A method for determining weights of factors influencing fault evolution based on semi-supervised learning

Abstract

The application relates to the technical field of system fault analysis in the safety field, and provides a fault evolution influence factor weight determination method based on semi-supervised learning, which is used for determining the influence of each factor on evolution for an object set obtained by studying an actual system fault evolution process, and proposes a factor weight determination method based on a semi-supervised learning method. A seven-step factor weight determination method is constructed, including establishing a basic data matrix, determining an object weight set, establishing a labeled data matrix, establishing an unlabeled data matrix, determining an object weight set, determining a characteristic vector and a characteristic value, and determining the weight of each factor. The method is used for weight determination of fault evolution influence factors. The weight determination method of the fault evolution influence factors based on the semi-supervised learning provided by the application can reliably and effectively determine the weight of the fault evolution influence factors, so that measures can be taken to control the evolution process according to the size of the weight.

Description

Technical Field

[0001] This invention relates to the field of system fault analysis technology in the field of safety, and in particular to the determination of the weights of factors influencing fault evolution, providing a method for determining the weights of factors influencing fault evolution based on semi-supervised learning. Background Technology

[0002] System failure evolution is the ability of a system to achieve its intended function under the influence of multiple factors; it is an inherent attribute of any system. The evolutionary process has a complex structure and hierarchy, leading to its diversity and uncertainty. Furthermore, the evolutionary process is the influence of internal system characteristics on external characteristics. Since internal characteristics are relatively fixed, while external characteristics are variations in the operating environment, evolution also exhibits certain regularities. These regularities stem from the stability of internal characteristics, while the diversity and uncertainty arise from changes in the operating environment. The types and numerical changes of factors during system operation are key to influencing the system failure evolution process; that is, factor changes are the driving force of system evolution. Studying the influence of factors on the system failure evolution process has become a focus of research in various fields. Especially in fields related to safety, reliability, and systems science, the main issue is the impact of the number, types, and changes of factors on the system. For system failure evolution, different factors and their changes inevitably lead to changes in system functionality, i.e., different system responses. This is reflected in the weight of factors influencing the evolutionary process, i.e., the issue of factor weights in the system failure evolution process. Currently, the common method is to measure system evolution, forming a set of objects through multiple measurements, and then using this set of objects as the basis for analyzing the weights of each factor. This allows us to understand the role of each factor in the evolution process and serves as a key reference for the failure evolution process of control systems, which is of great significance for research on safety and reliability.

[0003] Current research on the influencing factors of various faults, accidents, and failures is extensive. These findings have proposed effective methods for analyzing influencing factors in various systems, including the identification of various factors, and the study of factor importance and weight. While laying the foundation for subsequent research, there is also room for further development. This is because system failure evolution processes are ubiquitous in all types of systems. However, due to the complexity of structure and hierarchy, and the difficulties in describing and mathematically abstracting the evolution, current research data is limited to sets of objects obtained through measurement evolution, lacking reliable and effective methods for determining the weights of influencing factors in failure evolution. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining the weights of fault evolution influencing factors based on semi-supervised learning, so as to solve the technical problem that there is a lack of reliable and effective methods for determining the weights of fault evolution influencing factors in the prior art.

[0005] This invention provides a method for determining the weights of influencing factors in fault evolution based on semi-supervised learning. To study the fault evolution process of actual systems and obtain a set of objects, this invention proposes a method for determining the influence of each factor on the evolution. The method comprises seven steps: establishing a basic data matrix, determining the set of object weights, establishing a labeled data matrix, establishing an unlabeled data matrix, determining the set of object weights, determining eigenvectors and eigenvalues, and determining the weights of each factor. This method is used to determine the weights of influencing factors in fault evolution.

[0006] The steps for determining factor weights are as follows:

[0007] Establish the basic data matrix. Let the set of factors influencing the evolution process be F = {f1, ..., f2}. M}, m=1,…,M,f m ∈F, M is the number of factors. The set of objects formed by measurements at N time points is O={o1,…,o…} N}, n=1,…,N,o n ∈O, where N is the number of objects. Object o n It is a vector consisting of all factor values ​​at that moment. It is object o n In factor f m The factor values ​​are shown below. The basic data matrix Γ is formed as shown in Table 1.

[0008] Table 1 Basic Data Matrix Γ

[0009]

[0010] Determine the set of object labels. Assign class labels to objects in the base data matrix that have obvious characteristics; do not assign class labels to objects without obvious membership characteristics. Let the set of object labels be L = [l1,...,l...]. N ], l n For object o n The tag value, l n =1,...,θ, where θ is the maximum number of categories and the maximum label value; l n =0 o n No label, l n >0 o n There are labels, and the specific numerical value represents the category that the label represents. The method for determining the label value of an object is generally based on manual experience analysis, that is, first set a class label value, determine whether an object definitely belongs to the class and assign it a class label; if it cannot be determined, the class label is set to 0.

[0011] A labeled data matrix Γ is established based on the basic data matrix Γ and the object label set L. L , is the label value l nA matrix consisting of objects > 0. That is, objects that exist in Γ and l in L. n The matrix Γ composed of objects > 0 L Therefore Γ L ={o i |o i ∈Γ,l i ∈L,l i >0,i=1,...,N}.

[0012] Unlabeled data matrix Γ U For the label value l n A matrix consisting of objects whose sum is 0. That is, objects that exist in Γ and whose sum is in L. n The matrix Γ consisting of objects equal to 0 V Therefore Γ U ={o i |o i ∈F,l i ∈L,l i =0,i=1,...,N},Γ=Γ L ∪Γ U .

[0013] Determine the set of object weights W O =[w1,...,w N ], w n Representative object o n The weights are determined by using the K-nearest neighbor algorithm to construct the graph and the HeatKernel method to determine the weights of each object by the weight distribution of each edge in the graph, as shown in equation (4).

[0014] W O =W(Γ) L ,opt) (4)

[0015] In the formula: opt is a set of control parameters, including proximity pattern, distance pattern, number of clusters, and weight pattern.

[0016] Based on MMP, and integrating Γ L and Γ V The eigenvectors V and eigenvalues ​​λ of the optimal projection space are obtained, and the function is called as shown in equation (5).

[0017] [V,λ]=MMP(L,Γ L ,Γ U ,opt M (5)

[0018] In the formula: V=[ν1,...,ν M Let λ be the set of eigenvectors, where λ = [λ1, ..., λ2]. M [ ] represents the set of eigenvalues; opt MThe set of control parameters, including the object weight W O The intra-class and inter-class weights b∈[0,1].

[0019] Determine the weights W of each factor F The weights W of each factor are calculated using the eigenvector set V and the eigenvalue set λ. F =[w1,…,w M As shown in equation (6).

[0020]

[0021] The beneficial technical effects of the present invention are as follows: by applying the method for determining the weight of fault evolution influencing factors based on semi-supervised learning provided by the present invention, the weight of fault evolution influencing factors can be reliably and effectively determined, so that measures can be taken to control the evolution process according to the magnitude of the weight. Attached Figure Description

[0022] Figure 1 A flowchart illustrating the method for determining factor weights is shown.

[0023] Figure 2 A schematic diagram showing the variation of factor values ​​in the factor voltage is shown;

[0024] Figure 3 A schematic diagram showing the variation of the factor value of the factor current is shown;

[0025] Figure 4 A schematic diagram showing the variation of the factor value of temperature is shown;

[0026] Figure 5 A schematic diagram showing the changes in the humidity factor value is provided.

[0027] Figure 6 A schematic diagram showing the changes in the factor values ​​of the factor air pressure is shown;

[0028] Figure 7 A schematic diagram illustrating the changes in factor values ​​during factor vibration is shown;

[0029] Figure 8 A schematic diagram of the distribution of object label values ​​is shown. Detailed Implementation

[0030] 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.

[0031] The fault evolution process requires labeling the system states represented by objects to form class labels. However, some objects will inevitably be difficult to classify into known categories. The analysis process utilizing these object sets and class labels is the semi-supervised learning process.

[0032] To construct a method for determining the weights of influencing factors in the system fault evolution process based on semi-supervised learning, this invention proposes a factor weight determination method with the Maximum Margin Projection (MMP) method as its core. The goal is to use the MMP algorithm to analyze both labeled and unlabeled objects in the object set as samples, enabling the learning classifier to distinguish between positive and negative examples, while also increasing intra-class and inter-class features to achieve more accurate analysis results.

[0033] Regarding fault evolution and factor weighting analysis:

[0034] System failure evolution is an essential characteristic of any system. It is a process of change in a system's ability to perform its intended functions under the influence of multiple factors, focusing on the overall characteristics of the failure process. Correspondingly, the system's functionality at a certain moment in the evolution process is called the system functional state, focusing on the local characteristics of the evolution. The system functional states at all moments constitute the system failure evolution process. The system failure evolution process is the response of the system's intrinsic characteristics to its extrinsic characteristics. Intrinsic characteristics refer to the functions of the basic components constituting the system and the structure of the system composed of these components, determined during system design and remaining largely unchanged during operation. Extrinsic characteristics are the changes in environmental factors during system operation; although considered during design, they still exhibit randomness and uncertainty during operation. From this perspective, the changes in the system failure evolution process are mainly influenced by factors, and these factor changes are the driving force of evolution.

[0035] More specifically, the complexity and uncertainty of the evolutionary process stem from its structure and hierarchy. Structurally, it includes experienced events, influencing factors, logical relationships, and evolutionary conditions. Logical relationships are the interactions between events, and evolutionary conditions are the conditions under which causal events lead to consequential events; once events and factors are determined, they are essentially fixed. Events are the physical entities constituting the evolutionary process, but they are influenced by factors, and these factors, in turn, affect the evolutionary process through events. Hierarchically, it includes, from top to bottom, the evolutionary layer, the event layer, the factor layer, the factor phase layer, and the factor phase value layer. Each layer's objects are formed by the superposition of the states of all objects in the lower layer, which can be realized using the superposition of wave functions in quantum mechanics. At the hierarchical level, factors still determine events, thereby determining the evolutionary state. Therefore, although factors do not directly constitute the evolutionary process, their influence on events is transmitted throughout the entire evolutionary process.

[0036] Studying the evolution of system failures requires a reasonable description, and current methods include two-dimensional planar representation and multi-dimensional hyperspace representation. In two-dimensional planar representation, evolution time is plotted on the x-axis, and the system functional state on the y-axis, with the system functional state at a certain moment as the zero point. This represents a curve fluctuating between complete reliability and complete failure. The object measured at a certain moment is calibrated on the time axis using that moment as the variable. In multi-dimensional hyperspace, factors are orthogonal coordinate axes, and the projection of the object onto each axis represents the factor value. Since the changes in each factor during the evolution process have a range, the evolution process is a tortuous curve within that range. In contrast, the two-dimensional representation extends infinitely over the evolution time.

[0037] Currently, spatial fault network theory is used to describe the system fault evolution process. Characteristic functions are formed by utilizing the relationship between factors and event occurrence probabilities. The event occurrence probability distribution is formed by synthesizing the characteristic functions of events, and the system fault probability distribution is formed based on the structural relationship between events and the system. When factors are variables, the fault probability distribution is represented using a multidimensional hyperspace; when factor values ​​are time-calibrated, the evolution process can be represented using a two-dimensional plane.

[0038] The analysis of factor weights is prevalent in various studies. System representations are data emanating from the system, while data changes originate from factors influencing the system. Factor changes are transformed into data changes through the system; therefore, the internal structure of the system can be abstracted as a mapping relationship—a mapping from factors to data. Thus, the types and values ​​of factors inevitably affect the data and representations mapped from the system. Studying the influencing factors through these data and representations, and thereby eliminating factors detrimental to the system's state and hindering the evolution of system failures, is of great significance.

[0039] The impact of changes in factor values ​​on the system fault evolution process is termed factor weight. Methods for calculating factor importance are available for continuous functions and for discrete data. However, these methods are not applicable to sets of objects obtained from measuring actual evolution processes, making it difficult to effectively analyze the degree of influence of factors on the evolution process.

[0040] On object collections and semi-supervised learning:

[0041] Determining the factor weights for the system fault evolution process requires measurement data and data annotation. Measurement data consists of all factor values ​​obtained at a specific moment during the evolution process; these factor values ​​constitute the objects at that moment. Multiple measurements of the evolution process yield a set of objects, which serves as the foundational data matrix describing the evolution process. Each object is a vector composed of all factor values ​​at its corresponding moment.

[0042] Compared to obtaining a set of objects, labeling the system functionality represented by those objects is more difficult. First, it's clear that the diversity of all factors' variations is necessarily greater than the diversity of system functional states. Research has shown that under both linear and nonlinear conditions, the differences among all objects can characterize the differences in system states, but the specific implementation methods differ. Machine learning can be implemented using supervised, semi-supervised, and unsupervised data. They can all have the same set of objects, but their corresponding data labels are different; these labels are called class labels. If all objects in the set have class labels, it is supervised learning; if all objects have no class labels, it is unsupervised learning; if some objects have class labels and others do not, it is semi-supervised learning. Supervised learning is, of course, the optimal case, if the class labels are correct. Unsupervised learning completely discards class labels and classifies objects by calculating feature distances based on their own data characteristics. Semi-supervised learning performs intra-class learning on objects with class labels and inter-class analysis on objects without class labels, thus obtaining the clustering characteristics of objects more clearly.

[0043] Class labeling is a crucial concept in machine learning. In object classification, object ranking attributes are derived from known experience and used to train and build models. This object data contains several attributes (such as factors and factor values ​​mentioned above), among which a class attribute represents the clustering characteristics of the objects. In other words, the class attribute reflects the prior experience that an object belongs to a certain class; this attribute is the class label.

[0044] In practice, the classification of safety assessment levels is a typical example of class labeling. The value ranges of various factors are divided into levels, corresponding to the system state levels. For example, if a system is affected by three factors, and the factor value ranges are divided into three level value ranges, then the factor value of a certain object falls into different factor level value ranges. Based on prior experience, the overall system state can also be divided into three categories: reliable, unreliable, and uncertain. At this point, each object can belong to one of the three categories—reliable, unreliable, or uncertain—based on the level of its factor value, thus assigning a class label to all objects. This forms a mapping from object to class label, and from factor level to system level. Learning a model based on these two levels allows us to obtain the corresponding system state level when facing a new object; this level is the class label for the new object. During the evolution process, there will inevitably be some objects whose affiliation is difficult to determine, especially when class labels are determined manually. This is because human intuition has a fuzzy nature; it is easier to judge closer to extreme states, but difficult to judge in intermediate states. Objects whose affiliation is easily determined will have class labels, i.e., the aforementioned reliable and unreliable classes; those whose affiliation is difficult to determine will have no label, i.e., the aforementioned uncertain class. In practice, especially when human experience is required to determine membership, the data consists of a time-series fault data sequence formed by labeled and unlabeled objects according to the measurement order. Therefore, semi-supervised learning methods are usually needed to process this data, while supervised and unsupervised methods are difficult to apply in extreme cases.

[0045] Several mathematical methods exist for semi-supervised learning. For example, set pair analysis theory uses binary connection numbers to identify which objects in a set are definite and which are indefinite; ternary connection numbers identify objects in a set that are the same as, opposite to, or indefinite to the target. Fuzzy mathematics, such as membership functions and fuzzy sets, also describes similar problems. The piecewise function of the changing part of the membership function represents the indeterminate portion, i.e., the class label of the object is difficult to determine. Problems studied using these mathematical methods in machine learning all require the use of semi-supervised learning.

[0046] Therefore, to implement semi-supervised learning, at least a set of labeled objects, a set of unlabeled objects, a set of labels corresponding to the objects, and some control parameters are required. Thus, solving the above practical problem necessitates a reasonable methodology, with the weights of each factor determined using a semi-supervised learning algorithm as the core.

[0047] Regarding the MMP algorithm:

[0048] There are many semi-supervised learning methods. In studying the weights of influencing factors in the evolution of system failures, the weights of each factor are determined based on a pre-determined set of classifiable objects and a set of unclassifiable objects existing between classes. This focuses on the relationship between in-class object characteristics and factor changes, while actively weakening the connection between inter-class object characteristics and factors. This reduces the uncertainty of the determined factor weights. Learning only with labeled objects is not conducive to learning from negative examples of unlabeled objects. Therefore, to achieve the above objectives, the MMP algorithm is used as the core to determine the weights of factors influencing the evolution process.

[0049] Maximum Marginal Projection (MMP) is a linear semi-supervised algorithm based on the prior consistency assumption for image retrieval. Its fundamental problem is the gap between low-level visual features and high-level semantic concepts. To bridge this gap, relevance feedback is introduced into image retrieval. To address high dimensionality, a novel semi-supervised dimensionality reduction method, Maximum Marginal Projection (MMP), is proposed.

[0050] MMP can discover the local structure of a data manifold and characterize its geometric and discriminative structures. An intra-class graph G is constructed using intra-class and inter-class information. w Inter-class graph G b Subspace projection Y = A is achieved through a linear transformation matrix. T X, Y∈R d×N , X∈R L×N A = (a1, a2, ..., a d )∈R L×d d << L. This maximizes the difference between relevant and irrelevant data samples in each local neighborhood. The two objective functions of MMP are: and W w and W b It is G w and G b The weight matrix is ​​shown in equation (1).

[0051]

[0052] Where: N w () represents adjacent objects with different labels; N b () represents the remaining adjacent objects, and N b (x i )∪N w (x i )=N(x i ), N() is the k-neighbor set; γ is the weighted adjustment parameter.

[0053] The two equations in equation (1) can be expressed as equation (2). The objective function of MMP can be expressed as equation (3).

[0054]

[0055] In the formula: a is the projection vector; Λ w and Λ b These are the object matrices within and between classes, respectively.

[0056] argmaxa T X[β(Λ b -W b )+(1-β)W w ]X T a (3)

[0057] In the formula: β is a constant in [0,1].

[0058] The final dimensionality reduction process of MMP can be achieved through y i =A T x i Achieve this. Thus, obtain A. T The eigenvectors and eigenvalues ​​are used to determine the weights of each factor.

[0059] MMP is a novel manifold learning algorithm that models the geometric and discriminative structures of data by constructing inter-class and intra-class nearest neighbor graphs. It uses standard spectral techniques to determine an optimal projection, reducing the Euclidean distance between objects in the subspace to reflect the semantic structure of the data. MMP serves as the core of the factor weight determination method, and is directly invoked as a function during analysis.

[0060] This invention provides a method for determining the weights of influencing factors in fault evolution based on semi-supervised learning. To study the fault evolution process of actual systems and obtain a set of objects, this invention proposes a method for determining the influence of each factor on the evolution. The method comprises seven steps: establishing a basic data matrix, determining the set of object weights, establishing a labeled data matrix, establishing an unlabeled data matrix, determining the set of object weights, determining eigenvectors and eigenvalues, and determining the weights of each factor. This method is used to determine the weights of influencing factors in fault evolution.

[0061] The steps for determining factor weights are as follows:

[0062] First, the flowchart for determining factor weights is given, such as... Figure 1 As shown. Establish the basic data matrix. Let the set of factors influencing the evolution process be F = {f1, ..., f2}. M}, m=1,…,M,f m ∈F, M is the number of factors. The set of objects formed by measurements at N time points is O={o1,…,o…} N}, n=1,…,N,o n ∈O, where N is the number of objects. Object on It is a vector consisting of all factor values ​​at that moment. It is object o n In factor f m The factor values ​​are shown below. The basic data matrix Γ is formed as shown in Table 1.

[0063] Table 1 Basic Data Matrix Γ

[0064]

[0065] Determine the set of object labels. Assign class labels to objects in the base data matrix that have obvious characteristics; do not assign class labels to objects without obvious membership characteristics. Let the set of object labels be L = [l1, ..., l...]. N ], l n For object o n The tag value, l n =1,…,θ, where θ is the maximum number of categories and the maximum label value; l n =0 o n No label, l n >0 o n There are labels, and the specific numerical value represents the category that the label represents. The method for determining the label value of an object is generally based on manual experience analysis, that is, first set the class label value, determine whether the object definitely belongs to the class and assign the class label; if it cannot be determined, the class label is set to 0.

[0066] A labeled data matrix Γ is established based on the basic data matrix Γ and the object label set L. L , is the label value l n A matrix consisting of objects > 0. That is, objects that exist in Γ and l in L. n The matrix Γ composed of objects > 0 L Therefore Γ L ={o i |o i ∈Γ,l i ∈L,l i >0,i=1,…,N}.

[0067] Unlabeled data matrix Γ U For the label value l n A matrix consisting of objects whose sum is 0. That is, objects that exist in Γ and whose sum is in L. n The matrix Γ consisting of objects equal to 0 V Therefore Γ U ={o i |o i ∈F,l i ∈L,l i =0,i=1,...,N},Γ=Γ L ∪Γ U .

[0068] Determine the set of object weights W O =[w1,…,w N ], w n Representative object o n The weights are determined by using the K-nearest neighbor algorithm to construct the graph and the HeatKernel method to determine the weights of each object by the weight distribution of each edge in the graph, as shown in equation (4).

[0069] W O =W(Γ) L ,opt) (4)

[0070] In the formula: opt is a set of control parameters, including proximity pattern, distance pattern, number of clusters, and weight pattern.

[0071] Based on MMP, and integrating Γ L and Γ V The eigenvectors V and eigenvalues ​​λ of the optimal projection space are obtained, and the function is called as shown in equation (5).

[0072] [V,λ]=MMP(L,Γ L ,Γ U ,opt M (5)

[0073] In the formula: V=[ν1,…,ν M Let λ be the set of eigenvectors, where λ = [λ1, ..., λ2]. M [ ] represents the set of eigenvalues; opt M The set of control parameters, including object weight W O The intra-class and inter-class weights b∈[0,1].

[0074] Determine the weights W of each factor F The weights W of each factor are calculated using the eigenvector set V and the eigenvalue set λ. F =[w1,…,w M As shown in equation (6).

[0075]

[0076] Taking an electrical system as an example, the fault evolution process is studied. According to step 1, the set of influencing factors of system faults is F = {f1, f2, f3, f4, f5, f6}, where voltage f1 ∈ [12, 15] V; current f2 ∈ [0.7, 0.85] mA; temperature f3 ∈ [11, 24] ℃; humidity f4 ∈ [77, 94] %; air pressure f5 ∈ [100, 105] KPa; and vibration f6 ∈ [185, 236] Hz. The evolution is measured 50 times at equal time intervals, forming the object set O = {o1, ..., o...} 50The objects and factors constitute the basic data matrix Γ, and the changes in the factor values ​​of each object are as follows: Figures 2 to 7 As shown.

[0077] Construct a set of object labels. Let the maximum category θ = 3, i.e., the label value l n =1,2,3, divide all objects into 3 categories and an indistinguishable object class l. n =0. Based on prior experience, let l = 0. n =1 represents safety, l n =2 means possibly safe, l n =3 represents unsafe, l n =0 indicates uncertainty. Thus, 100 objects result in an object label set L = [l1,...,l...]. 100 [A schematic diagram showing the distribution of label values ​​for each object; the label values ​​for each object are as follows] Figure 8 As shown.

[0078] like Figure 8 As shown in the diagram, the first half of the label value distribution diagram contains many objects with a label value of 0, representing a significant portion that is difficult to determine based on experience. However, in the second half, all label values ​​are greater than 0, and all objects have been assigned a label value. This aligns with the general object classification process. There are 14 objects with a label value of 1, 41 objects with a label value of 2, 10 objects with a label value of 3, and 35 objects with a label value of 0.

[0079] Constructing the labeled data matrix Γ L and unlabeled data matrix Γ U Based on the formed L=[l1,...,l 100 The label value l n All objects greater than 0 constitute Γ L ={o i |o i ∈Γ,l i ∈L,l i >0, i=1,...,100}, while the label value l n All objects equal to 0 constitute Γ U ={o i |o i ∈F,l i ∈L,l i =0,i=1,…,100}, and Γ=Γ L ∪Γ U .

[0080] Determine the set of object weights W O =[w1,...,w 100The function is called as shown in equation (4). The opt control parameter set specifically uses Euclidean distance for object distance, KNN for proximity mode, 5 clusters, and HeatKernel for weight mode. This yields the object weight set W. O .

[0081] Based on MMP, the eigenvector V and eigenvalue λ of the optimal projection space are obtained, and the function shown in equation (5) is called. Where the parameters L, Γ L ,Γ U It is known that opt M Includes the object weight set W O The intra-class and inter-class weight coefficients b = 0.5. The optimal eigenvectors and eigenvalues ​​are obtained as shown in equation (7).

[0082]

[0083] Equation (7) is arranged in descending order of eigenvalues, which happens to be the ascending order of factor numbers. Finally, the weights of each factor, W, are determined using equation (6). F =[w1,…,w6]=[0.1212,0.0181,0.0013,0.0054,0.8581,-0.0040]. Factor 6 has a negative weight and a very small value, which is due to a problem with the data itself and is therefore ignored. The remaining factor weights represent the degree of influence of each factor in the evolution process. The weights are ranked as f5>f1>f2>f4>f3, and measures are taken to control the evolution process based on the magnitude of the weights.

Claims

1. A method for determining the weights of influencing factors in fault evolution based on semi-supervised learning, characterized in that, This includes establishing a basic data matrix, determining the set of object labels, establishing a labeled data matrix, establishing an unlabeled data matrix, determining the set of object weights, determining feature vectors and feature values, and determining the weights of each factor. Weighting of factors influencing fault evolution; The steps for determining factor weights are as follows: Establish a basic data matrix; let the set of factors influencing the evolution process be . , It is the number of factors; in The set of objects formed by measurements at each time point is , It is the number of objects; objects It is a vector consisting of all factor values ​​at that moment. ; It is an object In factors The following factor values; Forming the basic data matrix As shown in Table 1; Table 1 Basic Data Matrix Determine the set of object labels; assign class labels to objects with obvious characteristics in the basic data matrix, and do not assign class labels to objects without obvious membership characteristics; let the set of object labels be... , For object The tag value, , The maximum number of categories; hour No label hour It has a label, and the specific value is the category represented by the label; it determines whether an object definitely belongs to this category and assigns it a class label; if it cannot be determined, the class label is set to 0. Based on the basic data matrix and object tag collection Establish a labeled data matrix , is the tag value The objects form a matrix; in It exists and in middle Matrix of objects ,therefore ; Unlabeled data matrix For tag values A matrix composed of objects; in It exists and in middle Data matrix composed of objects ,therefore ; Determine the set of object weights , Representative object The weights; The graph is constructed using the K-nearest neighbor algorithm, and the weight of each object is determined by the weight distribution method of each edge in the graph using the HeatKernel method, as shown in Equation (4). （4） In the formula: The set of control parameters includes proximity pattern, distance pattern, number of clusters, and weight pattern; based on ,comprehensive and Obtain the eigenvectors of the optimal projection space and eigenvalues ; The function call format is shown in equation (5); （5） In the formula: For the set of feature vectors, It is the set of eigenvalues; The set of control parameters, including object weights Intra-class and inter-class weights ; Determine the weight of each factor ; Using feature vector sets and eigenvalue set Find the weights of each factor As shown in equation (6); （6）。 2. The method for determining the weights of fault evolution influencing factors based on semi-supervised learning according to claim 1, characterized in that, Used for studying the fault evolution process of electrical systems; according to step 1, the set of influencing factors of system faults is as follows: voltage ∈[12,15]V; Current ∈[0.7,0.85]mA; temperature ∈[11,24]℃; humidity ∈[77,94]%; air pressure ∈[100,105]KPa; Vibration ∈[185,236]Hz; 50 evolution measurements were performed at equal time intervals to form a set of objects. The objects and factors constitute the basic data matrix. ; Construct a collection of object labels; set the maximum category. That is, the tag value All objects are divided into 3 categories and an indistinguishable object class. Based on existing experience, let's assume... Represents safety, This suggests that it may be safe. This indicates insecurity. The value is uncertain; thus, 100 objects result in a set of object labels. Obtain a schematic diagram of the label value distribution of each object; In the diagram of label value distribution, the first half contains many objects with a label value of 0, which indicates that a large portion of them are difficult to determine based on experience. However, in the second half, all label values ​​are greater than 0, and all objects have been assigned a label value. This is consistent with the general object classification process. There are 14 objects with a label value of 1, 41 objects with a label value of 2, 10 objects with a label value of 3, and 35 objects with a label value of 0. Constructing a labeled data matrix and unlabeled data matrix Based on the formation ; where the tag value All objects constitute , and tag value All objects constitute ,and ; Determine the set of object weights The call is as shown in equation (4); The control parameter set specifically uses Eulerian distance for object distance, KNN for the nearest neighbor model, 5 clusters, and HeatKernel for weighting; thus, the object weight set is obtained. ; The eigenvectors of the optimal projection space are obtained based on MMP. and eigenvalues Call the function as shown in equation (5); where the parameters It is known that Includes object weight set Intra-class and inter-class weight coefficients The optimal eigenvectors and eigenvalues ​​are obtained as shown in equation (7); （7） Equation (7) is arranged in descending order of eigenvalues, which happens to be the ascending order of factor numbers; finally, the weight of each factor is determined by equation (6). .

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