Non-linear system fault tracing method based on multi-objective optimization and self-coding

Abstract

The invention discloses a nonlinear system fault tracing method based on multi-objective optimization and self-coding. The method comprises the following steps: collecting and storing historical operation data of an industrial process and carrying out normalization processing; establishing a self-encoding model, calculating to obtain an SPE statistical magnitude control limit # imgabs0 # under a preset confidence interval of the model, online obtaining operation data, normalizing the operation data, inputting the data into the self-encoding model, obtaining an SPE statistical magnitude in real time, and if the SPE statistical magnitude is greater than # imgabs1 #, starting fault tracing; setting a preposed residual vector as an initial population of multi-objective optimization; setting two objective functions of multi-objective optimization; and a Pareto optimal set is obtained after NSGA-II optimization, a population with the SPE statistical magnitude smaller than # imgabs2 and the minimum fault dimension number is selected as an optimal solution, finally, the operation parameters and deviation amplitude involved in the fault are positioned, and fault traceability is completed. According to the invention, the fault diagnosis time can be significantly reduced and the fault can be accurately isolated.

Description

Technical Field

[0001] The present invention relates to a fault diagnosis method for industrial data, and particularly to a fault tracing method for non-linear systems based on multi-objective optimization and auto-encoding. Background Art

[0002] Fault diagnosis of thermal processes based on latent variable methods such as principal component analysis and auto-encoders generally includes the following key steps: system modeling, fault detection, fault tracing, and fault classification. After the system model is constructed, it is necessary to further calculate the deviation between the actual measured value and the model predicted value, and compare the deviation statistic with a preset threshold to determine whether the system is in a normal state, so as to achieve fault detection. When the system is determined to be in an abnormal state, fault tracing technology is required to accurately locate the key parameters that cause the fault and quantify the deviation degree between these parameters and the normal state. This information will serve as fault characteristics and provide key basis for subsequent fault classification.

[0003] As the core means of fault feature extraction, fault tracing is a key link in realizing an efficient fault diagnosis system, and its accuracy and reliability directly affect the final effect of fault diagnosis. The contribution graph method is the most commonly used fault isolation method. This method is simple and fast, but it is prone to a large number of misdiagnoses when dealing with complex faults due to the influence of "residual contamination". The root cause of this problem is that the abnormal deviation of fault parameters will be transmitted to the model predicted value through the latent variable space, so that the predicted values of other normal parameters related to the fault parameters are also affected by the residual, which affects the accuracy of fault tracing. Different from the contribution graph method, the reconstructed contribution graph method avoids the indiscriminate transmission of residuals by actively compensating for the abnormal deviation in the measured data. Specifically, the reconstructed contribution graph method first pre-sets the fault parameters and calculates the optimal reconstruction amplitude. If the reconstruction residual is lower than the confidence limit, this fault direction is considered correct, otherwise the fault parameters are re-assumed. Since the true fault parameters are unknown, the reconstructed contribution graph method needs to evaluate all possible parameter combinations, which brings a large amount of repeated calculations. Research shows that its calculation time increases exponentially with the number of model parameters and the number of fault parameters.

[0004] In order to improve the calculation efficiency of the reconstructed contribution graph method, researchers have proposed a series of improvement methods such as BAB, Lasso, floating sequential search, etc., which have been successfully applied to the modeling and diagnosis of linear principal component analysis methods. However, optimization methods such as BAB and Lasso can only greatly improve the calculation efficiency in linear systems, and the calculation amount is still huge in high-dimensional non-linear systems. For non-linear auto-encoding methods, improvement methods such as BAB-AANN, CMA-ES-ITNN, and SFFS-AANN have also emerged. However, these methods are limited to fixed network structures, lack generality, and their calculation efficiency is low, making it difficult to meet the requirements of online real-time diagnosis. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a fault tracing method for a non - linear system based on multi - objective optimization and auto - encoding, which can significantly reduce the time of fault diagnosis and accurately isolate faults.

[0006] Technical Solution: A fault tracing method for a non - linear system based on multi - objective optimization and auto - encoding of the present invention includes:

[0007] Collect and store the historical operation data of the industrial process, and perform normalization processing on the historical operation data;

[0008] Use the normalized historical operation data to train a pre - constructed auto - encoding model, and calculate the control limit of the SPE statistic under a preset confidence interval for the trained auto - encoding model

[0009] Obtain real - time operation data online, use the normalized real - time operation data as the input data of the trained auto - encoding model, and calculate the SPE statistic of the real - time operation data in real - time; if the SPE statistic is greater than the control limit of the SPE statistic Then use the current real - time operation data as a fault sample and start fault tracing;

[0010] During the fault tracing process, set multiple pre - residual vectors according to the dimension of the non - linear system, and the multiple pre - residual vectors form the initial population of multi - objective optimization;

[0011] Set two objective functions for multi - objective optimization, including minimizing the SPE statistic after the measured data is superimposed with the pre - residual vector and minimizing the number of fault dimensions;

[0012] Combined with the two objective functions of multi - objective optimization, the initial population of multi - objective optimization is optimized by NSGA - II to obtain a Pareto - optimal set, and select the population with the SPE statistic less than And the smallest number of fault dimensions as the optimal solution, and finally locate the operation parameters involved in the fault and their deviation amplitudes to complete fault tracing.

[0013] Furthermore, the normalization processing includes:

[0014] Adopt the z - score method, and the specific process is as follows:

[0015]

[0016] where, x i represents the original value of the i - th input parameter; represents the value of the i - th input parameter after normalization; m(x) represents the mean of all input parameters; s(x) represents the standard deviation of all input parameters.

[0017] Furthermore, the expression of the mean value m(x) of all the input parameters is as follows:

[0018]

[0019] where n represents the number of all the input parameters.

[0020] Furthermore, the expression of the standard deviation s(x) of all the input parameters is as follows:

[0021]

[0022] Furthermore, the expression of the SPE statistic is as follows:

[0023]

[0024] The control limit of the SPE statistic is expressed as follows:

[0025]

[0026] At the (1-α)×100% confidence level, ζ α represents the standard value corresponding to (1-α)%; λ k represents the eigenvalue of the covariance matrix of; m is the number of eigenvalues; θ i represents the sum of the i-th powers of all the eigenvalues.

[0027] Furthermore, during the fault tracing process, multiple pre-residual vectors are set according to the dimensions of the nonlinear system. The multiple pre-residual vectors form the initial population for multi-objective optimization, including:

[0028] For a piece of real-time operating data that is monitored as a fault sample and has been normalized s n-dimensional pre-residual vectors can be randomly generated The s n-dimensional pre-residual vectors form the initial population

[0029] Furthermore, two objective functions for multi-objective optimization are set, including minimizing the SPE statistic after the measurement data is superimposed with the pre-residual vector and minimizing the number of fault dimensions, including:

[0030] The fault data stream and the predicted fault-free sample after being superimposed with the pre-residual vector have the minimum reconstruction value; the number of fault dimensions is minimized. A fault threshold Δ = 0.01 is set, then the two objective functions can be expressed as follows:

[0031]

[0032] Among them, represents the real-time data stream detected as a fault; represents the indicator function.

[0033] Furthermore, when |f i (t) | > 0.01, the value of the indicator function is 1, otherwise it is 0. By summing the indicator functions of n f i (t) , the number of fault dimensions is obtained.

[0034] Furthermore, by combining the two objective functions of multi-objective optimization, the initial population of multi-objective optimization is optimized by NSGA-II to obtain the Pareto optimal set. Select the population with the SPE statistic less than and the smallest number of fault dimensions as the optimal solution, and finally locate the operating parameters involved in the fault and their deviation amplitude to complete fault tracing, including:

[0035] Set the initial value i = 1 and the iteration number τ of the genetic algorithm. According to the two optimization objectives, non-dominated sorting is performed on each individual in the initial population P i , that is, each pre-residual vector, and divided into

[0036] through the genetic algorithm, that is, selection, crossover and mutation, to obtain the next-generation population of the initial population P i

[0037] Combine all individuals of the two populations P i and Q i to form the reconstructed population R i , R i = P i ∪Q i . Perform non-dominated sorting on all individuals in the reconstructed population R i , and also divide them into R i There are a total of 2s individuals in it;

[0038] If i = τ, then select the point on the Pareto chart with the SPE statistic less than and the smallest number of fault dimensions and output it.

[0039] Furthermore, if i ≠ τ, then take out the top s individuals from the population R i to form a set of s individuals P i+1 and increment i by 1, and repeat the selection, crossover and mutation steps until i = τ.​

[0040] Beneficial effects: Compared with the prior art, the remarkable technical effects of the present invention are as follows:

[0041] The present invention adopts NSGA-II (multi-objective optimization and genetic algorithm), which solves the problem that the traditional reconstruction method has low computational efficiency in high-dimensional non-linear systems because it needs to perform multiple iterations through the gradient descent method and also needs to use fault direction selection methods such as Sequential Floating Forward Selection (SFFS), Branch and Bound (BAB), etc. to determine the specific fault direction. The present invention adopts NSGA-II to accurately and quickly locate the fault variables and determine the magnitude of the fault.

[0042] The present invention adopts NSGA-II (multi-objective optimization and genetic algorithm), which adds an elitist retention strategy compared with NSGA-I. By using fast non-dominated sorting, the calculation speed is fast, so that the reconstruction result can be very conveniently integrated into the system control system, truly realizing real-time fault diagnosis and data reconstruction, and ensuring the validity of real-time data. Brief Description of the Drawings

[0043] Figure 1 is a schematic flow diagram of the present invention;

[0044] Figure 2 is a schematic diagram of the output result of the Pareto chart of the repeated genetic algorithm τ times in the present invention. Detailed Embodiments

[0045] The technical solution of the present invention will be introduced in detail below in combination with the specific embodiments and the accompanying drawings of the specification.

[0046] As Figure 1 shown, the non-linear system fault tracing method based on multi-objective optimization and auto-encoding of the present invention includes three parts: system modeling, fault detection, and fault tracing. Specifically, it includes the following steps:

[0047] S1. Collect and store the historical operation data of the industrial process, and perform normalization processing on the historical operation data.

[0048] In this embodiment, the normalization processing includes:

[0049] Adopt the z-score method, and the specific process is as follows:

[0050]

[0051] Among them, x i represents the original value of the i-th input parameter; It represents the value of the i-th input parameter after normalization; n represents the number of all input parameters; m(x) represents the mean value of all input parameters; s(x) represents the standard deviation of all input parameters.

[0052] S2. Use the normalized historical operation data to train the pre-constructed autoencoder model, and calculate the control limit of the SPE (Squared prediction error) statistic of the trained autoencoder model under the preset confidence interval. Among them, SPE is the squared prediction error and is a reconstruction-based index.

[0053] Establishing and training the autoencoder model mainly determines the weight matrix and bias vector of each layer through the gradient descent method.

[0054] In this embodiment, the autoencoder model (AE) is an unsupervised learning deep neural network, usually composed of an encoder and a decoder. Taking the middle hidden layer as the axis of symmetry, the encoding layer and the decoding layer are symmetric with each other. Therefore, the dimensions of the input layer and the output layer are the same. The input sample can be compressed to the hidden layer first and then reconstructed back to the original dimensional space. Among them, the m-layer encoder f enc Projects the i-th input sample x (i) Into the l-dimensional latent space to obtain the latent variable Then through the m-layer decoder f dec , Transforms h (i) Back to the original space, so that the model input x (i) Is reconstructed as The encoding process and the decoding process are respectively represented by the following formulas:

[0055]

[0056] In the formula: Represents the composition between mappings; Represents the encoding process of the j-th layer of AE; the activation function of the encoder is set to Is the output of the AE model; Represents the decoding process of the j-th layer of AE. The activation function of the decoder is the same as that of the encoder.

[0057] In this embodiment, the expressions of the SPE statistic and its control limit Are respectively as follows:

[0058]

[0059]

[0060] At the (1-α)×100% confidence level, ζ α represents the standard value corresponding to (1-α)%. λ k represents the eigenvalue of the covariance matrix; m represents the number of eigenvalues; θ i represents the sum of the i-th powers of all eigenvalues. θ i and h0 are directly calculated through the eigenvalues of the covariance matrix.

[0061] S3. Obtain real-time operation data online, and use the normalized real-time operation data as the input data of the trained autoencoder model to calculate the SPE statistic of the real-time operation data in real time; if the SPE statistic is greater than the SPE statistic control limit then use the current real-time operation data as a fault sample and start fault tracing.

[0062] Normalize a real-time operation data to obtain Through the trained autoencoder model, x k of SPE(x k ) can be calculated. If then judge that the real-time operation data is a normal sample and detect the next real-time operation data; if then judge that the real-time operation data is a fault sample and enter step S4 for fault tracing to determine the specific dimension and size of the fault.

[0063] S4. During the fault tracing process, set multiple pre-residual vectors according to the dimensions of the nonlinear system, and the multiple pre-residual vectors form the initial population of multi-objective optimization. Specifically, it includes the following:

[0064] For a real-time operation data that is monitored as a fault sample and has been normalized s n-dimensional pre-residual vectors can be randomly generated The s n-dimensional pre-residual vectors form the initial population

[0065] S5. Set two objective functions for multi-objective optimization, including minimizing the SPE statistic after superimposing the measurement data with the pre-residual vector and minimizing the number of fault dimensions. Specifically, it includes the following:

[0066] In order to obtain an accurate fault direction, the number of fault variables needs to be restricted. The optimal fault direction should meet two conditions: (a) The RB index is less than the control threshold; (b) The number of fault dimensions is the smallest. Therefore, the two objective functions of multi-objective optimization are:

[0067] One is the fault data stream The predicted fault-free samples after being superimposed with the pre-residual vectors Secondly, the reconstruction value should be as small as possible, and the number of fault dimensions should be small. Set the fault threshold Δ = 0.01, then the two objective functions can be expressed as follows:

[0068]

[0069] Among them, represents the real-time data stream detected as a fault; represents the indicator function. When |f i (t) | > 0.01, the value of the indicator function is 1, otherwise it is 0. Here, the number of fault dimensions can be obtained by summing the indicator functions of n f i (t) .

[0070] S6. Combine the two objective functions of multi-objective optimization. The initial population of multi-objective optimization is optimized by NSGA-II (multi-objective optimization and genetic algorithm) to obtain the Pareto optimal set. Select the population with the SPE statistic less than and the smallest number of fault dimensions as the optimal solution, and finally locate the operating parameters involved in the fault and its deviation amplitude to complete the fault tracing.

[0071] The specific implementation process of step S6 is as follows:

[0072] S6.1. Set the initial value i = 1 and the iteration number τ of the genetic algorithm. According to the two optimization objectives in step S5, non-dominated sorting is performed on each individual in the initial population P i , that is, each pre-residual vector, and they are divided into groups according to the fitness from high to low

[0073] S6.2. Through the genetic algorithm, that is, selection, crossover and mutation, obtain the next-generation population of the initial population P i

[0074] S6.3. Combine all the individuals in the two populations P i and Q i to form the reconstructed population R i , R i = P i ∪Q i . Perform non-dominated sorting on all the individuals in the reconstructed population R i , and also divide them into groups according to the fitness from high to low R i There are a total of 2s individuals in it;

[0075] S6.4. If i = τ, then select the population with the SPE statistic less than ​And output the point with the smallest number of fault dimensions. Among them, the number of fault dimensions is obtained by summing the indicator functions in step S5. As Figure 2 shown, the red dots in the figure are the schematic output points. Through this pre-residual vector, the specific dimensions where faults occur and their fault amplitude sizes can be determined. Take the absolute value of each element of the pre-residual vector. The element dimensions with absolute values less than the fault threshold are the directions where no faults occur, and the dimensions with absolute values greater than the fault threshold are the faulty dimensions. At this time, the element value is the fault size, and the positive and negative signs of the element respectively indicate whether the real-time operating fault data is smaller or larger than the normal sample in this fault direction.

[0076] If i≠τ, then select the top s individuals (sorted by crowding distance at the same level) from the population R i to form a set P of the top s individuals i+1 and increment i by 1, repeat step S6.2 until i = τ, then perform step S6.4.

[0077] The present invention introduces multi-objective optimization and the genetic algorithm (NSGA-II), takes the fault variables and their amplitudes as optimization parameters, aims to minimize the reconstruction residual and the number of fault variables, and obtains the optimal fault feature set through iterative optimization, ultimately realizing fault traceability.

[0078] To verify the effectiveness of the non-linear system fault traceability method based on multi-objective optimization and auto-encoding proposed by the present invention in non-linear process fault diagnosis, a 16-dimensional non-linear mathematical simulation process is used to study the diagnostic performance of different fault diagnosis methods in a high-dimensional non-linear system. The simulation process consists of 16 process variables x = [x1, x2, x3, …, x 16 , and its mathematical expression is as follows:

[0079]

[0080] where, e i ~N(0, 0.02), i = 1, 2, 3…, 16 are random noises subject to Gaussian distribution; v1, v2~U(-1, 1) are independently sampled from the uniform distribution U(-1, 1).

[0081] During the model training process, 1000 samples are generated as the training set and 2000 samples are generated as the test set. The Monte Carlo method is used to simulate five fault situations from the test set, corresponding to single-variable faults to five-variable faults respectively. For each fault type, 1000 test samples are randomly generated, and the fault amplitudes are sampled from the uniform distribution U(-1, 1).

[0082] The fault detection rate (FDR), false alarm rate (FAR), and time consumption (TC) are selected as the evaluation indicators for the fault diagnosis results, and their expressions are as follows:

[0083]

[0084]

[0085] In the formula, n is the number of test samples; m is the total number of system variables; o i is the number of correctly identified fault variables in the i-th test sample; r i is the total number of actual fault variables in the i-th test sample; p i is the number of misidentified fault variables in the i-th test sample; t i is the calculation time required for diagnosing the i-th test sample.

[0086] Table 1 gives the specific parameter setting values, and the confidence level of the statistical control limit is set to 99% to ensure the reliability of the fault diagnosis results.

[0087] Table 1 Parameter Settings of AE Model and NSGA-II Algorithm

[0088]

[0089] Table 2 gives the diagnostic results of the exhaustive reconstruction autoencoder (RBAE-ES), sequential forward reconstruction autoencoder (RBAE-SFFS), and multi-objective optimization reconstruction autoencoder based on NSGA-II (RBAE-NSGA2) methods applied in different fault scenarios of a 16-dimensional nonlinear system. The proposed RBAE-NSGA2 method in this paper shows excellent comprehensive performance in various fault scenarios. This method not only maintains a high detection rate of about 90% and a low false alarm rate within 1%, but also the calculation time consumption is always stable below 45 ms, and is basically not affected by the number of fault variables. This indicates that the RBAE-NSGA2 method effectively solves the bottleneck problem of the calculation efficiency of the reconstruction method by adopting multi-objective optimization to improve the fault isolation strategy.

[0090] Table 2 Fault Diagnosis Results of 16-Dimensional Nonlinear System

[0091]

Claims

1. A fault tracing method for non-linear systems based on multi-objective optimization and auto-encoding, characterized in that, Including: Collecting and storing historical operation data of an industrial process, and performing normalization processing on the historical operation data; Train a pre-constructed autoencoder model using the historical operation data after normalization, and calculate the control limit of the SPE statistic of the trained autoencoder model under the preset confidence interval Obtain real-time operating data online, use the normalized real-time operating data as the input data of the trained autoencoder model, and calculate the SPE statistic of the real-time operating data in real time; if the SPE statistic is greater than the SPE statistic control limit The current real-time operation data is used as the fault sample to start fault tracing; During the fault tracing process, setting multiple pre-residual vectors according to the dimensions of a non-linear system, and the multiple pre-residual vectors form an initial population for multi-objective optimization; Setting two objective functions for multi-objective optimization, including minimizing the SPE statistic after the measurement data is superimposed with the pre-residual vector and minimizing the number of fault dimensions; Combined with two objective functions of multi-objective optimization, the initial population of multi-objective optimization is optimized by NSGA-II to obtain the Pareto optimal set. Select the population with the SPE statistic less than and the smallest number of fault dimensions as the optimal solution, and finally locate the operating parameters involved in the fault and their deviation amplitudes to complete the fault traceability.

2. The method for tracing the source of faults in a nonlinear system based on multi-objective optimization and auto-encoding according to claim 1, wherein, The normalization processing includes: Using the z-score method, and the specific process is as follows: Among them, x i represents the original value of the i-th input parameter; represents the value of the i-th input parameter after normalization; m(x) represents the mean value of all input parameters; s(x) represents the standard deviation of all input parameters.

3. The method for fault tracing of a nonlinear system based on multi-objective optimization and auto-encoding according to claim 2, wherein The expression of the mean m(x) of all input parameters is as follows: where n represents the number of all input parameters.

4. The method for fault tracing of a nonlinear system based on multi-objective optimization and auto-encoding according to claim 2, wherein The expression of the standard deviation s(x) of all input parameters is as follows:

5. The method for fault tracing of a nonlinear system based on multi-objective optimization and auto-encoding according to claim 1, wherein The expression of the SPE statistic is as follows: The SPE statistic control limits The expression is as follows: At the (1-α)×100% confidence level, ζ α represents the standard value corresponding to (1-α)%; λ k represents the eigenvalue of the covariance matrix of; m is the number of eigenvalues; θ i represents the sum of the i-th powers of all the eigenvalues.

6. The method for fault tracing of a non-linear system based on multi-objective optimization and auto-encoding according to claim 1, wherein During the fault tracing process, setting multiple pre-residual vectors according to the dimensions of a non-linear system, and the multiple pre-residual vectors form an initial population for multi-objective optimization, including: For a real-time operation data that has been monitored as a fault sample and normalized s n-dimensional pre-residual vectors can be randomly generated The s n-dimensional pre-residual vectors form an initial population 7. The method for fault tracing of a non-linear system based on multi-objective optimization and auto-encoding according to claim 1, wherein Setting two objective functions for multi-objective optimization, including minimizing the SPE statistic after the measurement data is superimposed with the pre-residual vector and minimizing the number of fault dimensions, including: Fault data stream Predicted fault-free samples after being superimposed with the previous residual vector has the minimum reconstruction value; the number of fault dimensions is the smallest. Setting the fault threshold Δ = 0.01, the two objective functions can be expressed as follows: in, Represents a real-time data stream that is detected as a fault; Represents the indicator function.

8. The method for fault tracing of a nonlinear system based on multi-objective optimization and auto-encoding according to claim 7, characterized in that When |f i (t) | > 0.01, the value of the indicator function is 1, otherwise it is 0. By summing the indicator functions of n f i (t) , the number of fault dimensions is obtained.

9. The method for fault tracing of a non-linear system based on multi-objective optimization and auto-encoding according to claim 1, wherein Combined with two objective functions of multi-objective optimization, the initial population of multi-objective optimization is optimized by NSGA-II to obtain the Pareto optimal set, and the population with the SPE statistic less than and the smallest number of fault dimensions is selected as the optimal solution, and finally the operating parameters involved in the fault and their deviation amplitudes are located to complete the fault traceability, including: Set the initial value \(i = 1\) and the number of iterations \(\tau\) of the genetic algorithm, and according to two optimization objectives, perform non-dominated sorting on each individual in the initial population \(P\) i That is, each pre-residual vector, and divide them into different levels according to the fitness from high to low Obtain the initial population P through genetic algorithms, namely selection, crossover, and mutation i of the next generation population Combine all individuals of the two populations P i and Q i to form the reconstructed population R i , where R i = P i ∪ Q i . Perform non-dominated sorting on all individuals in the reconstructed population R i , and also divide them into groups according to fitness level There are a total of 2s individuals in R i ; If i = τ, then select the point in the Pareto chart where the SPE statistic is less than and the number of fault dimensions is the smallest for output.

10. The method for fault tracing of a non-linear system based on multi-objective optimization and auto-encoding according to claim 9, wherein, If i≠τ, then from the population R i Take out the first s individuals to form a set of s individuals P i+1 And step i by 1, repeat the selection, crossover and mutation steps until i = τ.

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