A method for analyzing the effect of a sub-evolution process of system fault evolution

Abstract

The application relates to system fault evolution process analysis in the safety field, and provides a system fault evolution sub-evolution process function analysis method, which is used for studying each sub-evolution process with different characteristics in a system fault evolution process, determining the function of each sub-evolution process on the total evolution process, and providing a sub-evolution process function analysis method based on spectral regression discriminant analysis; a basic data matrix and a normalized data matrix are constructed based on an object set measured and evolved at each moment; an object label set is generated by using uniformly distributed random numbers and is folded to form an object label matrix; the object label matrix is trained and predicted by using the spectral regression discriminant analysis method to obtain maximum accuracy, an optimal object label set and an optimal training object number; the function analysis of each sub-evolution process is realized by defining frequency and concentration; and the method is used for determining the function of each sub-evolution process in a system fault evolution process and clustering analysis of an object set.

Description

Technical Field

[0001] This invention relates to the analysis of system failure evolution processes in the field of safety, and particularly to the analysis of the role of sub-evolution processes in system failure evolution. Background Technology

[0002] System failure processes are complex and may involve multiple sub-processes. At any given time, only one sub-process may play a decisive role, or multiple sub-processes may overlap to form the system failure process. Because a system generally contains multiple subsystems, under the same influence of factors, the different internal characteristics of these subsystems lead to different failure evolution processes; and the system failure process is a comprehensive manifestation of the failure processes of these subsystems. The process of change in the system's ability to achieve its intended function under the influence of multiple factors is called the system failure evolution process. Therefore, determining the role of each subsystem at each time point in the system failure evolution process under the influence of multiple factors is crucial to identifying the key subsystems and their sub-evolutionary processes. In practice, conducting such research is quite difficult, mainly because subsystems constitute the structure of the system, and the interactions between subsystems mean that the system failure evolution process is a superposition of the failure evolution processes of all subsystems. Furthermore, failure evolution research is generally based on time-series failure data, that is, measuring the system state at multiple times and recording the values ​​of all factors to form the object at that time. The set of these measured objects is the time-series failure data. The role of each sub-evolutionary process in the system failure evolution process needs to be analyzed based on the set of objects in the time-series failure data.

[0003] The study of influencing factors, various events, and the roles of components in system failure processes, as well as time-series failure data, is currently a hot topic in various fields. Because the failure process of any system is an inevitable problem that the system must face, related research results are gradually increasing. The aforementioned results have played a positive role in the study of system failure processes in various fields, including methods and algorithms proposed for specific domains, as well as general research methods proposed at the system level. These results provide strong support for subsequent research. However, the main issue raised here lies in the role of the failure evolution processes of each subsystem in the system failure evolution process. Since measurements can only be conducted on the overall system failure evolution process, forming a set of time-series failure data, while the various sub-evolutionary processes collectively form the system failure evolution process, the problem to be solved is how to study the role of each sub-evolution on the overall evolution or to determine the sub-evolutionary process that plays a major role at each moment.

[0004] Therefore, there is an urgent need for a method to analyze the role of sub-evolution processes in system failure evolution, and to study the effect of each sub-evolution on the overall evolution. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing the role of sub-evolution processes in system fault evolution, so as to solve the problem that the existing technology lacks research on the role of each sub-evolution in the overall evolution.

[0006] To address the aforementioned problems, this invention forms a basic data matrix from the objects measured at each time point; then, a normalized data matrix is ​​formed; a label matrix for all objects during the system fault evolution process is constructed; the optimal composition of each sub-evolutionary process in the overall evolutionary process is determined; and finally, the role of each sub-evolutionary process in the overall evolutionary process is analyzed. This allows for understanding the role of each sub-evolutionary process and determining the importance of each subsystem within the system. Furthermore, unless otherwise specified, "system" refers to the overall system, distinguishing it from "subsystem"; the system fault evolution process is simply referred to as the evolutionary process, which refers to the overall evolutionary process, distinguishing it from the sub-evolutionary processes.

[0007] This invention provides a method for analyzing the role of sub-evolutionary processes in system failure evolution. To study the distinctive sub-evolutionary processes inherent in the system failure evolution process and determine the role of each sub-evolutionary process on the overall evolution process, a sub-evolutionary process role analysis method based on spectral regression discriminant analysis is proposed. A basic data matrix and a normalized data matrix are constructed based on the object sets obtained from the evolution at each time step. An object label set is generated using uniformly distributed random numbers and folded to form an object label matrix. The object label matrix is ​​trained and predicted using spectral regression discriminant analysis to obtain the maximum accuracy, optimal object label set, and optimal number of training objects. Frequency and concentration are defined to analyze the role of each sub-evolutionary process. This method is used to determine the role of each sub-evolutionary process and perform cluster analysis on the object set during system failure evolution.

[0008] Regarding the algorithm flow and basic data:

[0009] The algorithm flow is given here, and the basic data matrix and normalized data matrix are constructed based on the measured object set.

[0010] The input data, output data, and specific methods used for each step are given below.

[0011] Step 1: Construct the basic data matrix Γ. The input data consists of the object set O, the factor set F, and the object o. n In factor f m Factor values ​​below The output data is the basic data matrix Γ.

[0012] Step 2: Construct a normalized dataset Input data is Γ, output data is The method uses the 2-norm normalization function normalize().

[0013] Step 3: Construct the object label matrix L. The input data consists of the number of objects N, the number of iterations θ, and the number of subsystems Q; the output data is L; the method is to randomly generate an object label matrix L composed of object label numbers uniformly distributed in [1,Q].

[0014] Step 4: Determine the optimal set of object labels. Input data is... L and the set of control parameters opt; the output data is the maximum accuracy AC. opt , and its corresponding optimal object label set L{i opt} and the number of training objects nTrain opt The method used was the generalized regression discriminant analysis (SRDA) method.

[0015] Step 5: Analyze the role of each sub-evolution. Input data is L{i opt The algorithm consists of: object label value q∈[1,Q], sub-evolutionary set E; and output data including the frequency P and concentration Z of the appearing objects. A specific algorithm is proposed, and the effect of each sub-evolutionary process on the overall evolutionary process is analyzed.

[0016] Construct 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 composed of all factor values. It is object o n In factor f m The following factor values ​​form the basic data matrix Γ. M×N As shown in Table 1.

[0017] Table 1 Basic Data Matrix Γ M×N

[0018]

[0019] The system contains a set of subsystems S = {s1, ..., s...} Q}, s q ∈S, q=1,...,Q, where Q is the number of subsystems; the set of sub-evolutionary processes is E={e1,...,e Q}, e q It is s q The system fault evolution process. The division of subsystems is based on the fault characteristics of the objects.

[0020] Constructing a normalized data matrix Normalize each column of Γ using the 2-norm, i.e. The normalization function used is shown in equation (1).

[0021]

[0022] Regarding the construction of the object label matrix:

[0023] Let L be the object label matrix, which is an N×θ matrix, where N is the number of objects and θ is the number of iterations. Each sub-evolutionary process has its own fault characteristics. An object is included in a sub-evolutionary process when its fault characteristics are the same as those of the sub-evolutionary processes. Objects with the same characteristics then form a sub-evolutionary process, which is equivalent to cluster analysis of all objects. The problem lies in determining the optimal system fault evolutionary process with the highest accuracy, that is, the optimal composition of the overall evolutionary process formed by the sub-evolutionary processes.

[0024] If we let Q be the number of subsystems, then there are Q sub-evolutionary processes. Of course, not all Q sub-evolutionary processes play a role in the overall evolution; this requires analysis and judgment. A label is a marker indicating that an object belongs to a specific sub-evolutionary process, using the numerical values ​​q = 1, ..., Q. For O = {o1, ..., o...} N Each object has Q types of labels. Therefore, the array of distinct labels for N objects has Q0 types. N This requires the use of subsequent proposed algorithms to analyze this Q. N We use a variety of label distributions to obtain a set of object labels corresponding to the maximum accuracy. This method is computationally complex and relies on an enumeration strategy.

[0025] Here, the number of iterations θ is used to control the number of different object label sets; that is, the maximum accuracy is obtained in θ analyses, thus determining the corresponding optimal object label set. The question then becomes how to determine the object label matrix L required for these θ analyses. L is an N×θ matrix, where each row represents the label value of an object in different object label sets; and each column represents the object label set in different iterations. Since enumeration cannot be used, the object labels in the object label sets of each iteration need to be randomly generated. However, since θ is much smaller than Q... N Therefore, the random numbers need to be uniformly distributed among integer values ​​from 1 to Q. If the object label set is regenerated randomly in each iteration, the uniform distribution characteristic will be lost. Therefore, the object label values ​​and object label sets used in all iterations must be randomly generated simultaneously, i.e., the object label matrix must be generated all at once. This is to ensure that the sample sizes are θ and Q. N This yields approximately the maximum accuracy.

[0026] In summary, let the label values ​​of all objects form an array R, which is an N×θ dimensional array. The label values ​​are q = 1, ..., Q, and are uniformly distributed to form array R. All columns of matrix L are connected sequentially to form array R. Therefore, after determining array R, it is folded to form matrix L, as shown in equation (2).

[0027] L{i}=R((i-1)×N+1:i×N), i=1,...,θ (2)

[0028] In the formula: L{i} represents the i-th column of matrix L; the random numbers for the object label values ​​in R are implemented using the unifmd() function in MATLAB.

[0029] The above process forms the object label matrix L. However, due to computational limitations, L does not contain all object label sets; including all sets would require N×Q. N 1-order matrix.

[0030] Regarding determining the optimal set of object labels:

[0031] Based on the object label matrix L and the normalized data matrix The optimal set of object labels is determined using the Spectral Regression Discriminant Analysis (SRDA) algorithm. The SRDA analysis process is represented by functions. SRDA is based on the LDA algorithm, incorporating spectral analysis and regression model construction to achieve supervised, semi-supervised, and unsupervised learning. A connectivity graph is constructed using labeled or unlabeled data to characterize the discriminative structure within the dataset. The embedding function is obtained using the regression model based on the learning results, and data dimensionality reduction is achieved through function projection. The optimal set of object labels is then determined using SRDA. This involves two functions: the training function SRDAT() and the prediction function SRDAP(), as shown in equations (3) and (4), respectively.

[0032]

[0033] In the formula, nTrain represents the number of objects used for training in the object set, and nTrain∈[n1,n2,...,n] T ], n1 < n2 < ... < n T ≤N-1. It is a matrix The training object matrix consists of the first n rows of the object label matrix in the i-th iteration. L{i}(1:nTrain) is the training object label matrix consisting of the first n rows of the object label matrix in the i-th iteration. opt is an array of control parameters, including the RT regularization norm (default L2); the alpha regularization parameter (default 0.1); the gamma regularization parameter (default 0.05); and LASSOW, which uses the LASSO solution method (default LARs). The output value is MOD. i , is the trained model.

[0034]

[0035] In the formula AC i It is the accuracy of the i-th iteration, AC i ∈[0,1]. Then the training model and accuracy corresponding to the i-th iteration are MOD respectively. i and AC i Combining equations (3) and (4), we iterate through i = 1, ..., θ and nTrain ∈ [n1, n2, ..., n T The maximum accuracy after θ iterations is determined as shown in equation (5).

[0036]

[0037] In the formula AC opt It is the maximum accuracy; Li opt} is the optimal set of object labels for maximum accuracy, and is a column of L; nTrain opt This is the optimal number of training objects for maximizing accuracy. Therefore, L{i opt} is the optimal composition of the system fault evolution process formed by each sub-evolution process.

[0038] Analysis of the role of each sub-evolutionary process:

[0039] According to L{i opt The object label in} belongs to the sub-evolution process e q In the case of Li, statistics opt} belongs to e q Number of objects N q As shown in equation (6).

[0040]

[0041] From equation (6), we can see that Based on Li opt Statistics belong to e q The moment the object appears, that is, at Li opt} belongs to e q The row number q of the object. The objects belonging to e...q The times at which all objects appear constitute e q object position array Ns q As shown in equation (7).

[0042]

[0043] Where: Ns q |n represents Ns q Then add the number of elements n.

[0044] From equation (7), we can see that In the overall evolution process, the sub-evolution process e q The frequency of the object in the middle is The larger the value, the better. The frequency set of each sub-evolutionary process is P = [p1, ..., p...]. Q Sub-evolution process e q The concentration of objects appearing in the middle is The larger the value, the better, where J q The calculation is shown in equation (8).

[0045]

[0046] The set of occurrence concentrations of each sub-evolutionary process is Z = [z1, ..., z]. Q ].

[0047] Sub-evolution process e q The higher the frequency of an element, the greater its proportion in the overall evolutionary process, meaning it is included in e. q The more objects in the process, the more likely the overall evolutionary process will revolve around the sub-evolutionary process e. q Development proceeds. Sub-evolution process e q The greater the concentration, the more likely e is to be q The more concentrated and continuous the influence on the overall evolution, the better. In comparison, multiple elements belonging to e... q If objects appear consecutively, they will have a continuous effect on the overall evolutionary process; if they appear discontinuously, their effect is intermittent, influenced by the intermittent effects of other sub-evolutions. Simply put, the effect of two objects appearing consecutively is greater than the effect of two objects appearing intermittently. Determining the influence of each subsystem on the overall system's evolutionary process requires comprehensive consideration of both frequency and concentration.

[0048] The purpose of this method is to determine the role of multiple sub-evolutionary processes in the system failure evolution process. It involves identifying which objects, as measured during the evolution process, belong to each sub-evolutionary process. This is equivalent to cluster analysis of all objects, with each cluster corresponding to a different sub-evolutionary process. Finally, the influence of each sub-evolutionary process on the overall evolution process is determined by the frequency and concentration of object occurrences.

[0049] The beneficial technical effects of this invention are as follows:

[0050] By applying the sub-evolution process effect analysis method for system fault evolution provided by this invention, the effect of the sub-evolution process on the overall evolution process can be determined.

[0051] It should be noted that, unless otherwise specified, all letters in this invention are intermediate variables in the calculation process. Attached Figure Description

[0052] Figure 1 The system failure evolution process is illustrated.

[0053] Figure 2 The superposition of each sub-evolutionary process and the measurement objects at each time point are shown;

[0054] Figure 3 A flowchart of the sub-evolution process role analysis method for system fault evolution provided by the present invention is shown;

[0055] Figure 4 The changes in factor values ​​for each object of the factor voltage are shown;

[0056] Figure 5 The changes in factor values ​​for each object of the factor current are shown;

[0057] Figure 6 The changes in factor values ​​for each object at the factor temperature are shown;

[0058] Figure 7 The changes in the factor values ​​for each object related to humidity are shown;

[0059] Figure 8 The changes in factor values ​​for each object in the factor pressure are shown;

[0060] Figure 9 The changes in factor values ​​for each object in the factor vibration are shown;

[0061] Figure 10 The distribution of object label values ​​for the optimal set of object labels is shown. Detailed Implementation

[0062] 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.

[0063] This invention forms a basic data matrix from the objects measured at each moment; then forms a normalized data matrix; constructs a label matrix for all objects during the system fault evolution process; determines the optimal composition of each sub-evolutionary process in the overall evolution process; and finally analyzes the role of each sub-evolutionary process in the overall evolution process. This allows for understanding the role of each sub-evolutionary process and determining the importance of each subsystem within the system, among other key issues. Furthermore, unless otherwise specified, "system" refers to the overall system, distinguishing it from "subsystem"; the system fault evolution process is simply referred to as the evolution process, which refers to the overall evolution process, distinguishing it from the sub-evolutionary processes.

[0064] Regarding system failure evolution and its representation:

[0065] The process by which a system's ability to perform its intended function changes under the influence of multiple factors is called the system failure evolution process. System failure evolution is an inherent characteristic of the system; the existence of a system is measured by its ability to perform its intended function. Whether a system needs to be replaced during operation depends on its failure condition; therefore, the system failure evolution process is an effective method for representing system functionality. System functionality has two extreme states: complete reliability and complete failure, but generally, system functionality varies between these two states. Clearly, this state is related to the moment the system failure evolution process is measured; the system functionality at the measurement moment is called the system functional state. The system functional state describes the same things as the system failure evolution process; the former describes the system functionality at a certain moment, while the latter describes the overall characteristics of the failure evolution. The system functional states at all moments in the measurement sequence constitute the entirety of the system failure evolution process.

[0066] The evolution of system failures is influenced by both the system's intrinsic characteristics and the external environment. Intrinsic characteristics refer to the functionality of the components that make up the system and the structure of the system as a whole; external environmental influences refer to the changes in various factors during operation. The evolution of system failures can be understood as the response of the system's intrinsic characteristics to the influence of the external environment, while the system's functional state is the response at the moment of measurement.

[0067] The evolutionary process of system failure has a complex structure and hierarchy. Structurally, it includes experienced events, influencing factors, logical relationships, and evolutionary conditions. Experienced events are the markers of the evolutionary process and constitute its components. Influencing factors affect the functionality of experienced events, thus affecting the system failure evolutionary process. Logical relationships are the comprehensive ways in which events interact. Evolutionary conditions are the conditions under which causal events lead to resultant events. Once the events and factors are determined, the logical relationships and evolutionary conditions are generally determined, and since influencing factors act on the evolutionary process through events, the core of the evolutionary process is experienced events. Hierarchically, it includes the evolution layer, event layer, factor layer, factor phase layer, and factor phase value layer. The state of an object in each layer is the superposition of the states of all objects in the lower layer, including forms of joint action and exclusive action. The superposition of all object states from bottom to top forms the functional state of the system, which can be realized using the superposition of wave functions in quantum mechanics.

[0068] Due to the complexity of the evolutionary process, conducting research remains challenging, especially regarding the fundamental data. For example, safety assessment methods for various systems typically consist of fundamental data, factors, semantic levels, and algorithms. The fundamental data is generally time-series fault data, which comprises all factor values ​​measured at a given moment, labeled with the measurement moment as the key field, forming a set of objects. System safety analysis is then performed using this set of fundamental data. Similarly, system safety analysis based on various system signal data involves sampling the signals at a fixed frequency, thus creating a set of time-series fault data. Therefore, the set of time-series fault data objects provides effective fundamental data for studying the evolution of system faults.

[0069] Figure 1 The system failure evolution process is represented. With evolution time on the x-axis and system functional state on the y-axis, the solid line in the figure represents a two-dimensional description of the system failure evolution process. It fluctuates between reliable and failure states, and at measurement time t... n The object is obtained by measuring the evolution process. n The set of objects obtained by measurements at multiple moments can describe the evolutionary process. When the measurement time interval is infinitely small, the infinite number of objects obtained can completely represent the evolutionary process, but in reality, the measurement time cannot be infinitely small, and the number of objects obtained is finite.

[0070] Returning to the original question, since the system is composed of multiple subsystems and the system fault evolution process is also a comprehensive reflection of the evolution processes of each subsystem, this makes the measured object o... nThe evolution of all subsystems is influenced by their respective evolutionary processes. Therefore, the problem is to identify the key sub-evolutionary processes at each moment, and the corresponding subsystem is the one that plays a decisive role at that moment. This involves studying objects at all moments to determine the role of all subsystems in the evolutionary process. Of course, the subsystems here are systems in an abstract sense, and may not correspond to physical systems. They mainly refer to a subset of systems with independent fault characteristics during the system's fault evolution. Subsystems may have the same physical components, but exhibit different fault characteristics during evolution. It is difficult to determine the subsystems composed of non-common components at the physical level; therefore, subsystems are constructed based on different fault characteristics. These subsystems exhibit different fault characteristics at different moments; therefore, if the fault characteristics of objects measured at certain moments are the same, they can constitute a sub-evolutionary process. Classifying objects according to different fault characteristics, each category of objects forms its own sub-evolutionary process along the evolutionary time dimension. All objects in the system's fault evolution process are the collection of all objects in all sub-evolutionary processes.

[0071] Figure 2 This represents the sub-evolutionary processes of each subsystem under the influence of all factors, and the overall system fault evolution process is formed by combining all sub-evolutionary processes. During the evolution process, different sub-evolutionary processes play a major role at different stages, resulting in different measured object fault characteristics. Objects falling into the same sub-evolutionary process share the same characteristics, and object labels represent the sub-evolutionary process (number) to which the object belongs. Assuming that each object may belong to any sub-evolutionary process, we enumerate the object labels to form different object label sets. We divide the object label sets into a training set and a prediction set, and iterate through all possible object label sets; the set with the highest prediction accuracy is the optimal object label set. The overall evolution process formed by the sub-evolutionary processes corresponding to the optimal object label set is the desired optimal evolution process, or the most suitable evolution process. This determines the sub-evolutionary process to which the object belongs at each measurement moment, ultimately determining the role of each sub-evolutionary process in the overall evolution.

[0072] Regarding the algorithm flow and basic data:

[0073] The algorithm flow is given here, and the basic data matrix and normalized data matrix are constructed based on the measured object set.

[0074] The input data, output data, and specific methods used for each step are given below.

[0075] Step 1: Construct the basic data matrix Γ. The input data consists of the object set O, the factor set F, and the object o. n In factor f m Factor values ​​below The output data is the basic data matrix Γ.

[0076] Step 2: Construct a normalized dataset Input data is Γ, output data is The method uses the 2-norm normalization function normalize().

[0077] Step 3: Construct the object label matrix L. The input data consists of the number of objects N, the number of iterations θ, and the number of subsystems Q; the output data is L; the method is to randomly generate an object label matrix L composed of object label numbers uniformly distributed in [1,Q].

[0078] Step 4: Determine the optimal set of object labels. Input data is... L and the set of control parameters opt; the output data is the maximum accuracy AC. opt , and its corresponding optimal object label set L{i opt} and the number of training objects nTrain opt The method used was the generalized regression discriminant analysis (SRDA) method.

[0079] Step 5: Analyze the role of each sub-evolution. Input data is L{i opt The algorithm consists of: object label value q∈[1,Q], sub-evolutionary set E; and output data including the frequency P and concentration Z of the appearing objects. A specific algorithm is proposed, and the effect of each sub-evolutionary process on the overall evolutionary process is analyzed.

[0080] Construct 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 composed of all factor values. It is object o n In factor f m The following factor values ​​form the basic data matrix Γ. M×N As shown in Table 1.

[0081] Table 1 Basic Data Matrix Γ M×N

[0082]

[0083] The system contains a set of subsystems S = {s1, ..., s...} Q}, s q ∈S, q=1,...,Q, where Q is the number of subsystems; the set of sub-evolutionary processes is E={e1,...,e Q}, e q It is s q The system fault evolution process. The division of subsystems is based on the fault characteristics of the objects.

[0084] Constructing a normalized data matrix Normalize each column of Γ using the 2-norm, i.e. The normalization function used is shown in equation (1).

[0085]

[0086] Regarding the construction of the object label matrix:

[0087] Let L be the object label matrix, which is an N×θ matrix, where N is the number of objects and θ is the number of iterations. Each sub-evolutionary process has its own fault characteristics. An object is included in a sub-evolutionary process when its fault characteristics are the same as those of the sub-evolutionary processes. Objects with the same characteristics then form a sub-evolutionary process, which is equivalent to cluster analysis of all objects. The problem lies in determining the optimal system fault evolutionary process with the highest accuracy, that is, the optimal composition of the overall evolutionary process formed by the sub-evolutionary processes.

[0088] refer to Figure 2 The lower number line will Figure 1 The evolutionary process of fluctuations is projected onto the timeline, and the objects measured at each moment necessarily belong to a certain sub-evolutionary process. For example, o1, o2, and o3 belong to sub-evolutionary process e1, and the subsequent objects belong to e2, e3, e4, e5, and e6 respectively. Q e1, e Q Therefore, in the entire evolutionary process, the moments when all objects belonging to e1 are measured are the moments when e1 plays a crucial role; similarly, the moments when objects belonging to e2 or e... Q The moment when all objects are measured is also the moment when they play a crucial role.

[0089] If we let Q be the number of subsystems, then there are Q sub-evolutionary processes. Of course, not all Q sub-evolutionary processes play a role in the overall evolution; this requires analysis and judgment. A label is a marker indicating that an object belongs to a specific sub-evolutionary process, using the numerical values ​​q = 1, ..., Q. For O = {o1, ..., o...} N Each object has Q types of labels. Therefore, the array of distinct labels for N objects has Q0 types. N This requires the use of subsequent proposed algorithms to analyze this Q. N We use a variety of label distributions to obtain a set of object labels corresponding to the maximum accuracy. This method is computationally complex and relies on an enumeration strategy.

[0090] Here, the number of iterations θ is used to control the number of different object label sets; that is, the maximum accuracy is obtained in θ analyses, thus determining the corresponding optimal object label set. The question then becomes how to determine the object label matrix L required for these θ analyses. L is an N×θ matrix, where each row represents the label value of an object in different object label sets; and each column represents the object label set in different iterations. Since enumeration cannot be used, the object labels in the object label sets of each iteration need to be randomly generated. However, since θ is much smaller than Q... N Therefore, the random numbers need to be uniformly distributed among integer values ​​from 1 to Q. If the object label set is regenerated randomly in each iteration, the uniform distribution characteristic will be lost. Therefore, the object label values ​​and object label sets used in all iterations must be randomly generated simultaneously, i.e., the object label matrix must be generated all at once. This is to ensure that the sample sizes are θ and Q. N This yields approximately the maximum accuracy.

[0091] In summary, let the label values ​​of all objects form an array R, which is an N×θ dimensional array. The label values ​​are q = 1, ..., Q, and are uniformly distributed to form array R. All columns of matrix L are connected sequentially to form array R. Therefore, after determining array R, it is folded to form matrix L, as shown in equation (2).

[0092] L{i}=R((i-1)×N+1:i×N), i=1,...,θ (2)

[0093] In the formula: L{i} represents the i-th column of matrix L; the random numbers for the object label values ​​in R are implemented using the unifmd() function in MATLAB.

[0094] The above process forms the object label matrix L. However, due to computational limitations, L does not contain all object label sets; including all sets would require N×Q. N 1-order matrix.

[0095] Regarding determining the optimal set of object labels:

[0096] Based on the object label matrix L and the normalized data matrix The optimal set of object labels is determined using the Spectral Regression Discriminant Analysis (SRDA) algorithm. The SRDA analysis process is represented by functions. SRDA is based on the LDA algorithm, incorporating spectral analysis and regression model construction to achieve supervised, semi-supervised, and unsupervised learning. A connectivity graph is constructed using labeled or unlabeled data to characterize the discriminative structure within the dataset. The embedding function is obtained using the regression model based on the learning results, and data dimensionality reduction is achieved through function projection. The optimal set of object labels is then determined using SRDA. This involves two functions: the training function SRDAT() and the prediction function SRDAP(), as shown in equations (3) and (4), respectively.

[0097]

[0098] In the formula, nTrain represents the number of objects used for training in the object set, and nTrain∈[n1,n2,...,n] T ], n1 < n2 < ... < n T ≤N-1. It is a matrix The training object matrix consists of the first n rows of the object label matrix in the i-th iteration. L{i}(1:nTrain) is the training object label matrix consisting of the first n rows of the object label matrix in the i-th iteration. opt is an array of control parameters, including the RT regularization norm (default L2); the alpha regularization parameter (default 0.1); the gamma regularization parameter (default 0.05); and LASSOW, which uses the LASSO solution method (default LARs). The output value is MOD. i , is the trained model.

[0099]

[0100] In the formula AC i It is the accuracy of the i-th iteration, AC i ∈[0,1]. Then the training model and accuracy corresponding to the i-th iteration are MOD respectively. i and AC i Combining equations (3) and (4), we iterate through i = 1, ..., θ and nTrain ∈ [n1, n2, ..., n T The maximum accuracy after θ iterations is determined as shown in equation (5).

[0101]

[0102] In the formula AC opt It is the maximum accuracy; Li opt} is the optimal set of object labels for maximum accuracy, and is a column of L; nTrainopt is the optimal number of training objects for maximum accuracy. Therefore, L{i opt} is the optimal composition of the system fault evolution process formed by each sub-evolution process.

[0103] Analysis of the role of each sub-evolutionary process:

[0104] According to L{i opt The object label in} belongs to the sub-evolution process e q In the case of Li, statistics opt} belongs to e q Number of objects N q As shown in equation (6).

[0105]

[0106] From equation (6), we can see that Based on Li opt Statistics belong to e q The moment the object appears, that is, at Li opt} belongs to e q The row number q of the object. The objects belonging to e... q The times at which all objects appear constitute e q object position array Ns q As shown in equation (7).

[0107]

[0108] Where: Ns q |n represents Ns q Then add the number of elements n.

[0109] From equation (7), we can see that In the overall evolution process, the sub-evolution process e q The frequency of the object in the middle is The larger the value, the better. The frequency set of each sub-evolutionary process is P = [p1, ..., p...]. Q Sub-evolution process e q The concentration of objects appearing in the middle is The larger the value, the better, where J q The calculation is shown in equation (8).

[0110]

[0111] The set of occurrence concentrations of each sub-evolutionary process is Z = [z1, ..., z]. Q ].

[0112] Sub-evolution process eq The higher the frequency of an element, the greater its proportion in the overall evolutionary process, meaning it is included in e. q The more objects in the process, the more likely the overall evolutionary process will revolve around the sub-evolutionary process e. q Development proceeds. Sub-evolution process e q The greater the concentration, the more likely e is to be q The more concentrated and continuous the influence on the overall evolution, the better. In comparison, multiple elements belonging to e... q If objects appear consecutively, they will have a continuous effect on the overall evolutionary process; if they appear discontinuously, their effect is intermittent, influenced by the intermittent effects of other sub-evolutions. Simply put, the effect of two objects appearing consecutively is greater than the effect of two objects appearing intermittently. Determining the influence of each subsystem on the overall system's evolutionary process requires comprehensive consideration of both frequency and concentration.

[0113] The aim of this method is to determine the role of multiple sub-evolutionary processes in the system failure evolution process. It involves identifying which objects, as measured during the evolution process, belong to each sub-evolutionary process. This is equivalent to cluster analysis of all objects, with each cluster corresponding to a different sub-evolutionary process. Finally, the influence of each sub-evolutionary process on the overall evolution process is determined by the frequency and concentration of object occurrences.

[0114] This study takes an electrical system as an example. The system fault evolution is affected by six factors, F = {f1, f2, f3, f4, f5, f6}. Among them, voltage f1 has a range of [12, 15] V; current f2 has a range of [0.7, 0.85] mA; temperature f3 has a range of [11, 24] ℃; humidity f4 has a range of [77, 94] %; air pressure f5 has a range of [100, 105] kPa; and vibration f6 has a range of [185, 236] Hz. Subsystems are divided from the perspective of fault characteristics, with the subsystem set S = {s1, s2, s3} and Q = 3; the set of sub-evolution processes is E = {e1, e2, e3}. The evolution process is measured 100 times at equal time intervals, forming the object set O = {o1, ..., o 100 Each object contains the above 6 factor values, and these objects and factors constitute the basic data matrix Γ. 6×100 The changes in factor values ​​for 100 objects are as follows: Figures 4 to 9 As shown.

[0115] Use Γ and equation (1) to form the normalized matrix. All data and Figures 4 to 9 Similarly, it will not be given here.

[0116] Let the number of iterations θ = 100000 and N = 100, forming a label array R for all objects, which is a 10000000-dimensional array. The array R is generated using the MATLAB function unifmd() to generate uniformly distributed random numbers on q = 1, 2, 3. L{i} is obtained using i = 1, ..., 100000 and equation (2), ultimately forming the object label matrix L.

[0117] Using equation (5) and matrix The analysis is performed using L and opt, where opt uses the default value. Let nTrain∈[20,30,40,50,60,70,80], n T =80, in equation (5) iterates through equations (3) and (4) for training and prediction respectively, and obtains the accuracy AC for all analyses of θ = 100000. i Let i = 1, ..., 100000. Determine the maximum accuracy Max{AC}. i}, that is, the maximum accuracy ACopt = 0.85; the optimal object label set L{i opt The tag value of the object in} is as follows Figure 10 As shown; the optimal number of training objects nTrain opt =60.

[0118] L{i opt The number of objects in the sub-evolutionary process is N1 = 31, N2 = 33, and N3 = 36, respectively. The frequency set of each sub-evolution is P = [0.31, 0.33, 0.36], indicating that the role of sub-evolutionary process e3 is greater than that of e2, and e2 is greater than that of e1. According to equation (8), Z1 = (2+4+2+2+2) / 31 = 0.3871, Z2 = (4+3+3+2+3+2) / 33 = 0.5152, and Z3 = (2+3+2+2+2+2+3+2+2+2+2) / 36 = 0.6667. The concentration set of each sub-evolution is Z = [0.3871, 0.5152, 0.6667]. The role of each sub-evolutionary process in terms of concentration is the same as the frequency result.

Claims

1. A method for analyzing the role of sub-evolutionary processes in system fault evolution, characterized in that, To study the distinctive sub-evolutionary processes inherent in the system failure evolution process and to determine the role of each sub-evolutionary process in the overall evolution process, a sub-evolutionary process role analysis method based on spectral regression discriminant analysis is proposed. A basic data matrix and a normalized data matrix are constructed based on the object set obtained from the measurement evolution at each time point; Generate a set of object labels using uniformly distributed random numbers and fold them to form an object label matrix; The object label matrix is ​​trained and predicted using spectral regression discriminant analysis to obtain the maximum accuracy, optimal object label set, and optimal number of training objects; frequency and concentration are defined to analyze the role of each sub-evolutionary process; and it is used to determine the role of each sub-evolutionary process and perform cluster analysis on the object set during system fault evolution. The steps are as follows: Step 1: Construct the basic data matrix Γ; the input data consists of the object set O, the factor set F, and the object o. n In factor f m Factor values ​​below The output data is the basic data matrix Γ; Step 2: Construct a normalized dataset Input data is Γ, output data is The method uses the 2-norm normalization function normalize(); Step 3: Construct the object label matrix L; the input data is the number of objects N, the number of iterations θ, and the number of subsystems Q; the output data is L; the method is to randomly generate an object label matrix L composed of object label numbers uniformly distributed in [1,Q]. Step 4: Determine the optimal set of object labels; input data is L and the set of control parameters opt; the output data is the maximum accuracy AC. opt , and its corresponding optimal object label set L{i opt } and the number of training objects nTrain opt The method used was SRDA (Regression-Based Discriminant Analysis). Step 5: Analyze the role of each sub-evolution; input data is L{i opt The algorithm consists of three sub-evolutionary sets: object label value q∈[1,Q], and sub-evolutionary set E. The output data are the frequency P and concentration Z of the appearing objects. A specific algorithm is proposed, and the role of each sub-evolutionary process in the overall evolutionary process is analyzed. Construct a 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, N is the number of objects; object o n It is a vector composed of all factor values. It is object o n In factor f m The following factor values; Forming the basic data matrix Γ M×N As shown in Table 1; Table 1 Basic Data Matrix Γ M×N The system contains a set of subsystems S = {s1, ..., s...} Q }, s q ∈S, q=1,...,Q, where Q is the number of subsystems; the set of sub-evolutionary processes is E={e1,...,e Q }, e q It is s q The system failure evolution process; The division of subsystems is based on the fault characteristics of the objects; Constructing a normalized data matrix Normalize each column of Γ using the 2-norm, i.e. The normalization function used is shown in equation (1); Construct an object label matrix; let the object label matrix be L, which is an N×θ matrix, where N is the number of objects and θ is the number of iterations; let the label values ​​of all objects form an array R, which is an N×θ dimensional array; use q=1,...,Q as label values ​​and distribute the label values ​​evenly to form array R; connect all columns of matrix L in order to form array R, so after determining array R, fold it to form matrix L, as shown in equation (2); L{i}=R((i-1)×N+1:i×N), i=1,...,θ (2) In the formula: L{i} represents the i-th column of matrix L; the random numbers for the object label values ​​in R are implemented using the unifmd() function in MATLAB; Determine the optimal set of object labels; Based on the object label matrix L and the normalized data matrix To determine the optimal set of object labels, the spectral regression discriminant analysis method (SRDA) is used to determine the optimal set of object labels, including the training function SRDAT() and the prediction function SRDAP(), as shown in equations (3) and (4) respectively. In the formula, nTrain represents the number of objects used for training in the object set, and nTrain∈[n1,n2,...,n] T ], n1 < n2 < ... < n T ≤N-1; It is a matrix The first n rows of the training object matrix are used; L{i}(1:nTrain) is the first n rows of the object label matrix in the i-th iteration, used to form the training object label matrix; opt is an array of control parameters, including the RT regularization norm, which defaults to L2; the alpha regularization parameter, which defaults to 0.1; the gamma regularization parameter, which defaults to 0.05; LASSOW uses the LASSO solution method, with a default value of LARs; the output value is MOD. i It is the trained model; In the formula AC i It is the accuracy of the i-th iteration, AC i ∈[0,1]; Then the training model and accuracy corresponding to the i-th iteration are MOD respectively. i and AC i Combining equations (3) and (4), traverse i = 1, ..., θ and nTrain ∈ [n1, n2, ..., n T The maximum accuracy after θ iterations is determined as shown in equation (5); In the formula, ACopt is the maximum accuracy; L{i opt } is the optimal set of object labels for maximum accuracy, and is a column of L; nTrain opt It is the optimal number of training objects for maximizing accuracy; L{i opt } is the optimal composition of the system fault evolution process formed by each sub-evolutionary process; Analysis of the role of each sub-evolutionary process; based on Li opt The object label in} belongs to the sub-evolution process e q In the case of Li, statistics opt } belongs to e q Number of objects N q As shown in equation (6); From equation (6), we get Based on L{i opt Statistics belong to e q The moment the object appears, that is, at Li opt } belongs to e q The row number q of the object; will belong to e q The times at which all objects appear constitute e q object position array Ns q As shown in equation (7); Where: Ns q |n represents Ns q Then add the number of elements n; From equation (7), we can see that In the overall evolution process, the sub-evolution process e q The frequency of the object in the middle is The larger the value, the better; the frequency set of each sub-evolutionary process is P = [p1, ..., p...]. Q Sub-evolution process e q The concentration of objects appearing in the middle is The larger the value, the better, where J q The calculation is shown in equation (8); The set of occurrence concentrations of each sub-evolutionary process is Z = [z1, ..., z]. Q ]; Sub-evolution process e q The higher the frequency of an element, the greater its proportion in the overall evolutionary process, meaning it is included in e. q The more objects in the process, the more likely the overall evolutionary process is to revolve around the sub-evolutionary process e. q Development; Sub-evolution process e q The greater the concentration, the more likely e is to be q The more concentrated and continuous the influence on the overall evolution, the more likely it is to be affected by multiple factors belonging to e. q If the objects appear consecutively, they will have a continuous effect on the overall evolution process; When they appear discontinuously, their effect is intermittent, influenced by the intermittent effects of other sub-evolutions; simply put, the effect of two objects appearing consecutively is greater than the effect of two objects appearing intermittently. Determining the impact of each subsystem on the overall system evolution process requires comprehensive consideration of both frequency and concentration.

2. The method for analyzing the sub-evolutionary process of system fault evolution according to claim 1, characterized in that, Used for analyzing electrical systems, the system fault evolution is affected by six factors, F = {f1, f2, f3, f4, f5, f6}; where voltage f1 has a range of [12, 15] V; current f2 has a range of [0.7, 0.85] mA; temperature f3 has a range of [11, 24] ℃; humidity f4 has a range of [77, 94] %; air pressure f5 has a range of [100, 105] kPa; and vibration f6 has a range of [185, 236] Hz. Subsystems are divided from the perspective of fault characteristics, and the subsystem set is S = {s1, s2, s3}, Q = 3; the set of sub-evolution processes is E = {e1, e2, e3}; the evolution process is measured 100 times at equal time intervals, forming the object set O = {o1, ..., o 100 Each object contains the above 6 factor values, and these objects and factors constitute the basic data matrix Γ. 6×100 ; Obtain the changes in factor values ​​for 100 objects; Use Γ and equation (1) to form the normalized matrix. Let the number of iterations θ = 100000 and N = 100, forming a label array R for all objects, which is a 10000000-dimensional array; use the unifmd() function of MATLAB to generate a uniformly distributed random number on q = 1, 2, 3 to realize the array R; use i = 1, ..., 100000 and equation (2) to obtain L{i}, finally forming the object label matrix L; Using equation (5) and matrix L and opt are used for analysis, where opt uses the default value; let nTrain∈[20,30,40,50,60,70,80], n T =80, in equation (5) iterates through equations (3) and (4) for training and prediction respectively, and obtains the accuracy AC for all analyses of θ = 100000. i , i = 1,...,100000; determine the maximum accuracy Max{AC} i }, that is, maximum accuracy AC opt =0.85; Obtain the optimal object label set L{i opt The label values ​​of the objects in}; the optimal number of training objects nTrain opt =60; L{i opt The number of objects in the sub-evolutionary process is N1 = 31, N2 = 33 and N3 = 36 respectively; the frequency set of each sub-evolution is P = [0.31, 0.33, 0.36], indicating that the role of sub-evolutionary process e3 is greater than that of e2, and e2 is greater than that of e1; according to equation (8), Z1 = (2+4+2+2+2) / 31 = 0.3871, Z2 = (4+3+3+2+3+2) / 33 = 0.5152, Z3 = (2+3+2+2+2+2+3+2+2+2+2) / 36 = 0.6667; the concentration set of each sub-evolution is Z = [0.3871, 0.5152, 0.6667]; the role of each sub-evolutionary process in terms of concentration is the same as the frequency result.

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