Iron-making process anomaly detection method based on time kernel stationary generalized learning system

Abstract

The invention discloses an ironmaking process anomaly detection method based on a time kernel stationary generalized learning system. The method comprises the following steps: expression of nonlinear kernel generalized features, optimization target construction and solution based on the time kernel stationary width learning system, real-time modeling and anomaly detection strategy, and independent incremental learning mechanism. Firstly, a nonlinear kernel generalized representation extraction strategy is established, then a time matching mechanism between input and output of a model is explored through a time alignment parameter, and the parameter can be explained under a potential variable relation. In the integration stage, a Kullback-Leibler divergence objective function is established, so that a stationary relation in time sequence data is conveniently captured, and regression errors are combined. Then, a double-loop parameter optimization algorithm and an independent incremental learning mechanism are provided, and when additional data are collected, the independent incremental learning mechanism is utilized to maintain the mutual independence of an original model and an updating model, so that the long-term updatable regression modeling and monitoring capability is maintained.

Description

Technical Field

[0001] The present invention relates to an abnormal detection method for the ironmaking process based on a time kernel stationary generalized learning system. Background Art

[0002] In the field of supervised learning tasks, researchers have advanced many methodologies for input / output sample modeling. However, in many environments with limited computing resources, especially in real-world industrial environments, the deployment of a large number of high-performance deep learning models is often hindered due to the lack of dedicated computing service centers.

[0003] To circumvent this problem, inspired by the random vector functional-link neural network and the extreme learning machine, the broad learning system (BLS) was designed. This unique network expands the breadth, improves the computational efficiency, and ensures the model performance. Essentially, this three-layer feedforward neural network avoids the elaborate iterative back-optimization process by incorporating a large number of random feature mappings and ensures the optimal parameters through regression estimation. Since its inception, BLS and its derivatives have proven to be very effective and have been widely applied in various fields, including bioinformatics, power electronics, robotics, road traffic, and industrial applications.

[0004] Although BLS variants are often used in supervised learning tasks, there is still an obvious need for further research on time series modeling and anomaly detection in intricate situations, especially those caused by factors such as non-linearity, time misalignment, non-stationarity, and time variability.

[0005] The ability of the BLS-based method to handle process non-linearity is fundamentally related to the hidden layer it forms, which consists of feature nodes and enhancement nodes and is activated by a non-linear activation function. Yu et al. combined BLS with an autoencoder framework and graph regularization to obtain an enhanced feature representation estimation. At the same time, Feng and Zou et al. explored the T-S fuzzy system and replaced the mapping feature nodes with a set of T-S fuzzy subsystems. When introducing wavelet BLS, Lin et al. used wavelet functions to derive the mapping feature nodes. However, considering the intrinsic random non-linear mapping of BLS, it becomes crucial to generate a sufficient number of nodes to achieve sufficient and reliable non-linear coverage. Therefore, if a trustworthy initial non-linear exploration is set before the random non-linear mapping, the demand for subsequent nodes can be effectively reduced, paving the way for further research on more complex non-linear features.

[0006] In terms of time representation, after integrating the functions of recurrent neural networks and BLS, recurrent-BLS is produced. It can effectively extract time information through the iterative calculation of neural units within continuous time steps, achieving impressive results. On this basis, gated-BLS is developed by adding appropriate gating units, further enhancing its ability in time series modeling. Peng et al. effectively integrated the residual mechanism and the concept of time delay to develop the time-stacked generalized learning system. This system is good at capturing important non-linear features and time correlations, thus improving the accuracy of anomaly detection. In addition, Zhong et al. also cleverly merged the time series memory module with the dual BLS decoding module to establish the memory BLS for anomaly detection. However, these methods are ineffective in the face of multi-scale sampling where the sampling rates of model input and output are inconsistent (i.e., the time misalignment situation). In some cases, downsampling techniques can be used to force the alignment of input and output data for model fitting. However, the significant loss of information accompanying downsampling will significantly reduce the model performance.

[0007] Non-stationarity is another common feature of real-world data, so it is necessary to consider improving the generalization performance of the model. Some contemporary researchers use denoising techniques (such as regularization) to mitigate the interference caused by data outliers. This naturally leads to the idea that the regularization theory can be applied. Therefore, the model's resistance to noise is enhanced by introducing a regularization term and combining it with the augmented Lagrangian multiplier. In addition, the existing literature also emphasizes the important achievement of enhancing the model's robustness through the use of sparse coding. However, it must be recognized that this exploration of process noise is only a subset of the research on process non-stationarity, which mainly focuses on the time-varying statistical characteristics. Unfortunately, the existing BLS methods cannot solve the non-stationarity problem.

[0008] The incremental learning technique is an integral part of BLS, which endows it with the ability to adapt to new features in time-varying phenomena that frequently occur in real systems. It avoids the necessity of modifying the original model when integrating new samples; instead, it focuses on integrating new data for updating. However, it is elusive to analyze the relationship between the original model and the updated version in detail, and few scholars have conducted research in this regard. The original model is developed using a large amount of long-term system data, encapsulating the intrinsic information of the system. In contrast, the newly collected samples encapsulate the recent time-varying data that deviates from the intrinsic information. Therefore, both the original model and the updated model should maintain their respective modeling directions, that is, one manages the inherent long-term data, and the other navigates the recent time-varying data. The performance of each model is independent and better reflects the cognitive principle of humans. Summary of the Invention

[0009] To overcome the deficiencies of the prior art, the present invention provides an abnormal detection method for the ironmaking process based on a time kernel-based stationary generalized learning system. The steps include: representation of non-linear kernel generalized features, construction and solution of an optimization objective based on TKS-BLS, real-time modeling and abnormal detection strategy, and independent incremental learning mechanism.

[0010] The present invention specifically studies to ensure the prediction performance and fault monitoring ability of the blast furnace ironmaking process. Therefore, the present invention proposes a regression modeling and abnormal detection framework based on the time series kernel stationary width learning system (TKS-BLS). First, a non-linear kernel width representation (NKBR) extraction strategy is created, which provides a robust non-linear basis for random feature mapping through kernel technology. Subsequently, an internal time series matching mechanism between the model input and output is explored through a time alignment parameter, which can be interpreted under the latent variable relationship. In the integration stage, the present invention establishes a Kullback-Leibler objective function to facilitate capturing the stationary relationship in time series data and combining the regression error with the overall objective function. Finally, a dual-loop parameter optimization algorithm and an independent incremental learning mechanism are proposed.

[0011] An abnormal detection method for the ironmaking process based on a time kernel-based stationary generalized learning system, the steps include: representation of non-linear kernel generalized features, construction and solution of an optimization objective based on TKS-BLS, real-time modeling and abnormal detection strategy, and independent incremental learning mechanism;

[0012] The representation of the non-linear kernel generalized features includes the following steps:

[0013] (2.1) For the complexity in the blast furnace ironmaking process, the TKS-BLS method first develops a kernel-based non-linear feature extractor, which adopts the kernel method. It projects the data x(·) from the original space through the mapping function φ(.) onto a high-dimensional feature space so as to construct kernel features as follows;

[0014]

[0015] where i, j = 1, 2, …, n;

[0016] In the formula, κ(.) represents a specific kernel function and is defined as the inner product operation in the space, and the centering is calculated through the following method:

[0017]

[0018] where, In All elements of are set to 1 / n; to study the influence of the kernel function on non-linear information, a specific kernel function can be specified;

[0019] (2.2) Subsequently, the principal component analysis (PCA) is adopted to retain the basic information of, which can be expressed as:

[0020]

[0021] where the diagonal matrix Ξ = diag(ξ1, ξ2, …, ξ n ) is composed of eigenvalues, and V = [v1, v2, …, v n is constructed by the corresponding eigenvectors; the largest d (d < n) eigenvalues, together with their respective eigenvectors, form the non-linear kernel representation (NKR):

[0022]

[0023] Its reduction matrix is V d = [v1, v2, …, v d ;

[0024] Subsequently, using the non-linear activation function the feature nodes and enhanced nodes based on T can be calculated

[0025] where and represent the weight matrices and biases with m t feature nodes and l t enhanced nodes; (2.3) Based on the score matrix T, referring to the width learning method, the feature mapping hidden layer and the augmented mapping hidden layer can be constructed respectively. Through the cascading operation, the NKBR is obtained, which can be represented by as:

[0026]

[0027] The construction and solution of the optimization objective based on TKS-BLS include the following steps:

[0028] (3.1) Construction of the regression objective based on time series: When there is a significant difference in the sampling rates between the input and output variables of the system, the data set is collected, where N = ns > n; under the condition of sampling rate mismatch, each output sample y(i) and the input sample z(i) = [x T (i,1), xT (i, 2), …, x T (i, s)] T Alignment; this situation depends on specific attributes; with q as the maximum time lag scale, the projection of z(i) to NKBR can be expressed as Considering the form of latent variables, the projection vectors of y(i) and a q (i) are denoted as q and w respectively, and the following can be deduced:

[0029] c(i) = y T (i)q and t(i) = a q,T (i)w(8); here, in order to further confirm the alignment relationship between each time lag scale and the output sample, the alignment parameter β = [β1, β2, …, β q T ; Therefore, for each y(i), it can be expressed as:

[0030]

[0031] where β⊙w is the matrix Kronecker product between β and w; thus, define

[0032]

[0033] Equation (9) can be rewritten in matrix form as:

[0034]

[0035] Therefore, the first regression segment of the overall objective can be expressed as maximizing the following:

[0036]

[0037] (3.2) Construction of the stationary objective function: To effectively handle complex mixed processes, stationarity must be identified and the impact of non-stationary factors mitigated. This means that the extracted NKBR needs to maintain its consistency, as demonstrated by the stability of its mean and variance over various periods. When is divided into time periods, the corresponding mean and variance (μ e , Σ e ) should be consistent with the total mean and variance ; For this purpose, the KL divergence is further used here to construct the second segment of the overall objective, i.e., the stationary objective That is:

[0038]

[0039] However, directly minimizing​ It will lead to a non-convex optimization problem on β and w; to reduce the computational burden, the optimization problem (14) is reconstructed into a quadratic objective:

[0040]

[0041] (3.3) Overall objective composition: By weighing the parameter η, the first and second parts (i.e., and ) are combined, and the overall objective can be constructed as:

[0042]

[0043] (3.4) Solution of the double-loop parameters: To solve the optimization problem in Equation (17), the Lagrange multipliers are adopted; the Lagrangian function is defined as:

[0044]

[0045] where the Lagrange multipliers are λ q and λ w ; taking the derivatives of Equation (18) with respect to q, β, w, λ q and λ w and setting them to zero respectively, we get:

[0046]

[0047] Multiplying the left sides of Equations (19) and (20) by q T and w T respectively, the relationship can be calculated as:

[0048]

[0049] where q T q = 1 and (β⊙w) T (β⊙w) = 1 can obtain 2Λ = λ q + λ w ; therefore, the objective of (17) is achieved by maximizing λ q and λ w respectively. From (19)-(21), the values of q, β, and w can be obtained:

[0050]

[0051]

[0052] where ∝ represents the proportionality on both sides, Denote the pseudo - inverse operator; obviously, from (26) to (30), the solutions of the vectors q, β, and w are intertwined and lack a compact form. Therefore, the external structure of TKS - BLS is obtained by iterating through (26) to (30); by collecting all the latent variables load vector projection vector can be extracted from to obtain the latent variables:

[0053]

[0054] Subsequently, a connection between and can be established through multiple - variable least squares, that is, by using the regression parameter ζ:

[0055]

[0056] where denotes the regression estimate of , and denotes the regression error. The regularization term θ is used to reduce the potential ill - conditioning effect. Finally, the predicted values and and

[0057]

[0058] The real - time modeling and anomaly - detection strategy described above includes the following steps:

[0059] After collecting q input samples, a new observed input sample is established, denoted as X = [x T (new,1), x T (new,2), …, x T (new,q)] T ; then the Gram kernel matrix of the real - time mean - centered can be calculated With the load matrix V, the NKR after aggregating the main information, denoted as can be expressed as:

[0060]

[0061] Then, for t = 1, 2, …, q, can be expressed as:

[0062]

[0063] By summing up these NBKR vectors a(new,t), the lag term a q,newand the corresponding latent variable τ new can be utilized to achieve real-time prediction of the output variable :

[0064]

[0065] For anomaly detection, Hotelling's T 2 statistic can be utilized:

[0066]

[0067] The corresponding threshold J th follows a distribution indicating the covariance matrix of, with the confidence level denoted by α; ultimately, the anomaly detection logic can be expressed as:

[0068] The described independent incremental learning mechanism includes the following steps:

[0069] (5.1) By collecting additional samples t x = ns + 1, ns + 2, …, n + Ds, t y = n + 1, n + 2, …, n + D, an independent incremental learning technique is established; through X C and Y c , the relevant additional lag NKBR can be constructed According to the original TKS-BLS model, calculating the original latent variable is facilitated through Equation (30) which also determines that the original TKS-BLS can locate and The unmodeled residuals are expressed as and

[0070] (5.2) To study the neglect of the characteristics of recent data by the original model, an auxiliary TKS-BLS model is developed here:

[0071] s.t. q c,T q c = 1, (β c ⊙ w c ) T (β c ⊙ w c ) = 1;

[0072]

[0073] For l cFurther estimation of the projection vector generates additional latent variables and each variable is paired with its predicted value :

[0074] (5.3) Subsequently, by integrating the regression modeling capabilities of the initial model and the updated model , a comprehensive representation of the entire system can be given by a q,new as follows: That is:

[0075]

[0076] where and are the load matrices under the updated model, and ζ c is the regression matrix under the updated model. By arranging the latent variables in the original model and the updated model in sequence to form τ, an improved Hotelling's T 2 statistic is obtained:

[0077]

[0078] where the covariance of the matrix in Equation (42) is denoted by . The corresponding critical value set by the distribution is denoted by

[0079] It should be noted that the proposed independent incremental learning can ensure that the additional latent variables are kept different from the original variables. This maintains the orthogonality between the original model and the supplementary model, indicating that there is no performance interference or overlap. The original training data usually reflects the long-term characteristics of the system, while the additional data captures the recent trends. This mixture enhances the estimation of more comprehensive latent variables and improves the regression modeling ability.

[0080] Advantages of the present invention:

[0081] First, this study proposed a new regression modeling and anomaly detection method - TKS-BLS. Using kernel technology, the NKBR extraction strategy provides a powerful non-linear basis for random feature mapping. Subsequently, the internal matching mechanism between the model input and output is explored through time alignment parameters, which can be interpreted under the latent variable relationship. In addition, a KL divergence objective function is established to facilitate capturing the stationary relationship in time series data. In the integration stage, the consensus TKS-BLS objective function is explicitly proposed, combining the stationary objective and the regression objective. On this basis, a double-loop parameter optimization method and an independent incremental learning mechanism are introduced, and a comprehensive theoretical analysis is carried out. Through a large number of case studies on the actual ironmaking process and ablation research, effective experimental results are obtained, which are superior to other existing methods, verifying the effectiveness and superiority of the suggestions here. In addition, the case studies of this invention show that the proposed TKS-BLS has taken an important step in improving the prediction of the blast furnace ironmaking process and ensuring the safe operation of equipment through process monitoring. Brief Description of the Drawings

[0082] Figure 1 It is a schematic diagram of the technical route of the TKS-BLS-based modeling and anomaly detection framework for the blast furnace ironmaking process of the present invention.

[0083] Figure 2 It is a comparison chart of the RT1 prediction performance results of the MIQ for the blast furnace ironmaking process of the present invention; each part: (a) PLS; (b) KPLS; (c) IKOPLS; (d) L2RBLS; (e) Time-SBLS; (f) MemBLSAD; (g) TKS-BLS.

[0084] Figure 3 It is a comparison chart of the MIQ data representation and anomaly detection results of ADT5 for the blast furnace ironmaking process of the present invention;

[0085] Each part: (a) values of Si, P, S; (b) PLS; (c) KPLS; (d) IKOPLS; (e) L2RBLS; (f) Time-SBLS; (g) MemBLSAD; (h) TKS-BLS.

[0086] Figure 4 It is a data representation and probability density chart for the blast furnace ironmaking process of the present invention;

[0087] Each part: (a) values of Si, P, S; (b) four key process variables V1, V2, V7, V11; (c) 7 groups of latent variables t corresponding to trade-off parameters of 0, 0.5, 1, 2 respectively.

[0088] Figure 5RT1 prediction performance result comparison chart of MIQ for blast furnace ironmaking process of the present invention;

[0089] Among them, each part: (a) TKS - BLS - I; (b) TKS - BLS - II; (c) TKS - BLS - III; (d) TKS - BLS (the present invention).

[0090] Figure 6 Abnormal detection performance result comparison chart of abnormal data set 5 for blast furnace ironmaking process of the present invention;

[0091] Among them, each part: (a) TKS - BLS - I; (b) TKS - BLS - II; (c) TKS - BLS - III; (d) TKS - BLS (the present invention). Specific implementation mode

[0092] The present invention will be further described below in conjunction with the drawings and embodiments.

[0093] Case study comparison of the time - series kernel stationary width learning method for the blast furnace ironmaking process of the present invention includes the following steps:

[0094] (1) For offline modeling, various sensors (flow sensors, temperature sensors, concentration sensors, etc.) need to be installed at various positions in the blast furnace ironmaking process, and the corresponding data is stored through a database. In view of the complexity in the blast furnace ironmaking process, the present invention first develops a kernel - based non - linear feature extractor; in order to deal with non - linearity, the kernel method is first adopted, where the mapping function φ(.) projects the data x(·) from the original space to a high - dimensional feature space so as to construct kernel features as follows:

[0095]

[0096] where i, j = 1, 2, …, n;

[0097] In the formula, κ(.) represents a specific kernel function and is defined as the inner - product operation in the space, and the centering is calculated through the following method:

[0098]

[0099] where, all elements of I n are set to 1 / n; to study the influence of the kernel function on non - linear information, a specific kernel function is specified; however, after the kernel function mapping the size of the data matrix will change from to With N >> k x There is an extension, and the principal component analysis (PCA) is adopted to retain the basic information, which can be expressed as:

[0100]

[0101] where the diagonal matrix Ξ = diag(ξ1, ξ2, …, ξ n ) is composed of eigenvalues, and V = [v1, v2, …, v n is constructed from the corresponding eigenvectors. The largest d (d < n) eigenvalues, together with their respective eigenvectors, form the non-linear kernel representation (NKR):

[0102]

[0103] Its reduction matrix is V d = [v1, v2, …, v d .

[0104] Subsequently, using the non-linear activation function the feature nodes and enhanced nodes based on T can be calculated

[0105]

[0106] where and represent the weight matrix and bias with m t feature nodes and l t enhanced nodes; based on the score matrix T, referring to the width learning method, the feature mapping hidden layer and the augmented mapping hidden layer can be constructed respectively. Through the cascading operation, the NKBR is obtained, which can be represented by as:

[0107] As Figure 1 shown is the overall technical route schematic diagram of the present invention. Figure 4 This is the data representation and probability density map of the present invention for the blast furnace ironmaking process.

[0108] (2) The construction and solution of the optimization objective based on TKS-BLS include the following steps:

[0109] Construction of the regression objective based on time series: When there is a significant difference in the sampling rates between the input-output variables of the system, collect the data set which includes N = ns > n; under the condition of sampling rate mismatch, each output sample y(i) and the input sample z(i) = [x determined according to the time scale sT (i,1), x T (i,2), …, x T (i, s)] T Alignment; this situation depends on specific attributes.

[0110] With q as the maximum time-lag scale, the projection of z(i) onto NKBR can be expressed as Considering the form of latent variables, let the projection vectors of y(i) and a q (i) be denoted as q and w respectively, and the following can be deduced:

[0111] c(i) = y T (i)q and t(i) = a q,T (i)w (8);

[0112] Here, to further confirm the alignment relationship between each time-lag scale and the output samples, the alignment parameter β = [β1, β2, …, β q T . Therefore, for each y(i), it can be expressed as:

[0113]

[0114] where β⊙w is the matrix Kronecker product between β and w.

[0115] With these definitions:

[0116]

[0117] Equation (9) can be rewritten in matrix form:

[0118]

[0119] Therefore, the first regression segment of the overall objective can be expressed as maximizing the following:

[0120]

[0121] Stationary objective function construction: To effectively handle complex mixed processes, stationarity must be identified and the influence of non-stationary factors mitigated. This means that the extracted NKBR needs to maintain its consistency, as demonstrated by the stability of its mean and variance over various periods. When is divided into time periods, the corresponding mean and variance (μ e , Σ e ) should be consistent with the total mean and variance . For this purpose, the KL divergence is further used here to construct the second segment of the overall objective, i.e., the stationary objective​ That is:

[0122] However, directly minimizing will lead to a non-convex optimization problem on β and w. Although gradient descent has been used to solve this problem in some studies, it often consumes a large amount of computational resources. To reduce the computational burden, the optimization problem (14) is reformulated into a quadratic objective:

[0123]

[0124]

[0125] The overall objective composition: By weighing the parameter η, the first and second parts (i.e., and ) are combined. Here, the overall objective can be constructed as:

[0126]

[0127] Solving the double-loop parameters: To solve the optimization problem in Equation (17), the Lagrange multipliers are adopted. Define the Lagrangian function:

[0128]

[0129] where the Lagrange multipliers are λ q and λ w .

[0130] Take the derivatives of Equation (18) with respect to q, β, w, λ q and λ w , and set them to zero respectively, obtaining:

[0131]

[0132] Multiply the left sides of Equations (19) and (20) by q T and w T respectively, and the relationship can be calculated as:

[0133]

[0134] where q T q = 1 and (β⊙w) T (β⊙w) = 1 can yield 2Λ = λ q + λ w . Therefore, the objective of (17) is achieved by maximizing λ q and λ w respectively. From (19)-(21), the values of q, β, and w can be obtained:

[0135]

[0136] where ∝ represents the proportionality on both sides denotes the pseudo-inverse operator

[0137] Obviously, from (27) to (30), the solutions of vectors q, β, and w are intertwined and lack a compact form. Therefore, the external structure of TKS-BLS is obtained through iteration of (27) to (30).

[0138] By collecting all potential variables load vectors projection vectors the latent variables can be extracted from as follows

[0139]

[0140] Subsequently, the relationship between and can be established through multiple linear least squares, i.e., by using the regression parameter ζ

[0141]

[0142] where denotes the regression estimate of , and denotes the regression error. The regularization term θ is used to reduce the potential ill-conditioning effect. Finally, the predicted values and and

[0143]

[0144] Figure 2 It is shown that the present invention significantly outperforms other methods (such as PLS, KPLS, etc.) in the RT1 prediction performance of MIQ, while Figure 5 shows the comparison results of different versions (TKS-BLS-I to IV) of the present invention

[0145] (3) The real-time modeling and anomaly detection strategy described above includes the following steps: After collecting q input samples, a new observed input sample is established, denoted as X new =[x T (new,1),x T (new,2),…,x T (new,q)] n ; Then, the Gram kernel matrix of the real-time mean-centered can be calculated

[0146] With the load matrix V, the NKR after the main information aggregation, denoted as can be expressed as:

[0147]

[0148] Then, for t = 1, 2,..., q, can be expressed as:

[0149]

[0150] By aggregating these NBKR vectors a(new,t), the lag term a q,new and the corresponding latent variable τ new can be utilized to achieve the real-time prediction of the output variable :

[0151]

[0152] For anomaly detection, Hotelling's T-squared (T 2 ) statistic can be utilized because it has high sensitivity to anomalies:

[0153] The corresponding threshold J th follows distribution, denotes the covariance matrix of, expressed by Equation (31), and the confidence level is denoted by α.

[0154] Finally, the anomaly detection logic can be expressed as:

[0155]

[0156] As Figure 3 (a)-(h) show the detection results of the ADT5 data, and the present invention ( Figure 3 (h)) performs optimally in the detection of Si, P, and S values, while Figure 6 further verifies its performance advantage in the anomaly dataset 5.

[0157] (4) The independent incremental learning described above includes the following steps: (5.1) By collecting additional samples t x = ns + 1, ns + 2,..., n + Ds,t y = n + 1, n + 2,..., n + D, an independent incremental learning technique is established; through X C and Y c , the relevant additional lag NKBR can be constructed According to the original TKS - BLS model, the calculation of the original latent variable is facilitated by Equation (30). This also determines that the original TKS - BLS can locate and The unmodeled residuals are expressed as and

[0158]

[0159] (5.2) To study the neglect of the characteristics of recent data by the original model, an auxiliary TKS - BLS model is developed here:

[0160]

[0161] s.t.q c,T q c =1,(β c ⊙w c ) T (β c ⊙w c )=1

[0162]

[0163] For the further estimation of the projection vector of l c additional latent variables are generated and each variable is paired with its predicted value :

[0164] (5.3) Subsequently, by combining the regression modeling capabilities of the initial model and the updated model the overall representation of the entire system q,new can be given by a as follows:

[0165]

[0166] where and are the load matrices under the updated model, and ζ c is the regression matrix under the updated model. By arranging the latent variables in the original model and the updated model in sequence into τ, the improved Hotelling's T 2 statistic is obtained:

[0167]

[0168] where the covariance of the matrix in Equation (42) is denoted by ​ The corresponding critical value of the distribution setting is represented by As shown in the (d) part of Figure 5 , the incremental learning strategy of the present invention maintains stable performance in the fusion of long-term and short-term data.

[0169] It should be noted that the proposed independent incremental learning can ensure that the additional latent variables remain different from the original variables. This maintains the orthogonality between the original model and the supplementary model, indicating no performance interference or overlap. The original training data usually reflects the long-term characteristics of the system, while the additional data captures the recent trends. This mixture enhances the estimation of more comprehensive latent variables and improves the regression modeling ability.

[0170] The present invention proposes a new regression modeling and anomaly detection method - TKS-BLS. Using kernel technology, the NKBR extraction strategy provides a powerful non-linear basis for random feature mapping. Subsequently, the internal matching mechanism between the model input and output is explored through time alignment parameters, which can be interpreted under the latent variable relationship. In addition, a Kullback-Leibler objective function is established to facilitate capturing the stationary relationship in time series data. In the integration stage, the consensus TKS-BLS objective function is explicitly proposed, combining the stationary objective and the regression objective. On this basis, a double-loop parameter optimization method and an independent incremental learning mechanism are introduced, and a comprehensive theoretical analysis is carried out. Through a large number of case studies on actual ironmaking processes and ablation studies, effective experimental results are obtained, thus being superior to other existing methods, verifying the effectiveness and superiority of the suggestions herein. In addition, the case studies of the present invention show that the proposed TKS-BLS has taken an important step in improving the prediction of the blast furnace ironmaking process and ensuring the safe operation of equipment by monitoring the process.

[0171] The above-described embodiments merely represent several implementation manners of the present invention, and their descriptions are relatively specific and detailed, but should not be construed as limiting the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the appended claims.

Claims

1. An abnormal detection method for the ironmaking process based on a time kernel-based stationary generalized learning system, characterized by the steps include: Representation of nonlinear kernel generalized features, construction and solution of optimization objectives based on temporal kernel stationary broad learning system (TKS-BLS), real-time modeling and anomaly detection strategies, and independent incremental learning mechanisms; First, offline modeling is performed to prepare historical output data and input data. Then, the kernel matrix is calculated and the main kernel information matrix is obtained by principal component analysis to form a nonlinear kernel representation. Subsequently, the feature augmentation operation is performed to obtain the generalized representation of the nonlinear kernel. Then, the regression part of the algorithm objective function is constructed and combined with the stationary target part to form a complete TKS-BLS objective function. The model parameters are optimized using a double-layer closed-loop parameter optimization algorithm. Finally, the monitoring statistic based on the F distribution and its threshold are calculated, and the offline modeling phase ends. Entering the online application stage, after obtaining the newly collected real-time output data; then calculate the real-time nonlinear kernel generalized representation and lag parameters, and further calculate the real-time prediction value and real-time monitoring statistics; After collecting enough output and input data, the unmodeled residuals are calculated, and then a modeling auxiliary model is established to upgrade the model and further derive more comprehensive and improved statistics; The judgment is made based on the comparison result between the improved statistic and its threshold. If the improved statistic is greater than the threshold, it is judged as an abnormal situation; otherwise, it is judged as normal.

2. The method according to claim 1, wherein The representation of the non - linear kernel generalized feature includes the following steps: (2.1) For the complexity in the blast furnace ironmaking process, the TKS - BLS method first develops a kernel - based non - linear feature extractor, in which the kernel method is adopted. Through the mapping function φ(.), the data x(·) is projected from the original space to a high - dimensional feature space so as to construct the kernel feature as follows; Where i, j = 1, 2, ..., n; where κ(.) represents a specific kernel function and is defined as the inner product operation in the space, and the centering is obtained by the following calculation: Among them, I n All elements of are set to 1 / n; to study the influence of the kernel function on non-linear information, a specific kernel function is specified; (2.2) Subsequently, the principal component analysis method is adopted to retain The basic information of is expressed as: where the diagonal matrix Ξ = diag(ξ1, ξ2, …, ξ n ) consists of the eigenvalues, and V = [v1, v2, …, v n is constructed from the corresponding eigenvectors; the largest d (d < n) eigenvalues, together with their respective eigenvectors, form the Nonlinear Kernel Representation (NKR): Its reduction matrix is V d = [v1, v2, …, v d ; Subsequently, using the non-linear activation function the feature nodes and enhanced nodes based on T can be calculated Among them Among them Among them and represent the weight matrix and bias with m t feature nodes and l t enhanced nodes; (2.3) Based on the score matrix T, construct the feature mapping hidden layer and the augmented mapping hidden layer respectively by referring to the width learning method. Through the concatenation operation, obtain NKBR, which is represented by as follows:

3. The method according to claim 2, wherein The optimization target construction and solution based on TKS-BLS includes the following steps: (3.1) Regression target construction based on time series: When there is a significant difference in the sampling rates between the input and output variables of the system, collect a data set which includes N = ns > n; Under the condition of sampling rate mismatch, each output sample y(i) is aligned with the input sample z(i) = [x T (i,1), x T (i,2), …, x T (i,s)] determined by the time scale s T ; this situation depends on specific attributes; with q as the maximum time lag scale, the projection of z(i) onto NKBR is expressed as Considering the form of latent variables, the projection vectors of y(i) and a q (i) are denoted as q and w respectively, and the derivation is as follows: c(i) = y T (i) q and t(i) = a q,T (i) w (8); Here, in order to further confirm the alignment relationship between each time-delay scale and the output sample, an alignment parameter β = [β1, β2, …, β q T ; thus, for each y(i), it is expressed as:​ where β⊙w is the matrix Kronecker product between β and w; thus, we define Formula (9) is transformed into a matrix form: Therefore, the first regression segment of the overall objective is expressed as maximizing the following: (3.2) Steady objective function construction: When is divided into time periods, the corresponding mean and variance (μ e , Σ e ) should be consistent with the total mean and variance ; Here, the Kullback-Leibler (KL) divergence is further used to construct the overall objective, that is, the second part of the steady objective Namely: The optimization problem (14) is reformulated as a quadratic objective: (3.3) Overall objective composition: By weighing parameter η, the first and second parts, namely and are combined. Here, the overall objective is constructed as: (3.4) Double loop parameter solution: To solve the optimization problem in equation (17), Lagrange multipliers are used; Lagrange function is defined as: where the Lagrange multiplier is λ q and λ w ; take the derivatives of Equation (18) with respect to q, β, w, λ q and λ w and set them to zero respectively, obtaining: Multiply the left sides of equations (19) and (20) by q T and w T respectively, and calculate the relationship as follows: where q T q = 1 and (β ⊙ w) T (β ⊙ w) = 1 gives 2Λ = λ q + λ w ; thus, by maximizing λ q and λ w separately, the objective of equation (17) is achieved; from equations (19)-(21), the values of q, β, and w are obtained: where ∝ represents the proportionality on both sides, represents the pseudo-inverse operator; the external structure of TKS-BLS is obtained by iterating through (26) to (30); By collecting all potential variables Load vector Projection vector From Extract latent variables: Subsequently, through multivariate least squares, that is, by using the regression parameter ζ, establish a connection between : Among them, represents the regression estimate of, represents the regression error, and the regularization term θ is used to reduce the influence of potential ill-conditioning ; Finally, from directly derive the predicted value and 4. The method according to claim 1, wherein The described real-time modeling and anomaly detection strategy includes the following steps: After collecting q input samples, a new observed input sample is established, denoted as X = [x T (new,1), x T (new,2), …, x T (new,q)] T ; then calculate the Gram kernel matrix of the real-time mean center With the load matrix V, the NKR after the aggregation of the main information, denoted as Expressed as: Then, for t = 1, 2, …, q, is expressed as: By aggregating these NBKR vectors a(new,t), the lagged terms a q,new and the corresponding latent variables τ new are utilized to achieve real-time prediction of the output variable : For anomaly detection, the Hotelling's T 2 statistic is used: The corresponding threshold J th obeys a distribution denoted by the covariance matrix, with the confidence level denoted by α; finally, the anomaly detection logic can be expressed as:

5. The method according to claim 1, characterized in that, The independent incremental learning mechanism includes the following steps: (5.1) By collecting additional samples t x = ns + 1, ns + 2, …, n + Ds, t y = n + 1, n + 2, …, n + D, an independent incremental learning technique is established; through X C and Y c , the related additional lag NKBR is constructed According to the original TKS - BLS model, the calculation of the original latent variable is facilitated by Equation (30) This also determines that the original TKS - BLS can locate and The unmodeled residuals are expressed as and (5.2) An auxiliary TKS-BLS model was developed: For l c Further estimation of the projection vector yields additional latent variables and each variable is paired with its predicted value : (5.3) Subsequently, the regression modeling capabilities of the initial model and the updated model are combined, that is, the overall representation of the entire system q,new is given by a as follows: Among them, and are the load matrices under the updated model, and ζ c is the regression matrix under the updated model; by arranging the latent variables in the original model and the updated model in sequence to form τ, the improved Hotelling's T 2 statistic is obtained: Among them, the covariance of the matrix of formula (42) is represented by . The corresponding critical value set by the distribution is represented by .

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