Multi-working-condition industrial process monitoring method based on representation learning

Abstract

The invention discloses a multi-working-condition industrial process monitoring method based on representation learning, relates to the technical field of industrial monitoring, and is technically characterized in that a cross-mode reconstruction and diversified low-rank embedding representation learning (CR-DLERL) method is adopted and is used for multi-working-condition process monitoring, and the multi-working-condition industrial process monitoring is realized through a multi-level collaborative optimization strategy. Systematically mining specific diversity and complementary characteristics of multi-working-condition process data; according to the method, the CR-DLERL framework completely utilizes the complementary characteristics among the multi-working-condition process data through a cooperation mechanism, the accuracy of anomaly detection is improved through cross-working-condition transmission of complementary information, the process monitoring performance is remarkably improved, and accurate fault detection is achieved.

Description

Technical Field

[0001] This invention relates to the field of industrial monitoring technology, and specifically to a multi-condition industrial process monitoring method based on representation learning. Background Technology

[0002] In complex industrial processes, even a small localized malfunction can cause significant damage to the entire operating system, or even trigger an industrial accident. Process monitoring can analyze the operating status of industrial systems in real time. When an anomaly is detected, an alarm is automatically triggered, notifying operators to take immediate corrective action. With the rapid development of sensor and measurement technologies, control systems can collect and record a wealth of process data, which can be analyzed to monitor industrial processes and detect faults.

[0003] In modern industrial systems, changes in production batches, process stages, or load levels lead to frequent switching of operating conditions, resulting in multi-condition characteristics. Treating all data as a single operating condition may lead to overfitting in some conditions, ignoring subtle changes, and consequently failing to effectively detect key fault characteristics. A common approach to handling multi-condition patterns is to build independent statistical models for each pattern, such as Multi-Model PCA (MMPCA) and Local PCA (LPCA). These methods monitor by training models separately for each condition, but they ignore the inherent correlations between different conditions and fail to accurately reflect complex multi-condition processes.

[0004] Therefore, the present invention aims to provide a multi-condition industrial process monitoring method based on representation learning to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to solve the above-mentioned problems and provide a multi-condition industrial process monitoring method based on representation learning. This invention uses cross-modal reconstruction and diversified low-rank embedding representation learning (CR-DLERL) methods for multi-condition process monitoring. This method systematically mines the specific diversity and complementary features of multi-condition process data through a multi-level collaborative optimization strategy.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] This invention provides a multi-condition industrial process monitoring method based on representation learning, the method comprising the following steps:

[0008] 1. Establishment of the model objective function

[0009] Taking a single working condition scenario as an example, the collected training data is X = [x1, x2, ..., x...]. n ]∈R D×nClassical low-rank representation learning (LRR) introduces global structural constraints on the representation coefficient matrix Z by minimizing the nuclear norm. Its basic form is:

[0010]

[0011] In the formula, ||·|| * For the nuclear norm, ||·|| 2，1 For l 2，1 The norm and sparse term E are used to fit noise and outliers. In a multi-condition industrial process, the collected full-condition training data is X = [X1, X2, ..., X...]. S ], where the sample data for the s-th operating condition mode is This patent first introduces a mode-specific feature projection matrix P for each operating condition mode. s The low-rank representation and feature extraction are optimized in a coordinated manner:

[0012]

[0013] In Equation (2), global structural information is recovered and noise is filtered out in the reduced-dimensional subspace. Meanwhile, to ensure the diversity of embedding representations for each operating condition mode and to measure the statistical independence of different modes, the Hilbert-Schmidt Independence C criterion (HSIC) is introduced. The HSIC criterion is based on the cross-covariance C... xy Defined by kernel mapping functions φ and ψ, random variables and Projected into the regenerating nucleus Hilbert space and The mapping relationship is In nuclear space and The inner product between any vectors in the vector is given by k1(x) i ,x j )=<φ(x i ),φ(x j )> or k2(y i ,y j )=<ψ(y i ),ψ(y j Since cross-covariance can measure the covariance of any random variable, it is defined as follows:

[0014]

[0015] Where μ x =E x [φ(x)],μ y =E y [ψ(y)], It is the tensor product. Then the HSIC index is defined as tr.

[0016]

[0017] However, the joint distribution p is usually xy It is unknown, therefore E xy It's difficult to estimate. Therefore, based on experience, given p... xy Given n observations, Z:=(x1,y1),…,(x n ,y n The empirical metric for HSIC is:

[0018]

[0019] Among them, K s and K t Let Z be the Gram matrix and H be the centering matrix. In equation (2), the representation learning for each working condition mode is independent, and there is no clear correlation between the multimodal low-rank representation learning. However, in various representations Z s There may be some similar patterns. To remove redundancy and obtain strong performance, different operating condition patterns should be represented in a mutually exclusive manner. Therefore, HSIC constraint terms are used as mutual exclusion regularization terms to reduce redundancy and interference between various high-level patterns, i.e.

[0020]

[0021] Minimize HSIC(Z) s Z t This helps to learn the embedding representation of each operating condition mode in different subspaces, which will facilitate the projection matrix P s Focus on information specific to the operating conditions. This can also effectively simulate the diversity between different work tasks.

[0022] Equation (2) strengthens the independence of different model representations and reduces redundant interference. On the other hand, to explore complementary information between models, a cross-model reconstruction mechanism is designed:

[0023] X s ≈XQ s (7)

[0024] The reconstruction matrix Q in the above formula s Advantageous complementary features are extracted from the complete multi-condition data X to reconstruct the single-condition mode data. Finally, the cross-condition mode reconstruction (Equation (7)), low-rank embedding representation (Equation (2)), and HSIC diversity constraint (Equation (6)) are modeled in a unified manner to obtain the final objective function:

[0025]

[0026] In the above formula Cross-mode reconstruction of each operating condition can preserve complementary information between various operating modes and obtain more suitable fictitious measurements for feature extraction and low-rank embedding representation learning. Discriminative projection matrices for different operating conditions are then obtained to monitor key factors in each operating condition and measure the shared global structure of their low-dimensional embeddings. By collaboratively exploring the diversity and complementarity among multiple operating conditions, more discriminative and key features of each operating condition can be obtained, thereby significantly improving the monitoring capabilities in complex multi-condition industrial processes.

[0027] 2. Objective function optimization

[0028] To transform the constrained optimization problem (8) into an unconstrained optimization problem, we first introduce an auxiliary variable J. s And let Z s =J s The nuclear norm term and the reconstructed projection term are decoupled to facilitate optimization. Then, the Lagrange equation is constructed and Lagrange multipliers are introduced. The Lagrange equation that needs to be optimized is obtained:

[0029]

[0030] in μ is the adaptive penalty parameter. In the above equation, each variable is easily solved, while the others are fixed. Therefore, all variables are optimized alternately in an iterative manner.

[0031] 1) Update variable J s

[0032] With other variables fixed, variable J s The closed-form solution is as follows:

[0033]

[0034] in, It is the Singular Value Decomposition (SVD) operation, operator Θ t (x)=sgn(x)·max(|x|-τ,0) represents the singular value reduction operation, and τ=1n / μ is the thresholding parameter.

[0035] 2) Update variable Z s

[0036] To facilitate optimization, the HSIC constraint terms use an inner product kernel with a simple form (i.e., And ignore the proportionality constant factor (n-1). -2 Therefore, the following formula can be derived:

[0037]

[0038] in Then, the objective function with respect to Z s The gradient is as follows:

[0039]

[0040] Therefore, variable Z s The solution can be obtained iteratively using the gradient descent rule:

[0041] Z s =Z s -η▽z s L (13)

[0042] Where η is the gradient descent step size.

[0043] 3) Update variable E s 1 and E s 2

[0044] With other variables fixed, solve column by column using the minimum threshold operation:

[0045]

[0046] in,

[0047] 4) Update variable Q s

[0048] With other variables fixed, the objective function relative to Q s The gradient is as follows:

[0049]

[0050] Same variable Z s Similarly, variable Q s Alternatively, it can be solved iteratively using the gradient descent rule:

[0051]

[0052] Where η is the gradient descent step size.

[0053] 5) Update variable P s

[0054] With other variables fixed, optimize variable P. s The subproblems are as follows:

[0055]

[0056] The problem in equation (18) is further transformed into:

[0057]

[0058] variable P s The optimal solution is obtained by selecting the corresponding XQ s (IZ s (IZ) s ) T (XQ s ) T The eigenvectors of the first d smallest eigenvalues ​​are obtained.

[0059] 6) Update the Lagrange multipliers and penalty parameter μ

[0060]

[0061] Y s 3 :=Y s 3 +μ(Z s -J s )

[0062] μ:=min(ρμ,μ max (20)

[0063] Here, ρ > 1 is a parameter that adjusts the convergence. Given all initialized variables, each variable is updated alternately until the convergence requirement is met.

[0064] 3. Process monitoring applications and criteria

[0065] Historical multi-condition data X was collected from different working conditions, and each working condition mode is coupled together. It is necessary to divide the multi-condition data into different modes [X1,…,X] based on the inherent characteristics of each mode. S The K-means algorithm, a simple and effective unsupervised clustering method, is employed. Based on the clustering results, the multimodal data X can be divided into multiple individual operating condition modes. Then, in The proposed CR-DLERL method is then applied to train the projection matrix for specific operating conditions. For subsequent online monitoring. When a new sample X to be tested... new ∈R D Upon arrival, X needs to be identified. new The operating mode to which it belongs. The center of the operating condition cluster obtained during training. It can provide guidance for operating condition pattern recognition. To more reasonably determine which operating condition the sample to be detected belongs to, X... new and the center v for each working mode s The mixed distance metric between them is defined as follows:

[0066] score=d cos,s +d euc,s (twenty one)

[0067] in, Let d be the cosine distance. euc,s =||X new -v s ||2 represents the Euclidean distance. Cosine distance typically quantifies angular differences, while Euclidean distance more accurately reflects their spatial distance. Hybrid distance metrics can enhance adaptability to complex data distributions and improve the accuracy of pattern recognition. Therefore, the test sample X... new Assigned to the pattern corresponding to the most similar centroid:

[0068]

[0069] The SPE metric measures the change of a sample vector in the residual space and can be calculated by referring to the PCA monitoring method. 2 Statistics measure the change of a sample vector in the principal space.

[0070]

[0071] in This is the covariance matrix of the training data. Considering the complex and non-Gaussian distribution of actual industrial data, the corresponding control limits are estimated using the kernel density estimation (KDE) method. and J SPE,α Where α is the confidence factor. Therefore, the following decision-making mechanism can be used to determine the new sample X to be monitored. new Status:

[0072]

[0073] Compared with existing technologies, the beneficial effects of this solution are:

[0074] This invention utilizes a cross-modal reconstruction and diversified low-rank embedding representation learning (CR-DLERL) method for multi-condition process monitoring. This method systematically mines the specific diversity and complementary features of multi-condition process data through a multi-level collaborative optimization strategy. The CR-DLERL framework of this method fully utilizes the complementary characteristics between multi-condition process data through a collaborative mechanism. The learned discriminative condition-specific projection can achieve a comprehensive representation of multi-condition processes, significantly improving process monitoring performance and thus achieving more accurate fault detection. Attached Figure Description

[0075] Figure 1 This is a flowchart of multi-mode process monitoring using the CR-DLERL method in an embodiment of the present invention;

[0076] Figure 2 This is a schematic diagram of the monitoring results of the Multiple-LPP and CR-DLERL methods in the numerical simulation experiment in the embodiments of the present invention;

[0077] Figure 3 This is a schematic diagram illustrating the online identification and monitoring results of different methods in the TE process in embodiments of the present invention. Detailed Implementation

[0078] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be described in further detail below with reference to the embodiments and accompanying drawings. Obviously, the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort should fall within the scope of protection of the present invention.

[0079] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the embodiments.

[0080] Example:

[0081] 1. Establishment of the model objective function

[0082] Taking a single working condition scenario as an example, the collected training data is X = [x1, x2, ..., x...]. n ]∈R D×n Classical low-rank representation learning (LRR) introduces global structural constraints on the representation coefficient matrix Z by minimizing the nuclear norm. Its basic form is:

[0083]

[0084] In the formula, ||·|| * For the nuclear norm, ||·|| 2，1 For l 2，1 The norm and sparse term E are used to fit noise and outliers. In a multi-condition industrial process, the collected full-condition training data is X = [X1, X2, ..., X...]. S ], where the sample data for the s-th operating condition mode is This patent first introduces a mode-specific feature projection matrix P for each operating condition mode. s The low-rank representation and feature extraction are optimized in a coordinated manner:

[0085]

[0086] In Equation (2), global structural information is recovered and noise is filtered out in the reduced-dimensional subspace. Meanwhile, to ensure the diversity of embedding representations for each operating condition mode and to measure the statistical independence of different modes, the Hilbert-Schmidt Independence C criterion (HSIC) is introduced. The HSIC criterion is based on the cross-covariance C... xy Defined by kernel mapping functions φ and ψ, random variables and Projected into the regenerating nucleus Hilbert space and The mapping relationship is In nuclear space and The inner product between any vectors in the vector is given by k1(x) i ,x j )=<φ(x i ),φ(x j )> or k2(y i ,y j )=<ψ(y i ),ψ(y j Since cross-covariance can measure the covariance of any random variable, it is defined as follows:

[0087]

[0088] Where μ x =E x [φ(x)],μ y =E y [ψ(y)], It is the tensor product. Then the HSIC index is defined as tr.

[0089]

[0090] However, the joint distribution p is usually xy It is unknown, therefore E xy It's difficult to estimate. Therefore, based on experience, given p... xy Given n observations, Z:=(x1,y1),…,(x n ,y n The empirical metric for HSIC is:

[0091]

[0092] Among them, K s and K t Let Z be the Gram matrix and H be the centering matrix. In equation (2), the representation learning for each working condition mode is independent, and there is no clear correlation between the multimodal low-rank representation learning. However, in various representations Zs There may be some similar patterns. To remove redundancy and obtain strong performance, different operating condition patterns should be represented in a mutually exclusive manner. Therefore, HSIC constraint terms are used as mutual exclusion regularization terms to reduce redundancy and interference between various high-level patterns, i.e.

[0093]

[0094] Minimize HSIC(Z) s Z t This helps to learn the embedding representation of each operating condition mode in different subspaces, which will facilitate the projection matrix P s Focus on information specific to the operating conditions. This can also effectively simulate the diversity between different work tasks.

[0095] Equation (2) strengthens the independence of different model representations and reduces redundant interference. On the other hand, to explore complementary information between models, a cross-model reconstruction mechanism is designed:

[0096] X s ≈XQ s (7)

[0097] The reconstruction matrix Q in the above formula s Advantageous complementary features are extracted from the complete multi-condition data X to reconstruct the single-condition mode data. Finally, the cross-condition mode reconstruction (Equation (7)), low-rank embedding representation (Equation (2)), and HSIC diversity constraint (Equation (6)) are modeled in a unified manner to obtain the final objective function:

[0098]

[0099] In the above formula Cross-mode reconstruction of each operating condition can preserve complementary information between various operating modes and obtain more suitable fictitious measurements for feature extraction and low-rank embedding representation learning. Discriminative projection matrices for different operating conditions are then obtained to monitor key factors in each operating condition and measure the shared global structure of their low-dimensional embeddings. By collaboratively exploring the diversity and complementarity among multiple operating conditions, more discriminative and key features of each operating condition can be obtained, thereby significantly improving the monitoring capabilities in complex multi-condition industrial processes.

[0100] 2. Objective function optimization

[0101] To transform the constrained optimization problem (8) into an unconstrained optimization problem, we first introduce an auxiliary variable J. s And let Z s =J s The nuclear norm term and the reconstructed projection term are decoupled to facilitate optimization. Then, the Lagrange equation is constructed and Lagrange multipliers are introduced. The Lagrange equation that needs to be optimized is obtained:

[0102]

[0103] in μ is the adaptive penalty parameter. In the above equation, each variable is easily solved, while the others are fixed. Therefore, all variables are optimized alternately in an iterative manner.

[0104] 1) Update variable J s

[0105] With other variables fixed, variable J s The closed-form solution is as follows:

[0106]

[0107] in, It is the Singular Value Decomposition (SVD) operation, operator Θ t (x)=sgn(x)·max(|x|-τ,0) represents the singular value reduction operation, and τ=1 / μ is the thresholding parameter.

[0108] 2) Update variable Z s

[0109] To facilitate optimization, the HSIC constraint terms use an inner product kernel with a simple form (i.e., And ignore the proportionality constant factor (n-1). -2 Therefore, the following formula can be derived:

[0110]

[0111] in Then, the objective function with respect to Z s The gradient is as follows:

[0112]

[0113] Therefore, variable Z s The solution can be obtained iteratively using the gradient descent rule:

[0114] Z s =Z s -η▽z s L (13)

[0115] Where η is the gradient descent step size.

[0116] 3) Update variable E s 1 and E s 2

[0117] With other variables fixed, solve column by column using the minimum threshold operation:

[0118]

[0119] in,

[0120] 4) Update variable Q s

[0121] With other variables fixed, the objective function relative to Q s The gradient is as follows:

[0122]

[0123] Same variable Z s Similarly, variable Q s Alternatively, it can be solved iteratively using the gradient descent rule:

[0124]

[0125] Where η is the gradient descent step size.

[0126] 5) Update variable P s

[0127] With other variables fixed, optimize variable P. s The subproblems are as follows:

[0128]

[0129] The problem in equation (18) is further transformed into:

[0130]

[0131] variable P s The optimal solution is obtained by selecting the corresponding XQ s (IZ s (IZ) s ) T (XQ s ) T The eigenvectors of the first d smallest eigenvalues ​​are obtained.

[0132] 6) Update the Lagrange multipliers and penalty parameter μ

[0133]

[0134] Y s 3 :=Y s 3 +μ(Z s -Js )

[0135] μ:=min(ρμ,μ max (20)

[0136] Here, ρ > 1 is a parameter that adjusts the convergence. Given all initialized variables, each variable is updated alternately until the convergence requirement is met.

[0137] 3. Process monitoring applications and criteria

[0138] Historical multi-condition data X was collected from different working conditions, and each working condition mode is coupled together. It is necessary to divide the multi-condition data into different modes [X1,…,X] based on the inherent characteristics of each mode. S The K-means algorithm, a simple and effective unsupervised clustering method, is employed. Based on the clustering results, the multimodal data X can be divided into multiple individual operating condition modes. Then, in The proposed CR-DLERL method is then applied to train the projection matrix for specific operating conditions. For subsequent online monitoring. When a new sample X to be tested... new ∈R D Upon arrival, X needs to be identified. new The operating mode to which it belongs. The center of the operating condition cluster obtained during training. It can provide guidance for operating condition pattern recognition. To more reasonably determine which operating condition the sample to be detected belongs to, X... new and the center v for each working mode s The mixed distance metric between them is defined as follows:

[0139] score=d cos,s +d euc,s (twenty one)

[0140] in, Let d be the cosine distance. euc,s =||X new -v s ||2 represents the Euclidean distance. Cosine distance typically quantifies angular differences, while Euclidean distance more accurately reflects their spatial distance. Hybrid distance metrics can enhance adaptability to complex data distributions and improve the accuracy of pattern recognition. Therefore, the test sample X... new Assigned to the pattern corresponding to the most similar centroid:

[0141]

[0142] The SPE metric measures the change of a sample vector in the residual space and can be calculated by referring to the PCA monitoring method. 2Statistics measure the change of a sample vector in the principal space.

[0143]

[0144] in This is the covariance matrix of the training data. Considering the complex and non-Gaussian distribution of actual industrial data, the corresponding control limits are estimated using the kernel density estimation (KDE) method. and J SPE,α Where α is the confidence factor. Therefore, the following decision-making mechanism can be used to determine the new sample X to be monitored. new Status:

[0145]

[0146] The overall process flow of the multi-condition process monitoring framework using the CR-DLERL method is as follows: Figure 1 As shown, it mainly consists of two parts: offline modeling and online monitoring.

[0147] Example 2:

[0148] 1. Dataset Description

[0149] Based on simulation numerical experiments and evaluation results of the Tennessee Eastman (TE) process. Simulation numerical experiments were used to verify the superiority of the CR-DLERL method for joint multi-condition modeling. The Tennessee Eastman (TE) process is a complex chemical process with strong nonlinearity and is widely used as a benchmark dataset to verify the performance of process monitoring methods.

[0150] 2. Comparison Methods

[0151] In the simulated numerical experiments, the comparison method adopted Multiple Local Preserving Projection (Multiple-LPP) is a method that models each mode individually.

[0152] In the TE process experiments, the proposed CR-DLRL method was compared with three other methods, including JMSDL, MMJP and LRME.

[0153] 3. Data Construction

[0154] In the simulated numerical experiment, the experimental data was constructed as follows:

[0155]

[0156] Where [s1 s2] T These are the source variables, [e1,…e5] T It is white noise distributed N(0,0.01). The three types of data are constructed from completely different data sources, namely:

[0157]

[0158] Normally, 200 samples are sampled for each mode as training data. To fully verify the effectiveness of the proposed CR-DLERL for multimodal process monitoring, the following two different test cases were designed.

[0159] Case 1: There are 400 monitoring samples. Sampling points 1-200 are sampled from Mode 1 under normal conditions. Sampling points 201-400 are sampled from Mode 2. Then, the variable of each sample increases by a step change of 0.08, resulting in an abnormal state.

[0160] Case 2: There are 600 monitoring samples, with sampling points 1-200, 201-400, and 401-600 sampled from Mode 1, Mode 2, and Mode 3 under normal conditions, respectively. A ramp change is then added to samples 300 to 400 of the variable, and a step change with an amplitude of 0.08 is added to samples 500 to 600 of the variable.

[0161] In the TE process experiment, 22 measured variables and 11 controllable variables were selected as monitoring objects. Four operating modes were constructed based on a public dataset, with 400 normal operation samples collected in each mode, totaling 1600 samples for training. During the online testing phase, faults 4, 11, and 13 were added to the 100th sample in each of the three modes, generating 300 fault-infected samples for each mode. This was used to evaluate the detection performance of each method under different operating conditions and complex fault environments. Then, under mode 1 conditions, all 21 faults were added to the 160th sample as another test data point to evaluate the method's monitoring capability for a specified operating condition. The fault diagnosis rate (FDR) and false alarm rate (FAR) were used for evaluation.

[0162] 4. Experimental Results

[0163] In the simulated numerical experiments, the effectiveness of multi-condition collaborative modeling was verified by comparing it with the local multi-condition modeling method Multiple-LPP. The monitoring results are as follows: Figure 2 As shown, the green solid line represents mode switching. First, the proposed pattern recognition with hybrid distance metric can accurately identify the operating mode; then, for Case 1 and Case 2, for the proposed CR-DLERL, the sum and SPE statistics of anomalous samples are mostly above the control limit, while the statistics of normal samples are significantly below the control limit. However, the SPE statistics of Multiple-LPP are insufficient to detect the anomalous states in Case 1 and Case 2, mainly because independent modeling cannot effectively distinguish the differences between multiple operating conditions and provide a comprehensive understanding of the process data of multiple operating conditions.

[0164] In the TE process experiment, the online pattern recognition and monitoring results are as follows: Figure 3 As shown, the solid green line represents mode switching, and the dashed black line represents a fault introduced at the current sampling point. The proposed method can accurately identify operating mode, providing a solid foundation for multi-condition process detection. Figure 3 (a) It can be seen that the JMSDL method has difficulty in completely detecting faults from the 100th to the 400th sample when monitoring transient faults, and only achieves 10.33% and 64.44% FDR for SPE and SPE respectively. Figure 3 (b) indicates that the MMJP's SPE statistic cannot continuously monitor fault 4 in mode 1, but achieves relatively satisfactory detection performance in operating mode 2 and operating mode 3. Figure 3 In (c), the LRME method and the SPE statistic detected faults with FDRs of 84.22% and 70.20%, respectively. Although similar to JMSDL, their monitoring performance for the SPE statistic in operating mode 1 is unsatisfactory, and the boundaries between the control limits and the statistic values ​​are unclear. This is mainly because they use a mode-sharing strategy (JMSDL's shared dictionary and LRME's shared low-rank representation), which makes their detection performance susceptible to the influence of other modes. Figure 3 As shown in (d), the proposed CR-DLERL method achieves excellent fault detection performance (i.e., FDR of 92.86% and 81.22%, respectively), which is 2.31% and 11.02% higher than the suboptimal method. The FAR of the CR-DLERL's FDR and SPE statistics is acceptable and satisfactory, at only 1.00% and 0.33%, respectively. Furthermore, CR-DLERL can detect most faults under each operating condition, demonstrating its strong and robust monitoring capability across different operating conditions.

[0165] To further demonstrate its performance in detecting various faults, in Mode 1, 21 classic TE faults were added to sampling points 160-860. Table 1 shows the FDR of the SPE statistics. Overall, the proposed CR-DLERL consistently outperforms other comparative process monitoring methods in terms of the average SPE statistic.

[0166] Table 1 shows the FDR (%) for 21 faults detected in Mode 1 of TEP.

[0167]

[0168] The above specific embodiments are merely explanations of the present invention and are not intended to limit the present invention. After reading this specification, those skilled in the art can make modifications to these embodiments without contributing any inventive step, but as long as they are within the scope of the claims of the present invention, they are protected by patent law.

Claims

1. A multi-condition industrial process monitoring method based on representation learning, characterized by: The method includes the following steps: S1. Establish the objective function model: Obtain sample data for the s-th operating condition mode. Introduce a mode-specific feature projection matrix P for each operating condition mode. s By co-optimizing low-rank representation and feature extraction, the objective function model is obtained: S2. Optimize the objective function model: Introduce Lagrange multipliers to constrain the variables in the objective function model, and introduce auxiliary variable J. s Z s =J s Decouple the nuclear norm terms and the reconstructed projection terms; S3. Fault Detection Applications and Criteria: Kernel Density Estimation Method for Estimating Corresponding Control Limits and J SPE,α Determine the sample X to be monitored. new The state.

2. The multi-condition industrial process monitoring method based on representation learning as described in claim 1, characterized in that: The objective function model of S1 is constructed by low-rank representation learning, which introduces global structural constraints by minimizing the nuclear norm pair representation coefficient matrix Z.

3. The multi-condition industrial process monitoring method based on representation learning as described in claim 1, characterized in that: The Hilbert-Schmidt independence criterion is introduced into the objective function model of S1, and the cross covariance C is used as a basis. xy Define the HSIC criteria: Where μ x =E x [φ(x)],μ y =E y [ψ(y)], It is a tensor product; The HSIC index is defined as follows: Given from p xy Given n observations, Z:=(x1,y1),…,(x n ,y n The empirical measure of HSIC is: HSIC(Z) s Z t )=tr(K s HK t H) / (n-1) 2 K s and K t Let H be the Gram matrix and H be the centering matrix; The diversity constraints of HSIC are: The cross-condition mode reconfiguration mechanism is as follows: X s ≈XQ s .

4. The multi-condition industrial process monitoring method based on representation learning as described in claim 3, characterized in that: By unifying the cross-condition mode reconstruction, the objective function model, and the HSIC diversity constraint model, the final objective function is obtained:

5. The multi-condition industrial process monitoring method based on representation learning as described in claim 1, characterized in that: S2 introduces Lagrange multipliers. Construct the Lagrangian function from the final objective function model: in μ is the adaptive penalty parameter.

6. The multi-condition industrial process monitoring method based on representation learning as described in claim 5, characterized in that: In S2, the variables are optimized alternately in an iterative manner.

7. The multi-condition industrial process monitoring method based on representation learning as described in claim 6, characterized in that: For variable J s : The J s The closed-form solution is: Where τ = 1 / μ is the thresholding parameter; For variable Z s : Ignore the proportionality constant factor (n-1) -2 ,and Then the objective function with respect to Z s The gradient is: variable Z s The iterative formula using the gradient descent rule is: WITH s =Z s -η▽z s L, η is the gradient descent step size; For variable E s 1 and E s 2 : With other variables fixed, solve column by column using the minimum threshold operation: For variable Q s : With other variables fixed, the final objective function model relative to Q s The gradient is: variable Q s The solution obtained iteratively using the gradient descent rule is: η is the gradient descent step size; For variable P s : With other variables fixed, optimize variable P. s The question is: By selecting the corresponding XQ s (IZ s (IZ) s ) T (XQ s ) T The variable P is obtained by using the eigenvectors of the first d smallest eigenvalues. s The optimal solution; Lagrange multipliers The optimization formula for the penalty parameter μ is: Y s 3 :=Y s 3 +μ(Z s -J s ) μ:=min(ρμ,μ max )。 8. The multi-condition industrial process monitoring method based on representation learning as described in claim 1, characterized in that: The specific steps of S3 are as follows: Based on the clustering results, the multimodal data X of the multi-condition mode is divided into multiple individual condition modes. exist The CR-DLERL method is executed to train the projection matrix for a specific operating condition. To conduct online monitoring.

9. A multi-condition industrial process monitoring method based on representation learning as described in claim 8, characterized in that: when the process to be monitored... Monitoring sample X new ∈R D At that time, the working condition cluster center Provides guidance for operating condition pattern recognition, determining the sample X to be monitored. new The operating mode, X new and the center v for each working mode s The mixing distance metric between them is: score=d cos,s +d euc,s , when At that time, the sample X to be monitored new It is assigned to the corresponding operating mode.

10. The multi-condition industrial process monitoring method based on representation learning as described in claim 9, characterized in that: The T 2 The statistic measures the change of the sample vector in the principal component space as follows: Andorff is the covariance matrix of the training data. The corresponding control limits are estimated using the kernel density estimation method. and J SPE,α Determine the sample X to be monitored. new Status: Where α is the confidence factor.

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