A time series kernel stationary width learning method for blast furnace ironmaking process

Abstract

The application discloses a kind of sequential kernel stationary width learning methods for blast furnace iron-making process, steps include: nonlinear kernel width representation estimation, time sequence matching mechanism, stationary-regression overall objective construction and parameter estimation and independent incremental learning;The method designs a kind of feature estimation strategy with nonlinear kernel width representation (Nonlinear kernel broad representation, NKBR), and this strategy lays the nonlinear foundation for subsequent random feature mapping by kernel technology;Then, establish time sequence matching mechanism, establish time sequence between model NKBR and output Realize hidden variable prediction task;And Kullback-Leibler (KL) divergence is used as objective function to construct stationary-regression overall objective, and a double-ring parameter optimization method is proposed to estimate parameters;When additional data is collected, the mutual independence of original model and updated model is maintained using independent incremental learning mechanism, so as to maintain long-term updateable regression modeling and monitoring ability.

Description

Technical Field

[0001] This invention relates to a time-series kernel stationary width learning method for blast furnace ironmaking processes. Background Technology

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

[0003] To circumvent this problem, the Broad Learning System (BLS) was designed, drawing inspiration from stochastic vector function linked neural networks and extreme learning machines. This unique network expands the breadth of learning, improves computational efficiency, and ensures model performance. Essentially, this three-layer feedforward neural network avoids an exhaustive iterative back-optimization process by incorporating a large number of stochastic feature maps and ensures optimal parameters through regression estimation. Since its inception, BLS and its derivatives have proven highly effective and have been widely applied in various fields, including bioinformatics, power electronics, robotics, road transportation, and industrial applications.

[0004] Although BLS variants are frequently used for supervised learning tasks, there remains a clear need for further research into time series modeling and anomaly detection in complex situations, particularly those caused by nonlinearity, temporal misalignment, nonstationarity, and temporal variability.

[0005] The ability of BLS-based methods to handle process nonlinearity is fundamentally related to the hidden layers they form, which consist of feature nodes and enhancement nodes activated by nonlinear activation functions. Yu et al. combined BLS with an autoencoder framework and graph regularization to obtain enhanced feature representation estimation. Meanwhile, Feng and Zou et al. explored TS fuzzy systems, replacing the mapped feature nodes with a set of TS fuzzy subsystems. When introducing wavelet BLS, Lin et al. used wavelet functions to derive the mapped feature nodes. However, considering the intrinsic stochastic nonlinear mapping based on BLS, generating a sufficient number of nodes to achieve adequately reliable nonlinear coverage becomes crucial. Therefore, setting up a reliable initial nonlinear exploration before the stochastic nonlinear mapping can effectively reduce the need for subsequent nodes, paving the way for further research into more complex nonlinear features.

[0006] In terms of time representation, the integration of recurrent neural networks and BLS has resulted in recurrent-BLS, which effectively extracts temporal information through iterative computation by neural units within continuous time steps, achieving impressive results. Building upon this, gated-BLS has been developed by adding appropriate gating units, further enhancing its capabilities in time series modeling. Peng et al. effectively integrated residual mechanisms and the concept of time delay to develop the Time-Stacked Generalized Learning System (Time-SBLS). This system excels at capturing important nonlinear features and temporal correlations, thereby improving the accuracy of anomaly detection. Furthermore, Zhong et al. cleverly merged a temporal memory module with a dual-BLS decoding module to establish MemBLSAD for anomaly detection. However, these methods struggle with multi-scale sampling where the model input and output sampling rates are inconsistent (i.e., temporal misalignment). In some cases, downsampling techniques can be used to force the input and output data to align for model fitting. However, the significant information loss associated with downsampling significantly degrades model performance.

[0007] Nonstationarity is another common characteristic of real-world data, thus necessitating consideration of improving the generalization performance of models. Some contemporary researchers utilize denoising techniques (such as regularization) to mitigate the interference caused by outliers. This naturally leads to the idea of ​​applying regularization theory. Therefore, L2RBLS was constructed by introducing a regularization term and combining it with enhanced Lagrange multipliers to enhance the model's resistance to noise. Furthermore, existing literature also highlights significant achievements in enhancing model robustness through the use of sparse coding. However, it must be recognized that this exploration of process noise represents only a subset of research on process nonstationarity, which primarily focuses on time-varying statistical properties. Unfortunately, existing BLS methods cannot solve the nonstationarity problem. Summary of the Invention

[0008] To overcome the shortcomings of existing technologies, this invention provides a temporal kernel stationary width learning method, the steps of which include: nonlinear kernel width representation estimation, temporal matching mechanism, stationary-regressive overall objective construction and parameter estimation, and independent incremental learning.

[0009] This invention specifically studies the predictive performance and fault monitoring capabilities of the blast furnace ironmaking process. Therefore, it proposes a regression modeling and anomaly detection framework based on the Temporal Kernel Broad Representation (TKS-BLS) system. First, a nonlinear kernel broad representation (NKBR) extraction strategy is created, providing a robust nonlinear foundation for stochastic feature mapping through kernel technology. Then, an internal temporal matching mechanism between the model input and output is explored through a time alignment parameter, which can be interpreted under latent variable relationships. In the integration phase, a Kullback-Leibler-based objective function is established to facilitate the capture of stationary relationships in time series data and combines regression error with the overall objective function. Finally, a dual-loop parameter optimization algorithm and an independent incremental learning mechanism are proposed, both supported by comprehensive theoretical analysis.

[0010] A temporal kernel stationary width learning system includes the following steps: nonlinear kernel width representation estimation, temporal matching mechanism, stationary-regressive overall objective construction and parameter estimation, and independent incremental learning.

[0011] The nonlinear kernel width representation includes the following steps:

[0012] (2.1) To address the complexity of the blast furnace ironmaking process, the TKS-BLS method first developed a kernel-based nonlinear feature extractor; to handle nonlinearity, a kernel method was first adopted, in which the mapping function φ(.) maps the data x(·) from the original space. Projected into a high-dimensional feature space

[0013]

[0014] for i,j=1,2,…,n(1b)

[0015] In the formula, κ(.) represents a specific kernel function and Defined as Inner product operations in space, and centralization It is then calculated in the following way:

[0016]

[0017] Among them, I n All elements are set to 1 / n. To study the impact of the kernel function on nonlinear information in depth, a specific kernel function must be specified. In this analysis, a Gaussian kernel is used as a representative example, which can be expressed as follows:

[0018]

[0019] In the formula, γ is the kernel width. The following formula (4) always holds, that is,

[0020]

[0021] By introducing the Taylor expansion, it can be obtained that

[0022]

[0023] Therefore, the non-linear mapping φ(x(i)) can be explicitly expressed as

[0024]

[0025] Through formula (6), the Gaussian kernel function helps to explore high-order non-linear relationships in data. Obviously, this method also facilitates testing the ability to extract non-linear information using other kernel functions, such as polynomial kernel functions and Laplacian kernel functions.

[0026] (2.2) However, after the kernel function maps , the size of the data matrix will be expanded considerably from to when N>>k x . This significant expansion will noticeably increase the computational requirements of subsequent procedures. To solve this problem, we adopt principal component analysis (PCA) to retain basic information, and its expression is as follows:

[0027]

[0028] where the diagonal matrix Ξ=diag(ξ1,ξ2,…,ξ n ) is composed of eigenvalues, and V=[v1,v2,…,v n is constructed from corresponding eigenvectors. The largest d (d<n) eigenvalues together with their respective eigenvectors form the non-linear kernel representation (NKR) and its reduced matrix is V d =[v1,v2,…,v d . It is worth emphasizing that the application of PCA not only greatly reduces the size of the NKR matrix, but also effectively filters system noise by discarding residual subspaces. This key process can prevent noise from accumulating in the subsequent extraction process of non-linear kernel width representation (NKBR).

[0029] (2.3) Here, based on NKR T, the corresponding hidden layer, namely NKBR, is constructed with reference to the width mapping mechanism

[0030]

[0031] Where m t Feature nodes and l t Enhance nodes.

[0032] The timing matching mechanism includes the following steps:

[0033] (3.1) When there is a significant difference in the sampling rate between the system's input and output variables, it is necessary to collect a dataset. This includes N = ns > n. Each output sample y(i) is compared with the input sample z(i) graded according to time s = [x T (i,1),x T (i,2),…,x T (i,s)] T This situation conforms to certain properties: 1. After the maximum time-lag scale (denoted by q), the input will lose its corresponding mapping to the output. Furthermore, the input samples corresponding to different output samples will not overlap, i.e., q is less than s. 2. In a stable system, the maximum time-lag scale q of all output samples y(i) remains consistent.

[0034] The projection of NKBR z(i), given as the maximum time-delay scale q, can be expressed as: Considering the latent variable form, y(i) and a q The projection vectors of (i) are denoted as q and w, respectively, from which we can derive:

[0035] c(i)=y T (i)q(9a)

[0036] t(i)=a q,T (i)w(9b)

[0037] Here, to further confirm the registration relationship between each time delay scale and the output sample, a registration parameter β = [β1, β2, ..., β] is introduced. q ] T Therefore, for each y(i), the relationship between its latent variables and the input samples can be expressed as:

[0038]

[0039] Where β⊙w is the matrix Kronecker product between β and w. According to these definitions...

[0040]

[0041]

[0042] Equation (10) can be reconstructed in matrix form as follows:

[0043]

[0044] (3.2) Therefore, the first part of the overall objective This can be expressed as maximizing the following:

[0045]

[0046] It is worth noting that this equivalence arises from the concept that maximizing covariance is synonymous with minimizing the difference between predicted and observed values.

[0047] The construction and parameter estimation of the stationary-regression overall objective include the following steps:

[0048] (4.1) To effectively address the complex mixing process in blast furnace ironmaking, it is essential to explore stationarity to mitigate the impact of non-stationary factors. This requires that the extracted NKBR maintain consistency, manifested in the stability of its mean and variance across different periods. When divided into ε time periods, the corresponding mean and variance (μ) e ,Σ e It should be consistent with the population mean and variance. Consistent. Therefore, we utilize KL divergence. The second paragraph further constructs the overall goal. That is, the stable target, its calculation formula is:

[0049]

[0050] However, direct minimization This leads to a nonconvex optimization problem for β and w. Although some studies use gradient descent to solve this problem, it often consumes a lot of computational resources. To alleviate the computational burden, we refactor the optimization problem (14) into a quadratic objective, namely:

[0051]

[0052] in

[0053]

[0054] By merging the first and second parts using a tradeoff parameter η, the overall objective is... This can be expressed as:

[0055]

[0056] stq T q=1,(β⊙w) T(β⊙w)=1(17b)

[0057] (4.2) To solve the optimization problem in equation (17), Lagrange multipliers are needed. Define the Lagrange function.

[0058]

[0059] The Lagrange multiplier is λ. q and λ w For q, β, w, λ respectively q , and λ w Taking the derivative of equation (18) above and setting it to zero, we can obtain...

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] Multiply the left side of formulas (19a) and (19b) by q respectively. T and w T The relationship between them can be calculated as follows:

[0066]

[0067]

[0068] In q T q=1 and (β⊙w) T Given (β⊙w)=1, we obtain 2Λ=λ q +λ w Therefore, by maximizing λ respectively q and λ w The objective of equation (18) can be achieved. According to equation (19), the values ​​of q, β, and w can be determined by the following formula.

[0069]

[0070]

[0071]

[0072] Where ∝ represents the proportional relationship between the two sides. Let represent the pseudo-inverse operator. Clearly, it can be seen from equation (21) that the solutions for vectors q, w, and β are intertwined and lack a compact form. Therefore, the structure of TKS-BLS can be obtained through iterative equation (21).

[0073] (4.3) Subsequently, by collecting all latent variables Load vector Projection vector from The latent variables that can be extracted are:

[0074]

[0075] Subsequently, a multivariate least squares method (i.e., using the regression parameter ζ) can be used to establish... and The connection between them:

[0076]

[0077] in Indicates to Regression estimation, This represents the regression error. The regularization term θ is used to reduce the potential ill-conditioned matrix. The impact. Ultimately, the predicted value and You can directly from The conclusion is that

[0078]

[0079] (4.4) For the timely modeling and anomaly detection strategy, after collecting q input samples, a new observation input sample can be established, denoted as X. new =[x T (new,1),x T (new,2),…,x T (new,q)] T This allows us to calculate the real-time centralized mean kernel matrix. Together with the load matrix V, the NKR of main information aggregation It can be represented as:

[0080]

[0081] Then, for t = 1, 2, ..., q, NKBR for

[0082]

[0083] By summing these NBKR vectors a(new,t), the lagged term a can be used. q,newand the corresponding latent variable τ new For output variables Perform real-time predictions:

[0084]

[0085] In terms of anomaly detection, due to Hotelling'sT 2 The statistic has extremely high sensitivity, and therefore it is used here:

[0086]

[0087] The corresponding threshold J th follow Distribution, Σ τ represent The covariance matrix is ​​shown in equation (28), and the confidence level is represented by α. Based on the preceding explanation and analysis, the following anomaly detection logic is expressed as follows:

[0088]

[0089] The independent incremental learning includes the following steps:

[0090] (5.1) By developing optimization objectives and iterative algorithms, TKS-BLS has the ability to model and detect anomalies in nonlinear, unsteady systems with time-displaced characteristics. However, the time variability of the system is crucial to maintaining the effectiveness of the model, thus scalability is essential. Therefore, collecting additional samples... t x =ns+1,ns+2,…,n+Ds,t y =n+1,n+2,…,n+D, establishing an independent incremental learning technique. By applying X C and Y c Related additional hysteresis NKBR can be constructed Based on the original TKS-BLS model, equation (8) helps to determine the original latent variables. The calculation. This can also be achieved by locating the original TKS-BLS model. and The unmodeled residuals are represented as and

[0091]

[0092] Equation (30) shows and This includes unmodeled information. Due to the time-varying nature of the system, these elements contain supplementary data not present in the training set, thus necessitating additional modeling. To investigate the original model's neglect of recent data features, this invention establishes an auxiliary TKS-BLS model:

[0093]

[0094] stq c,T q c =1,(β) c ⊙wc) T (β c ⊙w c )=1(31b)

[0095] in

[0096]

[0097] For l c Further estimation of the projection vectors will uncover additional latent variables. And each latent variable is paired with its predicted value using the following method. pair

[0098]

[0099] in, and It is the load matrix, ζ c It's a regression matrix. Then, the initial model... and updating the model Combining the regression modeling capabilities, we can use a q,new Give the entire system The comprehensive representation of, that is

[0100]

[0101] The latent variables in the original model and the updated model are arranged sequentially as follows: An improved Hotelling'sT can be obtained. 2 Statistic:

[0102]

[0103]

[0104] in Covariance of a matrix It is represented as shown in equation (28). The corresponding critical value set by the distribution is used It is noteworthy that the proposed independent incremental learning ensures that the additional latent variables remain distinct from the original variables. This maintains the orthogonality between the original and supplementary models, indicating no performance interference or overlap. The original training data typically reflects the long-term characteristics of the system, while the additional data captures recent trends. This mixture enhances the estimation of more comprehensive latent variables and improves regression modeling capabilities.

[0105] The beneficial effects of this invention are:

[0106] First, a kernel function and width learning method are used to establish a structure for mining rich nonlinear features. Next, an optimization objective combining stationarity and regression characteristics is constructed by aligning input and output variables under sampling rate mismatch using time-series registration parameters, and solved using cyclic scaling. Subsequently, an independent incremental learning strategy is constructed to overcome the time-varying characteristics of the process. Furthermore, case studies of this invention demonstrate that the proposed Tc-GLNASSA represents a significant step forward in improving blast furnace ironmaking prediction and process efficiency, and ensuring safe equipment operation. Attached Figure Description

[0107] Figure 1 This is a schematic diagram illustrating the technical route of the time-series kernel stationary width learning method for the blast furnace ironmaking process of the present invention.

[0108] Figure 2.1 and Figure 2.2 These are comparison figures showing the fault detection results of the time-series kernel stationary width learning method for blast furnace ironmaking process according to the present invention;

[0109] The components are: (a) PLS; (b) KPLS; (c) IKOPLS; (d) L2RBLS; (e) Time-SBLS; (f) MemBLSAD; (g) TKS-BLS with module I; (h) TKS-BLS with modules I-II; (i) TKS-BLS with modules I-III; and (j) complete TKS-BLS. Detailed Implementation

[0110] like Figure 1 , Figure 2.1 and Figure 2.2 The figure shows a case study comparison of the time-series kernel stationary width learning method for the blast furnace ironmaking process of the present invention, which includes the following steps:

[0111] (1) For offline modeling, various sensors (flow sensors, temperature sensors, concentration sensors, etc.) need to be installed at different locations in the blast furnace ironmaking process, and the corresponding data needs to be stored in a database. To address the complexity of the blast furnace ironmaking process, this invention first develops a kernel-based nonlinear feature extractor; to handle nonlinearity, a kernel method is first adopted, where the mapping function φ(.) maps the data x(·) from the original space... Projected into a high-dimensional feature space

[0112]

[0113] for i,j=1,2,…,n(1b) where κ(.) represents a specific kernel function and Defined as Inner product operations in space, and centralization It is then calculated in the following way:

[0114]

[0115] Among them, I n All elements are set to 1 / n. To study the impact of the kernel function on nonlinear information in depth, a specific kernel function must be specified. In this analysis, a Gaussian kernel is used as a representative example, which can be expressed as follows:

[0116]

[0117] In the formula, γ is the kernel width. The following equation (4) always holds, i.e.

[0118]

[0119] By introducing the Taylor expansion, we can obtain

[0120]

[0121] Therefore, the nonlinear mapping φ(x(i)) can be explicitly expressed as

[0122]

[0123] Equation (6) shows that the Gaussian kernel function helps to explore higher-order nonlinear relationships in data. Clearly, this method also helps to test the ability to extract nonlinear information using other kernel functions (such as the polynomial kernel function and the Laplace kernel function).

[0124] However, in kernel function mapping Then, the size of the data matrix will be from arrive With N >> k xhas been expanded considerably. This significant expansion will obviously increase the computational requirements of subsequent procedures. To address this problem, we adopt Principal Component Analysis (PCA) to retain basic information, and its expression is as follows:

[0125]

[0126] where the diagonal matrix Ξ=diag(ξ1,ξ2,…,ξ n ) is composed of eigenvalues, and V=[v1,v2,…,v n is constructed from corresponding eigenvectors. The largest d (d < n) eigenvalues together with their respective eigenvectors form the Nonlinear Kernel Representation (NKR) and its reduced matrix is V d =[v1,v2,…,v d . It is worth emphasizing that the application of PCA not only greatly reduces the size of the NKR matrix, but also effectively filters system noise by discarding residual subspaces. This key process can prevent noise from accumulating in the subsequent extraction of Nonlinear Kernel Width Representation (NKBR).

[0127] Based on NKR T herein, a corresponding hidden layer is constructed with reference to the width mapping mechanism, namely NKBR

[0128]

[0129] where m t feature nodes and l t enhancement nodes.

[0130] (2) The timing matching mechanism described includes the following steps: when there is a significant difference in sampling rates between the input and output variables of the system, it is necessary to collect a dataset which includes N=ns>n. Each output sample y(i) corresponds to a time-graded input sample z(i)=[x T (i,1),x T (i,2),…,x T (i,s)] T . This situation satisfies specific properties: 1. After the maximum time lag scale (denoted by q), the input will lose the corresponding mapping with the output. In addition, input samples corresponding to different output samples do not overlap with each other, that is, q is less than s. 2. In a stable system, the maximum lag scale q of all output samples y(i) remains consistent.

[0131] The projection of NKBR onto z(i), given the maximum time lag scale q, can be expressed as Considering the latent variable form, y(i) and a q The projection vectors of (i) are denoted as q and w, respectively, from which we can derive:

[0132] c(i)=y T (i)q(9a)

[0133] t(i)=a q,T (i)w(9b)

[0134] Here, to further confirm the registration relationship between each time delay scale and the output sample, a registration parameter β = [β1, β2, ..., β] is introduced. q ] T Therefore, for each y(i), the relationship between its latent variables and the input samples can be expressed as:

[0135]

[0136] Where β⊙w is the matrix Kronecker product between β and w. According to these definitions...

[0137]

[0138]

[0139] Equation (10) can be reconstructed in matrix form as follows:

[0140]

[0141] Therefore, the first part of the overall goal This can be expressed as maximizing the following:

[0142]

[0143] It is worth noting that this equivalence arises from the concept that maximizing covariance is synonymous with minimizing the difference between predicted and observed values.

[0144] (3) The construction and parameter estimation of the stationary-regression overall objective includes the following steps: To effectively address the complex mixing process in blast furnace ironmaking, it is necessary to explore stationarity to mitigate the impact of non-stationary factors. This requires that the extracted NKBR maintain its consistency, manifested in the stability of its mean and variance at different times. When divided into ε time periods, the corresponding mean and variance (μ) e ,Σ e It should be consistent with the population mean and variance. Consistent. Therefore, we utilize KL divergence. The second paragraph further constructs the overall goal. That is, the stable target, its calculation formula is:

[0145]

[0146] However, direct minimization This leads to a nonconvex optimization problem for β and w. Although some studies use gradient descent to solve this problem, it often consumes a lot of computational resources. To alleviate the computational burden, we refactor the optimization problem (14) into a quadratic objective, namely:

[0147]

[0148] in

[0149]

[0150] By merging the first and second parts using a tradeoff parameter η, the overall objective is... This can be expressed as:

[0151]

[0152] stq T q=1,(β⊙w) T (β⊙w)=1(17b)

[0153] To solve the optimization problem in equation (17), Lagrange multipliers are needed. The Lagrange function is defined.

[0154]

[0155] The Lagrange multiplier is λ. q and λ w For q, β, w, λ respectively q , and λ w Taking the derivative of equation (18) above and setting it to zero, we can obtain...

[0156]

[0157]

[0158]

[0159]

[0160]

[0161] Multiply the left side of formulas (19a) and (19b) by q respectively. T and w T The relationship between them can be calculated as follows:

[0162]

[0163]

[0164] In q T q=1 and (β⊙w) T Given (β⊙w)=1, we obtain 2Λ=λ q +λ w Therefore, by maximizing λ respectively q and λ w The objective of equation (18) can be achieved. According to equation (19), the values ​​of q, β, and w can be determined by the following formula.

[0165]

[0166]

[0167]

[0168] Where ∝ represents the proportional relationship between the two sides. Let represent the pseudo-inverse operator. Clearly, it can be seen from equation (21) that the solutions for vectors q, w, and β are intertwined and lack a compact form. Therefore, the structure of TKS-BLS can be obtained through iterative equation (21).

[0169] Subsequently, by collecting all latent variables Load vector Projection vector from The latent variables that can be extracted are:

[0170]

[0171] Subsequently, a multivariate least squares method (i.e., using the regression parameter ζ) can be used to establish... and The connection between them:

[0172]

[0173] in Indicates to Regression estimation, This represents the regression error. The regularization term θ is used to reduce the potential ill-conditioned matrix. The impact. Ultimately, the predicted value and You can directly from The conclusion is that

[0174]

[0175] For the timely modeling and anomaly detection strategy, after collecting q input samples, a new observation input sample, denoted as X, can be established. new =[x T (new,1),x T (new,2),…,x T (new,q)] T This allows us to calculate the real-time centralized mean kernel matrix. Together with the load matrix V, the NKR of main information aggregation It can be represented as:

[0176]

[0177] Then, for t = 1, 2, ..., q, NKBR for

[0178]

[0179] By summing these NBKR vectors a(new,t), the lagged term a can be used. q,new and the corresponding latent variable τ new For output variables Perform real-time predictions:

[0180]

[0181] In terms of anomaly detection, due to Hotelling'sT 2 The statistic has extremely high sensitivity, and therefore it is used here:

[0182]

[0183] The corresponding threshold J th follow Distribution, Σ τ represent The covariance matrix is ​​shown in Equation (28), and the confidence level is represented by α. Based on the preceding explanation and analysis, the following anomaly detection logic is expressed as follows:

[0184]

[0185] (4) The independent incremental learning includes the following steps: By developing optimization objectives and iterative algorithms, TKS-BLS possesses the ability to model and detect anomalies in nonlinear, unsteady systems with temporal misalignment. However, the temporal variability of the system is crucial to maintaining the effectiveness of the model, thus scalability is essential. Therefore, by collecting additional samples... t x =ns+1,ns+2,…,n+Ds,ty =n+1,n+2,…,n+D, establishing an independent incremental learning technique. By applying X... C and Y c Related additional hysteresis NKBR can be constructed Based on the original TKS-BLS model, equation (8) helps to determine the original latent variables. The calculation. This can also be achieved by locating the original TKS-BLS model. and The unmodeled residuals are represented as and

[0186]

[0187] Equation (30) shows and This includes unmodeled information. Due to the time-varying nature of the system, these elements contain supplementary data not present in the training set, thus necessitating additional modeling. To investigate the original model's neglect of recent data features, this invention establishes an auxiliary TKS-BLS model:

[0188]

[0189] stq c,T q c =1,(β) c ⊙w c ) T (β c ⊙w c )=1(31b)

[0190] in

[0191]

[0192] For l c Further estimation of the projection vectors will uncover additional latent variables. And each latent variable is paired with its predicted value using the following method. pair

[0193]

[0194] in, and It is the load matrix, ζ c It's a regression matrix. Then, the initial model... and updating the model Combining the regression modeling capabilities, we can use a q,new Give the entire system The comprehensive representation, namely

[0195]

[0196] The latent variables in the original model and the updated model are arranged sequentially as follows: You can get an improved Hotelling'sT 2 Statistic:

[0197]

[0198]

[0199] in Covariance of a matrix It is represented as shown in equation (28). The corresponding critical value set by the distribution is used It is noteworthy that the proposed independent incremental learning ensures that the additional latent variables remain distinct from the original variables. This maintains the orthogonality between the original and supplementary models, indicating no performance interference or overlap. The original training data typically reflects the long-term characteristics of the system, while the additional data captures recent trends. This hybrid approach enhances the estimation of more comprehensive latent variables and improves regression modeling and anomaly detection capabilities.

[0200] This invention proposes a process algorithm model related to improving blast furnace ironmaking, namely, a time-series kernel-stationary width-of-base (TKS-BLS) system for blast furnace ironmaking. First, an NKBR extraction strategy is created, providing a robust nonlinear foundation for stochastic feature mapping through kernel technology. Then, an internal time-series matching mechanism between the model input and output is explored through a time alignment parameter, which can be interpreted under latent variable relationships. In the integration phase, this invention establishes a Kullback-Leibler-based objective function to facilitate the capture of stationary relationships in time-series data and combines regression error with the overall objective function. Finally, a dual-loop parameter optimization algorithm and an independent incremental learning mechanism are proposed, both supported by comprehensive theoretical analysis. Furthermore, case studies of this invention demonstrate that the proposed TKS-BLS represents a significant step forward in improving the prediction and monitoring effects of blast furnace ironmaking processes and ensuring safe equipment operation.

[0201] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A time-series kernel-stationary width learning method for blast furnace ironmaking processes, characterized by the following steps: include: Nonlinear kernel width representation estimation, temporal matching mechanism, stationary-regressive overall objective construction and parameter estimation, and independent incremental learning; The method described here proposes a feature estimation strategy that uses nonlinear kernel broad representation (NKBR). This strategy lays a nonlinear foundation for subsequent random feature mapping using kernel techniques. A temporal matching mechanism is then established to create a temporal link between the model NKBR and the output, enabling latent variable prediction. A stationary-regression overall objective is constructed using Kullback-Leibler (KL divergence) as the objective function, and a dual-loop parameter optimization method is proposed for parameter estimation. When additional data is collected, an independent incremental learning mechanism is used to maintain the independence between the original and updated models, thereby ensuring long-term updatable regression modeling and monitoring capabilities. The nonlinear kernel width representation includes the following steps: (2.1) For offline modeling, flow sensors, temperature sensors, and concentration sensors are installed at various locations in the blast furnace ironmaking process, and the corresponding data are stored in a database. To address the complexity of the blast furnace ironmaking process, the TKS-BLS method first develops a kernel-based nonlinear feature extractor, which employs a kernel method through a mapping function. Data From the original space Projected into a high-dimensional feature space Thus constructing kernel features As shown below; ； ； In the formula, Represents a specific kernel function and Centralization It is then calculated in the following way: ； in, All elements are set to 1 / n; a specific kernel function is specified to study the effect of the kernel function on nonlinear information. (2.2) However, in kernel function mapping Then, the size of the data matrix will be from arrive ,and There is an extension, which uses principal component analysis (PCA) to retain... The basic information can be represented by the score matrix T; (2.3) Based on the score matrix T, the feature mapping hidden layers can be constructed by referring to the width learning method. and augmented mapping hidden layers NKBR is obtained through cascading operations, and can be obtained from... express: ； in Number of feature nodes and Increase the number of nodes; The construction and parameter estimation of the stationary-regression overall objective include the following steps: To ensure the stability of data across different periods, this can be reflected in the consistency of its mean and variance, i.e., when the time lag matrix... Divided into After a certain period, the corresponding mean and variance Should be related to the population mean and variance Consistent, and establishing a solution objective with KL divergence as the target; ultimately, the predicted value and You can directly from The conclusion is that ； Among them, the latent variables are The load vector is Projection vector ,and For the timely modeling and anomaly detection strategy section, data was collected. After one input sample, a new observation input sample is created, denoted as . Calculate the real-time centralized mean kernel matrix. By calculating real-time NBKR vectors, Hotelling's... Statistics, and thus the corresponding thresholds You can also follow The distribution is obtained; ultimately, the anomaly detection logic can be expressed as follows: 。 2. The method according to claim 1, characterized in that, The timing matching mechanism includes the following steps: When there is a significant difference in the sampling rate between the system's input and output variables, the dataset is collected. including ; Under the condition of sample rate mismatch, each output sample can be represented as Furthermore, the input sampling determined by the time scale s can be expressed as: ; After considering the maximum time lag scale q (q < s), there will be no corresponding mapping between the input and the output; in addition, the input samples corresponding to different output samples will not overlap with each other; in a stable system, all output samples have the same maximum lag scale q; thus the time lag matrix can be constructed.

3. The method according to claim 1, characterized in that, The independent incremental learning includes the following steps: (5.1) By collecting additional samples , An independent incremental learning technique was established. The proposed independent incremental learning can ensure that the additional latent variables remain different from the original variables, which 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. Subsequently, the initial model was used. and updating the model Combining the regression modeling capabilities, we can determine the regression modeling from the lagged terms. Give the entire system The comprehensive representation, namely ； in, and It is the load matrix under the updated model. This involves updating the regression matrix under the updated model; subsequently, the improved Hotelling's regression matrix can be obtained. Statistic, The corresponding critical value set by the distribution is used express.

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