样本意味着判断结果是故障，已经能够判断出正常、故障。具体的监测结果见图3-10所示。If neither of the b+1 statistics N2 (t) nor SPE (t) exceeds the corresponding control limit, the detected t-th sample is regarded as a normal sample, otherwise it is a fault sample. A normal sample means that the judgment result is normal, and a fault sample means that the judgment result is a fault, and it has been able to judge normal and faulty. The specific monitoring results are shown in Figure 3-10.
参见图1，通过以上三个步循环进行即可得到化工生产过程故障的监测结果。Referring to Figure 1, the monitoring results of chemical production process failures can be obtained by cyclically performing the above three steps.
在对故障5“凝器冷却水入口温度的阶跃变化”进行监测时，图3示出了采用NMF监测时在第161个样本和第376个样本之间清楚地When monitoring fault 5 "step change in condenser cooling water inlet temperature", Figure 3 shows a clear difference between the 161st and 376th samples with NMF monitoring
监测到了故障。然而，由于控制回路的补偿，在第385个样本之后很难通过N2和SPE统计监测到故障。采用APNMF方法分为C1(12 29 23 15 30),C2(2 21 9 32),C3(3 5 8 614)，C4(1 25 4 16 27 7 13 20),C5(18 31 19 26),C6(17 33)和C7(10 28 11 24 22)7个子块，图4-10示出了这7个子块的监测结果。图3中的低监测结果存在于图5、图6、图7、图8、图10中。但是，如图9所示，C6子块可以在整个故障操作中通过SPE统计监测故障。基于NMF的故障监测率N2和SPE分别为0.3300和0.3612；而基于APNMF的分别为0.4762和0.9924。APNMF的SPE统计数据显示故障仍然存在于过程中，并且子块C6中能监测出出大部分故障数据。通过上述分析，在故障5中，APNMF方法优于NMF方法，可以为监测人员提供更精确的信息。A fault has been detected. However, due to the compensation of the control loop, it is difficult to detect the failure byN2 and SPE statistics after the 385th sample. Using APNMF method, it is divided into C1 (12 29 23 15 30), C2 (2 21 9 32), C3 (3 5 8 614), C4 (1 25 4 16 27 7 13 20), C5 (18 31 19 26), C6 (17 33) and C7 (10 28 11 24 22) 7 sub-blocks, Figure 4-10 shows the monitoring results of these 7 sub-blocks. The low monitoring results in Figure 3 are present in Figure 5, Figure 6, Figure 7, Figure 8, Figure 10. However, as shown in Figure 9, theC6 sub-block can monitor the fault through SPE statistics throughout the fault operation. The NMF-based fault monitoring ratesN2 and SPE are 0.3300 and 0.3612, respectively; while those based on APNMF are 0.4762 and 0.9924, respectively. APNMF's SPE statistics show that the fault still exists in the process, and most of the fault data can be monitored in sub-blockC6 . Through the above analysis, in fault 5, the APNMF method is superior to the NMF method, which can provide more accurate information for the monitoring personnel.
实验例1：本实验例采用TE模型模拟了一种基于自适应分块非负矩阵分解(APNMF)的化工生产过程故障监测方法具体应用，表1列出了TE过程的33个采集点采集的变量数据，这些变量数据包括温度、压力、液位、流体速度流量和功率，表2列出了与这33个采集点采集的变量数据高度相关的21种故障，表3为分别采用PCA、NMF、APNMF对该21种故障监测时的故障监测结果。Experimental example 1: This experimental example uses the TE model to simulate the specific application of a fault monitoring method in the chemical production process based on adaptive block non-negative matrix factorization (APNMF). Variable data, these variable data include temperature, pressure, liquid level, fluid velocity, flow rate and power. Table 2 lists 21 faults that are highly correlated with the variable data collected at these 33 collection points. , APNMF fault monitoring results when monitoring the 21 faults.
表1 TE过程的采集的变量及对应的采集点信息Table 1 The variables collected in the TE process and the corresponding collection point information
表2 21种故障Table 2 21 faults
表3为21种故障下故障监测的准确率/故障检测延迟时间Table 3 shows the accuracy of fault monitoring/fault detection delay time under 21 faults
表3列21种故障下的PCA，NMF和APNMF的故障监测结果。具有鲜明对比度的检测率用粗体字标记。注意到NMF方法的总体效果优于PCA方法，这与已发表的很多论文中的结论是一致的。与PCA或NMF相比，APNMF方法在大多数故障模式下显示出最高的故障检测率和最少的延迟时间，并且在故障3,5,9,10,16和19的模式下具有更好的性能，而该些故障均与温度相关。上述三种方法很容易检测到故障1,2,6,7,8,12,13,14,17和18因为它们对整个过程的变化和平均值有明显的影响。根据以上对TE过程的采集点采集的变量数据的分析，所提出的APNMF方法在故障监测方面比PCA和NMF表现更好。Table 3 lists the fault monitoring results of PCA, NMF and APNMF under 21 faults. Detection rates with sharp contrast are marked in bold. It is noted that the overall performance of the NMF method is better than that of the PCA method, which is consistent with the conclusions in many published papers. Compared with PCA or NMF, the APNMF method shows the highest failure detection rate and the least delay time in most failure modes, and has better performance in failure modes 3, 5, 9, 10, 16 and 19 , and these faults are related to temperature. The above three methods can easily detect faults 1, 2, 6, 7, 8, 12, 13, 14, 17 and 18 because they have obvious effects on the variation and average value of the whole process. According to the above analysis of the variable data collected at the collection points of the TE process, the proposed APNMF method performs better than PCA and NMF in fault monitoring.
上面结合附图和实施例对本发明作了详细的说明，但是，所属技术领域的技术人员能够理解，在不脱离本发明宗旨的前提下，还可以对上述实施例中的各个具体参数进行变更，形成多个具体的实施例，均为本发明的常见变化范围，在此不再一一详述。The present invention has been described in detail above in conjunction with the accompanying drawings and the embodiments, but those skilled in the art can understand that, without departing from the purpose of the present invention, each specific parameter in the above-mentioned embodiments can also be changed, Forming a plurality of specific embodiments is the common variation range of the present invention, and will not be described in detail here.
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