Extended C-Means-based multivariate data anomaly analysis method
Patent Information
- Application Number
- CN202211162698.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-23
- Publication Date
- 2026-02-10
AI Technical Summary
Existing technologies cannot effectively detect and screen the quality of multi-dimensional damage performance data, especially during large-scale acquisition and transmission. They cannot obtain real-time information on equipment replacement and transmission, resulting in a large amount of manpower and resources being consumed in data quality detection. At the same time, they cannot effectively extract the temporal characteristics of damage performance data.
A multivariate time series anomaly analysis method based on extended C-Means is adopted. Multivariate time series are divided by sliding window, and extended fuzzy C-Means clustering and particle swarm optimization algorithm are combined. The time offset is eliminated by using autocorrelation coefficient feature space, and anomaly score is calculated to detect anomalies in multivariate time series.
It improves the accuracy of anomaly detection in multivariate time series data, can identify abnormal amplitude and shape patterns, is applicable to various application fields, and builds an intelligent damage data platform system.
Smart Images
Figure CN121502569A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of multivariate time series data processing, and in particular to a multivariate metadata anomaly analysis method based on extended C-Means. Background Technology
[0002] Currently, the damage performance data collected by the system is inconsistent in quality due to the large number of data acquisition terminals, high acquisition frequency, and diverse transmission methods. Furthermore, the inability to obtain real-time information on equipment replacement and transmission status makes it impossible to determine whether the collected damage performance data meets quality standards, thus affecting subsequent data analysis. Therefore, the damage performance data collected by the system needs to be quality-checked first, identifying and promptly supplementing substandard data. Currently, troubleshooting transmission problems and acquisition terminals consumes significant manpower and resources; therefore, using machine learning methods to check the quality of damage performance data is becoming mainstream. However, mainstream machine learning methods have two problems: 1) they can only detect one-dimensional data sequences; 2) damage performance data has temporal characteristics, and existing methods cannot effectively extract the temporal features of the damage performance data. Summary of the Invention
[0003] The purpose of this invention is to provide a multivariate data anomaly analysis method based on extended C-Means. By utilizing extended fuzzy clustering, this invention can detect anomalies in the amplitude and shape of multivariate time series data, and is applicable to identifying anomalous amplitude and shape patterns in various application fields.
[0004] To achieve the above objectives, the present invention is implemented according to the following technical solution:
[0005] This invention includes the following steps:
[0006] S1: Use a fixed-length sliding window to divide a multivariate long-term series into a set of multivariate shorter subsequences;
[0007] S2: Use extended fuzzy C-Means clustering to reveal available structures in the data, establish reconstruction criteria, and perform particle swarm optimization;
[0008] S3: Assign anomaly scores to each subsequence based on cluster and reconstruction criteria.
[0009] The sliding window is defined as follows: Let x1, x2, ..., x p It is a multivariate time series of length p, where the k-th point in the multivariate time series is denoted as x. k =[x k1 ,x k2 ,…,x knLet n be the number of variables in a multivariate time series. A fixed-length sliding window is used to generate a set of N subsequences of length q. Let r be the length the sliding window moves each time. The number of subsequences generated can be determined as follows:
[0010]
[0011] For the Extended Fuzzy C-Means algorithm for multivariate time series, a sliding window generates a set of multivariate subsequences. After obtaining the subsequences, extended fuzzy C-Means is used for clustering. In the extended distance function, the squared Euclidean distance between the multivariate subsequence w and the cluster center v can be calculated as follows:
[0012]
[0013] The influence of each variable in the multivariate time series clustering process is controlled by a distance function, λ. i The higher the value, the more i th The influence of variable increases, while the influence of other variables decreases in the clustering process. By inserting the extended distance function into the fuzzy extended C-Means objective function, the following expression is obtained:
[0014]
[0015] Where c is the number of clusters, m (m>1) is the fuzzification coefficient, N is the number of multivariate subsequences, and U and v i These are the partition matrix and the original value i, respectively. The optimization process of the proposed extended objective function is implemented iteratively, using the following expressions to calculate the partition matrix and cluster centers:
[0016]
[0017]
[0018] The extended fuzzy C-Means reconstruction criterion and the particle swarm optimization (PSO) algorithm are used as tools to estimate each coefficient λ in the search for the optimal value. i Find the optimal values for i = 1, 2, ..., n, and the weights λ that satisfy the constraints. i The optimal combination of values, particle and its velocity vector update are as follows
[0019]
[0020]
[0021] Among them, v ki ∈[v min ,v maxM is the number of particles, n is the number of variables in the multivariate time series, the maximum and minimum velocities are used to limit the velocity of each particle to avoid possible chaotic behavior of the swarm, and pbest and gbest are the best positions obtained by the particles and the best positions found by the entire swarm, respectively.
[0022] The Particle Swarm Optimization (PSO) algorithm uses a reconstruction criterion as the fitness function considered in the PSO method, and reconstructs the original subsequence by minimizing the following sum of distances:
[0023]
[0024] in, It is w j A refactored version. By adjusting F for... When the gradient is zeroed, we can obtain:
[0025]
[0026] After reconstructing all data points, we calculate the reconstruction error as the sum of the following distances:
[0027]
[0028] A lower E value indicates higher quality clustering in terms of data granularity and degranulation. The coefficient λ is optimized by minimizing the reconstruction error represented by E. i ,i=1,2,...,n.
[0029] An anomaly score is assigned to each multivariate subsequence using the optimal cluster centers and partition matrix. The anomaly score for each multivariate subsequence is calculated as the squared Euclidean distance between the subsequence and its reconstructed version, where w is the subsequence. j The abnormal score is calculated in the following form:
[0030]
[0031] By eliminating the time shift by representing the subsequence in its autocorrelation coefficient feature space, and then using Euclidean distance in the new feature space, the autocorrelation coefficient of a subsequence wj of length q can be calculated using the following formula:
[0032]
[0033] Where e = 1, 2, ..., q-1 and j = 1, 2, ..., N are the time series averages;
[0034] Compare the scores of the outlier subsequences with the average scores of the subsequences, and consider using a confidence index to optimize these parameters. The confidence index is expressed as follows:
[0035]
[0036] Where h represents the anomaly score of each subsequence, h is the average of the outlier scores. anomaly The anomaly score of an anomalous subsequence is determined by assigning higher scores to the anomalous parts and lower scores to other parts with a higher f value. f can be used to find the optimal value of the parameter because a higher f value results in a greater difference in scores between normal and anomalous subsequences. When multiple anomalies exist in the time series, h... anomaly It is the average of the abnormal scores of the abnormal subsequences.
[0037] The beneficial effects of this invention are:
[0038] This invention is a multivariate data anomaly analysis method based on extended C-Means. Compared with existing technologies, this invention can detect anomalies in multivariate time series data and is suitable for identifying the magnitude and shape patterns of anomalies in various application fields. This invention improves the accuracy of anomaly detection in multivariate time series data and is of great significance for realizing the construction of an intelligent damage data platform system. Attached Figure Description
[0039] Figure 1 This is a flowchart illustrating the abnormal data detection process architecture of the present invention;
[0040] Figure 2 This is a graph showing the simulation data analysis results of the present invention. Detailed Implementation
[0041] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.
[0042] like Figure 1 As shown: This invention implements its functionality using the extended fuzzy C-Means algorithm and the PSO algorithm. First, a fixed-length sliding window is used to divide a multivariate long-duration series into a set of shorter multivariate subsequences. In the next step of this proposed framework, extended fuzzy C-Means clustering is used to reveal the available structure in the data. Subsequently, reconstruction criteria and particle swarm optimization are developed. Finally, anomaly scores are assigned to each subsequence based on the clusters and reconstruction criteria. Each component will be described in detail below:
[0043] Sliding window: Assume x1, x2, ..., x p It is a multivariate time series of length p, where the k-th point is denoted as x. k =[x k1 ,x k2 ,…,x knLet n be the number of variables in the multivariate time series. Using a fixed-length sliding window, a set of N subsequences of length q can be generated. Assuming r is the length the sliding window moves each time, the number of subsequences generated can be determined as follows:
[0044]
[0045] For the Extended Fuzzy C-Means algorithm for multivariate time series, a sliding window generates a set of multivariate subsequences. After obtaining the subsequences, they are clustered using Extended Fuzzy C-Means to reveal the available structure in the data. An extended version of the Euclidean distance function is used here to calculate the similarity of each variable between the multivariate time series. In the proposed extended distance function, the squared Euclidean distance between the multivariate subsequence w and the cluster center v can be calculated as follows:
[0046]
[0047] The influence of each variable in multivariate time series clustering can be controlled using distance functions. λ i The higher the value, the more i th The influence of variable A increases, while the influence of other variables decreases in the clustering process. By inserting the extended distance function into the fuzzy extended C-Means objective function, we obtain the following expression:
[0048]
[0049] Where c is the number of clusters, m (m>1) is the fuzzification coefficient, and N is the number of multivariate subsequences. U and v i These are the partition matrix and the original value i, respectively. The optimization process of the proposed extended objective function is implemented iteratively. Here, we use the following expressions to calculate the partition matrix and cluster centers:
[0050]
[0051]
[0052] Using the proposed extended fuzzy C-Means, the influence of each variable in clustered multivariate time series data can be controlled. However, the optimal influence of each variable during the clustering process is required. In other words, the influence of each coefficient λ must be estimated. iThe optimal values for i = 1, 2, ..., n are sought. To achieve this, we propose a reconstruction criterion and a Particle Swarm Optimization (PSO) algorithm as a tool for searching for optimal values. The PSO algorithm can find (near) optimal weights because it is advantageous in solving complex global optimization problems. It uses a swarm of particles characterized by position and velocity. Based on a fitness function, each particle can move in the search space and stores the best positions of all the particles it has visited in its personal memory. A global optimal position is determined for the entire swarm. When each particle moves to a new position, it references both its personal optimal position and the global optimal position. The evolutionary iterations intersect with a convergence criterion or a maximum number of iterations.
[0053] In this invention, due to the existence of n weights λ i For values i = 1, 2, ..., n, considering all possible combinations of these values in the extended distance function (to find the optimal influence of each variable in the clustering process) is time-consuming, and even infeasible for higher values of n. Therefore, we use PSO as a tool to find weights λ that satisfy the constraints. i The optimal combination of values. It starts by randomly generating many particles and their velocity vectors. For each particle, we evaluate its mass using a reconstruction criterion, which serves as the fitness function of the PSO technique. The particle and its velocity vector are updated as follows:
[0054]
[0055]
[0056] Among them, v ki ∈[v min ,v max M is the number of particles, and n is the number of variables in the multivariate time series. Maximum and minimum velocities are used to limit the velocity of each particle to avoid potential chaotic behavior in the swarm. pbest and gbest are the optimal positions obtained by the particles and the optimal positions found by the entire swarm, respectively.
[0057] In the first step of this method, a fixed-length sliding window is used to generate a set of multivariate subsequences. Then, extended fuzzy C-Means clustering is used to discover normal structures within the generated multivariate subsequences. Finally, a reconstruction technique is used to assign anomaly scores, quantified in relation to the level of abnormality in the normal structure of the data, to each multivariate subsequence. Inertia weights w control the influence of previous velocities on the current velocity and adjust the balance between global and regional search capabilities. c1 and c2 are learning factors, and r... 1i and r 2iIt represents a random value within an interval, striking a balance between exploration and exploitation search. When applying the PSO algorithm to different optimization scenarios, the aforementioned parameters play a crucial role in determining PSO performance; improper selection of these parameters can lead to slow convergence and poor performance.
[0058] Reconstruction Criteria: The reconstruction criterion serves as the fitness function considered in the PSO method. Specifically, this technique allows for the evaluation of cluster quality based on data granularity and degranulation. The essence of the reconstruction criterion is to reconstruct the original data (subsequences) by revealing the cluster centers and their membership values. Considering the cluster centers and partition matrix generated using the Extended Fuzzy C-Means algorithm, the original subsequences can be reconstructed by minimizing the following sum of distances:
[0059]
[0060] in, It is w j A refactored version. By adjusting F for... When the gradient is zeroed, we can obtain:
[0061]
[0062] After reconstructing all data points, we calculate the reconstruction error as the sum of the following distances:
[0063]
[0064] A lower E value indicates higher quality clustering in terms of data granularity and degranulation. The coefficient λ is optimized by minimizing the reconstruction error represented by E. i ,i=1,2,...,n.
[0065] Anomaly Score: The optimal weights in extended fuzzy C-Means techniques can lead to different optimal effects of various variables during clustering. A reconstruction structure for multivariate time series is proposed using cluster centers and partition matrices corresponding to the optimal weights. An anomaly score can be assigned to each multivariate subsequence using the optimal cluster centers and partition matrix. For this purpose, the anomaly score of each multivariate subsequence is calculated as the squared Euclidean distance between the subsequence and its reconstructed version. Formally, subsequence w... j The abnormal score is calculated in the following form:
[0066]
[0067] Time series correlation coefficient representation: When detecting amplitude anomalies, the similarity of time series is typically evaluated using the Euclidean distance function in the original feature space. However, for shape anomalies, using the Euclidean distance function as a similarity measure in the original feature space is not a suitable choice because subsequences may be affected by time shifts. This invention uses the autocorrelation coefficient of time series to solve this problem. By representing the subsequence in its autocorrelation coefficient feature space, the time shift can be eliminated, and then the Euclidean distance can be used in the new feature space. For a subsequence wj of length q, its autocorrelation coefficient can be calculated using the following formula:
[0068]
[0069] Where e = 1, 2, ..., q-1 and j = 1, 2, ..., N are the average values of the time series.
[0070] Parameter Selection: Before execution, Z-score normalization is applied to each variable (time series) of the multivariate time series to eliminate scaling effects between different variables. Several other parameters, such as the ambiguity coefficient m, cluster number c, subsequence length q, and length of each step r, affect the detection process. The scores of anomalous subsequences are compared to the average score of the subsequences, and a confidence index is considered to optimize these parameters. The confidence index is expressed using the following formula:
[0071]
[0072] Where h represents the anomaly score of each subsequence, h is the average of the outlier scores. anomaly Anomaly scores for anomalous subsequences. A higher f-value indicates that higher anomaly scores should be assigned to the anomalous parts, while lower scores should be assigned to other parts. f can be used to find the optimal value of the parameter because a higher f-value means a greater difference in scores between normal and anomalous subsequences. When multiple anomalies exist in the time series, h... anomaly It is the average of the abnormal scores of the abnormal subsequences.
[0073] Implementation Case: A method for detecting anomalies in multivariate damage performance data, comprising: dividing a multivariate long-term series into a group of multivariate shorter subsequences using a fixed-length sliding window for collected user data; using extended fuzzy C-Means clustering to reveal the available structure in the data; formulating reconstruction criteria and particle swarm optimization; and assigning anomaly scores to each subsequence based on the clusters and reconstruction criteria.
[0074] We simulated a multivariate time series of length 80, as shown in the figure. There are two time series (two variables) containing six different signals. Each signal repeats for some time, but the number of repetitions is unknown, while the relationships between the different signals (1-4, 2-5, 3-6) are known. Each number represents a specific type of signal. The multivariate time series without anomalies is shown below:
[0075] Time series 1:1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3
[0076] Time series 2:4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6
[0077] The following is an example of a multivariate time series with anomalies:
[0078] Time series 1:1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3
[0079] Time series 2:4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6
[0080] Each signal type repeats at different points in each time series. As a result, no anomalies are found in any individual time series. However, when considering two time series, two anomalies (highlighted) appear simultaneously, as signals 2 and 6 occur simultaneously. First, a fixed-length sliding window is used to divide the long multivariate time series into a set of shorter multivariate subsequences. Second, they are clustered using extended fuzzy C-Means to reveal the available structure in the data. Since each multivariate subsequence consists of two or more univariate subsequences, and these univariate subsequences may have different characteristics and structures, clustering such data using standard C-Means may result in bias towards one or more variables. To address this issue, we introduce a novel extended version of fuzzy clustering for multivariate time series (subsequences). In the proposed extended distance function, the squared Euclidean distance between the multivariate subsequence w and the cluster center v can be calculated as follows:
[0081]
[0082] Using the proposed extended fuzzy C-Means, the influence of each variable in clustering multivariate time series data can be controlled. However, the optimal influence of each variable during the clustering process is required. Therefore, the particle swarm optimization algorithm is then used to calculate each coefficient λ. iThe optimal values for i = 1, 2, ..., n are determined. Based on the reconstruction criteria of this data set as the fitness function, a particle swarm optimization algorithm is performed. During this process, the sequence is continuously reconstructed, and the reconstruction error is calculated. Then, the anomaly score for each multivariate subsequence, w, is calculated. j The abnormal score is calculated in the following form:
[0083]
[0084] Based on the obtained anomaly scores, the anomalies in the multivariate time series data can be determined. The anomalies in this simulated data are as follows: Figure 2 As shown.
[0085] The technical solutions of the present invention are not limited to the specific embodiments described above. Any technical modifications made in accordance with the technical solutions of the present invention fall within the protection scope of the present invention.
Claims
1. A multi-data anomaly analysis method based on extended C-Means, characterized in that, Includes the following steps: S1: Use a fixed-length sliding window to divide a multivariate long-term series into a set of multivariate shorter subsequences; S2: Use extended fuzzy C-Means clustering to reveal available structures in the data, establish reconstruction criteria, and perform particle swarm optimization. S3: Assign anomaly scores to each subsequence based on cluster and reconstruction criteria.
2. The multi-data anomaly analysis method based on extended C-Means according to claim 1, characterized in that: The sliding window is defined as follows: Let x1, x2, ..., x p It is a multivariate time series of length p, where the k-th point in the multivariate time series is denoted as x. k =[x k1 ,x k2 ,…,x kn Let n be the number of variables in a multivariate time series. A fixed-length sliding window is used to generate a set of N subsequences of length q. Let r be the length the sliding window moves each time. The number of subsequences generated can be determined as follows: For the Extended Fuzzy C-Means algorithm for multivariate time series, a sliding window generates a set of multivariate subsequences. After obtaining the subsequences, extended fuzzy C-Means is used for clustering. In the extended distance function, the squared Euclidean distance between the multivariate subsequence w and the cluster center v can be calculated as follows: The influence of each variable in the multivariate time series clustering process is controlled by a distance function, λ. i The higher the value, the more i th The influence of variable increases, while the influence of other variables decreases in the clustering process. By inserting the extended distance function into the fuzzy extended C-Means objective function, the following expression is obtained: Where c is the number of clusters, m (m>1) is the fuzzification coefficient, N is the number of multivariate subsequences, and U and v i These are the partition matrix and the original value i, respectively. The optimization process of the proposed extended objective function is implemented iteratively, using the following expressions to calculate the partition matrix and cluster centers:
3. The multi-data anomaly analysis method based on extended C-Means according to claim 1, characterized in that: The extended fuzzy C-Means reconstruction criterion and the particle swarm optimization (PSO) algorithm are used as tools to estimate each coefficient λ in the search for the optimal value. i Find the optimal values for i = 1, 2, ..., n, and the weights λ that satisfy the constraints. i The optimal combination of values, particle and its velocity vector update are as follows Among them, v ki ∈[v min ,v max M is the number of particles, n is the number of variables in the multivariate time series, the maximum and minimum velocities are used to limit the velocity of each particle to avoid possible chaotic behavior of the swarm, and pbest and gbest are the best positions obtained by the particles and the best positions found by the entire swarm, respectively.
4. The multi-data anomaly analysis method based on extended C-Means according to claim 3, characterized in that: The Particle Swarm Optimization (PSO) algorithm uses a reconstruction criterion as the fitness function considered in the PSO method, and reconstructs the original subsequence by minimizing the following sum of distances: in, It is w j A refactored version. By adjusting F for... When the gradient is zeroed, we can obtain: After reconstructing all data points, we calculate the reconstruction error as the sum of the following distances: A lower E value indicates higher quality clustering in terms of data granularity and degranulation. The coefficient λ is optimized by minimizing the reconstruction error represented by E. i ,i=1,2,...,n.
5. The multi-data anomaly analysis method based on extended C-Means according to claim 4, characterized in that: An anomaly score is assigned to each multivariate subsequence using the optimal cluster centers and partition matrix. The anomaly score for each multivariate subsequence is calculated as the squared Euclidean distance between the subsequence and its reconstructed version, where w is the subsequence. j The abnormal score is calculated in the following form: By eliminating the time shift by representing the subsequence in its autocorrelation coefficient feature space, and then using Euclidean distance in the new feature space, the autocorrelation coefficient of a subsequence wj of length q can be calculated using the following formula: Where e = 1, 2, ..., q-1 and j = 1, 2, ..., N are the time series averages; Compare the scores of the outlier subsequences with the average scores of the subsequences, and consider using a confidence index to optimize these parameters. The confidence index is expressed as follows: Where h represents the anomaly score of each subsequence, h is the average of the outlier scores. anomaly The anomaly score of an anomalous subsequence is determined by assigning higher scores to the anomalous parts and lower scores to other parts with a higher f value. f can be used to find the optimal value of the parameter because a higher f value results in a greater difference in scores between normal and anomalous subsequences. When multiple anomalies exist in the time series, h... anomaly It is the average of the abnormal scores of the abnormal subsequences.