Industrial process tiny fault detection method based on slow independent feature probability difference

Abstract

The invention provides an industrial process small fault detection method based on slow independent feature probability difference, and belongs to the technical field of industrial process fault detection. The technical problem that traditional PCA is low in small fault detection rate is solved. According to the technical scheme, industrial data are standardized, slow-varying and fast-varying feature spaces are extracted through slow feature analysis SFA, and a probability difference detection index is constructed for the slow-varying features in combination with JS divergence and a sliding window; performing ICA (Independent Component Analysis) on the quick change features to construct a slow independent principal component, and constructing a slow independent feature probability difference index in combination with JS divergence and a sliding window; and adopting a Bayesian strategy to fuse the two feature probability difference indexes to generate a comprehensive detection index BIC. The method has the beneficial effects that noise-containing quick change features are denoised through ICA, the probability difference is enhanced by using JS divergence, noise interference is suppressed, and the tiny fault detection rate is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of fault detection in industrial processes, and in particular to a method for detecting minor faults in industrial processes based on the probability difference of slow independent features. Background Technique

[0002] In recent years, major industrialized countries have successively put forward strategic goals for the new century to improve industrial competitiveness and take the lead in the new round of industrial revolution. Driven by these national strategies, industrial automation mainly based on intelligent manufacturing has developed rapidly, and industrial production is constantly moving towards large-scale, complex and intelligent directions. However, the scale of industrial processes is becoming increasingly large, the structure of control systems is becoming increasingly complex, and at the same time, faults occur more and more frequently in industrial processes, especially minor faults in industrial processes. Due to the low amplitude, slow change, being submerged in measurement noise, and being suppressed by closed-loop control of minor faults, as well as the characteristics of actively compensating for minor changes, they are extremely easy to be ignored in the production process. As production time goes by, if minor faults are not intervened in time, they may gradually evolve into serious faults or even trigger major safety accidents, resulting in serious casualties, huge property and economic losses. Therefore, how to detect minor faults in industrial processes in time and then improve the detection rate of minor faults is an urgent problem to be solved in the current complex industrial processes.

[0003] Slow Feature Analysis (SFA) has gradually been applied to industrial process monitoring due to its ability to extract slowly changing features in non-stationary time series data. SFA learns the slowness of time by extracting the features that change most slowly from time series, and it is an effective unsupervised algorithm. However, although the SFA method can extract potential processes with slow time variation, it does not consider the temporal correlation of potential features in dynamic systems, resulting in the difficulty of effectively identifying early faults and anomalies hidden in the time series trend. Recent studies have shown that using the Kullback-Leibler Divergence (KLD) to evaluate the probability distribution difference of slowness features improves the fault detection accuracy.

[0004] Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are classical multivariate statistical methods, which have received extensive attention in the academic and industrial fields for multivariate statistical process monitoring methods. PCA decomposes the original data space into a principal subspace and a residual subspace, and uses statistical metrics and SPE for fault detection in industrial processes. However, industrial process data usually has the characteristics of high-dimensional redundancy, correlation, and non-Gaussianity. Although some scholars have proposed kernel PCA and artificial neural network PCA in recent years, these extended PCA methods mainly focus on second-order statistical features and still have limited ability to process non-Gaussian data. In contrast, research has shown that ICA can directly and efficiently analyze non-Gaussian data. In addition, features with slower changes extracted by SFA are generally considered to contain more essential information, while features with relatively faster changes may be mixed with noise in the collected data. ICA can effectively separate the components of the target signal and the noise signal, and further deeply mine the effective information in the data. Recent research has shown that in patent CN118643320B, KL divergence is introduced into micro-fault detection to further mine the weak probability information in industrial process data, thereby improving the sensitivity to micro-faults. However, KL divergence is asymmetric, so it cannot accurately evaluate the dispersion degree of the distributions of two variables. Summary of the Invention

[0005] Aiming at the technical problems of the traditional linear detection method PCA in capturing micro-faults and low micro-fault detection efficiency, the present invention provides an industrial process micro-fault detection method based on the probability difference of slow independent features. This method is divided into three parts. The data preprocessing is divided into a static space and a dynamic space through the SFA space. After building the slow feature probability difference model in the static space and the slow independent principal component probability difference model in the dynamic space respectively, the detection results of the two spaces are fused through the Bayesian inference strategy. Simulation studies show that the algorithm of the present invention significantly improves the micro-fault detection rate. The features with relatively faster changes that may be mixed with noise in the collected data are denoised by independent component analysis ICA, and then the fault probability difference information is amplified through JS divergence, thereby improving the micro-fault detection rate.

[0006] The inventive concept of the present invention is as follows: The method includes the following steps: In the slow feature probability difference model part, the training data and the test data are standardized, the covariance matrix of the data is constructed to obtain the whitening matrix and the transformation matrix, two types of features, slow-varying and fast-varying, are extracted through slow feature analysis (SFA), the Jensen-Shannon (JS) divergence and a sliding window are introduced, the probability distribution difference of the slowness features is evaluated to build a slow feature probability difference model, and a new monitoring index is established; In the slow independent component (SICA) space part, the fast-varying features after slow feature analysis are subjected to independent component analysis (ICA) to obtain a separation matrix, and further the fast-varying feature space is divided into a slow independent principal component space and a residual space. The dual feature processing method retains more effective fault information and also improves the separability between the effective features and the noise. Then, a slow independent principal component probability difference model is constructed by combining the JS divergence and the sliding window, and a new monitoring index is established; In the fusion fault detection probability part, the Bayesian inference strategy is used to fuse the detection results of the slow feature probability difference model and the slow independent principal component probability difference model to obtain a comprehensive detection index BIC, complete the detection of minor faults in the industrial process, significantly improve the accuracy of minor fault detection, and thus be able to avoid the occurrence of serious faults and even major accidents, ensuring the safe operation of the industrial process.

[0007] In order to achieve the above-mentioned invention purpose, the technical solution adopted by the present invention is specifically as follows: A method for detecting minor faults in an industrial process based on the probability difference of slow independent features, comprising the following steps:

[0008] Step S1: Collect data samples from the historical database obtained during the normal operation of the production process to construct a training set X0 ∈ R n×m , where n is the total number of samples, m is the number of process monitoring variables, and R is a real number matrix, and perform standardized preprocessing on each variable, and finally generate a standardized data matrix X, making its mean 0 and standard deviation 1;

[0009] Step S2: Perform slow feature analysis on the standardized training data X, calculate the whitening matrix Q and the transformation matrix W, extract its slow feature vector S(t), and divide the obtained slow feature vector into a slow-varying feature S1(t) and a fast-varying feature S2(t) according to both static change and dynamic change, obtaining the corresponding static distribution space s and dynamic distribution space

[0010] Step S3: In the static space s of the training data, calculate the JS divergence of the slow-varying features of the training data through a sliding window, quantitatively analyze the probability distribution, and construct an evaluation index of the slow-varying features based on the JS divergence And calculate the corresponding control limit through the Kernel Density Estimation (KDE) method

[0011] Step S4: In the dynamic space of the training data Independent Component Analysis (ICA) algorithm is used to separate the independent source signals from the mixed signals, and the training data is divided into the slow independent feature principal component space and the residual space by sorting the importance of the independent components and calculating the cumulative contribution degree.

[0012] Step S5: In the slow independent feature principal component space of the training data, the Jensen-Shannon (JS) divergence of the slow independent features of the training data is calculated by a sliding window to quantitatively analyze the probability distribution, and an evaluation index based on the JS divergence of the slow independent features is constructed. And the corresponding control limits are calculated by the Kernel Density Estimation (KDE) method.

[0013] Step S6: The fault data collected during the production process is used to construct a test set X t ∈R n×m , and each variable is preprocessed by standardization using the mean and standard deviation of X0 of the training data in Step S1, and finally a standardized data matrix X T is generated. For the standardized test data X T , slow feature analysis is performed, and the slow feature vector S T (t) is extracted using the transformation matrix W in Step S2, and the obtained slow feature vector is divided into slow-varying features S 1T (t) and fast-varying features S 2T (t) according to both static and dynamic changes, and the corresponding static distribution space s and dynamic distribution space are obtained.

[0014] Step S7: In the static space s of the test data, the JS divergence of the slow-varying features of the test data is calculated by a sliding window to quantitatively analyze the probability distribution, and a statistic based on the JS divergence of the slow-varying features is constructed.

[0015] Step S8: In the dynamic space of the test data , the test data is divided into the slow independent feature principal component space and the residual space using Step S4. Then, in the slow independent feature principal component space of the test data, the JS divergence of the slow independent features of the training data is calculated by a sliding window to quantitatively analyze the probability distribution, and a statistic based on the JS divergence of the slow independent features is constructed.

[0016] Step S9: The fault detection probabilities of the slow-varying feature space and the slow independent feature space are fused through Bayesian inference to calculate the final monitoring statistic BIC (Bayesian Inference Control), and it is determined whether there is a fault in the system according to whether the statistic BIC exceeds the control limit β.

[0017] The above are the overall steps of the algorithm of the present invention. The following will further elaborate on the specific steps in detail from two parts: offline modeling and fault detection, as shown below.

[0018] Offline Modeling:

[0019] Further, in step S1, the training data X0 is obtained, and the standardized matrix X = [X1, X2,..., X n T ∈R n×m is obtained by standardizing it using its mean and standard deviation. The formula is as follows, where mean(X0) is its mean and std(X0) is its standard deviation.

[0020] X = (X0 - mean(X0)) / std(X0) (1)

[0021] Further, in step S2, the standardized training data is subjected to slow feature analysis, and the obtained slow features are spatially partitioned into a static distribution space s and a dynamic distribution space The detailed steps are as follows:

[0022] S21. Collect the data X0 of the normal operating conditions in the industrial process and standardize it. The standardized data is denoted as the input data

[0023] X(t) = [x1(t), x2(t),..., x n (t)] T , calculate the covariance matrix ∑ pp of X(t), perform singular value decomposition to obtain the whitening matrix Q, and perform whitening processing to obtain the whitened data matrix z(t). The formula is as follows.

[0024]

[0025] ∑ XX = UΛU T (3)

[0026] Q = Λ -1 / 2 U T (4)

[0027]

[0028] S22. Calculate the first derivative of the whitened data z and perform singular value decomposition on its covariance matrix . The formula is as follows.

[0029]

[0030] where P is the eigenvector matrix, Ω = diag(λ1, λ2,..., λ​n ) is the eigenvalue matrix, and the eigenvalues λ1 are arranged in ascending order. The smaller the eigenvalue, the slower the slow feature changes.

[0031] S23. Obtain the slow feature transformation matrix W, a series of extracted slow features S(t), and calculate the degree of change Δ(X of the standardized input data X j ), determine the number M of slow-changing features of the training data according to formula (11), and the remaining number of slow features is the fast-changing features, that is, the slow-changing features are S1(t) = [s1(t), s2(t),...., s M (t)] T , and the fast-changing features are S2(t) = [s M+1 (t), s M+2 (t),...., s m (t)] T , where q = 0.1 represents the 0.1 upper quantile of the set {Δ(X j ), and the input data is divided into the fast feature space and the slow feature space. The formula is as follows.

[0032] W = PΛ -1 / 2 U T (8)

[0033] S(t) = WX(t) (9)

[0034]

[0035] Furthermore, in step S3, in the static distribution space s, calculate the overall mean μ of the slow-changing feature S1 of the training data S1 and the overall variance λ S1 , then calculate the mean μ S1 (i) and variance λ S1 (i) of the slow-changing feature S1 of the training data within the i-th sliding window, and calculate the JS divergence component S of the slow-changing feature S1 of the training data according to formula (12) below JS1 , and determine the evaluation index of the static space Determine the static corresponding static space control limit through the KDE method

[0036]

[0037] Among them, in the sliding window algorithm, the window width W is set to H, and the step size is set to 1, that is, it moves backward once at each sampling moment. Given that the number of data samples is n, there are a total of N = n - H + 1 sampling moments.

[0038] Calculate the static space statistic according to the formula The formula is as follows, given the confidence level Calculate the corresponding control limits by the KDE method

[0039]

[0040] Further, in step S4, in the fast-changing feature space of the training data, the independent component analysis algorithm is used to separate the independent source signals from the mixed signals, and by sorting the importance of the independent components, they are divided into a slow independent feature principal component space and a residual space. The detailed process is as follows:

[0041] S41. Select the fast-changing space feature matrix S2(t) = [s M+1 (t), s M+2 (t),...., s m (t)] T Perform ICA decomposition to obtain the independent component matrix ICAedS and the separation matrix W. The independent component matrix ICAedS is a combination of multiple independent components, but its characteristics are mainly reflected in several independent components, which reflect a large amount of information of the observed random system. The formula is as follows.

[0042] ICAedS = WS2(14)

[0043] S42. Establish an independent principal component space model by selecting several main independent components in ICAedS. Considering the simplicity and reliability of the algorithm, the L2 norm of the row vectors of the demixing matrix is used to sort the independent components. Calculate the L2 norm for each row of the separation matrix W obtained by ICA to reflect the energy intensity c(i) of each independent component. Sort the separation matrix W in descending order of the L2 norm to obtain the sorted norm value D, calculate the total energy C, and through cumulative energy screening, retain the first d main independent components so that their cumulative energy accounts for 80%. Then, the corresponding separation matrix W d = W(M + 1:d, :) (select the rows of the W matrix corresponding to the d main independent components) and W e = W(d:m, :) (the remaining matrix in W d ), calculate the slow independent feature principal component space S d and the residual space S e , and the formulas are as follows:

[0044]

[0045]

[0046] S d = W d S2(18)

[0047] Further, in step S5, after determining the independent principal component subspace of the training data, a sliding window is used to calculate the slow independent feature S of the training data d of the divergence component S JSd of the overall mean μ Sd and the overall variance λ Sd , and calculate the mean μ d and variance λ Sd (i) of the slow-varying feature S of the training data within the i-th sliding window, and construct a statistic Sd . Use the kernel density method to calculate the corresponding control limit according to the given confidence level . The formula is as follows .

[0048]

[0049] Fault detection:

[0050] Further, in step S6, obtain the test data X t , and use the mean mean(X0) and standard deviation std(X0) of the training data to perform standardization processing to obtain the standardized matrix X T = [X1, X2,..., X n T ∈R n×m . For the standardized test data X T , perform slow feature analysis. The transformation matrix W obtained in step S2 determines its slow feature vector S T (t) = WX T (t). Use the slow feature vector obtained by the number M of slow-varying features to divide it into slow-varying feature S 1T (t) = [s1(t), s2(t),...., s M (t)] T and fast-varying feature S 2T (t) = [s 2M+1 (t), s 2M+2 (t),...., s 2m (t)] T , and obtain the corresponding static distribution space s and dynamic distribution space . The formula is as follows

[0051] X T = (X t - mean(X0)) / std(X0) (21)

[0052] Further, in step S7, calculate the overall mean μ 1T and overall variance λ S1T of the slow-varying feature S of the test data in the static distribution space s​S1T Then calculate the mean value μ 1T of the slow-varying feature S of the test data within the i-th sliding window S1T (i), and the variance λ S1T (i), and obtain the JS divergence component S JS1T of the slow-varying feature S of the test data. Calculate the JS divergence component S 1T of the slow-varying feature S of the test data according to the following formula (22), and determine the static spatial statistic JS1

[0053]

[0054] Calculate the static spatial statistic The formula is as follows.

[0055]

[0056] Finally, determine whether a fault has occurred based on whether the statistic exceeds the control limit

[0057] Furthermore, in step S8, perform ICA decomposition on the fast-varying spatial feature matrix S 2T (t) = [s 2M+1 (t), s 2M+2 (t),...., s 2m (t)] T of the test data. The slow independent feature principal component space S dt and the residual space S et of the test data are calculated by the separation matrix W. The formula is as follows. dt

[0058] S d = W 2T S et (24)

[0059] S e = W 2T S dt (25)

[0060] Next, calculate the overall mean value μ Sdt and the overall variance λ Sdt of the slow independent feature S of the test data. Then calculate the mean value μ dt and the variance λ Sdt of the slow independent feature S of the test data within the i-th sliding window, and calculate the JS divergence component through formula (26) to construct the statistic Sdt (i). The formula is as follows.

[0061] ​​​​

[0062] Finally, according to the statistic whether it exceeds the control limit to determine whether a fault has occurred.

[0063] Furthermore, in step S9, a Bayesian inference mechanism is adopted. From the statistics calculated in steps S7 and S8, the probabilities of faults occurring in the slow-varying feature space and the slow independent component subspace data are calculated. The probabilities of the two spaces are fused to obtain the monitoring statistic BIC. By judging whether the fused monitoring statistic BIC exceeds the control limit β, it is determined whether a fault has occurred. The specific steps are as follows:

[0064] S91. Calculate the probability fusion index corresponding to the static space statistic The conditional probabilities are calculated respectively according to the following formulas

[0065] and

[0066]

[0067] where N and F represent normal and fault conditions respectively.

[0068] The fault probability is calculated according to the following formula

[0069]

[0070] The fault probability is calculated according to the following formula

[0071]

[0072] S92. Calculate the probability fusion index corresponding to the slow independent space statistic The implementation process of the probability fusion index is similar to steps 1) - 3),

[0073] so it will not be elaborated. The calculated probabilities and are as follows.

[0074]

[0075] S93. Adopt the Bayesian probability algorithm to fuse the detection results of the two spaces to obtain the comprehensive statistic BIC. The formula

[0076] is as follows:

[0077]

[0078] ​Set the fault discrimination threshold β. When BIC ≤ β, the system is considered to be in a normal state; when BIC > β, the system is considered to be in a fault state.

[0079] In the above method, steps S1 to S5 are the offline modeling stage for building the slow feature probability difference and slow independent component probability difference. Steps S6 to S8 are the fault detection stage for the slow feature probability difference and slow independent component probability difference. Step S9 is to fuse the fault detection results of the two probability difference models and draw a conclusion.

[0080] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0081] 1. Aiming at the importance difference of features in different dimensions, the present invention uses SFA to extract the features with slower changes to retain more essential fault information. At the same time, ICA is performed on the features with faster changes to reduce noise interference. This dual feature processing method not only reduces the loss rate of fault information but also improves the separability of features, thereby improving the detection accuracy of micro faults.

[0082] 2. After the SFA transformation, the present invention introduces the JS divergence method through a sliding window to amplify the change trend of micro fault signals. By constructing a new statistic to deeply mine the fault state, micro faults can be accurately detected at an early stage, with higher sensitivity and stability compared to traditional methods.

[0083] 3. The detection strategy of the present invention can avoid the problem of easy misjudgment of traditional methods under strong noise backgrounds. By selecting the main independent components through ICA, the purpose of process feature extraction can be achieved, and at the same time, some noises can be filtered out, improving the detection performance of micro faults and making it more suitable for fault detection and diagnosis in industrial processes. Description of the Drawings

[0084] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention and do not constitute a limitation to the present invention.

[0085] Figure 1 It is the general flowchart for the detection of micro faults in the method of the present invention.

[0086] Figure 2 It is the flowchart for building the static space model in the method of the present invention.

[0087] Figure 3 It is the flowchart for the method of building the dynamic space model in the method of the present invention.

[0088] Figure 4 It is the schematic diagram of the TE chemical process for the implementation column in the present invention.

[0089] Figure 5(a) is the detection result graph of the traditional SFA method for the TE process fault 3 in the embodiment of the present invention.

[0090] Figure 5(b) is the detection result graph of the SICJSA method of the present invention for the TE process fault 3 in the embodiment of the present invention.

[0091] Figure 6(a) is the detection result graph of the traditional SFA method for the TE process fault 9 in the embodiment of the present invention.

[0092] Figure 6(b) is the detection result graph of the SICJSA method of the present invention for the TE process fault 9 in the embodiment of the present invention.

[0093] Figure 7(a) is the detection result graph of the traditional SFA method for the TE process fault 15 in the embodiment of the present invention.

[0094] Figure 7(b) is the detection result graph of the SICJSA method of the present invention for the TE process fault 15 in the embodiment of the present invention. Detailed implementation manners

[0095] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0096] Embodiment 1

[0097] In this embodiment, the Tennessee-Eastman (TE) chemical process is used, which is a simulation based on the actual industrial process of Eastman Chemical Company in the United States, abbreviated as the TE process. This process is a simulation based on the actual industrial process of Eastman Chemical Company in the United States. It was first proposed by Downs J.J. and Vogel E.F. of Eastman Chemical Company in the United States, and the FORTRAN source code was given. Subsequently, the Ricker Process Control Research Laboratory of the University of Washington rewrote the TE chemical model using the Simulink simulation environment of Matlab, enabling the TE chemical process to be simulated on Matlab. The simulated data has characteristics such as time-variability and strong coupling. Currently, the TE process is widely used in the research of methods such as process monitoring, optimal control, fault detection, and fault diagnosis.

[0098] The TE chemical process consists of five main units, namely: reactor, condenser, recycle compressor, vapor-liquid separator, and stripper. After the main gas raw materials enter the process, through the operation of these parts and the chemical reactions therein, two liquid products are produced from four reactants. In addition, an inert product and a by-product are also produced, which together contain eight components: A, B, C, D, E, F, G, and H. The various reaction equations of the reactor are as follows:

[0099] A(g) + C(g) + D(g) --> G(liq)

[0100] A(g) + C(g) + E(g) --> H(1liq)

[0101] A(g) + E(g) --> F(1iq)

[0102] 3D(g) --> 2F(liq)

[0103] Its process is as Figure 2 shown:

[0104] The entire TE chemical process includes a total of 12 operating variables and 41 measured variables. In this example, 11 commonly used operating variables and 22 measured variables, a total of 33 variables, are selected for testing. All process measurement values are interfered by Gaussian noise, and all variables are shown in Table 1.

[0105] The TE chemical process presets 21 types of faults, which are divided into fault types such as step and unknown. Faults IDV(1)-IDV(15) and IDV(21) are 16 known faults, and IDV(16)-IDV(20) are 5 unknown faults. In the actual experiment and simulation process, faults IDV(3), IDV(9), and IDV(15) are minor faults and are difficult to detect. In order to cover all fault types in this embodiment, 8 relatively representative faults are selected, and the 8 faults also include all the minor faults in the TE process. See Table 2 below for details.

[0106] Table 1 List of Variables

[0107]

[0108]

[0109] Table 2 Process Fault Types

[0110]

[0111] In this embodiment, normal samples are used as both training data and benchmark data, and sampled data under fault conditions are used as test data. The number of samples under each fault condition is 960, but the fault samples start to be in a fault state from the 161st sample.

[0112] When a fault is detected, in order to evaluate the advantages and disadvantages of the fault detection performance of different monitoring methods, two key indicators, the false alarm rate (FAR) and the fault detection rate (FDR), are selected for comparative analysis. Generally speaking, the lower the FAR and the higher the FDR, the better the fault detection effect of the method.

[0113]

[0114] Among them, N Tf and N Ff are the numbers of fault samples detected before and after the fault occurs respectively, and N T and N F are the numbers of normal samples and fault samples respectively.

[0115] Specific steps of this embodiment:

[0116] Offline modeling:

[0117] Step 1: First, construct a training set X0 ∈ R from the historical database obtained during the normal operation of the production process n×m , and obtain the standardized matrix X = (X0 - mean(X0)) / std(X0) by using standardization processing.

[0118] Step S2: Perform slow feature analysis on the standardized training data X. First, calculate the covariance matrix ∑ of X(t) pp Perform singular value decomposition to obtain the whitening matrix Q, and perform whitening processing to obtain the whitened data matrix z(t); find the first derivative of the whitened data z and perform singular value decomposition on its covariance matrix to obtain the eigenvector matrix P and the eigenvalue matrix Ω = diag(λ1, λ2,..., λ n );

[0119] Σ XX = UΛU T , Q = Λ -1 / 2 U T ,

[0120] Furthermore, the slow feature transformation matrix W = PΛ -1 / 2 U T , according to the degree of change of the input data X Determine the maximum number of slow-varying features Then the slow-varying feature S1(t) = [s1(t), s2(t),...., s M (t)] T , and the fast-varying feature is S2(t) = [s M+1 (t), s M+2 (t),...., s m (t)] T , in this embodiment M = 21;

[0121] Step 3: In the static distribution space s, calculate the overall mean μ S1 and the overall variance λ S1 of the slow-varying feature S1 of the training data, and then calculate the mean μ S1 (i) and variance λ S1 (i) of the slow-varying feature S1 of the training data within the i-th sliding window. Calculate the JS divergence component S JS1 of the slow-varying feature S1 of the training data according to the following formula (12) to determine the evaluation index of the static space Determine the static corresponding static space control limit by the KDE method In the sliding window algorithm, set the window width W to H and the step size to 1, that is, move backward once at each sampling moment. Given that the number of data samples is n, there are a total of N = n - H + 1 sampling moments (in this embodiment, N = 139).

[0122]

[0123] Step 4: In step S4, in the fast-varying feature space of the training data, use the independent component analysis algorithm to separate the independent source signals from the mixed signals, and divide them into the slow independent feature principal component space and the residual space by sorting the importance of the independent components

[0124] 1. Select the fast-varying space feature matrix S2(t) = [s M+1 (t), s M+2 (t),...., s m (t)] T of the training data under normal working conditions for ICA decomposition to obtain the independent component matrix ICAedS and the separation matrix W

[0125] ICAedS = WS2

[0126] 2. By selecting several main independent components in ICAedS to establish an independent principal component space model, calculate the L2 norm for each row of the separation matrix W obtained by ICA, which reflects the energy intensity c(i) of each independent component. Sort the separation matrix W in descending order according to the L2 norm to obtain the sorted norm values D, calculate the total energy C, and through cumulative energy screening, retain the first d main independent components so that their cumulative energy accounts for 80%, then the corresponding separation matrix W d = W(M + 1:d, :) (select the rows of the W matrix corresponding to d main independent components) and W e = W(d:m, :) (the remaining matrix in W d ), calculate the slow independent feature principal component space S d and the residual space S e , and the formula is as follows.

[0127]

[0128] Step S5: After the independent principal component subspace of the training data, use a sliding window to calculate the divergence component S d of the slow independent feature S JSd of the training data, the overall mean μ Sd and the overall variance λ Sd , and calculate the mean μ d and variance λ Sd (i) of the slow-varying feature S Sd (i) of the training data within the i-th sliding window, and construct a statistic Use the kernel density method to calculate the corresponding control limit according to the given confidence level

[0129]

[0130] Fault detection:

[0131] Step S6: Obtain the test data X t , and use the mean mean(X0) and standard deviation std(X0) of the training data to perform standardization processing to obtain the standardized matrix X T , and perform slow feature analysis on the standardized X T , and determine its slow feature vector S T (t) = WX T (t).

[0132] Step S7: Calculate the overall mean μ 1T and overall variance λ S1T of the slow-varying feature S S1T ​Then calculate the slowly varying feature S of the test data in the i-th sliding window 1T The mean μ S1T (i), variance λ S1T (i), we get the JS divergence component S JS1T , calculate the test data slow-changing feature S according to the following formula (22): 1T The JS divergence component S JS1 , determine the static spatial statistics

[0133]

[0134] Finally, according to the statistics Is it beyond the control limit? To determine whether a fault has occurred.

[0135] For the standardized test data X T Perform slow feature analysis, and the transformation matrix W obtained in step 2 determines its slow feature vector S T (t) = WX T (t), the number of slow-changing features M in the training data is the number of fast-changing slow features, so the slow-changing feature S 1T (t)=[s1(t),s2(t),....,s M (t)] T and fast-changing characteristics S 2T (t) = [s 2M+1 (t),s 2M+2 (t),....,s 2m (t)] T .

[0136] Step S8: The test data fast-varying spatial feature matrix S 2T (t) = [s 2M+1 (t),s 2M+2 (t),....,s 2m (t)] T Perform ICA decomposition and test the slow independent feature principal component space S of the data dt and the residual space S et It is calculated by the separation matrix W.

[0137] S dt =W d S 2T , S et =W e S 2T

[0138] Then calculate the slow independent feature S of the test data dt The overall mean μ Sdt and the population variance λ Sdt, then calculate the mean value μ dt of the slow independent feature S of the test data within the i-th sliding window Sdt (i) and the variance λ Sdt (i), calculate the JS divergence component and construct a statistic

[0139] Finally, based on whether the statistic exceeds the control limit to determine whether a fault has occurred.

[0140] Step 9: Adopt a Bayesian inference mechanism. From the statistics calculated in Steps S5 and S7, calculate the probabilities of faults occurring in the slow-varying feature space and the slow independent component subspace data, and fuse the probabilities of the two spaces to obtain the monitoring statistic BIC. The steps are as follows.

[0141] 1. Calculate the probability fusion index corresponding to the static space statistic as follows

[0142] 1) Calculate the conditional probabilities and

[0143]

[0144] where N and F represent normal and fault conditions respectively.

[0145] 2) Calculate the fault probability

[0146]

[0147] 3) Calculate the fault probability

[0148]

[0149] 2. Calculate the probability fusion index corresponding to the slow independent space statistic The implementation process is similar to Steps 1)-3), so it will not be elaborated. The calculated probabilities and are as follows.

[0150]

[0151] 3. Adopt the Bayesian probability algorithm to fuse the detection results of the two spaces to obtain the comprehensive statistic BIC. The formula is as follows.

[0152] From the statistics calculated in Steps S3 and S5, adopt the Bayesian probability algorithm to fuse the detection results of the two spaces to obtain the comprehensive statistic BIC.

[0153]

[0154] Set the fault discrimination threshold β. When BIC ≤ β, the system is considered to be in a normal state; when BIC > β, the system is considered to be in a fault state.

[0155] In the TE process simulation of this embodiment, the traditional SFA method is compared with the SICAJS method of this embodiment. In this example, the width of all sliding windows is set to 139, and the confidence level for calculating the control limit by the KDE method is set to 99%, and the confidence level β of the Bayesian inference mechanism in the SICAJS method is set to 0.1.

[0156] As can be seen from Table 2, Fault 3 is a minor fault caused by temperature disturbance during D feed. When the traditional SFA method and the SFA-ICAKL method of this embodiment are used for the detection effect of Fault 3, they respectively correspond to Figure 3 (a) and Figure 3 (b). In Figure 3 (a), due to the characteristics of slow change and small amplitude of minor faults, the detection effect of the traditional SFA method on Fault 3 is very poor, with a detection rate of only 15.75% and a false alarm rate of 16.88%. Compared with the traditional SFA algorithm, in the SFA-ICAKL algorithm of this embodiment, the slow feature analysis SFA can effectively extract the main slow features first, but the secondary slow features still contain important minor fault information. To further improve the accuracy of minor fault detection, independent component analysis (ICA) is performed on the secondary slow features to obtain independent source signals, improve the separability of fault features, and then extract the fault information at the small data scale through the sliding window KL divergence. As can be seen from Figure 3 (b), the fault detection rate of the method in this embodiment is 97.38%, and the fault false alarm rate is 3.75%. Therefore, it can be seen that the method in this embodiment greatly improves the detection effect of minor fault 3 in the TE process.

[0157] As can be seen from Table 2, Fault 9 is a minor fault caused by the change of D feed temperature. When the traditional SFA method and the SFA-ICAKL method of this embodiment are used for the detection effect of Fault 3, they respectively correspond to Figure 4 (a) and Figure 4 (b). The detection effect of the traditional SFA method on Fault 9 is very poor, with a detection rate of only 12.38% and a false alarm rate of 23.13%, which cannot meet the requirements of actual industrial process fault detection. For the SFA-ICAKL method of this embodiment, the detection rate of minor fault 9 is only 98.75%, and the false alarm rate is 3.13%, which greatly improves the detection rate of minor faults.

[0158] As can be seen from Table 2, Fault 15 is a minor fault caused by the jamming of the condenser cooling water valve. The detection effects of the traditional SFA method and the SFA-ICAKL method of this embodiment for Fault 3 correspond to Fig. 5(a) and Fig. 5(b) respectively. The detection effect of the traditional SFA method for Fault 15 is very poor, with a detection rate of only 26.75% and a false alarm rate of 3.13%. While the detection rate of the SFA-ICAKL method of this embodiment for Fault 15 is 96.5% and the false alarm rate is 0.63%, which verifies again that the method of this embodiment significantly improves the accuracy of minor fault detection.

[0159] Table 3

[0160]

[0161] As can be seen from Table 3, the traditional SFA algorithm only has a good detection rate for significant faults in the TE process, but it is difficult to capture the fault information of minor faults 3, 9, and 15, and can hardly detect minor faults. The method SICAJS of this embodiment is more sensitive to minor fault information by using sliding window divergence and the ICA algorithm, effectively captures the occurrence of minor faults, and greatly improves the detection rate of minor faults.

[0162] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An industrial process micro-fault detection method based on the probability difference of slow independent features, characterized in that, Including the following steps: Step S1: Collect data samples from the historical database obtained during the normal operation of the production process to construct a training set \(X_0\in R^{n\times m}\), where \(n\) is the total number of samples, \(m\) is the number of process monitoring variables, and \(R\) is a real number matrix. Then perform standardized preprocessing on each variable to finally generate a standardized data matrix \(X\) with a mean of 0 and a standard deviation of 1. n ×m ​ Step S2: Perform slow feature analysis on the standardized training data X, calculate the whitening matrix Q and the transformation matrix W, extract its slow feature vector S(t), and divide the obtained slow feature vector into slow-varying feature S1(t) and fast-varying feature S2(t) according to both static change and dynamic change, to obtain the corresponding static distribution space s and dynamic distribution space Step S3: In the static space s of the training data, calculate the JS divergence of the slow-varying features of the training data through a sliding window, quantitatively analyze the probability distribution, and construct an evaluation index of the slow-varying features based on the JS divergence And calculate the corresponding control limit through the kernel density estimation method Step S4: In the dynamic space of the training data , the independent component analysis algorithm is used to separate the independent source signals from the mixed signals, and the training data is divided into the slow independent feature principal component space and the residual space by sorting the importance of the independent components and calculating the cumulative contribution degree; Step S5: In the slow independent feature principal component space of the training data, calculate the JS divergence of the slow independent features of the training data through a sliding window, quantitatively analyze the probability distribution, and construct an evaluation index of the slow independent features based on the JS divergence And calculate the corresponding control limit by the KDE method Step S6: Construct a test set X from the fault data collected during the production process t ∈R n×m , preprocess each variable by standardizing it using the mean and standard deviation of X0 in the training data from Step S1, and finally generate a standardized data matrix X T , for the standardized test data X T perform slow feature analysis, and extract its slow feature vector S T (t) using the transformation matrix W in Step S2, and divide the obtained slow feature vector into slow-varying features S 1T (t) and fast-varying features S 2T (t) according to both static and dynamic changes, and obtain the corresponding static distribution space s and dynamic distribution space Step S7: In the static space s of the test data, calculate the Jensen-Shannon (JS) divergence of the slow-varying features of the test data through a sliding window, quantitatively analyze the probability distribution, and construct a statistic of the slow-varying features based on the JS divergence Step S8: In the dynamic space of test data Use Step S4 to divide the test data into a slow independent feature principal component space and a residual space. In the slow independent feature principal component space of the test data, calculate the JS divergence of the training data's slow independent features through a sliding window, quantitatively analyze the probability distribution, and construct a statistic based on the JS divergence of the slow independent features Step S9: Fuse the fault detection probabilities of the slow-varying feature space and the slow-independent feature space through Bayesian inference, calculate the final monitoring statistic BIC, and determine whether there is a fault in the system according to whether the statistic BIC exceeds the control limit β.

2. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, characterized in that, In the step S1, the training data X0 is obtained, and the standardized matrix X = [X1, X2,..., X n T ∈R n×m is obtained by performing standardization processing using its mean and standard deviation. The formula is as follows, where mean(X0) is its mean and std(X0) is its standard deviation, and X = (X0 - mean(X0)) / std(X0) (1)​ In step S2, the standardized training data is subjected to slow feature analysis, and the obtained slow features are spatially partitioned into a static distribution space s and a dynamic distribution space The steps are as follows: S21. Collect the normal operating condition data X0 in the industrial process and standardize it. The standardized data is denoted as the input data X(t) = [x1(t), x2(t),..., x n (t)] T , calculate the covariance matrix ∑ of X(t) pp Perform singular value decomposition to obtain the whitening matrix Q, and perform whitening processing to obtain the whitened data matrix z(t). The formula is as follows: ∑ XX = UΛU T (3) Q = Λ -1 / 2 U T (4) S22. Calculate the first derivative of z for the whitened data and its covariance matrix Perform singular value decomposition, and the formula is as follows: Among them, P is the eigenvector matrix, Ω = diag(λ1, λ2,..., λ n ) is the eigenvalue matrix, and the eigenvalues λ1 are arranged in ascending order; S23. Obtain the slow feature transformation matrix W, a series of slow features S(t) extracted, and calculate the degree of change Δ(X j ) of the standardized input data X. Determine the number M of slow-changing features of the training data according to Equation 11. The remaining number of slow features is the number of fast-changing features, that is, the slow-changing features are S1(t) = [s1(t), s2(t),...., s M (t)] T , and the fast-changing features are S2(t) = [s M+1 (t), s M+2 (t),...., s m (t)] T , where q = 0.1 represents the 0.1 upper quantile of the set {Δ(X j )}. Divide the input data into a fast feature space and a slow feature space. The formula is as follows: W = PΛ -1 / 2 U T (8) S(t) = WX(t) (9) 3. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, characterized in that, In the step S3, in the static distribution space s, calculate the overall mean μ of the slow-varying feature S1 of the training data S1 and the overall variance λ S1 , and then calculate the mean μ S1 (i) and the variance λ S1 (i) of the slow-varying feature S1 of the training data within the i-th sliding window. Calculate the JS divergence component S of the slow-varying feature S1 of the training data according to the following formula 12 JS1 , and determine the static space evaluation index Determine the static corresponding static space control limit through the KDE method Among them, in the sliding window algorithm, the window width W is set to H, and the step size is set to 1, that is, it moves backward at each sampling moment. Given that the number of data samples is n, there are a total of N = n - H + 1 sampling moments; Calculate static spatial statistics according to the formula The formula is as follows, given the confidence level Calculate the corresponding control limit by the KDE method 4. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, characterized in that In the step S4, in the fast-varying feature space of the training data, the independent component analysis algorithm is used to separate the independent source signals from the mixed signals, and it is divided into the slow-independent feature principal component space and the residual space, including the following steps: S41. Select the fast-changing spatial feature matrix S2(t) = [s M+1 (t), s M+2 (t),...., s m (t)] T under normal operating conditions for ICA decomposition to obtain the independent component matrix ICAedS and the separation matrix W. The independent component matrix ICAedS is a combination of multiple independent components, and the formula is as follows: ICAedS = WS2(14) S42. By selecting several main independent components in ICAedS to establish an independent principal component space model, calculate the L2 norm for each row of the separation matrix W obtained by ICA to reflect the energy intensity c(i) of each independent component. Sort the separation matrix W in descending order according to the L2 norm to obtain the sorted norm values D. Calculate the total energy C. Through cumulative energy screening, retain the first d main independent components so that their cumulative energy accounts for 80%, and then the corresponding separation matrix W d = W(M + 1:d, :) and W e = W(d:m, :), calculate the slow independent feature principal component space S of the training data d and the residual space S e , the formula is as follows: S d = W d S2(18).

5. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, characterized in that, In step S5, after determining the independent principal component subspace of the training data, a sliding window is used to calculate the divergence component S d of the slow independent feature S JSd of the overall mean μ Sd and the overall variance λ Sd , and calculate the mean μ d of the slow-varying feature S Sd (i) and the variance λ Sd (i) of the training data within the i-th sliding window, and construct a statistic Use the kernel density method to calculate the corresponding control limit according to the given confidence level , and the formula is as follows: The formula is as follows:

6. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, characterized in that In the step S6, test data X is obtained. t , and a standardized matrix X obtained by performing standardization processing using the mean mean(X0) and standard deviation std(X0) of the training data T = [X1, X2,..., X n T ∈ R n×m , and slow feature analysis is performed on the standardized test data X T .​ Determine the slow feature vector S from the transformation matrix W obtained in step S2 T (t) = WX T (t), and divide the slow feature vectors obtained by getting the number M of slow-varying features into slow-varying features S 1T (t) = [s1(t), s2(t),...., s M (t)] T and fast-varying features S 2T (t) = [s 2M+1 (t), s 2M+2 (t),...., s 2m (t)] T , and obtain the corresponding static distribution space s and dynamic distribution space The formula is as follows: X T = (X t - mean(X0)) / std(X0) (21).

7. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, characterized in that In the step S7, calculate the slow-varying feature S of the test data in the static distribution space s 1T for the overall mean μ S1T and the overall variance λ S1T Then calculate the mean μ 1T of the slow-varying feature S of the test data within the i-th sliding window S1T (i), and the variance λ S1T (i), to obtain the JS divergence component S JS1T of the slow-varying feature S of the test data, and calculate the JS divergence component S 1T of the slow-varying feature S of the test data according to the following formula 22, and determine the static space statistic JS1 ​ Calculate static spatial statistics The formula is as follows: Finally, based on the statistic whether it exceeds the control limit to determine whether a fault has occurred.

8. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, characterized in that The fast-varying spatial feature matrix S of the test data in step S8 2T (t)=[s 2M+1 (t), s 2M+2 (t),...., s 2m (t)] T Perform ICA decomposition. The slow-independent feature principal component space S of the test data dt and the residual space S et are calculated by the separation matrix W. The formula is as follows: S dt = W d S 2T (24) S et = W e S 2T (25) Calculate the slow independent feature S of the test data dt Overall mean μ Sdt And the overall variance λ Sdt , calculate the slow independent feature S of the test data within the i-th sliding window dt Mean μ Sdt (i) and variance λ Sdt (i), calculate the JS divergence component through formula (26) and construct a statistic The formula is as follows: According to the statistic whether it exceeds the control limit to determine whether a fault has occurred 9. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, wherein In the step S9, the Bayesian inference mechanism is adopted. From the statistics calculated in steps S7 and S8, calculate the probabilities of faults occurring in the slow-varying feature space and the slow-independent component subspace data, fuse the probabilities of the two spaces to obtain the monitoring statistic BIC, and determine whether a fault has occurred by judging whether the fused monitoring statistic BIC exceeds the control limit β. The steps are as follows: S91. Calculate the probability fusion index corresponding to the static spatial statistic of 1) Calculate the conditional probabilities respectively according to the following formulas and Among them, N and F respectively represent normal and fault conditions; 2) Calculate the failure probability according to the following formula 3) Calculate the failure probability according to the following formula S92. Calculate the probability fusion index corresponding to the slow independent space statistic The implementation process and steps 1) to 3) of the probability fusion index are calculated, and the probabilities and are as follows: S93. Adopt the Bayesian probability algorithm to fuse the detection results of the two spaces to obtain the comprehensive statistic BIC. The formula is as follows: Set the fault discrimination threshold β. When BIC ≤ β, it is considered that the system is in a normal state; when BIC > β, it is considered that the system is in a fault state.

10. The industrial process micro-fault detection method based on the difference in slow independent feature probabilities according to claim 1, characterized in that, The steps S1 to S5 are the offline modeling stage for building the slow feature probability difference and the slow-independent principal component probability difference. The steps S6 to S8 are the fault detection stage for the slow feature probability difference and the slow-independent principal component probability difference. The step S9 is to fuse the fault detection results of the two probability difference models and draw a conclusion.

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