Fault diagnosis method based on enhanced multi-mode switching dynamic system model

Abstract

The invention belongs to the field of industrial process fault diagnosis, and discloses a fault diagnosis method based on an enhanced multi-mode switching dynamic system model, an LDS model is used as a penetration point, a transfer matrix is used to describe mode switching so as to establish an SLDS model, in addition, a hidden Markov chain is combined with the transfer matrix, and a fault diagnosis result is obtained. And an enhanced hidden Markov transfer matrix is constructed to further consider the high-order dynamic characteristics of multi-mode switching of process data, the establishment of an aSLDS model is completed, and the fault diagnosis performance is improved. The aSLDS model not only provides a new method for the fault diagnosis technology, improves the effectiveness and superiority of fault detection and classification, but also supplements process operators to grasp dynamic information among multi-modal data features and multiple groups of data modals, guarantees the safety and reliability in the industrial production process, and improves the fault diagnosis efficiency. And further development of fault diagnosis in an actual industrial process can be promoted.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial process fault diagnosis, and in particular relates to a fault diagnosis method based on an enhanced multi-mode switching dynamic system model. Background Art

[0002] With the continuous improvement of modern industrial productivity and the continuous progress of science and technology, industrial processes have the characteristics of large-scale, complex and refined. However, the probability of industrial process accidents has also increased, and major industrial accidents can cause huge economic losses and even casualties. Therefore, it is very necessary to introduce fault diagnosis technology to ensure the safety and reliability of the production process. Fault diagnosis methods are divided into three categories: fault diagnosis research based on mathematical models, fault diagnosis research based on knowledge, and fault diagnosis research based on data-driven. Compared with the other two fault diagnosis methods, the data-driven fault diagnosis method does not rely on accurate mathematical models and rich empirical knowledge, and is easier to implement flexibly. Coupled with the application of technologies such as distributed control systems, a large amount of process data can be recorded, which also provides strong support for data-driven fault diagnosis methods.

[0003] Modern complex industrial process data has significant characteristics such as dynamics, uncertainty and multimodality. These characteristics make industrial processes highly complex and diverse, and also affect the accuracy of fault diagnosis. Traditional fault diagnosis methods such as principal component analysis (PCA) and Fisher discriminant analysis (FDA) are static modeling and do not consider the characteristics of process data. Therefore, some scholars have improved traditional methods, such as dynamic principal component analysis (DPCA) and dynamic slow feature analysis (DSFA). However, these methods only extract one feature of process data and cannot accurately represent the actual industrial process. In recent years, the linear dynamic system (LDS) model has been used in the field of fault diagnosis to simultaneously extract the dynamic and uncertainty characteristics of process data. However, there are multiple fault modes in actual industrial processes. When a fault occurs, accurate identification of the fault mode can effectively improve the accuracy of fault diagnosis. Therefore, the study of multimodal features is very important.

[0004] In order to solve the problem of multi-modal feature extraction and simultaneously fuse multiple features of process data, the goal is to improve the fault diagnosis performance. The present invention proposes a new fault diagnosis method based on an enhanced switched linear dynamic system (aSLDS) model. Summary of the invention

[0005] In order to overcome the above technical problems, the present invention provides a new fault diagnosis method based on an enhanced switched linear dynamic system (aSLDS) model fusing multiple data features. The LDS model is used as the entry point, and the transfer matrix is ​​used to describe the modal switching, so as to establish the SLDS model. In addition, the hidden Markov chain is combined with the transfer matrix to construct an enhanced hidden Markov transfer matrix to further consider the high-order dynamic characteristics of switching between multiple modes of process data, complete the establishment of the aSLDS model and improve the fault diagnosis performance.

[0006] The present invention adopts the following technical solutions:

[0007] A fault diagnosis method based on an enhanced multi-mode switching dynamic system model comprises the following steps:

[0008] Step 1: Use the distributed system to collect normal data of the actual industrial process and fault data when a fault occurs, and divide the data into a training set and a test set: The training set for fault detection is X = {x1,…,x T}, where T represents the number of samples, including T normal data. The test set for fault detection is a fault data set of different modes. Where S represents the number of fault modes, and each fault mode contains T samples;

[0009] Step 2: In fault detection, use the training set data and the EM algorithm to construct the aSLDS model for the normal operating mode, determine the model parameter θ, and determine the threshold line;

[0010] Step 3: For the test process in fault detection, based on the model establishment, the logarithmic posterior probability of the sample at the current moment is calculated and compared with the threshold line to achieve fault detection;

[0011] Step 4: In fault classification, the collected data is re-divided into training set and test set. The training set data uses a set of normal data and S sets of fault data. in Fault data representing the training set The test set also contains a set of normal data and S sets of fault data in Represent the normal data of the test set, build the aSLDS model, and determine the model parameters θ;

[0012] Step 5: For the test process in fault classification, based on the model establishment, the posterior probability of the sample at the current moment is calculated, and the mode corresponding to the maximum posterior probability is found to determine the mode to which the sample belongs.

[0013] In step 1, a set of normal data and seven sets of fault data of the TE process are collected for simulation experiments. The variables of each set of data include A feed amount, D feed amount, E feed amount, A, C mixture feed amount, recycling flow, reactor feed rate, reactor temperature, discharge rate, product separator temperature, product separator pressure, product separator bottom flow, stripping tower pressure, stripping tower temperature, stripping tower steam flow, reactor cooling water outlet temperature, separator cooling water outlet temperature. All collected data are processed using a standardized formula, which is as follows:

[0014]

[0015] In the formula, x new represents the standardized data, x represents the original data, represents the mean of the original data, σ x Represents the standard deviation of the original data. The standardized data are divided into the fault detection training set X={x1,…,x T} and test sets for fault detection Where S represents the number of fault modes, and each fault mode contains T samples.

[0016] The step 2 comprises:

[0017] Step 2.1: Construct the aSLDS model. The model expression is as follows:

[0018]

[0019]

[0020] In the formula, s t ∈{1,2,…,S} represents the switching variable at time t, which can determine the mode and model parameters at time t, and S is the total number of modes. A(s t )∈{A(1),A(2),…,A(S)} and B(s t )∈{B(1),B(2),…,B(S)} are the state transfer matrix and the state emission matrix respectively, δ t (s t ) and η t (s t ) is Gaussian noise following a normal distribution,

[0021] Step 2.2: Determine model parameters:

[0022] For the aSLDS model, switch the variable s t Switch the variable s from the previous moment t-1 and latent variable z t-1Therefore, the enhanced hidden Markov transfer matrix W can be used to describe the dynamic characteristics between local LDS models within the aSLDS model, which is constructed as follows:

[0023] W(a,b)=p(s t |z t-1 =a,s t-1 =b)a,b∈{1,2,…,S}, (3)

[0024] The initial switching variable distribution p(s1) is assumed to be π0, with a mean of The variance is The Gaussian distribution of is given by the following formula:

[0025] π0(a)=p(s1=a)a∈{1,2,…,S}, (4)

[0026] Combined with step 2.1, we can see that the parameters involved in establishing the aSLDS model are:

[0027] Step 2.3: Train aSLDS model parameters:

[0028] Step 2.3.1: The EM algorithm can be used to estimate the parameters of all local LDS models in the aSLDS model. The joint probability distribution of the aSLDS model is shown below:

[0029]

[0030] In the formula, p(x t |z t ,s t ) and p(z t |z t-1 ,s t ) follows a Gaussian distribution:

[0031]

[0032]

[0033] Step 2.3.2: The joint probability distribution can be transferred to the log-likelihood function as follows:

[0034]

[0035] Step 2.3.3: Calculate the expected value of the latent variable distribution of the full data log-likelihood function as follows:

[0036]

[0037] Step 2.3.4: By letting the parameter μ in E(L) πThe partial derivative of is zero, and the updated parameter μ can be obtained π new , the formula is as follows:

[0038]

[0039] Step 2.3.5: The remaining model parameters are updated in the same way. The results are as follows

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] Step 2.3.6: Determine the transfer matrix parameters W:

[0046] The enhanced hidden Markov transfer matrix W of the aSLDS model is estimated using the Gaussian mixture model. According to the joint distribution, the Gaussian forward filtering formula can be obtained as follows:

[0047]

[0048] However, accurate filtering derivation is difficult to achieve, so a finite Gaussian mixture is used to approximate the Gaussian forward filter. The approximate recursion of formula (16) can be expressed as:

[0049] p(z t ,s t |x 1:t )=p(z t |s t ,x 1:t )p(s t |x 1:t ), (17)

[0050] Where p(z t |s t ,x 1:t ) is a continuous part, p(s t |x 1:t ) is a discrete part, both of which obey Gaussian distribution. t |s t ,x 1:t ) is a mixture containing i components. It can be expressed as:

[0051]

[0052] Where p(z t |s t-1 ,i t-1 ,s t ,x 1:t ) is a Gaussian distribution, p(s t-1 ,i t-1 |s t ,x 1:t ) is a mixture weight containing i components, and the mixture weight p(s t-1 ,i t-1 |s t ,x 1:t ) can be further calculated as follows:

[0053] p(s t-1 ,i t-1 |s t ,x 1:t )∝p(z t |i t-1 ,s t-1 ,s t ,x 1:t-1 )p(s t |i t-1 ,s t-1 ,x 1:t-1 )p(i t-1 |s t-1 ,x 1:t-1 )p(s t-1 |x 1:t-1 ), (19)

[0054] The first factor p(z t |i t-1 ,s t-1 ,s t ,x 1:t-1 ) obeys Gaussian distribution. The last two factors p(i t-1 |s t-1 ,x 1:t-1 ) and p(s t-1 |x 1:t-1 ) is given in the previous filtering iteration. In addition, p(s t |i t-1 ,s t-1 ,x 1:t-1 ) can be derived as follows:

[0055]

[0056] Among them, the enhanced hidden Markov transfer matrix W obeys p(z t |i t ,s t ,x1:t )’s mean-variance distribution.

[0057] Step 2.4: The formula for determining the threshold line is:

[0058] L=(1-α)T train , (twenty one)

[0059] In the formula, is the α significance level, T train is the total number of training samples.

[0060] Step 3 includes:

[0061] Step 3.1: Calculate the log posterior probability:

[0062]

[0063] In the formula, is the data in the test set.

[0064] Step 3.2: Compare the logprobabilities statistic with the threshold value to determine whether a fault has occurred. If the current sample is in a normal state, the posterior probability will fluctuate only slightly and remain below the threshold. However, when a fault occurs, the posterior probability will fluctuate greatly and exceed the threshold.

[0065] In step 4, the model parameters are updated using the parameter updating method in step 2.

[0066] Step 5 includes:

[0067] Step 5.1: Fault classification based on the aSLDS model can be determined by finding the maximum value of all posterior probabilities of the current test sample relative to different modes. The maximum posterior probability is expressed as Its formula is as follows:

[0068]

[0069] Step 5.2: The current sample belongs to the mode corresponding to the maximum posterior probability. The mode to which the current sample belongs can be further determined as follows:

[0070]

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] The present invention introduces an enhanced hidden Markov transfer matrix W on the basis of the LDS model to accurately divide the mode when a fault occurs, dig out higher-order data features, and complete the multi-feature fusion of process data at the same time, thereby improving the performance of fault diagnosis. The method takes the LDS model as the starting point, uses the transfer matrix to describe the mode switching, establishes the SLDS model, and further combines the hidden Markov chain with the transfer matrix to construct an enhanced hidden Markov transfer matrix to further consider the high-order dynamic features of the multi-modal switching of the process data, and completes the establishment of the aSLDS model. The aSLDS model can simultaneously consider the dynamics, uncertainty and multi-modal features of the data, and improves the fault diagnosis performance. Compared with the existing fault diagnosis methods, the aSLDS model not only provides a new method for fault diagnosis technology, improves the effectiveness and superiority of fault detection and classification, but also supplements the process operator's grasp of the dynamic information between the multi-modal data features and multiple groups of data modes, ensures the safety and reliability in the industrial production process, and is conducive to promoting the further development of actual industrial process fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is a flow chart of the fault diagnosis method of the present invention;

[0074] Figure 2 An enhanced switched linear dynamic system (aSLDS) algorithm model constructed for the present invention;

[0075] Figure 3 This is a diagram showing the effect of the aSLDS model in the present invention in terms of fault detection;

[0076] Figure 4 This is a comparison chart of the fault classification effects of the aSLDS model in the present invention and other methods. DETAILED DESCRIPTION

[0077] The embodiments of the present invention are described in detail below. The methods in the embodiments are conventional methods in the art unless otherwise specified. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0078] like Figure 1 As shown, a fault diagnosis method based on an enhanced multi-mode switching dynamic system model includes the following steps:

[0079] Step 1: Use the distributed system to collect normal data of the actual industrial process and fault data when a fault occurs, and divide the data into a training set and a test set: The training set for fault detection is X = {x1,…,x T}, where T represents the number of samples, including T normal data. The test set for fault detection is a fault data set of different modes. Where S represents the number of fault modes, and each fault mode contains T samples; the process variables of the collected TE data are shown in Table 1, and the fault modes of the collected TE data are shown in Table 2;

[0080] Table 1 TE process variables

[0081]

[0082] Table 2 Seven types of faults

[0083]

[0084] Step 2: Construct the aSLDS model based on the normal data of the training set obtained in step 1, use the EM algorithm and filtering algorithm to determine the model parameters and the threshold line;

[0085] Step 2.1: Construct the aSLDS model. The model expression is as follows:

[0086]

[0087]

[0088] In the formula, s t ∈{1,2,…,S} represents the switching variable at time t, which can determine the mode and model parameters at time t, and S is the total number of modes. A(s t )∈{A(1),A(2),…,A(S)} and B(s t )∈{B(1),B(2),…,B(S)} are the state transfer matrix and the state emission matrix respectively, δ t (s t ) and η t (s t ) is Gaussian noise, following a normal distribution

[0089] Step 2.2: Determine model parameters:

[0090] For the aSLDS model, switch the variable s t Depends on the previous switch variable s t-1 and latent variable z t-1 Therefore, the enhanced Markov transfer matrix W can be used to describe the dynamic characteristics between multiple LDS models, which is constructed as follows:

[0091] W(a,b)=p(s t |z t-1 =a,s t-1 =b)a,b∈{1,2,…,S}, (2)

[0092] The initial switching variable distribution p(s1) is assumed to be π0, with a mean of The variance is The Gaussian distribution of is given by the following formula:

[0093] π0(a)=p(s1=a)a∈{1,2,…,S}, (3)

[0094] Combined with step 2.1, we can see that the parameters involved in establishing the aSLDS model are:

[0095] Step 2.3: Train aSLDS model parameters:

[0096] Step 2.3.1: The EM algorithm can be used to estimate the parameters of the local LDS model in the aSLDS model. The joint probability distribution of the aSLDS model is shown below:

[0097]

[0098] In the formula, p(x t |z t ,s t ) and p(z t |z t-1 ,s t ) follows a Gaussian distribution:

[0099]

[0100]

[0101] Step 2.3.2: The joint probability distribution can be transferred to the log-likelihood function as follows:

[0102]

[0103] Step 2.3.3: Calculate the expected value of the latent variable distribution of the full data log-likelihood function as follows:

[0104]

[0105] Step 2.3.4: By letting the parameter μ in E(L) π The partial derivative of is zero, and the updated parameter μ can be obtained π new , the formula is as follows:

[0106]

[0107] Step 2.3.5: The remaining LDS model parameters are updated in the same way. The results are as follows

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] Step 2.3.6: Determine the transfer matrix parameters W:

[0114] The enhanced hidden Markov transfer matrix W of the aSLDS model is estimated using the Gaussian mixture model. According to the joint distribution, the Gaussian forward filtering formula can be obtained as follows:

[0115]

[0116] However, accurate filtering derivation is difficult to achieve, so a finite Gaussian mixture is used to approximate the Gaussian forward filter. The approximate recursion of formula (16) can be expressed as:

[0117] p(z t ,s t |x 1:t )=p(z t |s t ,x 1:t )p(s t |x 1:t ), (16)

[0118] Where p(z t |s t ,x 1:t ) is a continuous part, p(s t |x 1:t ) is a discrete part, both of which obey Gaussian distribution. t |s t ,x 1:t ) is a mixture containing i components. It can be expressed as:

[0119]

[0120] Where p(z t |s t-1 ,i t-1 ,s t ,x 1:t ) is a Gaussian distribution, p(s t-1 ,i t-1 |s t ,x 1:t ) is a mixture weight containing i components, and the mixture weight p(st-1 ,i t-1 |s t ,x 1:t ) can be further calculated as follows:

[0121] p(s t-1 ,i t-1 |s t ,x 1:t )∝p(z t |i t-1 ,s t-1 ,s t ,x 1:t-1 )p(s t |i t-1 ,s t-1 ,x 1:t-1 )p(i t-1 |s t-1 ,x 1:t-1 )p(s t-1 |x 1:t-1 ), (18)

[0122] The first factor p(z t |i t-1 ,s t-1 ,s t ,x 1:t-1 ) obeys Gaussian distribution. The last two factors p(i t-1 |s t-1 ,x 1:t-1 ) and p(s t-1 |x 1:t-1 ) is given in the previous filtering iteration. In addition, p(s t |i t-1 ,s t-1 ,x 1:t-1 ) can be derived as follows:

[0123]

[0124] Among them, the enhanced hidden Markov transfer matrix W obeys p(z t |i t ,s t ,x 1:t )’s mean-variance distribution.

[0125] Step 2.4: The formula for determining the threshold line is:

[0126] L=(1-α)T train , (20)

[0127] Where, is the significance level, T train is the total number of training samples.

[0128] Step 2.4: The formula for determining the threshold line is:

[0129] L=(1-α)T train , (twenty one)

[0130] Where, is the significance level, T train is the total number of training samples.

[0131] Step 3 For the test set samples in fault detection, calculate the logarithmic posterior probability and compare it with the threshold line to achieve fault detection:

[0132] Step 3.1: Calculate the log posterior probability:

[0133]

[0134] In the formula, is the test set data.

[0135] Step 3.2: Comparing the logprobabilities statistic with the threshold line value can determine whether a fault has occurred. If the state of the current sample is normal, the posterior probability will only fluctuate slightly and remain below the control limit. However, when a fault occurs, the posterior probability will be very different from the normal probability. Therefore, there will be a significant deviation from the normal control limit, exceeding the control limit.

[0136] In step 4, for fault classification, a training set containing normal data and fault data is used to build an aSLDS model, and the parameter updating method in step 2 is used to update the model parameters.

[0137] Step 5: For the test set samples in the fault classification, calculate the posterior probability and find the mode corresponding to the maximum posterior probability to determine the mode to which the sample belongs:

[0138] Step 5.1: Fault classification based on the aSLDS model can be determined by finding the maximum value of all posterior probabilities of the current test sample relative to different modes. The maximum posterior probability is expressed as Its formula is as follows:

[0139]

[0140] Step 5.2: The current sample belongs to the mode corresponding to the maximum posterior probability. The mode to which the current sample belongs can be further determined as follows:

[0141]

[0142] The effectiveness of the present invention is verified by experiments below, and the main fault detection and fault classification results are shown in the figure.

[0143] Compared with the algorithm LDS, the transfer matrix is ​​not used when switching modes. Compared with the algorithm SLDS, the transfer matrix of simple probability is used to switch modes.

[0144] in, Figure 3 It is the result of the aSLDS model based on fault detection; Figure 4 is the result of the aSLDS model based on fault classification. Figure 3 It can be seen that the logarithmic posterior probabilities corresponding to the seven fault modes gradually exceed the threshold line starting from the 160th sampling point, with low false alarm and false alarm rates. Faults 1, 3, and 6 have no delay in the occurrence of faults, while faults 2, 4, 5, and 6 have slight delays, which are delayed by 9, 5, 33, and 17 samples respectively; Figure 4 It can be seen that the aSLDS model proposed in the present invention uses the enhanced hidden Markov matrix as the transition matrix between mode switching, which can mine high-order feature information and greatly improve the accuracy of fault classification. The aSLDS model has high accuracy in the classification of eight modes, and only a small number of samples are misclassified. Among them, for fault four, the aSLDS model misclassifies 15 samples as normal mode, while the SLDS model misdiagnoses 23 samples as normal mode, fault five mode, fault six mode and fault seven mode. For fault seven, the aSLDS model misclassifies 5 samples as normal mode, while the SLDS model misclassifies 11 samples as normal mode and fault five mode. These results clearly show that the aSLDS model has superior fault classification performance, especially when multiple fault modes are involved. In addition, Table 3 summarizes the specific false alarm rates and misclassification rates of the three fault diagnosis methods.

[0145] Table 3 Fault classification results of different algorithms

[0146]

[0147] Therefore, the performance of the aSLDS model of the present invention in fault detection and fault classification has been verified. For fault detection, the aSLDS algorithm uses the logarithm of the posterior probability as a new statistic to successfully achieve fault detection, and the fault detection results show good monitoring performance. For fault classification, the aSLDS model is compared with the LDS model and the SLDS model, and the fault classification results further prove its superior classification ability. This is attributed to the extraction of multiple features of process data and the mining of high-order dynamic information between multiple models by constructing an enhanced hidden Markov transfer matrix, so as to more accurately find the most appropriate sample attribution mode.

[0148] Although the embodiments of the present invention have been shown and described, those skilled in the art will appreciate that various changes, modifications, substitutions and variations may be made to the above embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A fault diagnosis method based on an enhanced multi-mode switching dynamic system model, characterized in that: The following steps are involved: S1. Use the distributed system to collect normal data of the actual industrial process and fault data when a fault occurs, and divide the data into a training set and a test set. The training set for fault detection is X = {x1,…,x T }, where T represents the number of samples, including T normal data, and the test set for fault detection is a fault data set of different modes Where S represents the number of fault modes, and each fault mode contains T samples; S2. In fault detection, the training set data is used to construct the aSLDS model for the normal operating mode using the EM algorithm, the model parameter θ is determined, and the threshold line is determined; S3. For the test process in fault detection, based on the model establishment, the logarithmic posterior probability of the sample at the current moment is calculated and compared with the threshold line to achieve fault detection; S4. In fault classification, the collected data is re-divided into training set and test set. The training set data uses a set of normal data and S sets of fault data. in Fault data representing the training set The test set also contains a set of normal data and S sets of fault data in Represent the normal data of the test set, build the aSLDS model, and determine the model parameters θ; S5. For the test process in fault classification, based on the establishment of the model, the mode to which the sample belongs is determined by calculating the posterior probability of the sample at the current moment and finding the mode corresponding to the maximum posterior probability.

2. A fault diagnosis method based on an enhanced multi-mode switching dynamic system model according to claim 1, characterized in that: S1 includes: Collect a set of normal data and multiple sets of fault data of the TE process; All collected data were processed using standardized formulas; The standardized data are divided into a training set for fault detection and a test set for fault detection.

3. A fault diagnosis method based on an enhanced multi-mode switching dynamic system model according to claim 2, characterized in that S2 include: Construct aSLDS model; Determine model parameters; Train aSLDS model parameters; Determination of threshold line.

4. A fault diagnosis method based on an enhanced multi-mode switching dynamic system model according to claim 3, characterized in that: S3 includes: Calculate the log posterior probability; Compare the statistics with the threshold value to determine whether a fault has occurred.

5. A fault diagnosis method based on an enhanced multi-mode switching dynamic system model according to claim 4, characterized in that: S4 updates the model parameters using the parameter updating method in S2.

6. The fault diagnosis method based on the enhanced multi-mode switching dynamic system model according to claim 5 is characterized in that S5 include: The fault classification based on the aSLDS model is judged by finding the maximum value of all posterior probabilities of the current test sample relative to different modes; The current sample belongs to the mode corresponding to the maximum posterior probability, and the mode to which the current sample belongs is further determined.

Images