A hierarchical fluctuation window based multi-modal industrial process identification and monitoring method
By using a hierarchical fluctuation window approach, combined with Gaussian mixture models and local preservation projection, the challenges of model complexity and transition mode monitoring in multimodal industrial processes are solved, achieving efficient mode identification and fault detection.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHEASTERN UNIV CHINA
- Filing Date
- 2022-12-29
- Publication Date
- 2026-05-15
AI Technical Summary
Existing technologies for multimodal industrial process monitoring suffer from complex model numbers, difficulty in setting window parameters, and the dynamic and non-stationary nature of transition modes, which affects the monitoring models and leads to monitoring difficulties.
A hierarchical fluctuation window-based approach is adopted, using Gaussian mixture models for coarse and fine mode identification, combined with local preservation projection for data dimensionality reduction, and a monitoring model for stable and transitional modes is constructed. Fault detection is performed using Mahalanobis distance and neighborhood offset models.
It improves the recognition accuracy of multimodal processes, reduces monitoring complexity, increases the fault detection rate of transition modes, simplifies the number of models, and provides a common platform for subsequent monitoring.
Smart Images
Figure CN115982579B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of process monitoring technology, and in particular to a multimodal industrial process identification and monitoring method based on hierarchical fluctuation windows. Background Technology
[0002] In recent years, with changes in factors such as industrial market demand and production planning, more and more industrial production processes have exhibited multimodal characteristics. Standard multivariate statistical algorithms such as principal component analysis (PCA) perform poorly in multimodal processes because they assume that the process should operate under a stable single mode.
[0003] Although multimodal processes have attracted widespread attention, most research remains focused on stable modes, neglecting the transitions between modes. Monitoring transitional modes is challenging due to the nonlinear, dynamic, and non-stationary nature of the data. In recent years, some scholars have begun researching transitional modes. Zhang et al. proposed a multi-model strategy based on Gaussian mixture models (GMMs). First, they applied k-Means coarse clustering, then arranged the data chronologically and performed fine clustering. Finally, they built a single Gaussian model for each stable mode and a GMM model for each transitional mode for monitoring. However, these models are too complex and impractical. Gao et al. used local peak clustering to identify stable and transitional modes and built a stacked denoising autoencoder model for each stable mode for monitoring, but did not mention a monitoring model for transitional modes. Ha et al. proposed an ensemble multimodal PCA based on KNN. This method uses KNN to identify multimodal processes and then builds a PCA monitoring model for each identified mode. However, the accuracy of KNN in identifying multimodal processes needs improvement, and the nonlinear and non-stationary characteristics of transitional modes affect PCA's ability to monitor transitional modes. Lu et al. proposed a stage-based sub-PCA model to handle multimodal data with transitional processes; however, the hard-stage partitioning algorithm ignores the transitional characteristics between modes.
[0004] In summary, monitoring of multimodal processes with transition modes faces challenges such as a large and complex number of models, difficulty in setting window parameters, and the dynamic and non-stationary nature of transition modes also places certain requirements on the monitoring model. Summary of the Invention
[0005] The technical problem to be solved by the present invention is to provide a multimodal industrial process identification and monitoring method based on hierarchical fluctuation windows, which addresses the shortcomings of the prior art.
[0006] To solve the above-mentioned technical problems, the method adopted by the present invention is as follows:
[0007] Step 1: Data preprocessing;
[0008] Collect multimodal process data X under normal operating conditions:
[0009] X = [x1, x2, ..., x m ] T ∈R m×n
[0010] Where m is the number of samples and n is the number of variables, we denote the i-th sample containing n variables as x. i，n (i = 1, 2, ..., m).
[0011] The specific steps for data preprocessing of X are as follows:
[0012] Step 1.1 Calculate the mean of all variables, where the j-th variable x in X is the mean of all variables. i，j The formula for calculating the mean of (j=1,2,…,n) is:
[0013]
[0014] Step 1.2 Calculate the standard deviation of all variables, where the j-th variable x in X is the standard deviation of the j-th variable. i，j The formula for calculating the standard deviation of (j = 1, 2, ..., n) is:
[0015]
[0016] Step 1.3 standardizes the multimodal historical data X, where the standardization formula for the j-th variable of the i-th sample is:
[0017]
[0018] Step 2: Coarse modal identification based on Gaussian mixture model;
[0019] After data standardization in step 1, we obtain standardized data X; X is then input into a Gaussian mixture model for clustering, and the parameters of the Gaussian mixture model are solved using the EM algorithm to obtain process data information.
[0020] The clustering results of the Gaussian mixture model are denoted as X = {S1, T1, S2, ..., S...} u ,T b ,…,S c-1 ,T c-1 ,S c}(u=1,2,…,c)(b=1,2,…,c-1), where S u and T b These represent the u-th stable mode and the b-th transition mode, respectively.
[0021] Step 3: Modal fine recognition based on the initial hierarchical window;
[0022] Step 4: Modal fine recognition based on the terminal hierarchical window;
[0023] Step 5: Data dimensionality reduction based on locally linear embedding; After determining the boundaries of the stable and transitional modes in Steps 3 and 4, it is necessary to construct a monitoring model for X and reduce the dimensionality of the process data X using locally linear embedding.
[0024] Step 5.1 Locally linear embedding projects the data X m×n onto a low-dimensional feature space Y m×l (l < n), where y i = x i A (i = 1, 2,..., m), where m is the number of samples, n is the number of original data variables, and l is the dimensionality of the feature space.
[0025] Locally linear embedding solves for the projection matrix A by optimizing the following objective function:
[0026]
[0027] where W ij is the weight coefficient, which penalizes the original neighboring points whose distances become farther after projection to achieve the purpose of maintaining the neighboring relationship of samples before and after projection; W ij is calculated using the heat kernel method, i.e., where t is the heat kernel parameter.
[0028] Step 5.2 The objective function in Step 5.1 can be transformed into the following formula,
[0029] min a T X T PXa
[0030] where P = D - W is the Laplacian matrix, D is a diagonal matrix and D ii = ∑ j W ij , and a is the projection vector.
[0031] Step 5.3 Adding the constraint condition a T X T DXa = 1 makes the solution of the projection vector unique. By using the Lagrange function method, the optimization problem can be transformed into a generalized eigenvalue problem, as shown in the following formula:
[0032] X T PXa = λX T DXa
[0033] The matrix formed by the eigenvectors corresponding to the first r smallest eigenvalues is the projection matrix A, i.e., A = (a1, a2, ..., a...). r ).
[0034] Step 5.4 The multimodal process data X is dimensionality reduced using the projection matrix A to obtain the low-dimensional spatial data Y, as shown in the following equation:
[0035] Y = XA
[0036] Step 6: Construct a stable modal monitoring model;
[0037] For monitoring stable modes, a new global monitoring metric combining Mahalanobis distance is applied:
[0038]
[0039] Where D is the number of Gaussian principal components, p(θ) d |x) is the probability that sample x belongs to the d-th Gaussian principal component, θ d ={μ d ,Σ d}and μ d With ∑ d Let λ be the mean and covariance matrix of the d-th Gaussian principal component, respectively; d The Mahalanobis distance is given by the following formula:
[0040]
[0041] G's control limits G UCL It can be obtained from the F-distribution, as shown in the following formula:
[0042]
[0043] Where m and n are the number of samples and the number of variables in the process data, respectively, F n,m-n,α It is an F-distribution with n and mn degrees of freedom, where α is the confidence level.
[0044] Step 7: Construct a transition mode monitoring model.
[0045] The specific method for step 3 is as follows:
[0046] Step 3.1 For a sample x in X, its neighborhood features D x The definition is as follows:
[0047]
[0048] Where k is the number of nearest neighbors of x, d i Let x be the distance between sample x and its i-th nearest neighbor, and exp be an exponential function.
[0049] Neighborhood features describe the characteristics of each modality from a distance perspective. Typically, neighborhood features of the same modality are similar, but when a modality transition occurs, the features of adjacent modalities show significant fluctuations. Let D denote the neighborhood distance of all samples in X.
[0050] Step 3.2 Divide D using a fixed window H with a window width of W, that is, D is divided into m / W initial level windows.
[0051] Step 3.3 Calculate the average neighborhood feature of the i-th initial hierarchical window, using the initial hierarchical window as the unit. The calculation formula is:
[0052]
[0053] Among them, H i Let μ represent the i-th initial window. i The average neighborhood feature of the data within the initial hierarchical window can vary significantly across different modalities.
[0054] Step 3.4 The absolute difference is the dividing point between the stable mode and the transition mode. The calculation formula is as follows:
[0055]
[0056] Where μ i and μ i+1 These are the average neighborhood features of the i-th and (i+1)-th initial hierarchical windows, respectively; γ i It represents the average neighborhood feature difference between adjacent initial level windows. If an initial level window contains the start or end point of a transition mode, the absolute difference between that window and its adjacent windows will be greater than the absolute difference between the windows of other modes.
[0057] Step 3.5 Based on the modal information obtained from the coarse identification of the Gaussian mixture model, i.e., X contains c-1 transition modes, γ... i Arrange from largest to smallest to obtain γ * And select the first 2(c-1) largest γ i value.
[0058] Step 3.6 Extract all 2(c-1) γ values from the original data X according to the initial hierarchical window arrangement. i The window corresponding to the value is designated as the priority window H*, as shown in the following formula:
[0059]
[0060] in, and These represent the start and end windows containing the j-th transition mode, respectively.
[0061] The specific method for step 4 is as follows:
[0062] Step 4.1 The result obtained in step 3.6 and Based on this, we can expand upon it as follows:
[0063]
[0064] Among them, H j and H o In X respectively and The number of adjacent windows, g, can be adjusted based on the multimodal process data X. or The number of samples in the sample is (g+1)W.
[0065] Step 4.2 Calculate the volatility of variables
[0066] s is or One of the variables in, at the f-th time t f Corresponding variable value s f As shown in the following formula:
[0067] s={(s1,t1),…,(s f ,t f ),…,(s (g+1)w ,t (g+1)W )}
[0068] Step 4.3 introduces a fixed window h with a window width of L to divide s, that is, s is divided into (g+1)W / L terminal level windows.
[0069] Step 4.4 Variable volatility v of adjacent terminal level windows i As shown in the following formula:
[0070]
[0071] Among them, s i (j) represents the value of the j-th variable in the i-th terminal level window, v i The difference between adjacent windows was measured, v i The larger the value of v, the greater the difference between adjacent windows. i =0 means that the two windows are exactly the same.
[0072] Step 4.5 involves determining the largest v in variable s. i To determine the time t when the variable undergoes a mode transition. a As shown in the following formula:
[0073] t a (s)=max(v i (s=1,2,…,n)
[0074] Where max is the maximum value function.
[0075] Step 4.6 Traversal The variables in the data and the statistics for each t. a The number of occurrences determines the starting position t of the mode transition. trans ,as follows:
[0076] t trans =max(count(t) a (s)))(s=1,2,…,n)
[0077] Here, count is a counting function.
[0078] The specific method for step 7 is as follows:
[0079] Step 7.1 For a sample τ in the dimensionality-reduced transition process data T, firstly, find the k nearest neighbor samples τ of τ in T. 1 ,τ 2 ,…,τ k .
[0080] Step 7.2 Calculate the mean vector ξ of the k nearest neighbor samples, as shown in the following formula:
[0081]
[0082] Where, τ i Let be the i-th nearest neighbor sample of sample τ, and k be the number of nearest neighbors.
[0083] Step 7.3 The offset vector of the sample τ in the low-dimensional space is denoted as η = τ - ξ, and the offset matrix of the transition process data T is denoted as B.
[0084] Step 7.4 Establish two monitoring statistics in the principal subspace and the residual subspace, respectively, as follows:
[0085]
[0086] q no =e(Ξ E ) -1 e T
[0087] Among them, Ξ B Let e be the covariance matrix of the mean B; where e is the residual vector and e = x h -ξA T ,x hLet τ be the sample corresponding to τ in high-dimensional space, and A be the projection matrix that preserves the local projection; Ξ E Let e be the covariance matrix of the residual matrix; for convenience, and q no control limits and q no-UCL The kernel density method was used to determine this.
[0088] The beneficial effects of this invention are:
[0089] This invention provides a method for identifying and monitoring multimodal industrial processes based on hierarchical fluctuation windows. The beneficial effects of this method are summarized as follows: (1) A new hierarchical fluctuation window (HFWS) is proposed from the perspective of samples and variables to accurately identify modal information, which improves the identification accuracy of multimodal processes with transition modes and facilitates the establishment of subsequent monitoring models; (2) A neighborhood offset model is established for transition modes, which reduces the monitoring complexity and improves the fault detection rate of transition modes; (3) Stable modes are monitored using a GMM model based on Mahalanobis distance, which greatly reduces the number of models; (4) A new benchmark TE process is applied, which provides a common platform for comparison with similar subsequent work, and the modal identification and monitoring capabilities of this invention are effectively verified in this process. Attached Figure Description
[0090] Figure 1 A flowchart of the method provided in an embodiment of the present invention;
[0091] Figure 2 A process flow diagram of the Tennessee-Eastman process provided in an embodiment of the present invention;
[0092] Figure 3 The neighborhood feature fluctuation map provided in the embodiments of the present invention;
[0093] Figure 4 A schematic diagram of the fluctuation window ratio provided in an embodiment of the present invention;
[0094] Figure 5 Scatter plot of variable 19 in fault 10 under four amplitudes provided in the embodiment of the present invention. Detailed Implementation
[0095] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.
[0096] The method in this embodiment is as follows:
[0097] This invention is used to illustrate the monitoring effect on a new benchmark, the Tennessee-Eastman (TE) process. Reinartz et al. proposed a new TE dataset in 2021, which provides a suitable and unified benchmark for future research; its process flow diagram is shown below. Figure 2 As shown in Table 1, the new dataset contains six operating modes, each with a sampling frequency of 3 minutes and a running time of 100 hours. The number of process faults has been updated to 28.
[0098] Table 1 TE Process Fault List
[0099]
[0100]
[0101] The process began introducing faults at hour 30. In addition to faults at full amplitude, Reinartz et al. simulated all faults at 25%, 50%, and 75% amplitude. Faults at 100% amplitude were simulated 200 times, and faults at 25%, 50%, and 75% amplitude were simulated 100 times each. We conducted experiments using mode 1 and mode 2 data downloaded from a website. The training data consisted of 2000 samples, with the first 600 belonging to mode 1, samples 601-1000 to the transition mode, and samples 1001-2000 to mode 2. The fault data also contained 2000 samples, with faults introduced starting at sample 601.
[0102] The implementation process of the embodiment is as follows: Figure 1 As shown, the details are as follows:
[0103] Step 1: Data preprocessing;
[0104] Collect multimodal process data X under normal operating conditions:
[0105] X = [x1, x2, ..., x m ] T ∈R m×n
[0106] Where m = 2000 is the number of samples, n = 50 is the number of variables, and we denote the i-th sample containing n variables as...
[0107] x i，n (i = 1, 2, ..., 2000). Data preprocessing for X is performed using the following steps:
[0108] Step 1.1 Calculate the mean of all variables, where the j-th variable x in X is the mean of all variables. i，j The formula for calculating the mean of (j=1,2,…,50) is:
[0109]
[0110] Step 1.2 Calculate the standard deviation of all variables, where the j-th variable x in X is the standard deviation of the j-th variable. i，j The formula for calculating the standard deviation of (j = 1, 2, ..., 50) is:
[0111]
[0112] Step 1.3 standardizes the multimodal historical data X, where the standardization formula for the j-th variable of the i-th sample is:
[0113]
[0114] Step 2: Coarse modal identification based on Gaussian mixture model;
[0115] After data standardization in step 1, we obtain standardized data X; X is input into a Gaussian mixture model for clustering, and the parameters of the Gaussian mixture model are solved by the EM algorithm to obtain process data information;
[0116] The clustering results of the Gaussian mixture model are denoted as X = {S1, T1, S2,};
[0117] Step 3: Modal fine-tuning based on the initial hierarchical window;
[0118] Step 3.1 For a sample x in X, its neighborhood features D x The definition is as follows:
[0119]
[0120] Where k is the number of nearest neighbors of x, and is chosen to be 100, d i Let x be the distance between sample x and its i-th nearest neighbor, and exp be an exponential function.
[0121] Neighborhood features describe the characteristics of each modality from a distance perspective. Typically, neighborhood features of the same modality are similar, but when a modality transition occurs, the features of adjacent modalities show significant fluctuations. Let D denote the neighborhood distance of all samples in X.
[0122] Step 3.2 Use a fixed window H with a window width of W = 100 to divide D, that is, D is divided into 20 initial level windows.
[0123] Step 3.3 Calculate the average neighborhood feature of the i-th initial hierarchical window, using the initial hierarchical window as the unit. The calculation formula is:
[0124]
[0125] Among them, H iLet μ represent the i-th initial window. i The average neighborhood feature of the data within the initial hierarchical window can vary significantly across different modalities.
[0126] Step 3.4 The absolute difference is the dividing point between the stable mode and the transition mode. The calculation formula is as follows:
[0127] γ i =|μ i+1 -μ i |(i=1,2,…,20)
[0128] Where μ i and μ i+1 These are the average neighborhood features of the i-th and (i+1)-th initial hierarchical windows, respectively; γ i It represents the average neighborhood feature difference between adjacent initial level windows. If an initial level window contains the start or end point of a transition mode, the absolute difference between that window and its adjacent windows will be greater than the absolute difference between the windows of other modes.
[0129] Step 3.5 Based on the modal information obtained from the coarse identification of the Gaussian mixture model, i.e., X contains one transition mode, γ... i Arrange from largest to smallest to obtain γ * And select the two largest γ values. i value.
[0130] Step 3.6 Extract all the top two largest γ values from the original data X according to the initial hierarchical window arrangement. i The window corresponding to the value is designated as the priority window H*, as shown in the following formula:
[0131]
[0132] in, and These represent the start and end windows containing the transition mode, respectively.
[0133] Step 4: Modal fine-grained recognition based on terminal-level windows;
[0134] Step 4.1 The result obtained in step 3.6 and Based on this, we can expand upon it as follows:
[0135]
[0136] Among them, H j and H o In X respectively and The number of adjacent windows, g, is selected as 1. or The sample size is 200. Taking the starting point of the transition mode as an example, samples 501-700 are selected from the initial level and sent to the terminal level. The neighborhood feature fluctuation diagram is shown below. Figure 3 As shown.
[0137] Step 4.2 Calculate the volatility of variables
[0138] s is or A certain variable in the f-th time t f Corresponding variable value s f As shown in the following formula:
[0139] s={(s1,t1),…,(s f ,t f ),…,(s 200 ,t 200 )}
[0140] Step 4.3 introduces a fixed window h with a window width of L = 20 to divide s, that is, s is divided into 10 terminal level windows.
[0141] Step 4.4 Variable volatility v of adjacent terminal level windows i As shown in the following formula:
[0142]
[0143] Among them, s i (j) represents the value of the j-th variable in the i-th terminal level window, v i The difference between adjacent windows was measured, v i The larger the value of v, the greater the difference between adjacent windows. i =0 means that the two windows are exactly the same.
[0144] Step 4.5 involves determining the largest v in variable s. i To determine the time t when the variable undergoes a mode transition. a As shown in the following formula:
[0145] t a (s)=max(v i (s=1,2,…,50)
[0146] Where max is the maximum value function.
[0147] Step 4.6 Traversal The variables in the data and the statistics for each t a The number of occurrences determines the starting position t of the mode transition. trans ,as follows:
[0148] t trans = max(count(t a (s)))(s = 1, 2, …, n)
[0149] where count is a counting function.
[0150] In this embodiment, the process variable starts to change significantly at the 621st moment, as Figure 4 shown. We determine that the transition process starts at the 621st sample. Compared with the true transition start time, there is a delay of 1 hour, that is, 20 samples. This is acceptable because the start of the transition occurs slowly. When the transition starts, most variables still remain in the previous stable mode and fail to respond to the process change in a timely manner. Similarly, the end time of the transition mode is determined to be the 51st hour.
[0151] Step 5: Data dimensionality reduction based on locally preserving projections; After determining the boundaries of the stable mode and the transition mode in Steps 3 and 4, it is necessary to construct a monitoring model for X and reduce the dimensionality of the process data X using locally preserving projections.
[0152] Step 5.1 Locally preserving projections project the data X m×n onto a low-dimensional feature space Y m×l (l < n), where y i = x i A (i = 1, 2, …, m), m = 2000 is the number of samples, n = 50 is the number of original data variables, and l is the dimensionality of the feature space, to be solved.
[0153] Locally preserving projections solve for the projection matrix A by optimizing the following objective function:
[0154]
[0155] where W ij is the weight coefficient, which penalizes the original neighboring points whose distances become farther after projection to achieve the purpose of maintaining the neighboring relationship of samples before and after projection; W ij is calculated using the heat kernel method, that is where t is the heat kernel parameter, selected as 10.
[0156] Step 5.2 The objective function in Step 5.1 can be transformed into the following formula,
[0157] min a T X T PXa
[0158] where P = D - W is the Laplacian matrix, D is a diagonal matrix and D ii = ∑ j W ij, where a is the projection vector.
[0159] Step 5.3 Add constraint a T X T DXa = 1 ensures that the solution of the projection vector is unique. The optimization problem can be transformed into a generalized eigenvalue problem using the Lagrange function method, as shown in the following equation:
[0160] X T PXa=λX T DXa
[0161] The matrix formed by the eigenvectors corresponding to the first 34 smallest eigenvalues obtained is the projection matrix A, i.e., A = (a1, a2, ..., a...). 34 ).
[0162] Step 5.4 The multimodal process data X is dimensionality reduced using the projection matrix A to obtain the low-dimensional spatial data Y, as shown in the following equation:
[0163] Y = XA
[0164] Step 6: Construct a stable modal monitoring model;
[0165] For monitoring stable modes, a new global monitoring metric combining Mahalanobis distance is applied:
[0166]
[0167] Where D is the number of Gaussian principal components, p(θ) d |x) is the probability that sample x belongs to the d-th Gaussian principal component, θ d ={μ d ,∑ d}and μ d With ∑ d Let λ be the mean and covariance matrix of the d-th Gaussian principal component, respectively; d The Mahalanobis distance is given by the following formula:
[0168]
[0169] G's control limits G UCL It can be obtained from the F-distribution, as shown in the following formula:
[0170]
[0171] Where m and n are the number of samples and the number of variables in the process data, respectively, F n,m-n,α It is an F-distribution with n and mn degrees of freedom, where α is the confidence level.
[0172] Step 7: Construct a transition mode monitoring model.
[0173] Step 7.1
[0174] For a sample τ in the dimensionality-reduced transition process data T, firstly, find the k nearest neighbor samples τ of τ in T. 1 ,τ 2 ,…,τ k , where k is selected as 5.
[0175] Step 7.2 Calculate the mean vector ξ of the k nearest neighbor samples, as shown in the following formula:
[0176]
[0177] Where, τ i Let be the i-th nearest neighbor sample of sample τ, and k be the number of nearest neighbors.
[0178] Step 7.3 The offset vector of the sample τ in the low-dimensional space is denoted as η = τ - ξ, and the offset matrix of the transition process data T is denoted as B.
[0179] Step 7.4 Establish two monitoring statistics in the principal subspace and the residual subspace, respectively, as follows:
[0180]
[0181] q no =e(Ξ E ) -1 e T
[0182] Among them, Ξ B Let e be the covariance matrix of the mean B; where e is the residual vector and e = x h -ξA T ,x h Let τ be the sample corresponding to τ in high-dimensional space, and A be the projection matrix that preserves the local projection; Ξ E Let e be the covariance matrix of the residual matrix; for convenience, and q no Control Limits and q no-UCL The kernel density method was used to determine this.
[0183] After obtaining information on the stable mode and transition mode, we tested the algorithm of this invention using fault amplitudes of 25% and 100%, and the fault detection rates are shown in Table 2. Taking fault 10 as an example, fault 10 is that the C feed temperature in the TE process has changed randomly. Figure 5Scatter plots are provided for four fault amplitudes of variable 19 under fault 10. When fault 10 is introduced into the system at hour 30, the stripper temperature and stripper liquid flow rate respond quickly to the fault. This is because feed C is directly delivered to the stripper. Table 1 shows the HFWS detection results for 25% and 100% amplitude faults. It is evident that the detection rate for most 25% amplitude faults is lower than that for 100% amplitude faults; however, the detection rate for some 25% amplitude faults is not significantly different from that for 100% amplitude faults. This further demonstrates that HFWS is effective for some minor faults.
[0184] Furthermore, we applied Multi-path Principal Component Analysis (MPCA), Multi-path Local Preserving Projection (MLPP), and the K-Nearest Neighbors (KNN) algorithm to monitor Mode 1 and Mode 2, as shown in Table 2, where bold indicates the highest detection rate for this fault. After comparison, the hierarchical fluctuation window identification and monitoring strategy proposed in this invention has the best detection performance.
[0185] Table 2 TE Process Fault Detection
[0186]
[0187] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.
Claims
1. A method for identifying and monitoring multimodal industrial processes based on hierarchical fluctuation windows, characterized in that, Includes the following steps: Step 1: Data preprocessing; Step 2: Coarse Modal Identification Based on Gaussian Mixture Model; After data standardization in step 1, we obtained standardized data. ;Will The data is input into a Gaussian mixture model for clustering, and the parameters of the Gaussian mixture model are solved using the EM algorithm to obtain process data information. The clustering results of the Gaussian mixture model are denoted as... X ={ S 1, T 1, S 2,…, S u , T b ,…, S c-1 , T c-1 , S c }( u =1,2,…, c ()( b =1,2,…, c -1), where S u and T b They represent the first u A stable mode and b One transition mode; Step 3: Modal fine-tuning based on the initial hierarchical window; Step 4: Modal fine-grained recognition based on terminal-level windows; Step 5: Dimensionality reduction based on locally preserving projections; after determining the boundaries of stable and transition modes in steps 3 and 4, it is necessary to... Build a monitoring model and utilize local preservation projection on process data. Dimensional reduction; Step 6: Construct a stable modal monitoring model, which includes the following steps: For monitoring stable modes, a new global monitoring metric combining Mahalanobis distance is applied: in, The number of Gaussian principal components. For the sample x Belongs to the d The probability of a Gaussian principal component. and and The first d The mean and covariance matrix of Gaussian principal components; The Mahalanobis distance is given by the following formula: G's control limits G UCL It can be obtained from the F-distribution, as shown in the following formula: in, m , n These are the number of samples and the number of variables in the process data, respectively. It has degrees of freedom. n and mn The F-distribution, Confidence level; Step 7: Construct a transition mode monitoring model, which includes the following steps: Step 7.1 For the transition process data after dimensionality reduction T Samples in τ First of all, in T Searching for τ k nearest neighbor samples τ 1 , τ 2 ,…, τ k ; Step 7.2 Calculate the mean vector of the nearest neighbor samples, which specifically includes the following steps: Calculate the mean vector of the k nearest neighbors. As shown in the following formula: in, For the sample τ The i-th nearest neighbor sample, where k is the number of nearest neighbors; Step 7.3 Calculate the offset vector of the sample, which specifically includes the following steps: Calculate samples offset vector As shown in the following formula: in, For low-dimensional space samples, for The nearest neighbor sample mean vector, and the transition process data T The offset matrix is denoted as B ; Step 7.4 Construct two monitoring statistics, specifically including the following steps: Two monitoring statistics are established in the principal subspace and the residual subspace, respectively, as shown in the following formula: in, The mean The covariance matrix; where The residual vector and , for τ The corresponding sample in high-dimensional space A The projection matrix is used to preserve the local projection. For the reason The covariance matrix of the residual matrix; for convenience, and Control Limits and The kernel density method was used to determine this.
2. The method for multimodal industrial process identification and monitoring based on hierarchical fluctuation windows according to claim 1, characterized in that, Step 1 specifically includes the following steps: Collect multimodal process data under normal operating conditions : in, m For the sample size, n For the number of variables, we will include n The i-th sample of the variables is denoted as ; right The specific steps for data preprocessing are as follows: Step 1.1 Calculate the mean of all variables, where, The j-th variable The formula for calculating the mean is: Step 1.2 Calculate the standard deviation of all variables, where, The j-th variable The formula for calculating the standard deviation is: Step 1.3 Processing multimodal historical data Standardization is performed, where the standardized value of the j-th variable in the i-th sample is calculated using the following formula: 。 3. The method for multimodal industrial process identification and monitoring based on hierarchical fluctuation windows according to claim 1, characterized in that, Step 3 specifically includes the following steps: Step 3.1 For A sample x Its neighborhood characteristics The definition is as follows: in, for x The number of nearest neighbors, For the sample x The distance to the i-th nearest neighbor. It is an exponential function; Neighborhood features describe the characteristics of each mode from a distance perspective; neighborhood features of the same mode are similar, but when a mode transition occurs, the features of adjacent modes will show significant fluctuations; The neighborhood distance of all samples in the sample is denoted as D; Step 3.2 Divide D using a fixed window H with a window width of W, that is, D is divided into m / W initial level windows; Step 3.3 Calculate the average neighborhood feature of the i-th initial hierarchical window, using the initial hierarchical window as the unit. The calculation formula is: in, This represents the i-th initial window. The average neighborhood feature of the data within the initial hierarchical window can vary significantly across different modalities. Step 3.4 The absolute difference is the dividing point between the stable mode and the transition mode. The calculation formula is as follows: in and These are the average neighborhood features of the i-th and (i+1)-th initial hierarchical windows, respectively. It represents the average neighborhood feature difference between adjacent initial level windows. If an initial level window contains the start or end point of a transition mode, the absolute difference between that window and its adjacent windows will be greater than the absolute difference between other modal windows. Step 3.5 Based on the modal information obtained from the coarse identification using the Gaussian mixture model, i.e. It contains c-1 transition modes, and will Arranged from largest to smallest γ * And select the first 2 (c-1) largest ones. value; Step 3.6 Following the initial hierarchical window arrangement, in the original data... Extract all 2(c-1) The window corresponding to the value is designated as the priority window. As shown in the following formula: in, and These represent the start and end windows containing the j-th transition mode, respectively.
4. The method for multimodal industrial process identification and monitoring based on hierarchical fluctuation windows according to claim 1, characterized in that, Step 4 specifically includes the following steps: Step 4.1 The result obtained in step 3.6 and Based on this, we can expand upon it as follows: in, and They are respectively in middle and The number of adjacent windows, g, can be determined based on the multimodal process data. Adjustments will be made based on the situation at this time. or The number of samples in the sample is (g+1)W; Step 4.2 Calculate the volatility of the variables s for or A certain variable in the f-th time period Corresponding variable value As shown in the following formula: Step 4.3 Introduce a fixed window h with a window width of L. s To divide, that is s It is divided into (g+1)W / L terminal-level windows; Step 4.4 Variable volatility of adjacent terminal level windows As shown in the following formula: in, This represents the value of the j-th variable in the i-th terminal level window. The differences between adjacent windows were measured. The larger the value, the greater the difference between adjacent windows. When the time is exactly the same, it means that the two windows are identical; Step 4.5 By determining the variables s The largest To determine the time when the variable undergoes a mode transition. As shown in the following formula: Where max is the maximum value function; Step 4.6 Traversal The variables in the data and the statistics for each one The number of occurrences determines the starting point of the mode transition. ,as follows: Here, count is a counting function.
5. The method for multimodal industrial process identification and monitoring based on hierarchical fluctuation windows according to claim 1, characterized in that, Step 5 specifically includes the following steps: Step 5.1 Local Preservative Projection by Finding the Projection Matrix A Data Projected into a low-dimensional feature space ,in , m For the sample size, n The number of original data variables, l The dimension of the feature space; Locally preserved projection is solved by optimizing the objective function of the following equation to obtain the projection matrix. A : in As a weighting coefficient, it penalizes the original nearest neighbors that are further away after projection, in order to maintain the nearest neighbor relationship between samples before and after projection; The calculations employ the thermonuclear method, i.e. ,in t These are the thermonuclear parameters; Step 5.2 The objective function in Step 5.1 can be transformed into the following formula: in, P = D - W For Laplace matrix, D diagonal matrix and , a The projection vector; Step 5.3 Add constraints This ensures that the solution for the projected vector is unique. The optimization problem can be transformed into a generalized eigenvalue problem using the Lagrange function method, as shown below: The solution is the first r The matrix formed by the eigenvectors corresponding to the smallest eigenvalues is the projection matrix. A ,Right now A =( a 1, a 2,…, a r ) ； Step 5.4 Multimodal process data Through projection matrix A Dimensionality reduction yields lower-dimensional data. As shown in the following formula: 。