A method for determining object distribution in system fault evolution process

Abstract

The application relates to the technical field of system fault analysis in the safety field, and provides a method for determining object distribution in a system fault evolution process, which is used for studying the object distribution belonging to different classes in the system fault evolution process; the method is based on UKSR, cooperates with a K-means and a mutual information method, constructs a randomly and uniformly distributed object label set, and proposes a criterion for the optimal object label set; the optimal object label set when the object label and object data correlation is maximum is determined through circulation; the label value in the set is the optimal object distribution condition; and the method is used for determining the object distribution in the system fault evolution process. The method for determining the object distribution in the system fault evolution process can represent the optimal object distribution.

Description

Technical Field

[0001] This invention relates to the field of system fault analysis technology in the field of security, and in particular to the determination of object distribution in the system fault evolution process, providing a method for determining object distribution in the system fault evolution process. Background Technology

[0002] The purpose of any system is to fulfill a predetermined function. Under the influence of multiple factors, the system's ability to achieve this function inevitably changes; this process of change is called the system failure evolution process. The system failure evolution process is an inherent attribute and essential characteristic of the system, representing the system's response to changes in external characteristics. The characteristics of the system failure evolution process at a certain moment can be defined as the system's functional state, representing the system's functionality at that moment. Research on system failure evolution and functional state is prevalent in fields such as safety, systems, and reliability. For example, safety assessments are generally based on the system state at different times and the corresponding factors to evaluate and predict system safety; similarly, sampling system operating signals is also a collection of system state and factors, serving as a basis for judging the system state. Therefore, current research on the system failure evolution process is generally conducted through measurements of the system at different times. The vector formed by the factor values ​​of all factors measured at a certain moment can be defined as an object. The fundamental data for studying the evolution process is the set of objects measured at all times; this set is the system's time-series failure data sequence. Studying the characteristics of the set of objects representing the time-series failure sequence reflects the characteristics of the system failure evolution process. However, it is necessary to classify objects and determine their distribution in an unsupervised manner, thereby determining the sub-evolutionary process, and finally summarizing the evolutionary characteristics to provide a way to predict and suppress fault evolution.

[0003] Research on various system failure processes and their evolutionary impacts is gradually increasing, especially in recent years with a surge in research on system failure evolution. These findings present theories, methods, and algorithms for studying system failure processes. Broadly speaking, these can be categorized into methods specific to system characteristics and data, and more general methods. The latter primarily analyzes and predicts system functionality by examining the values ​​of various factors at different times and their temporal relationships. Research on system failure evolution is conducted through objects; the existence of measurement time intervals limits the number of objects; the evolutionary process has a complex structure and hierarchy; and challenges remain with evolutionary representation methods, mathematical models, and unsupervised learning. Therefore, existing research is difficult to apply to the study of system failure evolution processes.

[0004] Therefore, there is an urgent need to provide a method for determining the distribution of objects during the system failure evolution process, which can characterize the optimal object distribution and thus meet the research needs of existing system failure evolution processes. Summary of the Invention

[0005] The purpose of this invention is to provide a method for determining the distribution of objects during the evolution of system faults, so as to solve the technical problem that there is no method for determining the distribution of objects during the evolution of system faults in the prior art.

[0006] This invention provides a method for determining the distribution of objects during system fault evolution. This method is proposed to study the distribution of objects belonging to different classes during system fault evolution. Based on UKSR, and combined with K-means and mutual information methods, the method constructs a randomly uniformly distributed set of object labels and proposes a criterion for the optimal object label set. The optimal object label set is determined through iteration when the correlation between object labels and object data is maximized. The label values ​​in the set represent the optimal object distribution. This method is used to determine the object distribution during system fault evolution.

[0007] The process and construction of the object distribution determination method;

[0008] Step 1: Obtain the object set and factor set through the evolutionary process. Let the set of factors influencing the evolutionary 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.

[0009] Step 2: Set the number of object categories θ and the number of iterations Q. The number of object categories is the number of unique object label values, which is also the number of clusters in the object clustering analysis. θ is obtained by performing clustering analysis only on object features, or by determining the semantic level based on the actual situation. The number of iterations Q is the number of times the mutual information between the base data and the label data is compared. Since this is unsupervised learning, each object has θ label values. If there are N objects, there will be at most θ label values. N The set of object label values, i.e., the combinatorial explosion problem, therefore let Q < θ N As the number of loop iterations.

[0010] Step 3, establish the basic data matrix. Object o n It is a vector composed of all factor values. 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.

[0011] Table 1 Basic Data Matrix Γ

[0012]

[0013] Step 4, create a set of object tags. The set of object tags used in each loop is different, L i Let represent the set of object labels for the i-th iteration, where i = 1, ..., Q. Theoretically, i = 1, ..., θ N , but θ N The value is too large; let Q be the actual number of iterations. This results in an MI obtained after looping Q times. n +MI t The maximum value may be less than the total θ of the loop. N The result after this. Only when the feature distribution of the object label set used in loop Q times is consistent with loop θ. N When the feature distribution of the object label set is the same, the resulting MI n +MI t It is close. Therefore, the set of object labels L must be generated all at once, and the object label values ​​should be uniformly random distributed in [1, θ]. That is, L = L1|,…,|L Q Let i = 1, ..., Q, where | denotes the concatenation of sets, and L is a set with Q × N elements; L i It is a set of N elements.

[0014] Steps 5 and 6 construct the training and test sets. n =Γ(1:nT) and Γ t =Γ(nT+1:end) represents the training set and test set derived from the basic data matrix, respectively. 1:nT represents the first nT objects in the basic data matrix, and nT+1:end represents all objects after nT in the basic data matrix.

[0015] Steps 7 and 8 construct the object label training and test sets. n =L i (1:nT) and G t =L i (nT+1:end) represent the training set and test set derived from the object label set, respectively.

[0016] Step 9 yields the unsupervised nuclear spectrum regression training model. The function is called as shown in equation (2), and the UKSR algorithm is used for unsupervised training, requiring parameter Γ. n , where opt is the set of control parameters, and the regression training model model is obtained.

[0017] model = U n (Γ n ,opt) (2)

[0018] Steps 10 and 11 yield the unsupervised nuclear spectral regression training set test results and test set test results. The calling functions are shown in equations (3) and (4) respectively, using the UKSR algorithm to perform unsupervised testing on the training and test sets, obtaining the training set test results F. n Training results F on the test set t Parameter C is G n The unique value is the tag class.

[0019] F n =U t (Γ n (3)

[0020] F t =U t (Γ t (4)

[0021] Steps 12 and 13 use the K-means algorithm to obtain the training set test results F. n Training results F on the test set t The clustering results are obtained by calling equations (5) and (6) respectively, setting the number of clusters K, and obtaining the clustering results L respectively. n and L t .

[0022] L n =L KM (F n ,K) (5)

[0023] L t =L KM (F t ,K) (6)

[0024] In steps 14 and 15, the cross-correlation between the training set and the test set in the basic data and label set is calculated using the mutual information theorem, and the functions are called as shown in equations (7) and (8) respectively.

[0025] MI n =MI(G n ,L n (7)

[0026] MI t =MI(G t ,L t (8)

[0027] Step 16: Determine the optimal object distribution. Since the number of iterations is set to Q, each iteration will have a different object label matrix L. i Starting with the basic data matrix, once Γ, nT, opt, C, and K are determined, L is used in Q iterations.n and L t Unchanged. G remains unchanged as the number of iterations changes. n and G t It is constantly changing because L i It is subject to change. MI n =MI(G n ,L n ) represents the cross-correlation between the object data used for training and the object labels used for training; MI t =MI(G t ,L t () represents the cross-correlation between the object data used for testing and the object labels used for testing. L i This represents the label values ​​of all objects in the object set at the i-th iteration, i.e., the distribution of object label values. If MI n and MI t If the values ​​are all close to 1, it indicates that the object data and object labels have the greatest correlation under both training and testing conditions. In this case, the resulting object label set L is... i For the optimal set of object labels L opt This represents the strongest correlation between the object data change characteristics and the object label change characteristics in these Q iterations, therefore L opt It is the optimal set of object labels for Γ. The object label values ​​in the set represent the optimal object distribution, as shown in Equation (9).

[0028]

[0029] Equation (9) is the criterion for the optimal object label set. The above yields the object distribution during the system fault evolution process, i.e., the optimal label value distribution of all objects. This can be understood as the class label values ​​of objects measured at different times during the evolution process, indicating which class they belong to at that time. This is equivalent to cluster analysis of the object set when the number of classes is known and the label values ​​of each object are unknown. Through Q iterations, Q object label sets are compared, and when MI... n +MI t The set of object labels obtained when the maximum value is reached is the optimal set of object labels L. opt This characterizes the optimal object distribution.

[0030] The beneficial technical effects of this invention are as follows: The method for determining object distribution during system fault evolution provided by this invention can characterize the optimal object distribution. Furthermore, by grouping objects with the same label into one category, a sub-evolutionary process is corresponding to it, thus achieving evolutionary process decomposition. Sub-evolutionary processes exhibit more obvious change characteristics, which is beneficial for mathematical abstraction and the formation of mathematical models. Then, based on the occurrence times of different object classes, the mathematical models of each sub-evolution are superimposed to form the overall evolutionary mathematical model, thereby providing an analytical method based on actual data for describing the system fault evolution process. Attached Figure Description

[0031] Figure 1 A two-dimensional schematic diagram of the system fault evolution process is shown;

[0032] Figure 2 A flowchart of the object distribution determination method is shown;

[0033] Figure 3 A schematic diagram showing the variation of factor values ​​in the factor voltage is shown;

[0034] Figure 4 A schematic diagram showing the variation of the factor value of the factor current is shown;

[0035] Figure 5 A schematic diagram showing the variation of the factor value of temperature is shown;

[0036] Figure 6 A schematic diagram showing the changes in the humidity factor value is provided.

[0037] Figure 7 A schematic diagram showing the changes in the factor values ​​of the factor air pressure is shown;

[0038] Figure 8 A schematic diagram illustrating the changes in factor values ​​during factor vibration is shown;

[0039] Figure 9 A schematic diagram of the distribution of object label values ​​is shown. Detailed Implementation

[0040] 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.

[0041] The evolution of system failures requires the study of an object set, fundamentally involving the classification and distribution of these objects, which is generally an unsupervised learning process. Object classification facilitates the decomposition of the evolutionary process, while object distribution reveals the evolutionary characteristics in response to time and other factors. Therefore, this paper proposes using Unsupervised Kernel Spectral Regression (UKSR) as the core algorithm to determine the distribution of object class label values ​​during the system failure evolution process.

[0042] Overview of the system failure evolution process:

[0043] System failure evolution is an inherent property of a system, representing the changing ability of a system to perform its intended functions under the influence of multiple factors. The system's functionality at a given moment is its functional state. The former describes the overall characteristics of a system failure, while the latter describes the local characteristics of a system failure at a given moment. System failure evolution is the response of the system's intrinsic characteristics to external characteristics. The system's intrinsic characteristics are the functional characteristics of the components that make up the system, and the structure of the system formed by these components; these are determined during system design and remain largely unchanged during operation. The system's external characteristics are the environmental factors and their changes during system operation; these are considered during system design but remain uncertain during operation. Therefore, although the system's intrinsic characteristics are fixed, changes in external characteristics still lead to uncertainty in the evolution process. From the perspective of the system's functional state, the evolution process always fluctuates between two extreme cases: complete reliability and complete failure.

[0044] The uncertainty of the evolutionary process stems from its complex structure and hierarchy. Structurally, it includes experienced events, influencing factors, logical relationships, and evolutionary conditions. Experienced events constitute the entities and key nodes in the system's failure evolution process, marking its existence. Influencing factors are the driving force of the evolutionary process, affecting the functionality of events and thus the functional state of the system. Logical relationships are the comprehensive ways in which events interact. Evolutionary conditions are the conditions under which causal events lead to resultant events. Logical relationships and evolutionary conditions are attached to events, and influencing factors also affect evolution through events; therefore, events are the core of the evolutionary process. Hierarchically, it includes the evolution layer, event layer, factor layer, factor phase layer, and factor phase value layer. The state of objects in each layer is jointly determined by the states of all objects in the lower layer, i.e., the superposition of the states of all objects in the lower layer. This can be realized using wave functions in quantum mechanics. Similarly, the superposition of the states of all events still directly affects the evolution. Therefore, events play a crucial role in both the structure and hierarchy of evolution.

[0045] Abstracting and mathematically describing the system failure evolution process is a prerequisite for this research. Currently, there are two methods for representing the evolution process: two-dimensional planar space representation and multi-dimensional hyperspace representation.

[0046] Figure 1This is a two-dimensional planar representation. The horizontal axis represents evolution time, and the vertical axis represents the system's functional state. The zero point represents the system's functional state at a certain moment in the evolution process, because the state where the absolute function is zero during the evolution process cannot be determined. The thick solid line in the figure represents the system's fault evolution process, fluctuating between reliable and failure states. At t... n The object is obtained by measuring at any time. n o n It is t n A vector composed of all factor values ​​at any given time. After countless measurements and obtaining countless objects over an evolutionary period, the entire evolutionary process within that period can be described. However, in reality, the number of objects is always finite. The resulting set of objects is a time-series fault data sequence, with evolution time as its variable; therefore, the evolutionary process extends infinitely in the direction of evolution time. Method two represents it in a multidimensional hyperspace. Using each factor as a spatial coordinate axis, perpendicular to each other, all factors constitute a multidimensional hyperspace. Generally, the range of change for all factors during the evolutionary process is always finite; therefore, the evolutionary process is also confined to a finite space, forming a winding, tortuous curve. Object o n The projection onto each axis represents the factor value, and all objects exhibit a distribution state in space. This distribution state is independent of evolution time, only related to the factor and its value. In summary, in two-dimensional planar representation, time should be used as the variable to represent the object set, studying the evolutionary linearity's variation with time; in multidimensional hyperspace representation, factor values ​​are used as the variable to represent the object set, studying the evolutionary distribution's variation with factors. The former primarily uses time-series data sequences (planar distribution of objects), while the latter primarily uses curved surface morphology (multidimensional spatial distribution of objects). The first representation method will be used for this study.

[0047] Based on the abstraction and representation of evolution, a spatial fault network theory is proposed to mathematically describe the system fault evolution process. Generally, it first constructs a characteristic function by combining the probability of an event with the change of a single factor. Then, it superimposes the characteristic functions of all factors for that event to form the event probability distribution. Finally, it obtains the system fault probability distribution based on the structural relationship between the event and the evolution. When all factor changes are represented by time, the system fault probability distribution is a function of time, and the evolution process is represented by a two-dimensional plane. When represented by changes in factor values, the system fault probability distribution is a function of all factor values, and is represented by a multidimensional hyperspace. Here, the system fault probability distribution can be equivalent to the system functional state.

[0048] The question is whether an object composed of factor values ​​can represent the functional state of a system. This is because the system's functional state is the response of its intrinsic characteristics to its extrinsic characteristics at a given moment. Since the intrinsic characteristics remain largely unchanged, the system's functional state is essentially dependent on its extrinsic characteristics. An object is precisely an instantiated version of these extrinsic characteristics. Furthermore, it has been proven that changes in the object can characterize changes in the system's functional state under both linear and nonlinear conditions, the diversity of object changes is greater than the diversity of functional states. Therefore, the object of study can fully explain changes in the system's functional state, and thus characterize the system's fault evolution process.

[0049] Regarding the distribution of objects in evolution:

[0050] As mentioned above, studying the evolution of system failures must be based on a set of objects. In a two-dimensional plane representation, the set of objects is actually a sequence of time-series fault data. It represents the external characteristics of the system at all measurement moments, i.e., the factor values ​​of all factors.

[0051] In fact, existing studies on system functional states are all based on sets of objects. Studying the system failure evolution process in a two-dimensional representation involves classifying objects and then studying their distribution over time throughout the entire evolution process. The overall evolutionary procedure is complex and may consist of multiple superimposed sub-evolutionary processes. A system may be composed of several different parts in terms of function or structure, and under the influence of the same factors, different parts exhibit different evolutionary characteristics, but generally, one sub-evolutionary process dominates. The dominant sub-evolutionary process may differ at different times. Although all objects in the evolutionary process represent the overall evolution, cluster analysis of the object set can yield several categories of objects, corresponding to different sub-evolutionary processes. The different temporal distributions of these categories of objects also indicate that different sub-evolutionary processes operate at different times. Object distribution can show the temporal distribution of each sub-evolutionary process, helping to understand the decomposability of the overall evolution process. The characteristics of the decomposed sub-evolutionary processes are clearer, which is conducive to forming a more suitable mathematical model for representation. The prerequisite for achieving the above research is determining the distribution of objects belonging to different sub-evolutionary processes.

[0052] Determining object distribution involves either clustering analysis after determining the number of sub-evolutions, or autonomous object clustering analysis when the number of sub-evolutions is unknown. Since the research is based on a fundamental data matrix, supervised learning requires class labels. However, the object set obtained from evolutionary measurements is unlabeled, necessitating unsupervised learning methods. Typically, the number of object classifications in evolution is determined, such as the evaluation level in system safety assessment. This results in a situation where, on the one hand, the fundamental data lacks class labels, and on the other hand, the number of classifications is fixed—that is, although the number of classifications is known, the class labels of specific objects are unknown. Furthermore, the nonlinear relationships between factors need to be considered, requiring the algorithm to handle nonlinear spatial mappings. Object distribution is achieved through object class label values; therefore, it is necessary to determine the class labels of all objects under unsupervised and nonlinear conditions to achieve the goals of object distribution and evolutionary decomposition.

[0053] Overview of basic algorithms:

[0054] In general, the above problems can be solved using the Spectral Regression (SR) method. Spectral methods are powerful tools for dimensionality reduction and manifold learning, using information contained in the eigenvectors of the data relation matrix to reveal low-dimensional structures in high-dimensional data. SR is an efficient regression framework for regularized subspace learning, transforming the problem of learning embedding functions into a regression framework, avoiding dense matrix eigenvalue decomposition; it can achieve supervised, unsupervised, and semi-supervised learning. Considering the nonlinearity of mapping, the Kernel Spectral Regression (KSR) algorithm is proposed to achieve nonlinear mappings in different dimensional spaces. Further considering the case of unlabeled objects, the UKSR algorithm is proposed to implement KSR model learning in the unlabeled case. Using the function U... n () and U t () indicates a call to the UKSR algorithm, used for training the unsupervised kernel spectral regression model and testing the regression model, respectively. The regression model is obtained through graph construction, response generation, and projection learning, and is mainly based on KSR.

[0055] For U t Cluster analysis is performed on the training set test results and the test set test results obtained from (), using the K-means clustering iterative method. Here, the function L is used. KM The () function is used for cluster analysis of datasets and can obtain clustering results for both the training set and the test set.

[0056] The research originates from the correlation between the training set results of the basic data matrix and the label training set of the object label set, as well as the correlation between the test set results and the label test set, and is implemented using mutual information theory. Mutual information is an information metric in information theory, referring to the correlation between two sets, with a value range of [0,1], where 0 represents that the two sets are uncorrelated, and 1 represents that the two sets are identical. MI(G) is used to... t ,L t The mutual information function is called to obtain the cross-correlation degree for data correlation analysis. The mathematical model is shown in equation (1).

[0057]

[0058] In equation (1), X is a set of data derived from reality, and X' is data derived from calculation; MI() is the normalized mutual information function (its value is the cross-correlation degree), and MI'() is the unnormalized mutual information function; p(x i ) and p(x' j ) is any data in the dataset that belongs to x. i and x' j The probability, P(x) i ,x' j ) is p(x i ) and p(x' j The joint probability of X and X'; H(X) and H(X') are the entropies of X and X'.

[0059] As described above, U n (), U t (), L KM () and MI() are the basic algorithms used in the object distribution determination method. They are used multiple times in the method flow, so they will be explained in detail here.

[0060] The process and structure of the method for determining object distribution:

[0061] The process of determining object distribution is as follows: Figure 2 As shown.

[0062] Step 1: Obtain the object set and factor set through the evolutionary process. Let the set of factors influencing the evolutionary 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.

[0063] Step 2: Set the number of object categories θ and the number of iterations Q. The number of object categories is the number of unique object label values, which is also the number of clusters in the object clustering analysis. θ is obtained by performing clustering analysis only on object features, or by determining the semantic level based on the actual situation. The number of iterations Q is the number of times the mutual information between the base data and the label data is compared. Since this is unsupervised learning, each object has θ label values. If there are N objects, there will be at most θ label values. N The set of object label values, i.e., the combinatorial explosion problem, therefore let Q < θ N As the number of loop iterations.

[0064] Step 3, establish the basic data matrix. Object o n It is a vector composed of all factor values. 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.

[0065] Table 1 Basic Data Matrix Γ

[0066]

[0067] Step 4, create a set of object tags. The set of object tags used in each loop is different, L i Let represent the set of object labels for the i-th iteration, where i = 1, ..., Q. Theoretically, i = 1, ..., θ N , but θ N The value is too large; let Q be the actual number of iterations. This results in an MI obtained after looping Q times. n +MI t The maximum value may be less than the total θ of the loop. N The result after this. Only when the feature distribution of the object label set used in loop Q times is consistent with loop θ. N When the feature distribution of the object label set is the same, the resulting MI n +MI t It is close. Therefore, the set of object labels L must be generated all at once, and the object label values ​​should be uniformly random distributed in [1, θ]. That is, L = L1|,…,|L Q Let i = 1, ..., Q, where | denotes the concatenation of sets, and L is a set with Q × N elements; L i It is a set of N elements.

[0068] Steps 5 and 6 construct the training and test sets. n =Γ(1:nT) and Γ t=Γ(nT+1:end) represents the training set and test set derived from the basic data matrix, respectively. 1:nT represents the first nT objects in the basic data matrix, and nT+1:end represents all objects after nT in the basic data matrix.

[0069] Steps 7 and 8 construct the object label training and test sets. n =L i (1:nT) and G t =L i (nT+1:end) represent the training set and test set derived from the object label set, respectively.

[0070] Step 9 yields the unsupervised nuclear spectrum regression training model. The function is called as shown in equation (2), and the UKSR algorithm is used for unsupervised training, requiring parameter Γ. n , where opt is the set of control parameters, and the regression training model model is obtained.

[0071] model = U n (Γ n ,opt) (2)

[0072] Steps 10 and 11 yield the unsupervised nuclear spectral regression training set test results and test set test results. The calling functions are shown in equations (3) and (4) respectively, using the UKSR algorithm to perform unsupervised testing on the training and test sets, obtaining the training set test results F. n Training results F on the test set t Parameter C is G n The unique value is the tag class.

[0073] F n =U t (Γ n (3)

[0074] F t =U t (Γ t (4)

[0075] Steps 12 and 13 use the K-means algorithm to obtain the training set test results F. n Training results F on the test set t The clustering results are obtained by calling equations (5) and (6) respectively, setting the number of clusters K, and obtaining the clustering results L respectively. n and L t .

[0076] L n =L KM (F n ,K) (5)

[0077] L t =L KM (F t ,K) (6)

[0078] In steps 14 and 15, the cross-correlation between the training set and the test set in the basic data and label set is calculated using the mutual information theorem, and the functions are called as shown in equations (7) and (8) respectively.

[0079] MI n =MI(G n ,L n (7)

[0080] MI t =MI(G t ,L t (8)

[0081] Step 16: Determine the optimal object distribution. Since the number of iterations is set to Q, each iteration will have a different object label matrix L. i .from Figure 2 The left-hand flow starts with the basic data matrix. Once Γ, nT, opt, C, and K are determined, L... n and L t The process on the right remains unchanged. The flow on the right, however, changes with the number of iterations (G). n and G t It is constantly changing because L i It is subject to change. MI n =MI(G n ,L n ) represents the cross-correlation between the object data used for training and the object labels used for training; MI t =MI(G t ,L t () represents the cross-correlation between the object data used for testing and the object labels used for testing. L i This represents the label values ​​of all objects in the object set at the i-th iteration, i.e., the distribution of object label values. If MI n and MI t If the values ​​are all close to 1, it indicates that the object data and object labels have the greatest correlation under both training and testing conditions. In this case, the resulting object label set L is... i For the optimal set of object labels L opt This represents the strongest correlation between the object data change characteristics and the object label change characteristics in these Q iterations, therefore L opt It is the optimal set of object labels for Γ. The object label values ​​in the set represent the optimal object distribution, as shown in Equation (9).

[0082]

[0083] Equation (9) is the criterion for the optimal object label set. The above yields the object distribution during the system fault evolution process, i.e., the optimal label value distribution of all objects. This can be understood as the class label values ​​of objects measured at different times during the evolution process, indicating which class they belong to at that time. This is equivalent to cluster analysis of the object set when the number of classes is known and the label values ​​of each object are unknown. Through Q iterations, Q object label sets are compared, and when MI... n +MI t The set of object labels obtained when the maximum value is reached is the optimal set of object labels L. opt This characterizes the optimal object distribution. Furthermore, grouping objects with the same label into a single category corresponds to a sub-evolutionary process, thus decomposing the evolutionary process. Sub-evolutionary processes exhibit more pronounced change characteristics, facilitating mathematical abstraction and the formation of mathematical models. Then, based on the occurrence times of different object classes, the mathematical models of each sub-evolution are superimposed to form the overall evolutionary mathematical model, providing an analytical method based on real-world data for describing the system fault evolution process.

[0084] The proposed method was used to study the fault evolution process of an electrical system. According to step 1, the set of influencing factors for 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. Fifty evolution measurements were performed at equal time intervals, forming an object set O = {o1, ..., o...} 50}

[0085] Based on step 2, let the number of object categories θ = 3 and the number of iterations Q = 10000. θ = 3 means setting the object category labels to 1, 2, and 3 to represent the different categories to which the objects belong. The optimal set of object labels is determined during the 10000 iterations of comparison.

[0086] Based on step 3, the objects and factors are used to construct the basic data matrix Γ, and the changes in the factor values ​​of each object are as follows: Figures 3 to 8 As shown.

[0087] Following step 4, an object label set is established. A function is used to randomly generate label values ​​that are evenly distributed within the range [1,3], resulting in an object label set L with 10000 × 50 elements. i It has 50 elements, L = L1|,…,|L 10000 ,i=1,…,10000.

[0088] Based on steps 5 and 6, construct the training and test sets, and set nT = 40. The training set is Γ. n =Γ(1:40), the test set is Γ t =Γ(41:50).

[0089] Based on steps 7 and 8, construct the object label training set and test set, which are G respectively in the i-th iteration. n =L i (1:40) and G t =L i (41:50).

[0090] According to step 9, the unsupervised nuclear spectrum regression training model is obtained. Call equation (2) and set opt ​​to obtain the training model model.

[0091] Based on steps 10 and 11, equations (3) and (4) are called respectively to calculate the test results of the training set and the test set. C = θ = 3 is set, and the UKSR algorithm is used for calculation.

[0092] Based on steps 12 and 13, the clustering results of the training set test results and the test set training results are calculated by calling equations (5) and (6) respectively. K=10 is set and the K-means algorithm is used to obtain the results.

[0093] According to steps 14 and 15, Equations (7) and (8) are called respectively to calculate the cross-correlation of the training set and the cross-correlation of the test set.

[0094] Based on step 16, determine the optimal object distribution. Repeat this process 10,000 times, using 10,000 different object label sets for comparison, where MI... n +MI t The maximum value is the desired value. When the loop reaches 7365 iterations, MI... n +MI t =1.8 is the maximum value in 10,000 iterations, where the cross-correlation of the training set is MI. n =0.8, the cross-correlation of the test set is MI t =1. This indicates that the correlation between changes in object data and object labels reached 80% during training and 100% during testing, meaning the correlation between changes in object data and label data was the highest. The resulting optimal object label value distribution is as follows: Figure 9 As shown.

[0095] like Figure 9As shown, the object numbers with a class label value of 1 include 22: 2, 3, 7, 9, 12, 13, 14, 15, 18, 22, 24, 25, 27, 30, 31, 32, 33, 34, 36, 39, 48, and 49; the object numbers with a class label value of 2 include 16: 4, 5, 6, 17, 19, 21, 23, 26, 37, 38, 41, 42, 43, 46, 47, and 50; and the object numbers with a class label value of 3 include 12: 1, 8, 10, 11, 16, 20, 28, 29, 35, 40, 44, and 45. This indicates that the above object label value distribution is obtained when all objects are divided into 3 classes throughout the entire evolution process. Among them, objects with class label 1 play the greatest role in the evolution, accounting for 44% of all measurement times. That is, for 44% of the time, the sub-evolutionary process represented by the set of objects with class label 1 is dominant, followed by the set of objects with class label 2, and the set of objects with class label 3 has the least effect.

Claims

1. A method for determining the distribution of objects during the evolution of system faults, characterized in that, Based on UKSR, and combined with K-means and mutual information methods, this method constructs a randomly uniformly distributed set of object labels and proposes a criterion for the optimal set of object labels. The optimal set of object labels is determined by iterative analysis when the correlation between object labels and object data is maximized. The label values ​​in the set represent the optimal object distribution. This method is used to determine the object distribution during system fault evolution. The process and construction of the object distribution determination method: Step 1: Obtain the object set and factor set through the evolution process; let the factor set influencing the evolution process be... , , , is the number of factors; in The set of objects formed by measurements at each time point is , , is the number of objects; Step 2, set the number of object categories and number of loops The number of object categories is the number of unique object label values, and also the number of clusters in object clustering analysis. This can be obtained by clustering analysis based solely on object features, or by determining the semantic level based on the actual situation; number of iterations. This refers to the number of times mutual information comparisons are performed between the base data and the label data; since it is unsupervised learning, each object has... Type of label value; if it exists At most one object can exist. The set of object label values, i.e., the combinatorial explosion problem, therefore let... < As the number of loops; Step 3, establish the basic data matrix; object It is a vector composed of all factor values. ; It is an object In factors The following factor values ​​are used to form the basic data matrix. As shown in Table 1; Table 1 Basic Data Matrix Step 4: Create a set of object labels; the set of object labels used in each loop is different. This represents the set of object labels for the i-th iteration. Generate a collection of object tags at once. And the object label value should be [1, The uniform random distribution in ]; that is ,in Indicates the connection of sets, It has A collection of elements; yes A collection of elements; Steps 5 and 6: Construct the training and test sets of data; and These represent the training set and test set, respectively, derived from the underlying data matrix. Represents the first part of the basic data matrix One object, Represents the basic data matrix All subsequent objects; Steps 7 and 8: Construct the object label training set and test set; and These represent the training set and the test set, respectively, derived from the set of object labels; Step 9: Obtain the unsupervised nuclear spectrum regression training model; call the function as shown in equation (2) to perform unsupervised training using the UKSR algorithm, which requires parameters. , To obtain the regression training model, we need to control the set of parameters. ; （2） Steps 10 and 11 yield the unsupervised nuclear spectral regression training set test results and test set test results; the calling functions are shown in equations (3) and (4) respectively, and the UKSR algorithm is used to perform unsupervised testing on the training set and test set to obtain the training set test results. Training results on the test set ; Parameter C is The unique values, i.e., the tag class; （3） （4） Steps 12 and 13 use the K-means algorithm to obtain the training set test results. Training results on the test set The clustering results are obtained; Equations (5) and (6) are called respectively to set the number of clusters. The clustering results obtained are as follows: and ; （5） （6） In steps 14 and 15, the cross-correlation between the training set and the test set in the basic data and label set is calculated using the mutual information theorem, and the functions are called as shown in equations (7) and (8), respectively. （7） （8） Step 16, determine the optimal object distribution; set the number of iterations to [number]. Each iteration will have a different object label matrix. ; Starting with the basic data matrix, when , , , and Once confirmed, In the next loop and Unchanged; as the number of iterations changes and It is constantly changing because It is subject to change; This represents the cross-correlation between the object data used for training and the object labels used for training; This represents the cross-correlation between the object data used for testing and the object labels used for testing; This represents the label values ​​of all objects in the object set at the i-th iteration, i.e., the distribution of object label values; if and If the values ​​are all close to 1, it indicates that the object data and object labels have the highest correlation under both training and testing conditions. In this case, the resulting object label set... For the optimal set of object labels It represents the relationship between the characteristics of object data change and the characteristics of object label change in this context. The maximum correlation in the next cycle, therefore Yes The optimal object label set, the object label values ​​in the set represent the optimal object distribution, as shown in Equation (9); （9） Equation (9) is the criterion for the optimal object label set; the object distribution in the system fault evolution process and the optimal label value distribution of all objects are obtained; through The next loop will When comparing a set of object labels, + The set of object labels obtained when the maximum value is reached is the optimal set of object labels. This characterizes the optimal object distribution.

2. The method for determining object distribution during system fault evolution 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. ; Based on step 2, let the number of object categories be... and number of loops ; To assign object classification labels 1, 2, 3 to represent the different classes to which the objects belong; determine the optimal set of object labels during 10,000 iterations of comparison. Based on step 3, construct the basic data matrix from the objects and factors. Obtain a schematic diagram of the changes in factor values ​​for each object; Based on step 4, establish an object label set; use a function to randomly generate label values ​​evenly distributed in [1,3] to obtain the object label set. ,have One element; It has 50 elements. ; Based on steps 5 and 6, construct the training and test sets of data, and set... The training data set is The test set is ; Based on steps 7 and 8, construct the object label training set and test set, respectively, in the i-th iteration. and ; According to step 9, the unsupervised nuclear spectrum regression training model is obtained; call equation (2) to set... Obtain the trained model; Based on steps 10 and 11, equations (3) and (4) are called respectively to calculate the training set test results and the test set test results; set The calculation is performed using the UKSR algorithm; Based on steps 12 and 13, equations (5) and (6) are called respectively to calculate the clustering results of the training set test results and the test set training results, and the settings are... It is obtained using the K-means algorithm; According to steps 14 and 15, Equations (7) and (8) are called respectively to calculate the cross-correlation of the training set and the cross-correlation of the test set; Based on step 16, determine the optimal object distribution; loop 10,000 times, using 10,000 different object label sets for comparison, where... The maximum value is the desired result; after looping 7365 times, The maximum value in 10,000 iterations, where the cross-correlation of the training set is... The cross-correlation of the test set is ; This indicates that the correlation between changes in object data and object labels reached 80% during training and 100% during testing, meaning that the correlation between changes in object data and changes in label data was the highest. The optimal distribution of object label values ​​was obtained. Objects with a class label value of 1 include numbers 2, 3, 7, 9, 12, 13, 14, 15, 18, 22, 24, 25, 27, 30, 31, 32, 33, 34, 36, 39, 48, and 49, totaling 22. Objects with a class label value of 2 include numbers 4, 5, 6, 17, 19, 21, 23, 26, 37, 38, 41, 42, 43, 46, 47, and 50, totaling 16. Objects with a class label value of 3... The numbers include 1, 8, 10, 11, 16, 20, 28, 29, 35, 40, 44, and 45, a total of 12. This indicates that during the entire evolution process, when all objects are divided into 3 categories, the above distribution of object label values ​​is obtained. Among them, objects with class label 1 play the greatest role in the evolution, accounting for 44% of all measurement moments. That is, for 44% of the time, the sub-evolutionary process represented by the set of objects with class label 1 is dominant, followed by the set of objects with class label 2, and the set of objects with class label 3 has the least role.

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