Reduction KICA reconstruction fault diagnosis method based on double attributes

Abstract

The invention discloses a reduction KICA reconstruction fault diagnosis method based on double attributes, and belongs to the technical field of reliability engineering, and the method comprises the steps: constructing a normal sample set and historical fault samples in an industrial process; performing FVS undersampling processing on the normal sample set, constructing a reduction training set, and creating a KICA model based on the reduction training set; extracting a fault subspace and a fault amplitude of each fault type in the historical fault sample, and constructing a dual-attribute fault library; and fault type diagnosis is carried out based on the KICA model and the dual-attribute fault library. According to the method, a reduction training set is constructed through FVS undersampling, key fault information is reserved, meanwhile, the extracted feature subspace dimension is greatly reduced, then the calculation complexity is reduced, and the fault diagnosis performance is improved; the fault amplitude is introduced to serve as another attribute to assist fault diagnosis, the classification robustness is remarkably improved through the dual criterion mechanism, and then the diagnosis accuracy is improved.

Description

Technical Field

[0001] The present application relates to the field of reliability engineering technology, and in particular to a simplified KICA reconstruction fault diagnosis method based on dual attributes. Background Art

[0002] Fault reconstruction methods, a key technology in industrial process monitoring, derive their core concept from statistical variable analysis of historical fault data. This method extracts key features from historical fault data through singular value decomposition (SVD), constructs a fault subspace, and classifies fault samples based on the reconstruction error within the subspace. For nearly two decades, linear dimensionality reduction techniques, such as principal component analysis (PCA) and partial least squares (PLS), have dominated this field. However, these methods rely on control limits to perform statistical inference on process data, based on the assumption of a multivariate Gaussian distribution. In real industrial scenarios, complex process data often exhibit significant non-Gaussian characteristics, which reduces the accuracy of control limit estimation and, in turn, affects the reliability of fault diagnosis.

[0003] In reality, large and complex process data often deviate from a strict Gaussian distribution. For non-Gaussian processes, independent component analysis (ICA) can effectively extract independent components by mining the high-order statistical information of the data, making it a better choice. Furthermore, to overcome the complex nonlinear relationship between fault characteristics and data, the kernel independent component analysis (KICA) method was proposed, which maps data to a high-dimensional feature space through a kernel function to capture nonlinear characteristics. However, existing KICA-based methods still have two major challenges: first, the dimension of the fault subspace extracted by the nonlinear model is usually too high, resulting in a sharp increase in space consumption and computational complexity; second, the subsystems in complex industrial systems are highly coupled, and the characteristics of different fault types are prone to overlap, which makes the commonalities between the fault subspaces significant, causing uncertainty in the fault diagnosis process. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present application provides a simplified KICA reconstruction fault diagnosis method based on dual attributes, which solves the problems of space consumption and computational complexity caused by high-dimensional fault subspaces, and the significant commonality between fault subspaces due to fault overlap, which causes uncertainty in the fault diagnosis process.

[0005] In order to achieve the above-mentioned invention objectives, the technical solutions adopted in this application are:

[0006] This application provides a simplified KICA reconstruction fault diagnosis method based on dual attributes, including:

[0007] S1: Construct normal sample sets and historical fault samples in industrial processes;

[0008] S2: performing FVS undersampling processing on the normal sample set to construct a reduced training set, and creating a KICA model based on the reduced training set;

[0009] S3: extracting the fault subspace and fault amplitude of each fault type in the historical fault samples to construct a dual-attribute fault library;

[0010] S4: Perform fault type diagnosis based on the KICA model and the dual-attribute fault library.

[0011] Furthermore, in S2, the normal sample set is subjected to FVS undersampling processing to construct a reduced training set, including:

[0012] S201: Calculate the global fitness of each sample in the normal sample set, select a sample that can generate the maximum global fitness, and use the sample as the first feature vector;

[0013] S202: Increase the feature vector to a simplified training set X S , and delete the feature vector from the normal sample set;

[0014] S203: Iteratively select subsequent feature vectors: calculate the local fitness of the current sample for each remaining sample in the normal sample set, select the sample that can provide the minimum local fitness, add the sample to the simplified training set, and delete the sample from the normal sample set until the simplified training set X S The square matrix of the eigenvector dot product of Irreversible, where Φ S For X S The kernel matrix, is the transpose of the kernel matrix, S stands for simplification, and T stands for transpose;

[0015] S204: output the reduced training set;

[0016] S205: Creating a KICA model based on the reduced training set.

[0017] Furthermore, the S201 specifically includes:

[0018] S2011: Select N samples from the normal samples for training to form a training set X = [x1, ..., x N ];

[0019] S2012: Any sample x in the training set i The estimated kernel vector of is linearly represented as:

[0020]

[0021] in, is the estimated kernel vector, is the reduced training set X S The kernel matrix, is the simplified training set X S The kernel vector, x i S To reduce the training set The i-th sample in x i is the i-th sample in the training set X, i=1,...,N, is x i The coefficient vector of a ii is the i-th coefficient vector, ii=i1,...,iN S , N is the total number of training set samples, N S Reduce the total number of training set samples, N S ≤N;

[0022] S2013: Calculating the actual kernel vector With the estimated kernel vector The collinearity factor δ i :

[0023]

[0024] in, is the actual kernel vector;

[0025] S2014: with δ i The partial derivative of is zero as a condition, calculate the coefficient vector a i :

[0026]

[0027] Among them, (Φ S T Φ S ) -1 is the invertible matrix of the square matrix of eigenvector dot products;

[0028] S2015: (Φ S T Φ S ) -1 Existence as a condition, obtain the coefficient vector a i Minimize δ i :

[0029]

[0030] in, is the transposed vector of the actual kernel vector;

[0031] S2016: As the conversion condition, the converted minimized δ is obtained i :

[0032]

[0033] in, is the radial basis kernel function, σ is the kernel parameter, and Represent the reduced training set X S The pth and qth samples in, 1≤p≤N S ,1≤q≤N S , K S,S is the reduced training set X S The square matrix of the dot product of the eigenvectors of is x i The dot product vector between and the eigenvector;

[0034] S2017: Calculate all samples x i Minimize δ on ∈X i The reduced training set X S :

[0035]

[0036] in, is the square matrix K of the eigenvector dot product S,S The reversible matrix of

[0037] S2018: Calculate the X S The global fitness and local fitness of and J S (x i ):

[0038]

[0039] in, is the global fitness, J S (x i ) is the local fitness;

[0040] S2019: Selection produces the maximum global fitness and use the sample as the first feature vector.

[0041] Furthermore, the S3 specifically includes:

[0042] S301: extracting fault subspace;

[0043] S302: solving the fault amplitude based on the fault subspace;

[0044] S303: Constructing a Bayesian binary classifier based on the fault amplitude;

[0045] S304: Associating the fault subspace with the Bayesian binary classifier to construct a dual-attribute fault library.

[0046] Furthermore, extracting the fault subspace in S301 specifically includes:

[0047] S3011: Select the historical fault set of the kth label fault as follows: Calculate the kernel matrix of the historical fault set to obtain the independent component subspace:

[0048]

[0049] Where k = 1, 2, ..., c, c is the total number of tag failures, is the kernel matrix, A is the mixing matrix, Q is the unmixing matrix, is the independent component subspace;

[0050] S3012: Perform singular value decomposition on the independent component subspace to extract the independent component subspace:

[0051]

[0052] in, is the left singular matrix, D is the singular value matrix, S is the right singular matrix, u i It is arranged in descending order of singular values in the order of i=1,...,N S singular vectors;

[0053] S3013: Select front θ k The singular vector u corresponding to the largest singular value i , construct the fault subspace Among them, θ k It should be set to make the failure reconstruction rate FRR reach The minimum dimension of FRR can be defined as:

[0054] FRR=N fn / N f ×100%

[0055] Among them, θ k represents the dimension of the fault subspace, is the preset value of the fault reconstruction rate, N fn Refers to the number of fault samples whose reconstructed statistics are less than the control limit, N f Refers to the total number of fault samples.

[0056] Furthermore, solving the fault amplitude based on the fault subspace in S302 specifically includes:

[0057] S3021: Record the kernel vector of the fault sample as the sum of the fault-free reference component and the fault component:

[0058] k=k * +Ξ k f

[0059] in, and is the fault subspace and fault magnitude, k * is the fault-free part, k is the core vector;

[0060] S3022: Estimation of fault magnitude by least squares optimization;

[0061] Select the statistic as I 2 , calculate the extreme value of the fault amplitude f:

[0062]

[0063] The fault amplitude is obtained by analyzing the extreme value:

[0064]

[0065] in, is the transpose of the fault subspace, I 2 is a statistic.

[0066] Furthermore, in S303, a Bayesian binary classifier is constructed based on the fault amplitude, specifically including:

[0067] S3031: Reconstruct all fault samples of a certain type of fault using all fault subspaces and record the corresponding fault amplitudes as positive samples, where the fault amplitude of the k-th fault sample is:

[0068]

[0069] Among them, N k represents the number of all label samples in the history of the k-th fault, f k,1 is the first fault amplitude of the kth fault sample, is the Nth kth fault sample k The fault amplitude of each, k represents the kth fault;

[0070] S3032: Use all fault subspaces to reconstruct fault samples that are not of a certain type of fault and record the corresponding fault amplitude as a negative sample, where the fault amplitude of the non-k-th fault sample is:

[0071]

[0072] Among them, N nk represents the number of all historical label samples that are not the k-th fault, f nk,1 is the fault amplitude of the first non-k-th fault sample, is the Nth non-kth fault sample nk The fault amplitude of each, nk represents the non-kth fault;

[0073] S3033: Constructing a Bayesian binary classifier based on the positive samples and negative samples;

[0074] Calculating quilt space Ξ k The probability that the fault magnitude f of the reconstructed sample x belongs to the kth fault is:

[0075]

[0076] Among them, c k and c nk Refers to the kth fault and non-kth fault respectively, p(c k ) and p(c nk ) refer to the prior probabilities of positive samples and negative samples respectively, p(f|c k ) and p(f|c nk ) refer to the conditional probabilities of positive samples and negative samples respectively, Represents the number of all label samples N from the history of the kth fault k and represents the number of all historical label samples N that are not the kth fault nk The minimum value between and F k and F nk The deviation matrix, and They are and The invertible matrix of the deviation matrix, F k is the fault amplitude of the kth fault sample, F nk is the fault amplitude of the non-k-th fault sample, and f is the quilt space Ξ k The fault magnitude of the reconstructed sample x, f k,i is the fault amplitude of the i-th fault sample of the k-th fault sample, f nk,i is the fault amplitude of the i-th non-k-th fault sample.

[0077] Furthermore, the fault type diagnosis in S4 based on the KICA model and the dual-attribute fault library specifically includes:

[0078] S401: Based on the KICA model and the dual-attribute fault library, obtain the kernel vector of the test fault sample, calculate the fault amplitude and the statistics after fault reconstruction of each test fault sample, where the fault subspace Ξ k The fault magnitude and reconstructed statistics are:

[0079]

[0080] Among them, x new is the test fault sample, k new is x new The kernel vector after centering and normalization, is the fault-free part of the test fault sample kernel vector, k f new,k is the fault part of the test fault sample kernel vector, f new,k is the fault subspace of the test fault sample Ξ k The fault amplitude;

[0081] S402: Calculate the number of subspaces under the control limit that can be reconstructed into the test fault sample:

[0082]

[0083] Among them, I(.) is the labeling function, is the statistic after fault reconstruction, is the control limit of the KICA model;

[0084] S403: Determine the fault type based on the number of subspaces in step S402;

[0085] If C new =0, then test fault sample x new The fault type belongs to the unprecedented fault type;

[0086] If C new =1, then test fault sample x new The fault type is the fault type corresponding to the subspace reconstructed under the control limit:

[0087]

[0088] Among them, Γ(x new ) refers to x new Type of fault;

[0089] If C new >1, a Bayesian binary classifier is used to analyze the fault type based on the dual-attribute fault library.

[0090] Furthermore, if C new>1, the Bayesian binary classifier is used to analyze the fault based on the dual-attribute fault library, including:

[0091] A1: Calculate the reconstruction x new The posterior probability of

[0092] For each candidate fault type, the fault magnitude The posterior probability p is calculated by step S3033. new :

[0093] p new =[p(x∈c (1) ),...,p(x∈c (α) )]

[0094] Among them, p(x∈c (j) ) is the test fault sample x, and the corresponding fault type belongs to fault c j＝1,...,α The failure probability of j is , j represents the jth failure type, and α is the total number of failure types;

[0095] A2: Determine the fault type based on the posterior ratio;

[0096] Find the fault type x new Belongs to the fault type corresponding to the maximum a posteriori probability:

[0097]

[0098] Among them, p(x new ∈c (.) ) is the test fault sample x new The posterior probability of .

[0099] The beneficial effects of the present application are: the present application provides a simplified KICA reconstruction fault diagnosis method based on dual attributes, which adopts FVS undersampling to construct a simplified training set, while retaining key fault information, greatly reducing the dimension of the extracted feature subspace, thereby reducing the computational complexity and improving the fault diagnosis performance; each fault is characterized by two attributes such as fault subspace and fault amplitude, wherein the fault subspace is preliminarily classified through reconstruction error, and the fault amplitude is input into the Bayesian classifier as a supplementary feature to further distinguish the fault types with overlapping subspaces. This dual judgment mechanism significantly improves the classification robustness, thereby improving the diagnostic accuracy; in addition, by deeply integrating fault reconstruction with pattern classification, the advantages are complementary, and it has the ability to identify unseen faults, thereby enhancing the efficiency and accuracy of fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other embodiments can also be obtained based on these drawings.

[0101] Figure 1 A flowchart of a simplified KICA reconstruction fault diagnosis method based on dual attributes provided in an embodiment of the present application.

[0102] Figure 2 Schematic diagram of fault diagnosis results using different methods in the Tennessee-Eastman experiment provided in the embodiments of the present application.

[0103] Figure 3 A structural schematic diagram of the rocket servo system provided in an embodiment of the present application.

[0104] Figure 4 This is a fault reconstruction diagram used in the rocket servo system provided in an embodiment of the present application.

[0105] Figure 5 A diagnostic diagram of using a Yes classifier for re-diagnosis in a rocket servo system provided in an embodiment of the present application.

[0106] Figure 6 Diagram of the diagnostic results of the rocket servo system provided in an embodiment of the present application. DETAILED DESCRIPTION

[0107] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field based on this application are within the scope of protection of this application.

[0108] In order to more clearly illustrate the simplified KICA reconstruction fault diagnosis method based on dual attributes provided in an embodiment of the present application, an illustrative explanation of the preliminary knowledge of the simplified KICA reconstruction fault diagnosis method based on dual attributes provided in an embodiment of the present application will be given below. It can be understood that the following example is only a preliminary knowledge of the simplified KICA reconstruction fault diagnosis method based on dual attributes provided in an embodiment of the present application, and the following example does not impose any restrictions on this.

[0109] Based on this, the embodiment of the present application provides a simplified KICA reconstruction fault diagnosis method based on dual attributes, which can be found in Figure 1 , Figure 1FIG. 1 is a flow chart of a simplified KICA reconstruction fault diagnosis method based on dual attributes provided by an embodiment of the present application, including:

[0110] S1: Construct a normal sample set and historical fault samples in the industrial process.

[0111] S2: Perform FVS undersampling processing on the normal sample set to construct a reduced training set, and create a KICA model based on the reduced training set.

[0112] Furthermore, in S2, the normal sample set is subjected to FVS undersampling processing to construct a reduced training set, including:

[0113] S201: Calculate the global fitness of each sample in the normal sample set, select a sample that can generate the maximum global fitness, and use the sample as the first feature vector;

[0114] S202: Increase the feature vector to a simplified training set X S , and delete the feature vector from the normal sample set;

[0115] S203: Iteratively select subsequent feature vectors: calculate the local fitness of the current sample for each remaining sample in the normal sample set, select the sample that can provide the minimum local fitness, add the sample to the simplified training set, and delete the sample from the normal sample set until the simplified training set X S The square matrix of the eigenvector dot product of Irreversible, where Φ S For X S The kernel matrix, is the transpose of the kernel matrix, S stands for simplification, and T stands for transpose;

[0116] S204: output the reduced training set;

[0117] S205: Creating a KICA model based on the reduced training set.

[0118] In one possible embodiment, the first eigenvector is calculated as follows:

[0119] S2011: Select N samples from the normal samples for training to form a training set X = [x1, ..., x N ];

[0120] In a possible embodiment, a number of input data x are collected from the industrial process to form a training set X = [x1, ..., x N ].

[0121] S2012: Reduced training set for a given feature vector: Any other sample x i The kernel vector of can be estimated as the following linear combination:

[0122]

[0123] in, is the estimated kernel vector, is the reduced training set X S The kernel matrix, is the simplified training set X S The kernel vector, x i S To reduce the training set The i-th sample in x i is the i-th sample in the training set X, i=1,...,N, is x i The coefficient vector of a ii is the i-th coefficient vector, ii=i1,...,iN S , N is the total number of training set samples, N S Reduce the total number of training set samples, N S ≤N.

[0124] S2013: A factor δ i is defined to measure the actual kernel vector With the estimated kernel vector Collinearity between:

[0125]

[0126] A small delta i The value indicates and There is a small angle between them, which means a strong collinearity. Thus, the goal is to find the coefficient vector a i To minimize δ i .

[0127] S2014: Setting δ i The partial derivative of is zero, so:

[0128]

[0129] In the formula, (Φ S T Φ S ) -1 is the invertible matrix of the square matrix of eigenvector dot products;

[0130] Among them, if FVs are linearly independent, then exist.

[0131] S2015: Substitute the above formula into δ i In the solution formula, we get:

[0132]

[0133] in, is the transposed vector of the actual kernel vector;

[0134] S2016: As the conversion condition, δ i The solution formula can be rewritten as:

[0135]

[0136] in, is the radial basis kernel function, σ is the kernel parameter, and Represent the reduced training set X S The pth and qth samples in, 1≤p≤N S ,1≤q≤N S , K S,S is the reduced training set X S The square matrix of the dot product of the eigenvectors of is x i The dot product vector between and the eigenvector.

[0137] S2017: Find the best solution for all samples x i The set X of minimizing formulas on ∈X S :

[0138]

[0139] in, is the square matrix K of the eigenvector dot product S,S The reversible matrix of

[0140] S2018: For each candidate sample x i , calculate its global fitness, select the one that can maximize J S * Sample x k , as the first eigenvector, and add it to the reduced training set X S , At the same time, delete the x from the normal sample set X k , the formula for maximizing global fitness is as follows:

[0141]

[0142] in, is the global fitness, JS (x i ) is the local fitness, N is the total number of samples;

[0143] S2019: Selection produces the maximum global fitness and use the sample as the first feature vector.

[0144] In one embodiment of the present application, iteratively selects subsequent feature vectors: for each remaining sample X in X i , calculate the current X S J S (x i ), select the one that can provide the minimum J S (x i ) of the sample x k1 :J S (x k1 )=min({J S (x i )}),x i ∈X, the x k1 Increase to the simplified training set X S :X S ={X S ,x k1}, and delete the x from the normal sample set X k1 , until K S,S Irreversible, where Φ S For X S The kernel matrix, is the transpose of the kernel matrix, S stands for simplification, T stands for transpose, minimizing J S (x i ) is calculated as follows:

[0145]

[0146] Among them, J S (x i ) is the local fitness, is x i and the dot product vector between FVs, is the reduced training set X S The invertible matrix of the kernel matrix, is x i The transposed dot product vector of the dot product vector between and FVs;

[0147] Output reduced training set where N S ≤N.

[0148] In one embodiment of the present application, creating a KICA model based on the reduced training set is specifically as follows:

[0149] Mapping the reduced training set to a high-dimensional feature space through a kernel function to obtain a high-dimensional score matrix corresponding to the reduced training set;

[0150] Extracting independent components of samples in the reduced training set using the FastICA algorithm;

[0151] Calculates systematic and unsystematic statistics and determines systematic and unsystematic control limits using kernel density.

[0152] KICA is an extension of ICA for solving nonlinear problems. Given a complex system with n samples and m variables, the reduced training set of the system under normal operation is assumed to be:

[0153]

[0154] in is the i-th sample, and Refers to the jth variable.

[0155] The core of KICA is the projection sample matrix X S To high-dimensional feature space Where Φ(.) is a nonlinear projection function. Since it is difficult to express Φ(.) intuitively, the radial basis function is usually used to calculate the kernel matrix K = Φ T Φ, whose (i,j)th element can be calculated as k(x i ,x j )=exp(-||x i -x j || 2 / σ), where σ is the kernel parameter.

[0156] After centering and normalization, the kernel matrix K is eigenvalue decomposed to understand the correlation:

[0157] μ i v i =Kv i

[0158] where μ i and v i are eigenvalues and eigenvectors respectively. Usually, the largest p eigenvalues and corresponding eigenvectors satisfy the condition is used to construct the whitening matrix:

[0159]

[0160] where H=[v1,v2,...,v p ] and Λ=diag(μ1,μ2,...,μ p). The whitened score matrix can be expressed as

[0161]

[0162] In order to maximize the independent and sufficient non-Gaussian properties, the FastICA algorithm is implemented to directly calculate the matrix W. The independent components of a certain sample x can be expressed as:

[0163]

[0164] in is the layer matrix, k x is the kernel vector.

[0165] To monitor the systematic and unsystematic changes in nonlinear processes, two statistics are defined:

[0166]

[0167] Where Σ=Q T Q is the coefficient matrix and I is the identity matrix. Since it is not restricted to any specific distribution, the kernel density estimation KDE is used to determine the control limits. and SPE limit .

[0168] Furthermore, the S3 specifically includes:

[0169] S301: Extracting a fault subspace.

[0170] Furthermore, S3011: select the historical fault set of the k-th label fault as: Calculate its kernel matrix, and the independent component subspace can be expressed as:

[0171]

[0172] Where k = 1, 2, ..., c, c is the total number of tag failures, is the kernel matrix, A is the mixing matrix, Q is the unmixing matrix, is the independent component subspace;

[0173] S3012: Yes Perform singular value decomposition and select the first θ k The singular vector u corresponding to the largest singular value i , construct the fault subspace The extracted subspace is:

[0174]

[0175] Where, is the left singular matrix, D is the singular value matrix, S is the right singular matrix, ui It is arranged in descending order of singular values in the order of i=1,...,N S singular vectors;

[0176] S3013: Select front θ k The singular vector u corresponding to the largest singular value i , construct the fault subspace Among them, θ k It should be set to make the failure reconstruction rate FRR reach The minimum dimension of FRR can be defined as:

[0177] FRR=N fn / N f ×100%

[0178] Where θ k represents the dimension of the fault subspace, is the preset value of the fault reconstruction rate, N fn Refers to the number of fault samples whose reconstructed statistics are less than the control limit, N f Refers to the total number of fault samples.

[0179] S302: Calculate the fault amplitude based on the fault subspace.

[0180] Specifically, S3021: record the kernel vector of the fault sample as the fault-free reference component k * and fault component Ξ k The sum of f:

[0181] k=k * +Ξ k f

[0182] in, and is the fault subspace and fault magnitude, k * is the fault-free part, k is the core vector;

[0183] S3022: Estimate the fault magnitude f through least squares optimization. The formula is as follows:

[0184]

[0185] in, is a statistic, For the fault-free part, is the kernel vector, and are the fault subspace and fault magnitude.

[0186] The analytical solution of the fault amplitude f is obtained from the above formula:

[0187]

[0188] Among them, k With Ξ k is the fault subspace and the transpose of the fault subspace, k is the kernel vector, and f is the fault subspace and the fault magnitude.

[0189] S303: Construct a Bayesian binary classifier based on the fault amplitude.

[0190] Specifically: S3031: reconstruct all fault samples of a certain type of fault using all fault subspaces and record the corresponding fault amplitudes as positive samples, where the fault amplitude of the k-th fault sample is:

[0191]

[0192] Among them, N k represents the number of all label samples in the history of the k-th fault, f k,1 is the first fault amplitude of the kth fault sample, is the Nth kth fault sample k The fault amplitude of each, k represents the kth fault;

[0193] S3032: Use all fault subspaces to reconstruct fault samples that are not of a certain type of fault and record the corresponding fault amplitude as a negative sample, where the fault amplitude of the non-k-th fault sample is:

[0194]

[0195] Among them, N nk represents the number of all historical label samples that are not the k-th fault, f nk,1 is the fault amplitude of the first non-k-th fault sample, is the Nth non-kth fault sample nk The fault amplitude of each, nk represents the non-kth fault;

[0196] S3033: Constructing a Bayesian binary classifier based on the positive samples and negative samples;

[0197] Calculating quilt space Ξ k The probability that the fault magnitude f of the reconstructed sample x belongs to the kth fault is:

[0198]

[0199] Among them, c k and c nk Refers to the kth fault and non-kth fault respectively, p(c k ) and p(c nk ) refer to the prior probabilities of positive samples and negative samples respectively, p(f|c k) and p(f|c nk ) refer to the conditional probabilities of positive samples and negative samples respectively,

[0200] Represents the number of all label samples N from the history of the kth fault k and represents the number of all historical label samples N that are not the kth fault nk The minimum value between and F k and F nk The deviation matrix, and They are and The invertible matrix of the deviation matrix, F k is the fault amplitude of the kth fault sample, F nk is the fault amplitude of the non-k-th fault sample, and f is the quilt space Ξ k The fault magnitude of the reconstructed sample x, f k,i is the fault amplitude of the i-th fault sample of the k-th fault sample, f nk,i is the fault amplitude of the i-th non-k-th fault sample.

[0201] Furthermore, the fault type diagnosis in S4 based on the KICA model and the dual-attribute fault library specifically includes:

[0202] S401: Based on the KICA model and the dual-attribute fault library, obtain the kernel vector of the test fault sample, calculate the fault amplitude and the statistics after fault reconstruction of each test fault sample, where the fault subspace Ξ k The fault magnitude and reconstructed statistics are:

[0203]

[0204] Among them, x new is the test fault sample, k new is x new The kernel vector after centering and normalization, is the fault-free part of the test fault sample kernel vector, k f new,k is the fault part of the test fault sample kernel vector, f new,k is the fault subspace of the test fault sample Ξ k The fault amplitude, I new For all subspaces {Ξ1,...,Ξ c} Construct k in sequence new All reconstructed I 2 Statistics;

[0205] S402: Calculate the number of subspaces under the control limit that can be reconstructed into the test fault sample:

[0206]

[0207] Among them, I(.) is the labeling function, is the statistic after fault reconstruction, is the control limit, if If established, otherwise

[0208] S403: Determine the fault type based on the number of subspaces in step S402;

[0209] In one possible embodiment, when analyzing I new There are three situations:

[0210] 1) C new = 0. This means that these subspaces cannot effectively reflect x new Fault information, at this time, the sample x new The fault type belongs to the unprecedented fault type;

[0211] 2) C new = 1. This means that there is only one subspace that can reconstruct x new To control limit This shows that this subspace can uniquely reflect the fault characteristics. new Classified as the fault type corresponding to this subspace, that is,

[0212]

[0213] Where Γ(x new ) refers to x new Type of fault;

[0214] 3) C new >1. This means that there are multiple subspaces that can reconstruct x new To control limit Below. At this point, further analysis based on the Bayesian binary classifier in the fault database is needed. Assume x new Can be subspace {Ξ (1) ,...,Ξ (α) Refactor x new To control limit below, and the corresponding fault magnitude is recorded as Especially, here (1) Unlike Ξ1, Ξ (1) Represents reconfigurable x new To control limit The first subspace below, which may be {Ξ1,...,Ξ c}. Then, based on the trained BBC in the fault library, x belonging to each fault type new The probability of can be calculated as follows:

[0215] i) For each candidate fault type, the fault magnitude Substituted into the following formula to calculate the posterior probability p new =[p(x∈c (1) ),...,p(x∈c (α) )]; where p(x∈c (j) ) is the test fault sample x, and the corresponding fault type belongs to fault c j＝1,...,α The failure probability of j is , j represents the jth failure type, and α is the total number of failure types;

[0216] Assume that the quilt space Ξ k The fault magnitude of the reconstructed sample x is f, and the probability that it belongs to the kth fault can be expressed as:

[0217]

[0218] Where p(c k ) and p(c nk ) refer to the prior probabilities of positive samples and negative samples respectively. Since the samples have been balanced, their values are equal to 0.5 in this study. k ) and p(f|c nk ) refer to the conditional probabilities of positive samples and negative samples respectively.

[0219] Because F k and F nk The specific distribution of is unknown, and the Parzen window (a non-parametric kernel density estimation method) is used here to estimate the probability density as follows:

[0220]

[0221] in and F k and F nk The deviation matrix.

[0222] For example, if x new can be reconstructed by subspaces Ξ2 and Ξ4 new To control limit Below, if the candidate fault types are fault 2 and fault 4, then there is (1) =Ξ2,Ξ (2) =Ξ4, p(x∈c(1) )=p(x∈c2),p(x∈c (2) )=p(x∈c4) holds. According to the formula, x new The probabilities of fault 2 and fault 4 can be calculated as:

[0223]

[0224] ii) Compare the posterior probabilities, x new Belongs to the fault type corresponding to the maximum a posteriori probability, that is,

[0225]

[0226] In this embodiment, the method proposed in this application is verified by data collected from the Tennessee-Eastman Experiment (TEP). TEP is a well-known benchmark test process for verifying fault monitoring and diagnostic performance. It contains 21 types of faults, recorded as IDV (1)-IDV (21). In this paper, IDVs (2, 4, 8, 11, 14) are considered to be historical faults, while IDV (18) is treated as an unseen fault. IDV (2) and IDV (8) are related to the feed concentration in process 4, while IDV (4, 11, 14) are all related to reactor cooling water. It can be expected that the samples from these faults may show overlap of Chinese medicinal materials, so they are selected to verify the fault diagnosis accuracy.

[0227] A total of 1460 normal samples were collected, of which 960 were used for training. These training samples were undersampled to create a reduced training set of 195 samples for building the KICA model, and the remaining 500 samples were used to calculate the control limits. In addition, a dual-attribute fault library was constructed, containing 480 samples for each fault type.

[0228] In the experiments, the following parameters were set: For the KSFDA method, the tuning parameter β was chosen to be 0.5, and the kernel parameter α was set to 5.4, both of which are taken from the original literature. For the RRFS and RD-KICA methods, the kernel parameter α was set to 3052, which is the result of tabu optimization. The CNN-LSTM method consists of a three-layer convolutional network and a two-layer LSTM network. The number of convolutional kernels is 3264 and 128, with a size of 1×3. The number of unit nodes in the LSTM layer is 128. Specifically, the default values for the confidence level and reconstruction rate are 0.95 in all experiments.

[0229] 1) Experiment on Fault Diagnosis Accuracy

[0230] In order to clearly show the fault diagnosis results of different methods, Figure 2 Visualize them as a confusion matrix in Figure 2Schematic diagram of the fault diagnosis results using different methods in the Tennessee-Eastman experiment provided in the embodiment of the present application. The experimental accuracy is summarized in Table 1. KSFDA, ENBS and CNN-LSTM show good diagnostic accuracy for historical faults. However, due to their lack of identification mechanism for unseen faults, all samples of IDV (18) are misdiagnosed. In contrast, RRFS can effectively identify 77.13% of unseen fault samples, and its diagnostic accuracy for historical faults is poor. The proposed RD-KICA combines the advantages of fault reconstruction method and classification method, achieving high average diagnostic accuracy and the ability to identify unseen faults.

[0231] Table 1 Fault diagnosis accuracy of TEP

[0232]

[0233] Although the RD-KICA fault diagnosis accuracy shown in Table 1 is not the highest across all fault scenarios, it demonstrates significant stability. Compared to RRFS, the RD-KICA method improves the average diagnostic accuracy for historical faults by 42.65%, indicating that adding size as another feature enhances diagnostic accuracy. Compared to the KSFDA, ENBS, and CNN-LSTM methods, the RD-KICA method effectively identifies 82.88% of unseen faults while maintaining good diagnostic accuracy for historical faults. Furthermore, the diagnostic accuracy of the RD-KICA method is comparable to, or even slightly higher than, that of the RD-KICA-without-FVS method. These findings demonstrate that undersampling the training set does not compromise fault diagnosis accuracy.

[0234] 2) Computational complexity experiment

[0235] In this section, the computation time (CT) of the six methods is compared. CT is the time consumed in online diagnosis of each sample. Equipped with the same computer: Intel Core Tmi7-1165G7 processor (2.8GHz), 16GB of RAM, the different algorithms perform 60 online diagnosis procedures. The results of these methods are shown in Table 2.

[0236] Table 2 Online diagnosis time for each sample

[0237]

[0238] It can be found that ENBC shows the highest CT because it classifies high-dimensional samples without dimensionality reduction. The RD-KICA-without-FVS method and the RRFS method, which use nonlinear models for fault reconstruction, maintain relatively high CT because their subspace dimensions match the number of training samples. According to Table 2, the CT of the RD-KICA method varies greatly for different faults. For example, it only takes 0.2145ms to diagnose a sample of IDV(8), while IDV(8) takes 1.1625ms. This difference mainly comes from its diagnosis strategy. In the diagnosis process, if C in the formula new =0 or C new = 1, the diagnosis type can be determined directly; and if C new >1, the BBC needs to be activated for further diagnosis. This additional step increases the total CT. RD-KICA is an advanced version of RD-KICA-without-FVS that adds undersampling, resulting in a CT of approximately one-third of that of RD-KICA-without-FVS.

[0239] Combined with the previous diagnostic experimental results, the following findings emerge: Compared to the reconstruction-based RRFS method, the proposed RD-KICA method substantially improves the diagnostic accuracy for historical faults, indicating that adding size as another fault feature has a positive effect on fault diagnosis accuracy. Furthermore, compared to pattern recognition-based methods such as KSFDA, ENBS, and CNN-LSTM, the proposed RD-KICA method possesses the ability to identify unseen faults. Furthermore, ablation experiments using RD-KICA without FVS demonstrate that undersampling with FVS improves online fault diagnosis performance without compromising diagnostic accuracy.

[0240] In this embodiment, the rocket servo system is used to verify the online fault diagnosis process of the method described in this application, including fault reconstruction, re-diagnosis using BBC, and diagnostic decision-making. The experimental data comes from the semi-physical simulation platform, such as Figure 3 As shown, Figure 3 A schematic diagram of the structure of a rocket servo system provided in an embodiment of the present application. The servo system includes dual-channel actuator data, such as displacement, velocity feedback, and nozzle swing angle, totaling 32 process variables. In this experiment, five fault modes were injected, as shown in Table 3. Among them, faults F1 to F4 are known faults, and F4 is a composite of F1 and F3, so there is a significant overlap between F1, F3, and F4. F5* is considered an unknown fault in this experiment.

[0241]

[0242] In this experiment, 500 samples were collected under fault conditions F1-F4, of which 300 samples were used to extract fault subspaces, namely Ξ1, Ξ2, Ξ3 and Ξ4. The remaining 200 samples were used to evaluate the diagnostic performance. In addition, 200 samples of fault F5 were collected to test the proposed method's ability to identify unknown faults. The RD-KICA method proposed in this chapter was used to perform online diagnosis on the test samples, and the fault reconstruction was as follows: Figure 4 As shown, Figure 4 This is a fault reconstruction diagram used in the rocket servo system provided in the embodiment of the present application. The local details are magnified in the black dotted box. Figure 4 Reconstructed statistics of sample points 1-200 and 401-600 Both are less than the control limit (The yellow line is below the red dashed line), indicating that subspace Ξ4 incorrectly eliminates the sample fault effects of faults 1 and 3. This is because subspace Ξ4 of F4 (the composite fault of F1 and F3) covers all fault information of F1 and F3. In contrast, the fault effects of sample points 601-800 can only be effectively eliminated by Ξ4, while neither Ξ1 nor Ξ3 is effective. For sample points 801-1000 of the unknown fault F5*, only one sample point has the reconstruction statistic Below the control limit, the rest are above the control limit, which indicates that no subspace can cover all the fault information of these samples. This reconstruction result is consistent with the fault injection situation in Table 3.

[0243] To solve the problem of mis-elimination of fault effects caused by overlap, the proposed RD-KICA method introduces a Bayesian classifier for re-diagnosis, such as Figure 5 As shown, Figure 5 A diagnostic diagram of the rocket servo system using the Yes classifier for re-diagnosis provided in the embodiment of the present application. Sample points 1 to 200 are enlarged for clearer observation. The vertical axis in the figure represents the probability that the sample belongs to a specific fault category. Sample point 168 is used as an example for detailed analysis. Figure 4 It can be seen that the reconstruction statistic of the sample is and All less than Therefore, we only need to calculate the probability that the sample belongs to F1 and F4, which are 0.889957% and 0.0404448% respectively. Based on this calculation result, the sample can be diagnosed as fault 1, as shown in Figure 6 As shown, Figure 6 Diagram of the diagnostic results of the rocket servo system provided in an embodiment of the present application.

[0244] exist Figure 6In the figure, the horizontal axis represents the sampling time, and the vertical axis represents the diagnostic label. Specifically, the Y value corresponding to sampling point 168 in the figure is 1, which means that the sampling point is diagnosed as fault F1. It can be clearly observed from the figure that most samples have been accurately diagnosed, while there are also a small number of misdiagnoses. According to statistical data, the diagnostic accuracy of RD-KICA in this online diagnosis process reached 93.20%. In addition, for the sampling points of unknown faults (i.e., sampling points 800 to 1000), only one sample was misdiagnosed, and the rest were correctly identified as unknown faults.

[0245] The present application provides a simplified KICA reconstruction fault diagnosis method based on dual attributes. The method adopts FVS undersampling to construct a simplified training set. While retaining key fault information, the dimension of the extracted feature subspace is greatly reduced, thereby reducing the computational complexity and improving the fault diagnosis performance. Each fault is characterized by two attributes such as fault subspace and fault amplitude. Among them, the fault subspace is preliminarily classified through reconstruction error, and the fault amplitude is input into the Bayesian classifier as a supplementary feature to further distinguish the fault types with overlapping subspaces. This dual judgment mechanism significantly improves the classification robustness, thereby improving the diagnostic accuracy. In addition, by deeply integrating fault reconstruction with pattern classification, the advantages are complementary, and it has the ability to identify unseen faults, thereby enhancing the efficiency and accuracy of fault diagnosis.

[0246] Each embodiment in this specification is described in a related manner. Similar parts between the embodiments can be referred to in conjunction with each other. Each embodiment focuses on the differences from other embodiments. The above description is only a preferred embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of this application are included in the scope of protection of this application.

Claims

1. A simplified KICA reconstruction fault diagnosis method based on dual attributes, characterized by: include: S1: Construct normal sample sets and historical fault samples in industrial processes; S2: performing FVS undersampling processing on the normal sample set to construct a reduced training set, and creating a KICA model based on the reduced training set; S3: extracting the fault subspace and fault amplitude of each fault type in the historical fault samples to construct a dual-attribute fault library; S4: Perform fault type diagnosis based on the KICA model and the dual-attribute fault library.

2. The dual-attribute-based simplified KICA reconstruction fault diagnosis method according to claim 1 is characterized in that: In S2, the normal sample set is subjected to FVS undersampling processing to construct a reduced training set, including: S201: Calculate the global fitness of each sample in the normal sample set, select a sample that can generate the maximum global fitness, and use the sample as the first feature vector; S202: Increase the feature vector to a simplified training set X S , and delete the feature vector from the normal sample set; S203: Iteratively select subsequent feature vectors: calculate the local fitness of the current sample for each remaining sample in the normal sample set, select the sample that can provide the minimum local fitness, add the sample to the simplified training set, and delete the sample from the normal sample set until the simplified training set X S The square matrix of the eigenvector dot product of Irreversible, where Φ S For X S The kernel matrix, is the transpose of the kernel matrix, S stands for simplification, and T stands for transpose; S204: output the reduced training set; S205: Creating a KICA model based on the reduced training set.

3. The dual-attribute-based simplified KICA reconstruction fault diagnosis method according to claim 2 is characterized in that: The S201 specifically includes: S2011: Select N samples from the normal samples for training to form a training set X = [x1, ..., x N ]; S2012: Any sample x in the training set i The estimated kernel vector linear representation of : in, is the estimated kernel vector, is the reduced training set X S The kernel matrix, is the simplified training set X S The kernel vector, x i S To reduce the training set The i-th sample in x i is the i-th sample in the training set X, i=1,...,N, is x i The coefficient vector of a ii is the i-th coefficient vector, ii=i1,...,iN S , N is the total number of training set samples, N S Reduce the total number of training set samples, N S ≤N; S2013: Calculating the actual kernel vector With the estimated kernel vector The collinearity factor δ i : in, is the actual kernel vector; S2014: with δ i The partial derivative of is zero as a condition, calculate the coefficient vector a i : Among them, (Φ S T Φ S ) -1 is the invertible matrix of the square matrix of eigenvector dot products; S2015: (Φ S T Φ S ) -1 Existence as a condition, obtain the coefficient vector a i Minimize δ i : in, is the transposed vector of the actual kernel vector; S2016: As the conversion condition, the converted minimized δ is obtained i : in, is the radial basis kernel function, σ is the kernel parameter, and Represent the reduced training set X S The pth and qth samples in, 1≤p≤N S ,1≤q≤N S , K S,S is the reduced training set X S The square matrix of the dot product of the eigenvectors of is x i The dot product vector between and the eigenvector; S2017: Calculate all samples x i Minimize δ on ∈X i The reduced training set X S : in, is the square matrix K of the eigenvector dot product S,S The reversible matrix of S2018: Calculate the X S The global fitness and local fitness of and J S (x i ): in, is the global fitness, J S (x i ) is the local fitness; S2019: Selection produces the maximum global fitness and use the sample as the first feature vector.

4. The dual-attribute-based simplified KICA reconstruction fault diagnosis method according to claim 1 is characterized in that: The S3 specifically includes: S301: extracting fault subspace; S302: solving the fault amplitude based on the fault subspace; S303: constructing a Bayesian binary classifier based on the fault amplitude; S304: Associating the fault subspace with the Bayesian binary classifier to construct a dual-attribute fault library.

5. The dual-attribute-based simplified KICA reconstruction fault diagnosis method according to claim 4 is characterized in that: Extracting the fault subspace in S301 specifically includes: S3011: Select the historical fault set of the kth label fault as follows: Calculate the kernel matrix of the historical fault set to obtain the independent component subspace: Where k = 1, 2, ..., c, c is the total number of tag failures, is the kernel matrix, A is the mixing matrix, Q is the unmixing matrix, is the independent component subspace; S3012: Perform singular value decomposition on the independent component subspace to extract the independent component subspace: in, is the left singular matrix, D is the singular value matrix, S is the right singular matrix, u i It is arranged in descending order according to the singular value i=1,...,N S singular vectors; S3013: Select front θ k The singular vector u corresponding to the largest singular value i , construct the fault subspace Among them, θ k It should be set to make the failure reconstruction rate FRR reach The minimum dimension of FRR can be defined as: FRR=N fn / N f ×100% Among them, θ k represents the dimension of the fault subspace, is the preset value of the fault reconstruction rate, N fn Refers to the number of fault samples whose reconstructed statistics are less than the control limit, N f Refers to the total number of fault samples.

6. The dual-attribute-based simplified KICA reconstruction fault diagnosis method according to claim 4 is characterized in that: Solving the fault amplitude based on the fault subspace in S302 specifically includes: S3021: Record the kernel vector of the fault sample as the sum of the fault-free reference component and the fault component: k=k * +Ξ k f in, and is the fault subspace and fault magnitude, k * is the fault-free part, k is the core vector; S3022: Estimation of fault magnitude by least squares optimization; Select the statistic as I 2 , calculate the extreme value of the fault amplitude f: The fault amplitude is obtained by analyzing the extreme value: in, is the transpose of the fault subspace, I 2 is a statistic.

7. The dual-attribute-based simplified KICA reconstruction fault diagnosis method according to claim 4 is characterized in that: The step S303 constructs a Bayesian binary classifier based on the fault amplitude, specifically including: S3031: Reconstruct all fault samples of a certain type of fault using all fault subspaces and record the corresponding fault amplitudes as positive samples, where the fault amplitude of the k-th fault sample is: Among them, N k represents the number of all label samples in the history of the k-th fault, f k,1 is the first fault amplitude of the kth fault sample, is the Nth kth fault sample k The fault amplitude of each, k represents the kth fault; S3032: Use all fault subspaces to reconstruct fault samples that are not of a certain type of fault and record the corresponding fault amplitude as a negative sample, where the fault amplitude of the non-k-th fault sample is: Among them, N nk represents the number of all historical label samples that are not the k-th fault, f nk,1 is the fault amplitude of the first non-k-th fault sample, is the Nth non-kth fault sample nk The fault amplitude of each, nk represents the non-kth fault; S3033: Constructing a Bayesian binary classifier based on the positive samples and negative samples; Calculating quilt space Ξ k The probability that the fault magnitude f of the reconstructed sample x belongs to the kth fault is: Among them, c k and c nk Refers to the kth fault and non-kth fault respectively, p(c k ) and p(c nk ) refer to the prior probabilities of positive samples and negative samples respectively, p(f|c k ) and p(f|c nk ) refer to the conditional probabilities of positive samples and negative samples respectively, Represents the number of all label samples N from the history of the kth fault k and represents the number of all historical label samples N that are not the kth fault nk The minimum value between and F k and F nk The deviation matrix, and They are and The invertible matrix of the deviation matrix, F k is the fault amplitude of the kth fault sample, F nk is the fault amplitude of the non-k-th fault sample, and f is the quilt space Ξ k The fault magnitude of the reconstructed sample x, f k,i is the fault amplitude of the i-th fault sample of the k-th fault sample, f nk,i is the fault amplitude of the i-th non-k-th fault sample.

8. The dual-attribute-based simplified KICA reconstruction fault diagnosis method according to claim 1, characterized in that: The fault type diagnosis in S4 is performed based on the KICA model and the dual-attribute fault library, specifically including: S401: Based on the KICA model and the dual-attribute fault library, obtain the kernel vector of the test fault sample, calculate the fault amplitude and the statistics after fault reconstruction of each test fault sample, where the fault subspace Ξ k The fault magnitude and reconstructed statistics are: Among them, x new is the test fault sample, k new is x new The kernel vector after centering and normalization, is the fault-free part of the test fault sample kernel vector, k f new,k is the fault part of the test fault sample kernel vector, f new,k is the fault subspace of the test fault sample Ξ k The fault amplitude; S402: Calculate the number of subspaces under the control limit that can be reconstructed into the test fault sample: Among them, I(.) is the labeling function, is the statistic after fault reconstruction, is the control limit of the KICA model; S403: Determine the fault type based on the number of subspaces in step S402; If C new =0, then test fault sample x new The fault type belongs to the unprecedented fault type; If C new =1, then test fault sample x new The fault type is the fault type corresponding to the subspace reconstructed under the control limit: Among them, Γ(x new ) refers to x new Type of fault; If C new >1, a Bayesian binary classifier is used to analyze the fault type based on the dual-attribute fault library.

9. The dual-attribute-based simplified KICA reconstruction fault diagnosis method according to claim 8, characterized in that: If C new >1, the Bayesian binary classifier is used to analyze the fault based on the dual-attribute fault library, including: A1: Calculate the reconstruction x new The posterior probability of For each candidate fault type, the fault magnitude The posterior probability p is calculated by step S3033. new : p new =[p(x∈c (1) ),...,p(x∈c (α) )] Among them, p(x∈c (j) ) is the test fault sample x, and the corresponding fault type belongs to fault c j＝1,...,α The failure probability of j is , j represents the jth failure type, and α is the total number of failure types; A2: Determine the fault type based on the posterior ratio; Find the fault type x new Belongs to the fault type corresponding to the maximum a posteriori probability: Among them, p(x new ∈c (.) ) is the test fault sample x new The posterior probability of .

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