技术领域technical field
本发明以非线性过程工业系统为对象，以提高建模稳定性和故障预测精度为目标，提出了一种包括复杂过程工业数据预处理技术、反馈差分优化极限学习机(Feedback Differential Evolution Optimized Extreme Learning Machine，FDE-ELM)技术，以及时延扩展有限状态机(Extended Finite State Machine，EFSM)技术的工业故障预测方法。The present invention takes the nonlinear process industrial system as the object, aims at improving the modeling stability and fault prediction accuracy, and proposes a complex process industrial data preprocessing technology, Feedback Differential Evolution Optimized Extreme Learning (Feedback Differential Evolution Optimized Extreme Learning) Machine, FDE-ELM) technology, and the industrial fault prediction method of the extended finite state machine (Extended Finite State Machine, EFSM) technology.
背景技术Background technique
过程工业包括石化、冶金、造纸等是我国的基础产业，它涉及到国民生活的方方面面。过程工业具备生产规模大、工艺复杂、过程非线性、危险系数高等特点，因而成为了故障预测和诊断的一个重要研究领域。近些年来我国相关行业事故频发，其中在化工行业情况尤为严峻，2013年青岛石化爆炸造成62人死亡、136人受伤，这使得加强过程生产过程的安全保障变得迫在眉睫。为了预防此类事故的发生造成严重后果，高精度的故障预测和诊断是一种有效的规避故障方法。因此，研究提高非线性过程工业故障预测和故障诊断精度和模型稳定性，具有重要的理论意义和实用价值。The process industry, including petrochemical, metallurgy, and papermaking, is the basic industry of our country, and it involves all aspects of national life. The process industry has the characteristics of large production scale, complex process, nonlinear process and high risk factor, so it has become an important research field of fault prediction and diagnosis. In recent years, there have been frequent accidents in related industries in my country, especially in the chemical industry. In 2013, Qingdao petrochemical explosion caused 62 deaths and 136 injuries. This makes it extremely urgent to strengthen the safety guarantee of the production process. In order to prevent such accidents from causing serious consequences, high-precision fault prediction and diagnosis is an effective method to avoid faults. Therefore, it is of great theoretical significance and practical value to study how to improve the accuracy and model stability of fault prediction and fault diagnosis in the nonlinear process industry.
人工神经网络是一种仿生物结构形成的数学模型，能够根据提供的数据，通过训练和学习找到数据中的内在联系，从而搭建出目标对象的数学模型。该方法是一种技术数据驱动的方法，在实际应用上不依赖先验知识和规则，并且具有很强的非线性逼近能力，因而被广泛应用于复杂工业对象的参数估计、操作优化、故障预测等领域中。在现有的各种算法中，极限学习机(Extreme Learning Machine，ELM)是一种单隐含层前馈神经网络的快速参数训练算法，它能够解决大多数传统算法收敛速度慢、容易陷入局部极小等问题。但是ELM网络为了达到比较好的效果，通常需要大量的隐含层节点，这增加了算法的复杂度。同时，由于ELM学习算法的输入层权值是随机产生的，而随机权值通常不是最优的，因此网络学习的精度不高。为了解决这两个问题，可以引入差分(differential evolution，DE)优化算法来找到网络最优的输入层权值，提高学习精度，同时也可以减少隐含层节点数，从而达到降低算法复杂度的目的。但在过程工业中，DE-ELM没有考虑到数据的时延和系统变量的内在联系，因此往往预测效果不佳。Artificial neural network is a mathematical model that imitates the formation of biological structures. According to the provided data, it can find the internal connection in the data through training and learning, so as to build a mathematical model of the target object. This method is a technical data-driven method that does not rely on prior knowledge and rules in practical applications, and has strong nonlinear approximation capabilities, so it is widely used in parameter estimation, operation optimization, and fault prediction of complex industrial objects. and other fields. Among the various existing algorithms, extreme learning machine (Extreme Learning Machine, ELM) is a fast parameter training algorithm for single hidden layer feedforward neural network, which can solve the problem of slow convergence speed of most traditional algorithms and easy to fall into local problems. Minor issues. However, in order to achieve better results, the ELM network usually requires a large number of hidden layer nodes, which increases the complexity of the algorithm. At the same time, since the weights of the input layer of the ELM learning algorithm are randomly generated, and the random weights are usually not optimal, the accuracy of network learning is not high. In order to solve these two problems, the differential evolution (DE) optimization algorithm can be introduced to find the optimal input layer weights of the network, improve the learning accuracy, and at the same time reduce the number of nodes in the hidden layer, thereby reducing the complexity of the algorithm. Purpose. However, in the process industry, DE-ELM does not take into account the time delay of data and the internal relationship of system variables, so the prediction effect is often poor.
EFSM是一种在计算机领域应用十分成熟的切片技术，它可以有效地简化复杂系统模型并且有助于系统模型的分析和理解。EFSM由三大部分组成，状态依赖图、数据依赖图、迁移表，通过这三部分就能够将系统间的内部关系和状态转换清晰的表征出来。因此可以将其 引入过程工业领域，应用于系统分析和故障推理中。然而传统的EFSM无法直接引入过程工业，其中还存在一些无法解决的问题：首先，传统EFSM数据依赖图搭建完全凭借数学模型，但在过程工业系统中，数学模型往往十分复杂，无法精确表示；其次，过程工业系统间的变量往往存在时延，传统EFSM并未考虑这一时延问题，因而会导致变量间关系的分析不准确。EFSM is a very mature slicing technology applied in the computer field, which can effectively simplify the complex system model and help the analysis and understanding of the system model. EFSM consists of three parts, state dependency graph, data dependency graph, and migration table. Through these three parts, the internal relationship and state transition between systems can be clearly represented. Therefore, it can be introduced into the field of process industry and applied in system analysis and fault reasoning. However, the traditional EFSM cannot be directly introduced into the process industry, and there are still some unsolvable problems: First, the traditional EFSM data dependency graph is built entirely by mathematical models, but in the process industry system, the mathematical models are often very complicated and cannot be accurately expressed; secondly , variables between process industry systems often have time delays, traditional EFSM does not take this time delay into account, which will lead to inaccurate analysis of the relationship between variables.
发明内容Contents of the invention
本发明的目的在于：克服传统故障预测精度低、模型稳定性不高的缺点，并针对现有技术存在的上述问题，提出了一种基于FDE-ELM和时延EFSM非线性过程工业故障预测的方法。该方法将人工神经网络和EFSM引入过程工业故障预测领域，分别构建基于时延EFSM的状态依赖图和数据依赖图，以及基于FDE-ELM技术的变量预测模型，提出了一种预测精度高、模型稳定性好、算法复杂度低的故障预测方法，为降低事故发生率、节约硬件成本、提高生产安全等级提供了技术支撑。The purpose of the present invention is to: overcome the shortcomings of traditional failure prediction accuracy and low model stability, and aim at the above-mentioned problems existing in the prior art, propose a kind of based on FDE-ELM and time-delay EFSM non-linear process industry fault prediction method. This method introduces the artificial neural network and EFSM into the field of fault prediction in the process industry, constructs the state dependence graph and data dependence graph based on time-delay EFSM, and the variable prediction model based on FDE-ELM technology, and proposes a model with high prediction accuracy and The fault prediction method with good stability and low algorithm complexity provides technical support for reducing the accident rate, saving hardware costs, and improving production safety levels.
本发明提供了一种用于非线性过程工业的故障预测和推理方法，其特征在于所述方法包括：The present invention provides a fault prediction and reasoning method for the nonlinear process industry, characterized in that the method comprises:
数据预处理过程：对工业数据进行降噪处理；Data preprocessing process: noise reduction processing for industrial data;
时延时延扩展有限状态机EFSM模型构建过程：运用时延互信息量TDMI对预处理后的数据进行延迟时间计算和相关性分析，搭建数据依赖图，并通过先验知识和对模型的机理分析构建状态依赖图和迁移表；The construction process of the time-delay time-delay extended finite state machine EFSM model: use the time-delay mutual information TDMI to calculate the delay time and correlation analysis of the preprocessed data, build a data dependency graph, and use the prior knowledge and the mechanism of the model Analyze build state dependency graphs and migration tables;
基于反馈差分优化极限学习机FDE-ELM的变量预测过程：构建FDE-ELM网络，选取系统的关键变量作为网络的输出节点，并通过所述数据依赖图建立的变量间的联系得到与输出节点对应的输入节点；The variable prediction process of the extreme learning machine FDE-ELM based on feedback difference optimization: construct the FDE-ELM network, select the key variables of the system as the output nodes of the network, and obtain the correspondence between the variables established by the data dependency graph and the output nodes the input node;
基于时延EFSM的故障推理过程：当所述FDE-ELM的变量预测过程输出的预测结果超出设定的控制阈值范围时，将所述预测结果导入时延EFSM进行故障推理；具体为，根据预先设定好的迁移表进行推理，当预测结果满足迁移条件时，状态发生转变，当状态不再发生转变时，输出的状态即为发生的故障类型。Fault reasoning process based on time-delay EFSM: when the prediction result output by the variable prediction process of the FDE-ELM exceeds the set control threshold range, the prediction result is imported into the time-delay EFSM for fault reasoning; specifically, according to the preset The set migration table is used for reasoning. When the prediction result meets the migration conditions, the state changes. When the state no longer changes, the output state is the type of fault that occurred.
所述数据预处理过程中，采用小波去噪对数据进行预处理。In the data preprocessing process, wavelet denoising is used to preprocess the data.
所述数据依赖图的搭建具体包括：针对系统中每一个变量运用TDMI计算其与其他变量间的相关系数和延迟时间，所得的最短延迟时间所对应的两个变量即为最短传播路径所对应的两个变量；连接所述两个变量形成传播路径；计算所述两个变量之间的干扰传播方向，确定两个变量之间最终的延迟时间t和相关系数r并进行标注，形成完整的数据依赖图。The construction of the data dependence graph specifically includes: using TDMI for each variable in the system to calculate the correlation coefficient and delay time between it and other variables, and the two variables corresponding to the obtained shortest delay time are the shortest propagation paths. Two variables; connecting the two variables to form a propagation path; calculating the interference propagation direction between the two variables, determining the final delay time t and correlation coefficient r between the two variables and marking them to form complete data Dependency graph.
所述状态依赖图和迁移表的搭建具体包括：通过对机理模型的分析和先验知识确定系统的状态，创建状态依赖图用于表征各个状态之间的联系；根据所述数据依赖图中变量间的t 和r，得出状态和变量间的关系，从而得到状态依赖图中对应的状态间迁移的迁移规则，进而构建迁移表。The construction of the state dependency graph and the migration table specifically includes: determining the state of the system through the analysis of the mechanism model and prior knowledge, creating a state dependency graph to represent the relationship between each state; according to the variables in the data dependency graph Between t and r, the relationship between the state and the variables is obtained, so as to obtain the migration rules of the corresponding state migration in the state dependency graph, and then build the migration table.
所述基于FDE-ELM的变量预测过程具体包括：加入反馈层来存储预测变量的时间序列信息，同时将EFSM提取后的变量间关系引入FDE-ELM；将所述数据依赖图中与目标预测变量相邻的变量作为网络的输入。The variable prediction process based on FDE-ELM specifically includes: adding a feedback layer to store time series information of predictor variables, and introducing the relationship between variables extracted by EFSM into FDE-ELM; Neighboring variables serve as input to the network.
所述基于时延EFSM的故障推理过程具体包括：当目标变量的预测结果超出了设定的控制限范围，则将FDE-ELM网络中所有关键变量的预测结果导入EFSM进行故障推理；所述故障推理依照迁移表中的迁移条件逐步进行，具体为，在当前状态下，搜索当前状态作为初始状态对应的迁移条件是否满足，若满足则迁移被激活，状态发生迁移，当状态不再发生迁移时输出对应的故障识别结果。The fault reasoning process based on the delay EFSM specifically includes: when the predicted result of the target variable exceeds the set control limit range, then the predicted results of all key variables in the FDE-ELM network are imported into the EFSM for fault reasoning; the fault The reasoning is carried out step by step according to the migration conditions in the migration table. Specifically, in the current state, search whether the migration conditions corresponding to the current state as the initial state are satisfied. If it is satisfied, the migration is activated and the state is migrated. When the state no longer migrates Output the corresponding fault identification result.
所述推理过程通过人工操作实现，或者通过过程编程自动化实现。The reasoning process is realized through manual operation, or automatically realized through process programming.
本发明与现有技术相比的创新点在于：The innovation point of the present invention compared with prior art is:
(1)本发明提高了一种新型神经网络预测方法——FDE-ELM，该方法可以在随机选择输入层权值的前提下，利用差分优化找到最优输入层权值送入网络，从而提高网络的训练和泛化精度。反馈的引入，能够有效地存储系统连续运行过程中数据的时序信息，改善由于时延引起的泛化精度不高的问题。该方法具有学习速率快、学习效果稳定、泛化精度高、模型稳定性强等诸多优良特性，为过程工业故障预测提供了新思路。(1) The present invention improves a novel neural network prediction method——FDE-ELM, which can use differential optimization to find the optimal input layer weight and send it into the network under the premise of randomly selecting the input layer weight, thereby improving Network training and generalization accuracy. The introduction of feedback can effectively store the timing information of the data during the continuous operation of the system, and improve the problem of low generalization accuracy caused by time delay. This method has many excellent characteristics such as fast learning rate, stable learning effect, high generalization accuracy, and strong model stability, which provides a new idea for process industry fault prediction.
(2)本发明将运用于计算机领域的EFSM成功引入过程工业故障预测领域。同时，在传统EFSM中引入了TDMI，得到变量间时延信息和相关系数形成了一种新的时延EFSM。通过该方法，我们能清楚地了解系统变量间的内部关系，选取相关性高的变量输入预测网络，从而避免了大量的冗余信息对预测过程的影响。实验表明，时延EFSM的引入能大幅度提高变量预测的精度。(2) The present invention successfully introduces the EFSM used in the computer field into the field of process industry failure prediction. At the same time, TDMI is introduced into the traditional EFSM, and a new time-delay EFSM is formed by obtaining the time-delay information and correlation coefficients among variables. Through this method, we can clearly understand the internal relationship between system variables, and select highly correlated variables to input into the prediction network, thereby avoiding the influence of a large amount of redundant information on the prediction process. Experiments show that the introduction of time-delayed EFSM can greatly improve the accuracy of variable prediction.
(3)本发明运用时延EFSM，建立了系统状态依赖图和迁移表，定义了一套新的迁移条件表述方法，有效地解决了过程工业数学模型复杂的问题。(3) The present invention uses the time-delay EFSM to establish a system state dependency graph and a migration table, and defines a new set of migration condition expression methods, effectively solving the problem of complex mathematical models in the process industry.
(4)本发明将时延EFSM和FDE-ELM有机的结合起来，将FDE-ELM预测所得的变量值导入FDE-ELM运用于故障推理过程，充分发挥了这两者的技术优势，获得了良好的技术效果。(4) The present invention organically combines time delay EFSM and FDE-ELM, imports the variable value predicted by FDE-ELM into FDE-ELM and applies it to the fault reasoning process, fully exerts the technical advantages of the two, and obtains a good technical effect.
附图说明Description of drawings
图1为本发明所述方法的工作流程图；Fig. 1 is the working flow diagram of method of the present invention;
图2为TE过程工艺流程图；Figure 2 is a flow chart of the TE process;
图3为TE过程的时延EFSM数据依赖图；Fig. 3 is the delay EFSM data dependency figure of TE process;
图4为TE过程的时延EFSM状态依赖图；Fig. 4 is the delay EFSM state dependency diagram of TE process;
图5为FDE-ELM网络结构图；Fig. 5 is a FDE-ELM network structure diagram;
图6为TE过程变量预测结果。Figure 6 shows the prediction results of TE process variables.
具体实施方式Detailed ways
如图1所示，为本发明所述方法的工作流程图。(1)数据预处理过程：该过程主要对工业数据进行降噪处理，避免由于噪声干扰影响后续操作结果的准确性。(2)时延EFSM模型构建过程：该过程主要是运用TDMI对预处理后的数据进行延迟时间计算和相关性分析，搭建出数据依赖图，并通过先验知识和对模型的机理分析构建状态依赖图和迁移表，从而将复杂的过程工业对象约减为简单的模型，清晰地展现系统变量间的内部联系、状态间的内部联系、以及状态和变量间的相互联系。(3)基于FDE-ELM的变量预测过程：该过程是使用FDE-ELM网络预测过程工业运行中可能发生的异常。在构建FDE-ELM网络时，选取系统的关键变量(一般将异常时会直接导致故障发生的变量定义为关键变量)作为网络的输出节点，并通过数据依赖图建立的变量间的联系得到与输出节点对应的输入节点。在训练过程中差分优化和反馈同时发挥作用，保障网络的稳定性和预测结果的可靠性，使得泛化结果有着较小的误差。(4)基于时延EFSM的故障推理过程：当FDE-ELM输出的预测结果超出设定的控制阈值范围时，将FDE-ELM输出的预测结果导入时延EFSM进行故障推理。推理根据预先设定好的迁移表进行，当预测结果满足迁移条件时，状态发生转变。最后，当状态不再发生转变时，输出的状态即为可能发生的故障类型。As shown in Fig. 1, it is a work flow diagram of the method of the present invention. (1) Data preprocessing process: This process mainly performs noise reduction processing on industrial data to avoid affecting the accuracy of subsequent operation results due to noise interference. (2) Time-delay EFSM model construction process: This process mainly uses TDMI to calculate the delay time and correlation analysis of the preprocessed data, build a data dependency graph, and build the state through prior knowledge and mechanism analysis of the model Dependency graphs and migration tables reduce complex process industry objects to simple models, clearly showing the internal connections between system variables, the internal connections between states, and the interrelationships between states and variables. (3) Variable prediction process based on FDE-ELM: This process is to use FDE-ELM network to predict possible abnormalities in process industry operation. When constructing the FDE-ELM network, select the key variables of the system (generally, the variables that will directly lead to failures during abnormalities are defined as key variables) as the output nodes of the network, and the relationship between variables established through the data dependency graph is obtained and output The input node to which the node corresponds. During the training process, differential optimization and feedback play a role at the same time to ensure the stability of the network and the reliability of the prediction results, so that the generalization results have a small error. (4) Fault inference process based on time-delay EFSM: When the prediction result output by FDE-ELM exceeds the set control threshold range, the prediction result output by FDE-ELM is imported into time-delay EFSM for fault reasoning. The reasoning is performed according to the pre-set migration table, and when the prediction result meets the migration conditions, the state changes. Finally, when the state no longer transitions, the state of the output is the type of fault that may occur.
为了清晰地说明该方法的具体过程，我们选择TE过程(Tennessee Eastman Process)作为仿真对象，其具体工艺流程图如图2所示。TE标准过程是一个实际非线性工业过程，经常被用来验证故障预测和故障诊断的效果。TE过程是一种实际化工过程的仿真模拟，由美国Tennessee Eastman化学公司过程控制小组的J.J.Downs和E.F.Vogel提出，广泛应用于过程控制技术的研究。TE过程包括12个操纵变量和41个测量变量，如表1所示。同时，在标准TE过程中包含了20种故障，分为随机故障和阶跃故障两大类。我们选取其中的阶跃故障(故障1、故障2、故障3、故障4、故障5和故障7)作为研究对象，如表2所示。In order to clearly illustrate the specific process of this method, we choose the TE process (Tennessee Eastman Process) as the simulation object, and its specific process flow chart is shown in Figure 2. The TE standard process is an actual nonlinear industrial process, which is often used to verify the effect of fault prediction and fault diagnosis. The TE process is a simulation of an actual chemical process, proposed by J.J.Downs and E.F.Vogel of the process control group of Tennessee Eastman Chemical Company in the United States, and is widely used in the research of process control technology. The TE process includes 12 manipulated variables and 41 measured variables, as shown in Table 1. At the same time, 20 types of faults are included in the standard TE process, which are divided into two categories: random faults and step faults. We select the step faults (fault 1, fault 2, fault 3, fault 4, fault 5 and fault 7) as the research objects, as shown in Table 2.
表1TE过程变量Table 1 TE process variables
表2TE过程故障Table 2 TE Process Failures
步骤(1)所述的数据预处理，具体表现为：The data preprocessing described in step (1) is specifically shown as:
仿真的数据是含有大量噪声的，因此我们采用小波去噪对数据进行预处理。The simulated data contains a lot of noise, so we use wavelet denoising to preprocess the data.
步骤(2)中的变量特征提取，具体表现为：The variable feature extraction in step (2) is specifically expressed as:
系统中大量的变量之间是相互关联的，我们需要这些变量进行TDMI计算来提取它们之间 的特征。对任意两个变量Xi、Xj(i＝1～53,j＝1～53,i≠j)，其时延信息熵定义为：A large number of variables in the system are interrelated, and we need these variables to perform TDMI calculations to extract the characteristics between them. For any two variables Xi , Xj (i=1~53, j=1~53, i≠j), the delay information entropy is defined as:
pij表示联合概率密度，Xi(t)代表第i个变量在t时刻的值，Xi(t+τ)代表第i个变量在t+τ时刻的值，其中τ为延迟时间，t为当前采样时刻。(X、Y、τ、t均没有定义，已定义)代表Xi(τ)和Xj(t+τ)间的时延信息熵，代表Xj(τ)和Xi(t+τ)间的时延信息熵对于相同的一组变量Xi、Xj，设定不同的τ计算出不同的和并将所得结果的第一个极大值分别记为和接着计算X和Y的依赖关系：pij represents the joint probability density, Xi( t) represents the value of the i-th variable at time t,Xi (t+τ) represents the value of the i-th variable at time t+τ, where τ is the delay time, t is The current sampling moment. (X, Y, τ, t are not defined, but defined) Represents the time delay information entropy between Xi (τ) and Xj (t+τ), Represents the time delay information entropy between Xj (τ) and Xi (t+τ) For the same set of variables Xi and Xj , different τ is set to calculate different and And record the first maximum value of the result as and Then calculate the dependence of X and Y:
如果大于零，则信息流的方向是从Xi指向Xj，如果小于零，则信息流的方向是从Xj指向Xi。当等于零时，则代表Xi与Xj是相互独立的。在确定了依赖关系之后，我们就可以确定两个变量间的相关系数和延迟时间。选取和较大的值记作两个变量间相关系数r'，其对应的τ记为两个变量间的延迟时间τ'。if is greater than zero, the direction of information flow is from Xi to Xj , if If it is less than zero, the direction of information flow is from Xj to Xi . when When it is equal to zero, it means thatXi and Xj are independent of each other. After determining the dependencies, we can determine the correlation coefficient and lag time between the two variables. select and The larger value is recorded as the correlation coefficient r' between the two variables, and its corresponding τ is recorded as the delay time τ' between the two variables.
步骤(2)中的数据依赖图按照下述方法来构建：The data dependency graph in step (2) is constructed according to the following method:
a)选取一个变量Xi(1≤i≤n，n为变量的总数)，计算出该变量Xi与另一变量Xj(1≤j≤n，j≠i)的延迟时间τ'ij，重复该操作，得到变量Xi与系统中其余变量间的延迟时间。a) Select a variable Xi (1≤i≤n, n is the total number of variables), and calculate the delay time τ'ij between this variable Xi and another variable Xj (1≤j≤n, j≠i) , repeat this operation to get the delay time between variableXi and other variables in the system.
b)找到变量Xi最小延迟时间τ'imin所对应的变量Xm。Xm可称为变量Xi的相关变量，并用直线连接这两个变量。b) Find the variable Xm corresponding to the minimum delay time τ'imin of the variable Xi . Xm can be called the dependent variable of variable Xi, and a straight line connects these two variables.
c)对系统中所有变量重复该操作，得到每个变量相关变量，并进行连接，最终整理得到一个变量间的关系网络。c) Repeat this operation for all the variables in the system to obtain the related variables of each variable and connect them to finally obtain a relationship network between variables.
d)根据变量特征提取中描述的依赖关系计算方法，计算关系网络中相连接变量间的依赖关系，并根据依赖关系在之前的连线上加上箭头表征信息流的方向(若则箭头由Xi指向Xm，若则箭头由Xm指向Xi)。d) According to the dependency calculation method described in variable feature extraction, calculate the dependency relationship between connected variables in the relationship network, and add arrows to the previous connection according to the dependency relationship to represent the direction of information flow (if Then the arrow points from Xi to Xm , if Then the arrow points from Xm to Xi ).
e)在带箭头的连线上标注出通过变量特征提取所计算得到的两个变量间的相关系数r'和延迟时间τ'，就完成了数据依赖图的构建(如图3所示)。e) Mark the correlation coefficient r' and the delay time τ' between the two variables calculated by variable feature extraction on the line with the arrow, and the construction of the data dependence graph is completed (as shown in Figure 3).
步骤(2)中的状态依赖图按照下述方法来构建：The state dependency graph in step (2) is constructed in the following way:
通过对TE系统的机理分析和先验知识构建状态依赖图(如图4所示)。图中，Sk表示系统 的状态，由对TE过程工艺流程的分析和故障预测的需要而设定，Tk(k＝1,2,3…)是两个状态间的迁移。当且仅当迁移被激活时，状态才会发生转移。The state dependence graph (as shown in Figure 4) is constructed through the mechanism analysis and prior knowledge of the TE system. In the figure, Sk represents the state of the system, which is set by the analysis of the TE process flow and the need for fault prediction, and Tk (k=1,2,3...) is the transition between the two states. A state transition occurs if and only if a transition is activated.
步骤(2)中的迁移规则表按照下述方法来构建：The migration rule table in step (2) is constructed according to the following method:
针对TE各个状态间的迁移建立迁移规则表，如表3所示。在状态依赖图中，某类状态(如S3，S5，S7)存在两条迁移路径，这两条迁移路径有相同初始状态，但是目标状态不同。这类状态在迁移表中对应存在两种状态模式，分别匹配不同的迁移条件和不同的目标状态。表中Sk(cv1)表示Sk的第一个状态模式(Sk为图4中对应的状态)，Sk(cv2)表示Sk的第二个状态模式。这里状态Xiset(i＝1～53)代表系统变量Xi的初始设定值，XiL代表变量Xi的控制阈值下限，XiH表示变量Xi的控制阈值上限，tset代表系统采样间隔周期。符号‘∨’表示逻辑关系“或”，具体含义是当‘∨’两侧任意一个条件满足时，该迁移被激活。符号‘∧’表示逻辑关系“与”，具体含义是当‘∧’两侧条件都满足时，该迁移才被激活。符号(+)表示变量值超过了预先设定的控制阈值上线，同时符号(-)表示变量值低于预先设定的控制阈值下限。A migration rule table is established for the migration between various TE states, as shown in Table 3. In the state dependency graph, there are two migration paths for a certain type of state (such as S3, S5, S7). These two migration paths have the same initial state, but different target states. This type of state corresponds to two state modes in the migration table, matching different migration conditions and different target states respectively. In the table, Sk(cv1) represents the first state mode of Sk (Sk is the corresponding state in Figure 4), and Sk(cv2) represents the second state mode of Sk. Here the stateXiset (i=1～53) represents the initial setting value of the system variableXi , XiL represents the lower limit of the control threshold of the variableXi , XiH represents the upper limit of the control threshold of the variableXi , and tset represents the system sampling interval cycle. The symbol '∨' represents the logical relationship "or", and the specific meaning is that when any condition on both sides of '∨' is satisfied, the transition is activated. The symbol '∧' represents the logical relationship "AND", and the specific meaning is that the migration is activated only when the conditions on both sides of '∧' are satisfied. The symbol (+) indicates that the variable value exceeds the upper limit of the preset control threshold, while the symbol (-) indicates that the variable value is lower than the lower limit of the preset control threshold.
表3TE过程的迁移表Table 3 Migration table of TE process
步骤(3)基于FDE-ELM的故障预测，具体表现为：Step (3) is based on FDE-ELM fault prediction, specifically as follows:
图5所示的即为FDE-ELM的网络结构图，从图中我们可以看到通过在输出层和输入层中 加入反馈层，反馈层的输入时上一个时刻的网络输出值，反馈层的输出连接到主网络的输入层，这样就可以进行迭代计算，从而存储变量的时序信息、提高学习精度。Figure 5 shows the network structure diagram of FDE-ELM. From the figure, we can see that by adding a feedback layer to the output layer and input layer, the input of the feedback layer is the network output value at the previous moment, and the feedback layer’s The output is connected to the input layer of the main network, so that iterative calculations can be performed, thereby storing the timing information of the variables and improving the learning accuracy.
为了便于描述，我们用y(t)代表预测变量(Xi,i＝1～53)在t-1时刻网络预测输出值，y(t+1)代表预测的变量在t时刻网络预测输出值。同时，对于FDE-ELM网络的输入，用xi(t)代表t时刻网络的第i个变量Xi当前时刻的采样真实值。如图5所示，y(t)代表预测变量上一时刻的网络输出值，同时y(t)被反馈到当前时刻的输入网络，y(t+1)代表预测变量当前时刻的网络输出值(即预测值)。对应于TE模型FDE-ELM具体算法如下：For the convenience of description, we use y(t) to represent the predictor variable (Xi , i=1～53) at the time t-1 network forecast output value, and y(t+1) represents the predicted variable at the time t network forecast output value . At the same time, for the input of the FDE-ELM network, usexi (t) to represent the sampled real value of the ith variable Xi of the network at the momentt . As shown in Figure 5, y(t) represents the network output value of the predictor variable at the previous moment, while y(t) is fed back to the input network at the current moment, and y(t+1) represents the network output value of the predictor variable at the current moment (i.e. predicted value). The specific algorithm corresponding to the TE model FDE-ELM is as follows:
(1)输入训练集和差分优化算法(DE)中的控制参数(比例因子F、交叉概率CR、最大迭代次数和种群数量Np)。(1) Input the training set and the control parameters (scale factor F, crossover probability CR, maximum number of iterations and population size Np) in the differential optimization algorithm (DE).
(2)种群初始化，设定当前迭代次数j＝1。(2) Population initialization, set the current iteration number j=1.
(3)从解空间随机生成d维目标向量ai(j)和bi(j)形成大小为N的初始种群。设定函数评价次数FES＝Np。(3) Randomly generate d-dimensional target vectors ai (j) and bi (j) from the solution space to form an initial population of size N. Set the number of function evaluations FES=Np.
(4)从i＝1toNp，执行以下步骤：(为方便描述，该步骤中参数a、b统一用字母v替代)(4) From i=1toNp, perform the following steps: (for convenience of description, parameters a and b are uniformly replaced by letter v in this step)
(4.1)变异：对于目标个体，通过如下公式将原始的个体随机的按照一定比例通过变异到一个新的个体，从而生成变异向量ui(j+1)＝[ui1(j+1),ui2(j+1),…,uid(j+1)]。(4.1) Variation: For the target individual, the original individual is randomly mutated into a new individual according to a certain ratio by the following formula, thereby generating a mutation vector ui (j+1)=[ui1 (j+1), ui2 (j+1),..., uid (j+1)].
ui(j+1)＝vbest(j)+F(vr1(j)-vr2(j))(4) ui (j+1)=vbest (j)+F(vr1 (j)-vr2 (j))(4)
其中r1,r2∈{1,2,…Np}是随机的，并且r1≠r2≠i。比例因子F∈(0,2]是一个常数，通过它控制不同变异vr1(j)-vr2(j)的倍数。vbest(j)是基向量，是当前种群中最优秀的个体，种群间可以通过它来共享最好的信息。由于变异操作是使用随机选择的两个个体之间的差异来进行计算，其计算结果可能会出现突变个体超出设定搜索域的情况，因此我们需要对其加以限制。当优化参数uiq(j+1)超出设定搜索域时，定义如下：where r1,r2∈{1,2,…Np} are random, and r1≠r2≠i. The proportional factor F∈(0,2] is a constant, through which it controls the multiple of different variations vr1 (j)-vr2 (j). vbest (j) is the base vector, which is the best individual in the current population, The best information can be shared between populations. Since the mutation operation is calculated using the difference between two randomly selected individuals, the calculation result may appear that the mutant individual exceeds the set search domain, so we need Limit it. When the optimization parameter uiq (j+1) exceeds the set search domain, it is defined as follows:
(4.2)交叉：在变异操作之后，应用交叉操作来增加种群的多样性。每个目标向量vi(j)对应的试验向量ki(j+1)＝[ki1(j+1),ki2(j+1),…,kid(j+1)]可由二项交叉(公式6)生成。(4.2) Crossover: After the mutation operation, the crossover operation is applied to increase the diversity of the population. The test vector ki (j+1)=[ki1 (j+1),ki2 (j+1),...,kid (j+1)] corresponding to each target vector vi (j) can be obtained by two The term intersection (Equation 6) generates.
其中，rand(q)表示在[0,1]之间的独立随机均匀分布，randn(i)表示变量i是从集合{1,2,…d}随机选择的，CR∈[0,1]表示交叉概率。Among them, rand(q) represents an independent random uniform distribution between [0,1], randn(i) represents that variable i is randomly selected from the set {1,2,...d}, CR∈[0,1] Indicates the crossover probability.
(4.3)选择：在交叉过程完成后，进行选择操作来决定试验向量ki(j+1)是否能成为j+1代种群中的个体。这是一个最优化问题，需要运用贪婪选择算法将试验向量ki(j+1)与原始目标个体vi(j)进行比较，得到下一代个体，具体过程如下：(4.3) Selection: After the crossover process is completed, a selection operation is performed to determine whether the test vector ki (j+1) can become an individual in the j+1 generation population. This is an optimization problem. It is necessary to use the greedy selection algorithm to compare the test vector ki (j+1) with the original target individual vi (j) to obtain the next generation of individuals. The specific process is as follows:
(5)令FES＝FES+Np。(5) Let FES=FES+Np.
(6)如果FES＝FESmax，跳转到步骤8，否则令j＝j+1，跳转到步骤4。(6) If FES=FESmax , go to step 8, otherwise let j=j+1, go to step 4.
(7)根据适应度函数f(·)最小原则，得到最优a和b。(7) According to the minimum principle of the fitness function f(·), the optimal a and b are obtained.
(8)根据得到了最优a和b，计算隐含层输出值hns＝g{as[xn(t),o(t)]+bs}其中，g(·)为隐含层神经元的激活函数。将关于个体神经网络m的所有训练样本的隐含层输出值构成一个隐含层输出矩阵H：(8) Calculate the hidden layer output value hns =g{as [xn (t),o(t)]+bs } according to the optimal a and b obtained, where g(·) is the hidden layer Activation function for layer neurons. The hidden layer output values of all training samples of the individual neural network m form a hidden layer output matrix H:
(9)利用Moore-Penrose广义逆来计算神经网络输出层权值向量：β＝(H)+Y，其中Y＝[y1,y2,…,yn]T，(H)+为H的Moore-Penrose广义逆。(9) Use the Moore-Penrose generalized inverse to calculate the weight vector of the neural network output layer: β=(H)+ Y, where Y=[y1 ,y2 ,…,yn ]T , (H)+ is H Moore-Penrose generalized inverse.
(10)取验证样本集 (10) Take the verification sample set
Xn＝[xn1,xn2,…,xnP]T∈RP；Yn＝[yn1]T∈R1}，N1为样本集的总数，P为网络的输入节点数。首先根据已产生的输入层权值向量as和隐含层阈值bs，计算神经网络的隐含层输出矩阵 Xn ＝[xn1 ,xn2 ,…,xnP ]T ∈ RP ; Yn ＝[yn1 ]T ∈ R1 }, N1 is the total number of sample sets, and P is the number of input nodes of the network. First, calculate the hidden layer output matrix of the neural network according to the generated input layer weight vector as and hidden layer threshold bs
然后按照如下公式计算所有验证样本在神经网络的输出值T。Then calculate the output value T of all verification samples in the neural network according to the following formula.
(11)计算神经网络的均方根误差RMSE。其中，均方根误差计算公式为：(11) Calculate the root mean square error RMSE of the neural network. Among them, the root mean square error calculation formula is:
为了验证本方法的有效性，针对TE过程用方法FDE-ELM结合TD-EFSM、DE-ELM结合TD-EFSM,单一FDE-ELM和单一DE-ELM分别进行测试，其泛化误差如表4所示。这里计算泛化误差用的是均方差，它不仅能够表示精度的高低也能用于判断模型的稳定性。In order to verify the effectiveness of this method, the method FDE-ELM combined with TD-EFSM, DE-ELM combined with TD-EFSM, single FDE-ELM and single DE-ELM were tested for the TE process, and the generalization errors are shown in Table 4 Show. Here, the mean square error is used to calculate the generalization error, which can not only indicate the level of accuracy but also be used to judge the stability of the model.
表4不同模型的泛化误差比较Table 4 Comparison of generalization errors of different models
从表4我们可以看出FDE-ELM结合TD-EFSM的方法误差是最小的，与其余三种方法相比预测精度有了大幅度提高。另外我们还可以看出TD-EFSM对预测精度的提高贡献最大，因为TD-EFSM只选取相关程度高的变量作为输入，避免的大量冗余信息的干扰预测的准确性。反馈的加入考虑了变量的时序信息，对精度也有的一定提高，起到了进一步优化方法的作用。两者共同作用，得到了一种预测精度最高，模型最稳定的预测方法。From Table 4, we can see that the method error of FDE-ELM combined with TD-EFSM is the smallest, and the prediction accuracy has been greatly improved compared with the other three methods. In addition, we can also see that TD-EFSM contributes the most to the improvement of prediction accuracy, because TD-EFSM only selects highly correlated variables as input, avoiding a large amount of redundant information that interferes with the prediction accuracy. The addition of feedback takes into account the timing information of variables, which improves the accuracy to a certain extent, and plays a role in further optimizing the method. The two work together to obtain a prediction method with the highest prediction accuracy and the most stable model.
步骤(4)基于时延EFSM的故障推理过程，具体表现为：Step (4) is based on the fault reasoning process of the time-delay EFSM, specifically as follows:
观察FDE-ELM的预测结果，如果所有变量均在正常范围内，则暂时无故障发生。如果有变量超出设定的控制阈值范围，则系统可能发生了故障。接着，为了进一步推理出故障类型，我们将预测结果引入TD-EFSM的迁移规则。预测结果通过迁移规则和过程状态是紧密联 系的，所以通过迁移规则在TD-EFSM状态依赖图中进行深度优先搜索识别出故障源。在这里我们以故障3为例，来展示故障识别和推理的整个流程。Observe the prediction results of FDE-ELM, if all variables are within the normal range, then no fault occurs temporarily. If any variable is outside the set control threshold range, the system may be malfunctioning. Then, in order to further infer the fault type, we introduce the prediction results into the migration rules of TD-EFSM. The prediction results are closely related to the process state through the migration rules, so the depth-first search in the TD-EFSM state dependency graph through the migration rules is used to identify the source of the fault. Here we take fault 3 as an example to show the entire process of fault identification and reasoning.
首先假设系统目前处于正常运行状态(S4)，为了验证方法的性能，人为地在系统中加入故障IDV(3)。控制阈值由正常工况下各变量的均值(μ)和方差(σ)来确定，控制阈值上限为μ+3σ，控制阈值下限为μ-3σ。为了更清楚的展示FDE-ELM的预测数据异常状况，对预测数据进行归一化。First, assuming that the system is currently in normal operation (S4), in order to verify the performance of the method, a fault IDV is artificially added to the system (3). The control threshold is determined by the mean (μ) and variance (σ) of each variable under normal working conditions, the upper limit of the control threshold is μ+3σ, and the lower limit of the control threshold is μ-3σ. In order to show the abnormality of FDE-ELM forecast data more clearly, the forecast data is normalized.
(1)当t＝ktset时，根据迁移表中的规则判断可知迁移6(T6)被激活。接着，系统状态由S4迁移到S3。读入变量当前时刻的变量预测结果，并进行归一化处理如图6所示。(1) When t=ktset , it can be known that transition 6 (T6) is activated according to the rules in the transition table. Then, the system state is transferred from S4 to S3. Read in the variable prediction results at the current moment of the variable, and perform normalization processing, as shown in Figure 6.
(2)在状态3下，系统根据预测结果发现，在变量X51和变量X52之间存在异常，而变量X45的当前值在正常范围内。由迁移条件可知，迁移8(T8)被激活，系统状态由S3迁移到S6。(2) In state 3, the system finds, according to the prediction result, that there is an anomaly between the variable X51 and the variable X52, while the current value of the variable X45 is within the normal range. It can be seen from the transition conditions that transition 8 (T8) is activated, and the system state transitions from S3 to S6.
(3)在状态6下，进一步判断变量X51和变量X52的异常状况，发现X51超过了控制阈值上限，因此将其标记为X51(+)。同时，变量X52并未发生任何异常。因此，系统依据迁移条件可判断得出迁移15(T15)被激活，系统状态由S6迁移到S7。(3) In state 6, further judge the abnormality of variable X51 and variable X52, and find that X51 exceeds the upper limit of the control threshold, so it is marked as X51 (+). At the same time, nothing abnormal happened to the variable X52. Therefore, according to the transition condition, the system can determine that transition 15 (T15) is activated, and the system state transitions from S6 to S7.
(4)在状态7下，进一步推理发现系统还存在其他异常变量。变量X21低于控制阈值下限，将其标记为S21(-)，同时其他的变量均在正常范围内。此时，迁移17(T17)被激活，系统状态由S7迁移到S12。(4) In state 7, further reasoning found that there are other abnormal variables in the system. Variable X21 is lower than the lower limit of the control threshold, which is marked as S21(-), while other variables are within the normal range. At this point, Transition 17 (T17) is activated, and the system state transitions from S7 to S12.
(5)由于S12是末端状态，因此推理过程结束。(5) Since S12 is an end state, the reasoning process ends.
状态S12的具体含义是故障3发生，因此故障3被准确的识别出来了。The specific meaning of state S12 is that fault 3 has occurred, so fault 3 has been accurately identified.
综上可知本方法在故障预测的精度和模型稳定性上提升上取得了很好的效果，并且能够有效的识别出故障类型，可视化系统故障推理识别过程中的状态的迁移路径，具有很强的创新性。In summary, it can be seen that this method has achieved good results in improving the accuracy of fault prediction and model stability, and can effectively identify the type of fault, and visualize the migration path of the state in the process of fault reasoning and identification of the system. innovative.
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