A system fault evolution feature data extraction method

Abstract

The application relates to the technical field of fault process basic data extraction, and provides a system fault evolution characteristic data extraction method, which is used for extracting more effective and representative system fault evolution data as basic data for evaluating the function state of a system, and proposes a system fault evolution characteristic data extraction method based on KLPP and KPCA; the basic data is the key to evaluation, object screening is realized through KLPP, factor dimension reduction is realized through KPCA, and a characteristic data matrix is obtained; the method is used for characteristic data extraction in a system fault process, so that a more representative characteristic data matrix is formed. The system fault evolution characteristic data extraction method can extract data, so that the basic data participating in analysis can be reduced, the analysis efficiency is improved, and the accuracy of analysis results is improved.

Description

Technical Field

[0001] This invention relates to the field of basic data extraction technology for fault processes, and in particular to the extraction of system fault evolution feature data through factor dimensionality reduction and object screening, providing a method for extracting system fault evolution feature data. Background Technology

[0002] System failure evolution exists in all types of systems and is a process of change in the system's ability to perform its intended function under the influence of multiple factors. Every system is an organic whole that exists to achieve its intended function. Therefore, studying, judging, and predicting system failure evolution has become a key research topic in various disciplines, especially safety science and systems science. A specific moment in the system failure evolution process is the system's functional state at that moment. During system design, analytical methods can be used to quantitatively study the probability of system failure, where the results mainly depend on system components and structure. However, during operation, the system's functional state depends on the factors that occur during that period and their fluctuations. The system failure evolution process is the response of the system's inherent internal characteristics to external factors during operation. Therefore, studying the system failure evolution process during operation is closer to reality. Moreover, due to the correlation and complexity of the factors' influence, analytical studies are difficult to implement, and various evaluation methods are typically used to study the system's functional state, such as various safety evaluations and reliability evaluations. These evaluations are generally based on the measured system functional states at various moments, thereby instantiating objects to form a basic data matrix. Each row of this matrix represents different factors, and each column represents different objects, forming the basic data form of the evaluation method. Clearly, these objects and factors play different roles in representing the system failure evolution process, making the selection of these factors and objects a crucial issue. This involves dimensionality reduction of factors in the basic data matrix and object selection.

[0003] Numerous studies have been conducted on various evaluation methods and basic data. These studies have achieved good results in their respective fields, demonstrating that different methods have varying degrees of applicability depending on the field and data characteristics. Researching these methods at the system level is necessary, especially for constructing reasonable basic data, which is of practical significance. Because different factors have different effects on evaluation, and data may be missing, identifying characteristic objects and factors can reduce the amount of basic data required for analysis, thereby improving analytical efficiency and reducing the impact of non-essential factors and data on the results.

[0004] To achieve the above objectives, it is necessary to conduct characteristic studies on the factors and objects in the evaluation basis data matrix. However, the existing technology lacks a reliable and effective method for extracting system fault evolution characteristic data, resulting in low analysis efficiency and poor accuracy of analysis results. Summary of the Invention

[0005] The purpose of this invention is to provide a method for extracting system fault evolution feature data, so as to solve the problem that the lack of reliable and effective methods for extracting system fault evolution feature data in the prior art leads to low analysis efficiency and poor accuracy of analysis results.

[0006] This invention uses KPCA to reduce the dimensionality of factors and identify characteristic factors, and uses KLPP to filter objects and identify characteristic objects, thereby obtaining a feature data matrix. The method for extracting feature data of system fault evolution provided by this invention is used to extract feature data during system fault processes, thereby forming a more representative feature data matrix.

[0007] This invention provides a method for extracting system fault evolution feature data. To extract more effective and representative system fault evolution data as the basic data for evaluating the functional state of the system, a method based on KLPP and KPCA is proposed. The basic data is the key to the evaluation. KLPP is used to screen objects, and KPCA is used to reduce the dimensionality of factors to obtain a feature data matrix. This matrix is ​​used to extract feature data during the system fault process, thereby forming a more representative feature data matrix.

[0008] Research on system failures and the problems encountered:

[0009] In safety science, various methods for studying, assessing, and predicting system safety and functionality play a crucial role. However, the inherent characteristics of system failure processes present some challenges to related research. Theoretically, research on system safety or reliability can be divided into two technical paths based on the system boundary: internal and external.

[0010] Within a system, the probability of failure stems from the failure status of its constituent components and the system structure they form. Quantitative calculations are typically performed here, as system failure variations are relatively clear, resulting in a quantitative analytical model. However, a drawback is that component failure characteristics and system structure are determined during the design phase, and the analyzed failure results may be biased in the face of changes in factors during system operation. This is particularly true when unforeseen interactions between components occur, unexpected factors arise, or known factors exceed their intended scope, leading to erroneous results.

[0011] Internal analysis methods require knowledge of the system's internal structure, which may be difficult to achieve in practice. Therefore, it is also necessary to understand the system's fault characteristics from the outside. In this case, the system's internal structure is a black box, and fault characteristic analysis is based on the effect of factor changes on the system and the system's response characteristics after being affected by these factors. Because the system's internal structure is unknown, it is difficult to generate analytical results. Due to the uncertainty of factor changes and the limited perception and processing capabilities of current technologies, the dimensionality of the basic data becomes chaotic. Similarly, the system's response under these factors is subject to monitoring and subjective human interpretation biases, making the correspondence between factor data and system fault data unclear. When predicting system faults, safety, or reliability, the system's performance has not yet occurred, and the aforementioned correspondence does not exist. These problems bring difficulties to the evaluation of system fault states, and evaluation can only be carried out through human experience or a combination of experience and analytical methods. For example, a system safety evaluation system composed of data, evaluation standards, and algorithms.

[0012] Therefore, there are still many problems in evaluating system failures, safety, or reliability. Analytical methods struggle to cope with changes in factors during operation, while evaluation methods face difficulties in terms of basic data requirements and the classification of factors and results. However, any system is an organic whole built to fulfill its intended function. The system's ability to perform its intended function must be guaranteed, that is, its reliability must be ensured, which corresponds to its failure capability. Complete reliability and complete failure are non-existent states for a running system. Generally, the system's ability to perform its intended function varies between failure and reliability, or is a superposition of failure and reliability states. Safety evaluations are necessary and unavoidable for any system during operation. This is crucial for the development of safety science and for ensuring system safety.

[0013] Regarding the system failure evolution process and basic data matrix:

[0014] As mentioned above, analytical methods that focus on the internal workings of a system are inaccurate for studying actual system failure processes. In contrast, changes in external influencing factors and system failure states during system operation better reveal the characteristics of system failures.

[0015] The authors define the changes in system faults during system operation as a system fault evolution process. This describes the change in the system's ability to perform its intended functions under the influence of multiple factors. Correspondingly, the system functionality of the system fault evolution process at a given moment is defined as the system functional state. The system fault evolution process emphasizes the overall nature of the fault process, while the system functional state emphasizes the characteristics of the system fault at a specific moment; both are descriptions of the same problem from different perspectives.

[0016] The problems with both internal analysis and external evaluation stem from the complexity of the system failure evolution process. Structurally, the system failure evolution process includes experienced events, influencing factors, logical relationships, and evolutionary conditions. Events are the key nodes in the evolution process and are necessary conditions for its existence. Influencing factors are the direct causes affecting the evolution process and are the driving force of evolution. Logical relationships are the interactions between events. Evolutionary conditions are the conditions under which causal events lead to resultant events. When events and factors are determined, logical relationships and evolutionary conditions are also basically determined. Hierarchically, it includes an evolution layer, an object layer, a factor layer, a factor phase layer, and a factor phase value layer. Each layer contains several objects, the states of which depend on the states of objects in the lower layers. The states of objects in the upper layers are represented by the superposition of the states of objects in the lower layers, realized through the wave function form of quantum mechanics. This complex, nonlinear, black-box relationship makes it difficult for existing methods to analyze effectively.

[0017] Accurate and suitable basic data is fundamental for the accurate analysis, evaluation, and prediction of system failure evolution. However, obtaining representative data is challenging, especially given the lack of response results when system failures occur under predictive conditions. Since the core of the system failure evolution process in terms of structure and hierarchy consists of events and factors, the authors use objects as a synthesis of these. All factor values ​​at a given moment in the system failure evolution process constitute an object, representing the system's functional state at that moment. The set of objects at each moment in the evolution then forms the basic data for analysis, i.e., the object set. If the time intervals for measuring the system failure evolution process are infinitesimally small, then all objects at all moments in the evolution process are obtained, forming an object set. Using this object set as the basic data for research is the most comprehensive approach. However, the actual measurement intervals cannot be infinitesimally small, and the number of objects cannot be infinite; therefore, such an object set does not exist. On the other hand, if the measurements of all objects correspond to the occurrence times of all key events, meaning all objects represent characteristic system functional states, an optimal object set is also formed. However, in practice, it is difficult to determine the corresponding moments for these objects. Therefore, the system failure evolution process is generally measured at equidistant time intervals to obtain the object set. These objects cannot possibly include all objects with characteristics, because characteristic objects can appear between two points in time.

[0018] This is a suitability problem for various evaluation object sets, or more specifically, a problem of extracting characteristic data of system failure evolution. Evaluation data typically used for system failure, safety, and reliability consists of objects, labeled with multiple factors, forming the foundational data for the evaluation—the object set. The object set is represented by a matrix, where rows represent factor sets, and each row represents a factor dimension. The columns represent measurement moments in the system failure evolution process, with each moment representing an object. Each row of the matrix is ​​a vector of factor values ​​for all objects at that factor; each column is a representation vector of that object across all factor dimensions. For system failure evolution, the more factors and objects there are, the larger the matrix becomes. Once the factors' discriminative power over the objects is satisfied, the matrix should be simplified to obtain the most representative feature data matrix for the evolution.

[0019] Since the feature data matrix has only two dimensions—factors and objects—its formation can only be achieved by identifying the feature factors and feature objects. Feature factors are those factors from the original factor set that play a decisive role and have the greatest distinguishing effect on the objects. Feature objects are the objects corresponding to the system's functional state at the moment of a significant event during the system's failure evolution. Cluster analysis is used to determine the central objects of each class. These objects represent the characteristics of a class of objects, thus characterizing the features of a stage in the evolution process. The method involves identifying feature factors and feature objects to construct the feature data matrix, which is ultimately used for system functional state evaluation.

[0020] It is important to note that the basic data matrix can form a feature data matrix, and the proposed method can still yield higher-order feature data matrices based on this feature data matrix. Theoretically, the higher the iteration order of the basic data matrix, the more abstract the resulting feature data matrix becomes, and the more information is lost. It is recommended to iterate only the feature data matrix once, or to specify the number of feature factors and feature objects as required, thereby determining which factors and objects belong to the feature factors and objects.

[0021] Let the set of factors influencing the system failure evolution process be F = {f1, ..., f2}. M}, m=1,…,M,f m ∈F, M is the number of factors. The system fault evolution process is measured at N time points, forming an object set O = {o1,…,o...} N}, n=1,…,N,o n ∈O, where N is the number of samples. Object o n It is a vector composed of factor values. It is object o n In factor f m The factor values ​​below. The resulting basic data matrix is ​​Γ. M×N As shown in Table 1.

[0022] Table 1 Basic Data Matrix Γ M×N

[0023]

[0024] Table 1 Basic Data Matrix Γ M×N The value of each factor in the middle needs to be normalized. The data was normalized to [0,1]. Subsequent studies used the normalized data.

[0025] Basic principles and feature extraction of KPCA:

[0026] Kernel principal component analysis (KPCA) is a nonlinear extension of principal component analysis (PCA). While PCA is linear, KPCA can represent the overall nonlinear relationships in the data. A nonlinear mapping function ξ is introduced to map the data from the original space to a higher-dimensional space. This is because any vector in the higher-dimensional space is linearly represented by all the samples in that space.

[0027] Suppose an M (M>m) dimensional vector θ i (i = 1, ..., m) are eigenvectors in the high-dimensional space, λ i (i=1,…,m) are the eigenvalues, and the PCA in the high-dimensional space is shown in equation (1).

[0028] ξ(Γ)ξ(Γ) T θ i =λ i θ i (1)

[0029] The eigenvector θ i (i=1,…,m) is linearly represented by ξ(Γ), as shown in (2).

[0030]

[0031] θ i Substituting (i=1,…,m) into equation (2), and multiplying both sides of the equation by ξ(Γ) on the left, we get equation (3).

[0032] ξ(Γ) T ξ(Γ)ξ(Γ) T ξ(Γ)α=λ i ξ(Γ) T ξ(Γ)α (3)

[0033] Construct the kernel matrix K KPCA=ξ(Γ) (where Γ is a symmetric matrix). There are many kernel functions, including linear kernel functions, polynomial kernel functions, Gaussian radial basis function kernel functions, and multilayer perceptron kernel functions. K is obtained from equation (3). KPCA 2 α=λ i K KPCA α, i.e., K KPCA α=λ i α, this is similar to the solution formula for PCA. The final objective function of KPCA is maxtr(ξ(Γ)). T K KPCA K KPCA Given ξ(Γ), find K. KPCA The factor corresponding to the largest eigenvalue is the characteristic factor in the basic data matrix Γ. The above process is represented by the function KPCA() as shown in equation (4).

[0034] [θ KPCA ,λ KPCA ]=KPCA(Γ,opt) (4) where: θ KPCA λ represents the set of eigenvectors corresponding to the characteristic factors. KPCA This represents the set of eigenvalues ​​corresponding to the feature factors; KPCA() is the KPCA function; Γ is the basic data matrix mentioned above; opt is the parameter set, including the kernel function and weight pattern.

[0035] The obtained λ KPCA Sort in descending order, based on the number of required feature factors. Take the one that is earlier The factors corresponding to each characteristic value are what we are looking for. This will form A feature data matrix of dimension, i.e. Ultimately, the goal is to reduce the dimensionality of factors and achieve feature factor extraction.

[0036] Basic principles and feature object extraction of KLPP:

[0037] KPCA determines the maximum value of the objective function for global data. It analyzes the effects of different factors on all objects, achieving factor dimensionality reduction. However, it is not very effective in identifying feature objects. This is because feature objects are determined by the relationship between an object and its nearest neighbors, i.e., whether the object can represent the distribution characteristics of the set of nearest objects. Therefore, it is necessary to consider the distribution characteristics of local objects in the nearest neighborhood, making the Kernel Locality Preserving Projection (KLPP) method more suitable. By improving feature extraction and dimensionality reduction methods, KLPP is incorporated into the objective function of KPCA from manifold learning. It achieves linear computation while preserving the distribution characteristics of local objects, reflecting the local features of the data. Therefore, KLPP is suitable for the underlying data matrix Γ. M×N The process involves filtering objects to form a set of feature objects, thereby enabling feature object extraction.

[0038] Study the basic process of KLPP, and define O = {o1,…,o N Mapped to First, construct a set of nearest neighbor objects using the KNN algorithm, as shown in equation (5).

[0039]

[0040] In the formula: L() is the result of the k-nearest neighbor set of the object; KNN() is the k-nearest neighbor algorithm; k is the number of nearest neighbor objects.

[0041] The weights are determined, and W is a weight symmetric matrix of order N×N, where W ij It is o i to o j The weight. If o i to o j If there is no connection, then w ij =0; if there are multiple connections, then If there is one and only one connection, then w ij =1.

[0042] Determine the feature mapping and set the mapping function ζ, as shown in the derivation process of equation (3) to obtain equation (6).

[0043] ζ(Γ) T ζ(Γ)Lζ(Γ) T ζ(Γ)α=λζ(Γ) T ζ(Γ)Dζ(Γ)ζ(Γ)α (6)

[0044] In the formula: D is a diagonal matrix. L is a Laplacian matrix, L = DW.

[0045] Let ξ(Γ) be the kernel matrix K. KLPP Let be the kernel matrix formed by one of the four kernel functions mentioned above. Then the objective function of KLPP is mintr(ζ(Γ)). T K KLPP LK KLPP ζ(Γ)), st.L=DW, ζ(Γ) T K KLPP LK KLPP ζ(Γ) = I. Find K. KLPP The object corresponding to the largest eigenvalue is the feature object in the basic data matrix Γ. The above process is represented by the function KLPP() as shown in equation (7).

[0046] [θ KLPP ,λ KLPP ]=KLPP(Γ,W,opt,) (7)

[0047] In the formula: θ KLPP λ is the set of feature vectors corresponding to the feature object. KLPP Γ is the set of feature values ​​corresponding to the feature object; KLPP() is the KLPP function; Γ is the basic data matrix; W is the weight; opt is the set of parameters, including the kernel function used and the nearest neighbor clustering method KNN.

[0048] The obtained λ KLPP Sort in descending order, based on the number of required feature objects. Take before The object corresponding to each feature value is the desired one. This forms a column. The feature data matrix, i.e. Ultimately, the goal is to reduce the number of objects and achieve feature object extraction.

[0049] Regarding the construction of feature data extraction methods:

[0050] The above KPCA method has completed Ultimately, this achieves the goal of reducing factor dimensionality and enabling factor extraction from feature data. The KLPP method described above completes this process. Ultimately, the goal is to reduce the number of objects and achieve object extraction of feature data.

[0051] The mathematical model of the final system fault evolution feature data extraction method is shown in Equation (8).

[0052]

[0053] In the formula: num() represents the dimension of the vector.

[0054] Equation (8) will use the basic data matrix Γ M×NTransform into a feature data matrix Feature data extraction was achieved. The size of the basic data matrix was reduced from M×N to... This reduces the size of the matrix used as the basis for analysis. This preserves both the overall distribution characteristics of important factors and the distribution characteristics of key objects that are locally representative.

[0055] Feature data extraction rate Ω is Alternatively, the number of feature factors can be determined based on the specified extraction rate Ω. and number of feature objects This method provides an effective way to reduce and retain the characteristics of the original data, and helps in the research, prediction and evaluation of system fault evolution process and system functional status.

[0056] The beneficial technical effects of the present invention are as follows: by applying the system fault evolution feature data extraction method provided by the present invention, data can be extracted, thereby reducing the amount of basic data involved in the analysis, improving analysis efficiency, and enhancing the accuracy of the analysis results.

[0057] It should be noted that, unless otherwise specified, all letters in this invention are intermediate variables in the calculation process. Attached Figure Description

[0058] Figure 1 The numerical changes of the voltage factor at each sampling point are shown;

[0059] Figure 2 The numerical variation of the current factor at each sampling point is shown;

[0060] Figure 3 The numerical changes of temperature at each sampling point are shown;

[0061] Figure 4 The values ​​of humidity at each sampling point are shown.

[0062] Figure 5 The numerical changes of the air pressure factor at each sampling point are shown;

[0063] Figure 6 The numerical changes of vibration factors at each sampling point are shown. Detailed Implementation

[0064] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0065] The embodiments provided in this application take an electrical system as the research object. The functionality of this electrical system is affected by six factors, F={f1,f2,f3,f4,f5,f6}. f1 is voltage, ranging from [12,15]V; f2 is current, ranging from [0.7,0.85]mA; f3 is temperature, ranging from [11,24]℃; f4 is humidity, ranging from [77,94]%; f5 is air pressure, ranging from [100,105]KPa; f6 is vibration, ranging from [185,236]Hz.

[0066] For this electrical system, if 50 measurements are performed within a certain period of time, with each measurement occurring at a different time, 50 objects are formed, namely O = {o1, ..., o2}. 50 Each object contains the above six factor values, forming the basic data matrix Γ. 6×50 Since the matrix is ​​large, the values ​​of each factor at different sampling points (objects) are displayed in graphical form, such as... Figures 1 to 6 As shown.

[0067] First, KPCA is used to extract feature factors. 6×50 Substituting the basic data matrix into equation (4), the Gaussian kernel function is used to set the number of feature factors. Given 4, we obtain λ. KPCA The eigenvalues ​​are sorted in descending order as λ6, λ5, λ4, λ3, λ2, and λ1. Therefore, the factors corresponding to the first four eigenvalues ​​are taken as the characteristic factors, i.e. Γ 6×50 Extracting factor features

[0068] Feature object extraction is implemented using KLPP. 6×50 Substituting the basic data matrix into equation (7), the Gaussian kernel function is adopted; the number of feature factors The weighting is determined by the program (assuming the object's contribution is greater than 0.05); the weighting pattern uses HeatKernel. λ is obtained. KLPPThe eigenvalues ​​are sorted in descending order as follows: 46, 39, 40, 37, 38, 35, 26, 24, 16, 17, 11, 12. The feature objects corresponding to these eigenvalues ​​are... Γ 6×50 Extracting object features

[0069] The factors represented by the rows of the final feature data matrix, from top to bottom, are as follows: The columns in the matrix represent objects from left to right as follows: The extraction rate Ω = (4×12) / (6×50)×100% = 16%, which indicates that similar conclusions can be obtained by using only 16% of the basic data.

Claims

1. A method for extracting system fault evolution feature data, characterized in that, Object selection is achieved through KLPP, and factor dimensionality reduction is achieved through KPCA to obtain a feature data matrix; Feature data extraction method construction; let the set of factors influencing the system fault evolution process be . , , , It is the number of factors; in The system fault evolution process is measured at each moment, forming a set of objects. , , , It refers to the number of samples; objects. It is a vector composed of factor values. ; It is an object In factors The following factor values; thus forming the basic data matrix. As shown in the table below; Basic data matrix The basic data matrix in the table The value of each factor in the middle needs to be normalized. Normalization Subsequent studies used normalized data. Completed using the KPCA method Ultimately, this achieves the goal of reducing factor dimensionality and enabling factor extraction from feature data. （4） In the formula: This represents the set of feature vectors corresponding to the feature factors; This represents the set of eigenvalues ​​corresponding to the characteristic factors; For KPCA functions; for abbreviation; It is a set of parameters, including the kernel function and weight pattern; Received Sort in descending order, based on the number of required feature factors. Take the one that is earlier The factors corresponding to each characteristic value are what we are looking for; this will form A feature data matrix of dimension, i.e. ; The KLPP method has been completed. Ultimately, this achieves the goal of reducing the number of objects and enabling object extraction of feature data; （7） In the formula: The set of feature vectors corresponding to the feature object; The set of feature values ​​corresponding to the feature object; For KLPP functions; As weight; It is a set of parameters, including the kernel function used and the nearest neighbor clustering method KNN; Received Sort in descending order, based on the number of required feature objects. Take the front The object corresponding to each feature value is the desired one; forming a column as follows: The feature data matrix, i.e. ; The mathematical model for the final system fault evolution feature data extraction method is shown below; In the formula: num() represents the dimension of the vector; Feature data extraction rate for According to the specified extraction rate Determine the number of characteristic factors and the number of feature objects , .

2. The method for extracting system fault evolution feature data according to claim 1, characterized in that, The KPCA method has been completed. Specifically, it includes: Suppose an M (M>m) dimensional vector These are feature vectors in a high-dimensional space. For eigenvalues, PCA in high-dimensional space is shown in equation (1); （1） eigenvectors use Linear representation, as shown in (2); （2） Will Substitute into equation (1) and multiply both sides of the equation on the left. Then we get equation (3); （3） Constructing the kernel matrix Kernel functions include linear kernel functions, polynomial kernel functions, Gaussian radial basis function kernel functions, and multilayer perceptron kernel functions; obtained from equation (3) ,Right now The final objective function of KPCA is: ;beg The factor corresponding to the largest eigenvalue is the basic data matrix. Characteristic factors; characteristic factors The above process is represented by a function. As shown in equation (4).

3. The method for extracting system fault evolution feature data according to claim 2, characterized in that, The KLPP method has been completed. Specifically, it includes: Will Mapped to First, construct a set of nearest neighbor objects, which is implemented using the KNN algorithm, as shown in equation (5); （5） In the formula: For objects Nearest neighbor set results; for Nearest neighbor algorithm; The number of nearest neighbors; Determine the weights. It is a weighted symmetric matrix. Rank, among which yes arrive The weight; if arrive No connection If there are multiple connections... If there is one and only one connection, then ; Determine the feature mapping, and set the mapping function. As shown in the derivation process of equation (3), equation (6) is obtained. （6） In the formula: D is a diagonal matrix. ; It is a Laplacian matrix. ; set up For the kernel matrix Let be the kernel matrix formed by one of the following: linear kernel function, polynomial kernel function, Gaussian radial basis function, or multilayer perceptron kernel function; then the objective function of KLPP is... , , ;beg The object corresponding to the largest eigenvalue is the basic data matrix. Feature objects in; feature objects The above process is represented by a function. As shown in equation (7).

4. The method for extracting system fault evolution feature data according to claim 1, characterized in that, Used for analyzing electrical systems; The functionality of the electrical system is affected by six factors. ; The voltage range is [12, 15]V; The current is in the range [0.7, 0.85] mA; Temperature, range [11, 24]℃; Humidity, range [77, 94]%; The pressure is [100, 105] kPa. For vibration, the range is [185,236] Hz; The electrical system was measured 50 times within a set time period, with each measurement taken at a different time, resulting in 50 corresponding objects. Each object contains the above six factor values, forming the basic data matrix. ; First, KPCA is used to extract feature factors; Substituting the basic data matrix into equation (4), and using the Gaussian kernel function, the number of feature factors is set. The value is 4, so we get The eigenvalues ​​are sorted in descending order as follows: , , , , , Therefore, the factors corresponding to the first four characteristic values ​​are taken as characteristic factors, that is... ; Will Extracting factor features ; Feature object extraction is achieved using KLPP; Substitute the basic data matrix into equation (7) and use the Gaussian kernel function; number of feature factors The program is user-defined, assuming the object's contribution is greater than 0.05; the weighting mode is HeatKernel; the results are obtained. The eigenvalues ​​are sorted in descending order as follows: 46, 39, 40, 37, 38, 35, 26, 24, 16, 17, 11, 12; the corresponding feature objects are: ;Will Extracting object features ; The factors represented by the rows of the final feature data matrix, from top to bottom, are as follows: The columns in the matrix represent objects from left to right as follows: Extraction rate =16%, indicating that similar conclusions can be obtained by using only 16% of the basic data.

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