Improved fault detection and identification method for hybrid kernel aided stationary subspace analysis

Abstract

The application discloses a kind of improved hybrid kernel auxiliary stationary variable analysis fault detection and identification method, steps include: using hybrid kernel to explore typical stationary variable (CSVs), singular value decomposition (SVD) and iterative modeling process, stationary subspace analysis (SSA), the contribution of two statistics and index difference is calculated;First, consider past, future matrix and the multi-view nonlinear mapping of hybrid kernel, explore the time correlation and weak stationarity of typical stationary variable;The efficiency improvement of singular value decomposition and iterative modeling process is proposed to reduce the calculation cost and accurately estimate typical stationary variable.In addition, by retaining the smooth information in the residual that has no autocorrelation, to further analyze the stationary variable (SSVs) generated using stationary subspace analysis.By intuitive explanation of dynamic and static stationary information, the corresponding two statistics and index difference contribution are calculated to detect and identify faults.

Description

TECHNICAL FIELD

[0001] The present application relates to a blast furnace ironmaking process fault detection and identification method based on improved hybrid kernel auxiliary canonical variate analysis. BACKGROUND

[0002] For a complex blast furnace ironmaking process (BFIP), the complex interaction of its nonlinear, dynamic and non-stationary characteristics is mutually coupled, which brings challenges to fault detection and identification. Due to the simultaneous occurrence of physical and chemical reactions and the distributed system structure it contains, BFIP data exhibits complex nonlinearity, dynamics and non-stationarity.

[0003] In order to ensure the safe operation of the process, it is crucial to develop a monitoring scheme that is accurate, efficient and timely in detecting faults in the case of considering the complex characteristics of BFIP. Data-driven multivariate statistical fault detection has attracted the attention of researchers due to its high efficiency, accuracy and robustness, and has been successfully verified in actual industrial scenarios. However, in terms of non-stationarity, due to the interference of non-stationary information, the mean and variance of process data change with time, which brings challenges to the mining of stationary parts in the original data, so only a few scholars dare to explore this problem. At present, non-stationary fault detection methods include independent component analysis (ICA), Kalman filter (KF), stationary subspace analysis (SSA) and its variants.

[0004] SSA is derived from weak stationarity, i.e. the consistency of the mean and variance, which frees it from strict theoretical constraints, enabling it to be applied to more general cases. Chen et al. proposed an exponential analysis SSA algorithm that can accurately estimate the potential component to remain smooth and designed an updating strategy and an adaptive monitoring scheme to track the trajectory of non-stationary processes while minimizing the updating frequency. Wu et al. proposed a new algorithm from the perspective of probability, called probabilistic SSA, which effectively models the process uncertainty using the expectation maximization and closed-form model updating strategy. For complex BFIP scenarios, due to complex process dynamics and nonlinearity, the estimation of the stationary part in the above model is hindered. This limitation can lead to bias, where part of the non-stationary information is incorrectly integrated with the stationary component, while some stationary information is ignored. To address the above challenges, many methods have been developed in the past few decades to exploit the key dynamic information embedded in the process data. One of these methods is the canonical variable analysis (CVA) based on the state space model, which maximizes the correlation between the constructed past and future matrices to describe the time correlation. Although CVA was introduced into the field of fault detection nearly 20 years ago, it remains an active research area due to its solid theoretical foundation and efficient application performance. When faced with complex nonlinearity, mixed kernel CVDA introduces the multi-angle nonlinear exploration brought by mixed kernel technology into CVDA, with superior monitoring performance. Wu et al. successively constructed CVA and mixed kernel PCA to take into account linear and nonlinear features. Although CVA and its variants have been able to handle specific application scenarios, they are obviously lacking in processing capacity. For non-stationarity, the excessive modeling consumption associated with mixed kernels cannot match the fragile industrial conditions. SUMMARY

[0005] By integrating the characteristics of BFIP data and eliminating the above difficulties, the present application proposes a fault detection and identification method of improved mixed kernel assisted stationary variable analysis. This method uses the nonlinear characteristics of mixed kernel based on multi-view under the constraint of weak stationarity to obtain canonical stationary variables. It makes the canonical stationary variables (CSVs) exhibit a high degree of time dependence and resistance to non-stationary disturbances. In addition, it retains the stationary information in the residuals that is not autocorrelated, and further extracts stationary variables (SSVs) from the residuals through the stationary subspace analysis (SSA) algorithm. Two statistics and exponential difference contributions are calculated, so that dynamic and static stationary information can be explicitly explained through simultaneous fault detection and identification

[0006] A blast furnace ironmaking process fault detection and identification method based on improved mixed kernel assisted canonical stationary variable analysis, the steps comprising: using mixed kernel technology to explore CSVs, singular value decomposition (SVD) and iterative modeling process, stationary subspace analysis, calculating two statistics and exponential difference contributions to realize fault detection and identification.

[0007] The method of mixed kernel technique exploration of typical stationary variables includes the following steps:

[0008] (2.1) For the complexity of the blast furnace ironmaking process, the M2KCSVA method first performs a mixed kernel multi-view feature representation. In exploring the time characteristics of the past vector p(k) and the future vector f(k), the kernel trick is used to further capture nonlinearity; a linearly solvable nonlinear mapping function Map the low-dimensional original space R to a certain high-dimensional feature space F, and then analyze and model in this new space; assume that N samples x(t) are collected, the local kernel And That is, the Gaussian radial basis function (RBF), the global kernel And That is, the polynomial kernel satisfies:

[0009] p(k) = [x(k-q) T x(k-q+1) T …x(k-1) T ] T (1a)

[0010] f(k) = [x(k) T x(k+1) T …x(k+q-1) T ] T (1b)

[0011] Where q is the lag number of the past and future window;

[0012]

[0013] Where And v(i) and v(j) are arbitrary process samples, and the kernel parameter a r And a p Suitable for RBF and polynomial kernel;

[0014] In order to reconcile the intensity of And The method of weighted accumulation is given:

[0015]

[0016] Where the mixed kernel Respectively represent the past and future vectors, and γ ∈ [0, 1] represents the mixing weight. (2.2) Objective function of M2KCSVA: assume The mean and covariance of

[0017]

[0018] Here the M2KCSVA aims at two objectives simultaneously; first, to capture the process dynamics by maximizing the correlation between and second, the estimated features should remain smooth and not be disturbed by non-stationary fluctuations; the objective function of the M2KCSVA is thus given by:

[0019]

[0020] where j s and h s are the projection vectors, and are partitioned into E k segments, where the mean and variance of each segment and their average can be obtained from the above equations;

[0021] The solution of equation (6) is considered using the method of Lagrange multipliers:

[0022]

[0023] Using the Lagrange multipliers λ j and λ h ; here we take the derivative of (8) with respect to j s and h s and set them to zero:

[0024]

[0025] Introducing the properties of equation (6), pre-multiplying the above equations by and respectively, we get:

[0026]

[0027] It is shown that (6) is equivalent to finding the maximum of λ, while (11) gives a compact form:

[0028]

[0029] The singular value decomposition and iterative modeling procedure comprises the following steps:

[0030] (3.1) Using singular value decomposition, the symmetric matrices and are decomposed into:

[0031]

[0032] where and are the singular value matrices, and denotes the corresponding singular matrix;

[0033] (3.2) Taking into account and contains elements that tend to zero, and will be condensed to:

[0034]

[0035] where According to the decomposition of the segment, we have:

[0036]

[0037] (3.3) After that, the main information in and will be combined to:

[0038]

[0039] (3.4) Finally, we bring equation (15) into equation (12), here we get:

[0040]

[0041] where the optimal j s and h s are equal to the eigenvectors corresponding to the largest eigenvalues by solving the EVD problem;

[0042] (3.5) The compacting and modeling process includes the following steps:

[0043] Given the weight matrix CSVs are directly represented by and :

[0044]

[0045] The residuals (ε p , ε f ) containing dynamic independent stationary and non-stationary information can be divided into:

[0046]

[0047] where I is the identity matrix.

[0048] The stationary subspace analysis generates stationary variables includes the following steps:

[0049] (4.1) Stationary subspace analysis is used to capture the SSVs in :

[0050]

[0051] where, is the projection matrix of the stationary part, and the projection matrix of the non-stationary part is given by left.

[0052] The calculation of the two statistical quantities and the index difference contribution to achieve fault detection and identification includes the following steps:

[0053] (5.1) In order to process the periodically sampled data, the real-time past samples are superimposed as p(k) in (1) at time k:

[0054] p(k) = [x(k-q) T x(k-q+1) T …x(k-1) T ] T (1)

[0055] where q is the lag number of the past and future window;

[0056] Then the local kernel and the global kernel are calculated respectively to obtain the mixed kernel

[0057]

[0058] (5.2) In addition, the CSVs and SSVs of M2KCSVA are constructed:

[0059]

[0060] (5.3) The fault detection statistics and are added to obtain the corresponding threshold which is subject to χ2 distribution:

[0061]

[0062] where g c =∑ Dc / 2μ Dc , g s =∑ Ds / 2μ Ds , μ Dc and μ Ds represent the mean of and , Σ Dc and Σ Dsrespectively, where denotes the corresponding variance; if the computed statistics exceeds a predefined threshold, the process is classified as abnormal; otherwise, it is considered normal;

[0063] (5.4) When a process anomaly is identified, it subsequently enters the fault identification phase; in this phase, the contribution of the statistics is expressed as and

[0064]

[0065] where denotes the Hadamard operator; in addition, to further improve the sensitivity of the contribution, the exponential difference contribution and is expressed as:

[0066]

[0067] where and denote the average contribution in training.

[0068] Advantages of the present application:

[0069] First, a new objective function based on M2KCSVA is proposed to mine CSVs from time series data, considering both the time correlation and weak stationarity of the samples. Then, the corresponding iterative data compression and modeling procedure is developed to obtain accurate CSVs estimates. Modeling efficiency improvement methods for the fault identification methods based on singular value decomposition and exponential difference contribution are proposed respectively, and are analyzed and mathematically discussed. The geometric properties of CSVs and SSVs are studied, and their mutual orthogonality is emphasized. This property means that both CSVs and SSVs can be explicitly and independently monitored. Practical BFIP experiments, combined with a comprehensive parameter optimization process, verify the effectiveness of the methods proposed here. By facilitating accurate and timely fault detection and identification of abnormal furnace conditions, the methods here enable field engineers to quickly identify the source of anomalies. This enables timely intervention and recovery, thereby improving operational safety, ensuring the stability of ironmaking products, and resulting in considerable economic benefits. BRIEF DESCRIPTION OF DRAWINGS

[0070] Figure 1 Fault detection route schematic diagram of the improved mixed kernel auxiliary typical stationary variable analysis method of the present application for blast furnace ironmaking.

[0071] Figure 2Fault detection results comparison plot for the blast furnace ironmaking process ND1 scenario of the present application; where each part: (a) SSA; (b) DSSA-ADMM; (c) MKSSA; (d) PCA-ICA; (e) CVA; (f) M2KCSVA.

[0072] Figure 3 Stationary projection performance of the improved mixed kernel auxiliary typical stationary variable analysis method for the blast furnace ironmaking process of the present application; where each part: (a) and (b) correspond to CSVs; (c) and (d) correspond to SSVs; (e)-(h) are Q-Q plots for all CSVs and SSVs.

[0073] Figure 4 Fault detection results comparison plot for the blast furnace ironmaking process FD3 scenario of the present application;

[0074] where each part: (a) SSA; (b) DSSA-ADMM; (c) MKSSA; (d) PCA-ICA; (e) CVA; (f) M2KCSVA.

[0075] Figure 5 Contribution plot identification results for the blast furnace ironmaking process of the present application; where each part: (a) PCA-ICA; (b) M2KCSVA. DETAILED DESCRIPTION

[0076] As shown in Figure 1 , Figure 2 , Figure 3 and Figure 4 , the M2KCSVA-based fault detection and identification case study comparison for the blast furnace ironmaking process of the present application includes the following steps:

[0077] The present application proposes a new fault diagnosis method (i.e., M2KCSVA-based fault diagnosis), a new modeling efficiency improvement technique, and a new contribution plot construction method based on an exponential function. In particular, M2KCSVA analyzes time correlation and stationarity to facilitate the revelation of the essence of the process and the estimation of CSVs and SSVs, thereby avoiding the interference of non-stationary properties and more accurately modeling. Here, the computational burden brought by the multi-kernel technology is reduced through the boosting strategy based on SVC. In addition, the newly proposed exponential difference contribution realizes fast and sensitive fault identification capability, and the geometric properties of the model are derived. In the actual BFIP scenario, experimental studies show that the method here can generate smooth CSVs and SSVs, and provide more accurate monitoring capability under normal and fault scenarios. The analysis of variable contribution and modeling time consumption further verifies the effectiveness of the method proposed here.

[0078] The one for exploring the typical stationary variables (CSVs) with hybrid kernel technology comprises the following steps:

[0079] 2.1) For the complexity of the blast furnace ironmaking process, the M2KCSVA method first performs hybrid kernel multi-view feature representation, and uses kernel trick to further capture nonlinearity when exploring the time characteristics of past vector p(k) and future vector f(k); a linear solution is feasible for a nonlinear mapping function Map the low-dimensional original space R to a high-dimensional feature space F, and then analyze and model in this new space; suppose N samples x(t) are collected, the local kernel And That is, the Gaussian radial basis function (RBF), the global kernel And That is, the polynomial kernel satisfies:

[0080] p(k) = [x(k-q) T x(k-q+1) T …x(k-1) T ] T (1a)

[0081] f(k) = [x(k) T x(k+1) T …x(k+q-1) T ] T (1b)

[0082] Where q is the lag number of the past and future window;

[0083]

[0084] Where And v(i) and v(j) are arbitrary process samples, and the kernel parameter a r And a p Suitable for RBF and polynomial kernel;

[0085] In order to reconcile the intensity of And The method of weighted accumulation is given:

[0086]

[0087] Where the hybrid kernel Respectively represent the past and future vectors, and γ ∈ [0, 1] represents the mixing weight;

[0088] 2.2) Objective function of M2KCSVA: suppose The mean and covariance of

[0089]

[0090] Here the M2KCSVA aims at two objectives simultaneously; first, to capture the process dynamics by maximizing the correlation between and and second, the estimated features should remain smooth and not be disturbed by non-stationary fluctuations; the objective function for the M2KCSVA is thus given by:

[0091]

[0092]

[0093] where j s and h s are the projection vectors, and are partitioned into E k segments, where the respective mean and variance and their averages can be obtained from the above equations;

[0094] 2.3) The solution of equation (6) can be considered using the method of Lagrange multipliers:

[0095]

[0096] with Lagrange multipliers λ j and λ h ; here we take the derivative of (8) with respect to j s and h s and set them to zero:

[0097]

[0098] Introducing the properties of equation (6), pre-multiplying the above equations by and respectively, we get:

[0099]

[0100] It turns out that (6) is equivalent to finding the maximum of λ, while (11) gives it in a compact form:

[0101]

[0102] 3. The singular value decomposition (SVD) and iterative modeling procedure comprises the following steps:

[0103] 3.1) Using singular value decomposition, the symmetric matrix and are decomposed into:

[0104]

[0105] where and is a singular value matrix, and denotes the corresponding singular matrix;

[0106] 3.2) Taking into account that and contain elements that tend to zero, and the condensation is:

[0107]

[0108] where From the decomposition of the fragments, we have:

[0109]

[0110] 3.3) After that, the main information in and is merged into:

[0111]

[0112] 3.4) Finally, we bring equation (15) into equation (12), where we get:

[0113]

[0114] where the optimal j s and h s are equal to the eigenvectors corresponding to the largest eigenvalues found by solving the EVD problem; 3.5) The tightening and modeling process includes the following steps:

[0115] Given the weight matrix The CSVs are directly represented by and

[0116]

[0117] The residuals (ε p , ε f ) containing dynamic independent stationary and non-stationary information can be partitioned as:

[0118]

[0119] where I is the identity matrix.

[0120] 4. The stationary subspace analysis (SSA) includes the following steps:

[0121] According to the above considerations, the SSA is used to capture ​SSVs in:

[0122]

[0123] in, The projection matrix of the stationary part is given by [formula missing], and the projection matrix of the non-stationary part is given by [formula missing]. Leave.

[0124] 5. For example Figure 5 As shown, the comparison of the research results on the contribution of the difference between the two statistics and the index in this invention includes the following steps: 5.1) In order to process the periodically sampled data, the real-time past samples are... The superposition of p(k) in time k (1):

[0125] p(k)=[x(kq) T x(k-q+1) T …x(k-1) T ] T (1)

[0126] Where q is the lag number for the past and future windows;

[0127] Then the concentrated local kernel and global kernel The concentrated hybrid kernels were calculated separately.

[0128]

[0129] 5.2) In addition, CSVs and SSVs of M2KCSVA were constructed:

[0130]

[0131] 5.3) Fault detection statistics and Add them together to get the corresponding threshold. It follows a χ² distribution:

[0132]

[0133] In the formula g c =∑ Dc / 2μ Dc , g s =∑ Ds / 2μ Ds , μ Dc and μ Ds They represent and The mean, Σ Dc and ΣDs respectively, where the process is classified as abnormal if the computed statistics exceed a predefined threshold; otherwise, it is considered normal;

[0134] 5.4) When a process abnormality is identified, it subsequently enters the fault identification phase; in this phase, the contribution of the statistics is expressed as and

[0135]

[0136] where represents the Hadamard operator; in addition, to further improve the sensitivity of the contribution, inspired by the properties of the exponential function, the exponential differential contribution and is expressed as:

[0137]

[0138] where and denote the average contribution in training.

[0139] The present application proposes a new objective function based on M2KCSVA for mining CSVs from time series data. Then, the corresponding iterative data compression and modeling procedure is developed to obtain accurate CSVs estimates. The modeling efficiency improvement methods based on the singular value decomposition and the fault identification method based on the exponential differential contribution are proposed respectively, and are analyzed and mathematically discussed. The geometric properties of CSVs and SSVs are studied, and their mutual orthogonality is emphasized. This property means that both CSVs and SSVs can be explicitly and independently monitored. The effectiveness of the methods proposed herein is verified by the practical blast furnace ironmaking process experiment combined with the comprehensive parameter optimization process. By promoting accurate and timely fault detection and identification of abnormal furnace conditions, the methods herein enable the on-site engineers to quickly identify the source of the abnormality. This enables timely intervention and recovery, thereby improving the operation safety, ensuring the stability of the ironmaking products, and thus producing considerable economic benefits.

[0140] The above-described embodiments only express several embodiments of the present application, which are described in a more specific and detailed manner, but should not be understood as limiting the scope of the application. It should be noted that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the scope of protection of the present application. Therefore, the scope of protection of the present application should be subject to the appended claims.

Claims

1. A method for improved fault detection and identification with hybrid kernel assisted principal component analysis, characterized by the steps of The method comprises the following steps: The method uses the nonlinear characteristics of the mixed kernel based on multiple views under the weak stationary constraint to obtain the CSVs, so that the CSVs exhibit high time dependence and resistance to non-stationary interference; in addition, stationary information without autocorrelation in the residual is reserved, and the residual is further extracted by an SSA algorithm to generate SSVs; by calculating the contributions of two statistics and exponential differences, synchronous fault detection and identification can be realized to explicitly explain dynamic and static stationary information. The method for exploring typical stationary variables by using a mixed kernel comprises the following steps:

2. The method according to claim 1, characterized in that, 2.1) To deal with the complexity of blast furnace ironmaking process, firstly, a mixed kernel multi-view feature representation is performed, and the kernel trick is used to further capture the nonlinearity when exploring the temporal features of past vector p(k) and future vector f(k) through a linearly solvable nonlinear mapping function The low-dimensional original space R is mapped to a certain high-dimensional feature space F, and then analysis and modeling are performed in this new space: Assume N samples x(t) are collected, the local kernel and i.e. Gaussian Radial Basis Function (RBF), the global kernel and i.e. polynomial kernel satisfies: p(k) = [x(k-q) x(k-q+1)... x(k-1) ]T (1a) T x(k-q+1) T …x(k-1) T ] T (1a) f(k) = [x(k) T x(k+1) T …x(k+q-1) T ] T (1b) where q is the lag number of past and future windows; wherein and v(i) and v(j) are arbitrary process samples, the kernel parameter a r and a p Kernel applicable to RBF and polynomial To reconcile and the strengths, a method of weighted accumulation is given: where the mixed kernel respectively denote past and future vectors, and γ ∈ [0, 1] represents the mixing weight. 2.2) Objective function of M2KCSVA: Assume that the mean and covariance of are: Here the M2KCSVA aims at two objectives simultaneously; first, to capture the process dynamics by maximizing the correlation between and Second, the estimated features should remain smooth, not disturbed by non-stationary fluctuations; the objective function for the M2KCSVA is thus given by: where j s and h s are projection vectors, and are separated into E k segments, where the mean and variance of each and their average can be obtained from the above equations. The solution of formula (6) is obtained by using a Lagrange multiplier method to consider: The results show that (6) is equivalent to solving the maximum value of λ, and (11) is given in a compact form: with Lagrange multipliers λ j and λ h ; here we take the derivative of (8) with respect to j s and h s and set them to zero: Introducing the properties in (6) into the above equations, we have and We have The singular value decomposition and iterative modeling process comprises the following steps:

3. The method of claim 2, wherein, According to the decomposition of the segment, the following can be obtained: 3.1) Using singular value decomposition, the symmetric matrix and is decomposed into: wherein and is a singular value matrix, and denotes the corresponding singular matrix; 3.2) taking into account and containing elements tending to zero, and will condense to: wherein 3.4) Finally, formula (15) is brought into formula (12), and here the following is obtained: 3.3) After that, the main information in and are merged into: 3.5) The compacting and modeling process comprises the following steps: wherein the optimal j s and h s is equal to finding the eigenvector corresponding to the largest eigenvalue by solving the EVD problem; Wherein I is a unit matrix. Given weight matrix CSVs are represented by and directly: Residuals (ε p ,ε f ) containing dynamic independent stationary and non-stationary information can be partitioned into: The further extraction of the residual by using an SSA algorithm to generate SSVs comprises the following steps:

4. The method of claim 1, wherein, 5. The method according to claim 1, characterized in that, the calculation of the contributions of two statistics and exponential differences to realize fault detection and identification comprises the following steps: SSA is employed to capture SSVs in the context of wherein is the projection matrix for the stationary part, the projection matrix for the non-stationary part is left over. is the projection matrix for the stationary part, the projection matrix for the non-stationary part is left over. 5.2) In addition, the CSVs and SSVs of M2KCSVA are constructed: 5.1) To process periodically sampled data, past samples are overlaid in real time into p(k) in (1) at time k: p(k) = [x(k-q) x(k-q+1)... x(k-1)]T (2) where q is the lag number of past and future windows. T T T T where q is the lag number of past and future windows; then the local kernel and the global kernel are calculated respectively to get the hybrid kernel ​​​​ ​ 5.3) Add the failure detection statistics and to obtain the corresponding threshold subject to a χ 2 distribution: where g c =∑ Dc / 2μ Dc , g s =∑ Ds / 2μ Ds , μ D c and μ D s represent the mean of and , respectively, and∑ Dc and∑ Ds represent the respective variance; if the computed statistics exceed a predefined threshold, the process is classified as abnormal; otherwise, it is considered normal; 5.4) When a process abnormality is identified, the subsequent entry into the fault identification phase; in this phase, with sensitivity analysis, the contribution of the statistical quantity is expressed as and wherein represents the Hadamard operator; furthermore, in order to further improve the contribution sensitivity, the exponential difference contribution and is expressed as: wherein and denotes the average contribution in training.

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