A power distribution network operation mode identification method based on measurement big data analysis

Abstract

The application belongs to the technical field of power distribution network state estimation, and discloses a power distribution network operation mode identification method based on measurement big data analysis, which comprises the following steps: step 1, pre-processing measurement data; step 2, taking the measurement data of each sampling time as a sample, and using an improved t-distributed stochastic neighbor embedding algorithm to reduce the dimension of each sample; step 3, selecting a small number of samples from all samples, manually marking the corresponding power distribution network operation mode of the samples, and then automatically establishing the corresponding relationship between the remaining samples and the power distribution network operation mode through semi-supervised learning; and step 4, pre-processing and reducing the dimension of real-time measurement data, and identifying the real-time operation mode of the power distribution network according to the corresponding relationship obtained through semi-supervised learning. The online identification method provided by the application can quickly and accurately identify the operation mode of the power distribution network according to real-time measurement data, and provides guarantee for real-time observation of the operation mode of an active power distribution network containing a large number of distributed renewable energy sources.

Description

Technical Field

[0001] This invention belongs to the field of distribution network state estimation technology, specifically relating to a method for identifying distribution network operation modes based on big data analysis of measurements. Background Technology

[0002] The output of renewable energy is intermittent and fluctuates. As the penetration rate of distributed renewable energy in distribution networks gradually increases, the operation of distribution networks needs to be frequently optimized based on the output of renewable energy. By continuously adjusting the opening and closing states of sectionalizing switches and tie switches on the distribution network feeders, the power flow distribution can be optimized to avoid problems such as transformer or line overload and voltage exceeding limits. However, due to factors such as investment, telemetry and tele-signaling equipment are usually not installed on the sectionalizing switches and tie switches of the distribution network. Therefore, the distribution network control master station cannot obtain the opening and closing states of each switch in real time, which brings difficulties to the optimization of the distribution network operation mode.

[0003] Smart meters, RTUs, and other devices installed in the distribution network can collect measurement data such as voltage, current, and power, and upload the real-time measurement data to the control master station. The master station can use this measurement data to infer the opening and closing status of each section switch and tie switch, as well as the operating mode of the distribution network. The technology of identifying the operating mode of the distribution network using data from distribution network measurement terminals has been mentioned in some literature (such as patent applications CN115498633A, CN114123165A, and patent CN111313405B), but they are all based on power flow equations and require parameters such as feeder line impedance. These parameters are affected by environmental factors such as temperature, and are often difficult to obtain accurately in practice. Some literature (such as patent CN109190672A) uses dimensionality reduction and clustering methods to analyze the distribution network measurement data, but it does not preprocess the original measurement data, making it difficult to reveal the features contained in the measurement data. Moreover, it does not reasonably select initial cluster centers in clustering, which may lead to slow clustering iteration convergence.

[0004] Therefore, how to quickly and accurately identify the operation mode of the distribution network without relying on parameters such as line impedance, and based entirely on historical measurement data, is an urgent problem to be solved. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for identifying the operation mode of a distribution network based on big data analysis of measurements. By preprocessing, reducing dimensionality, and performing semi-supervised learning on historical measurement data, the method discovers the correspondence between the measurement data of smart meters in the distribution network and the operation mode of the distribution network. It can quickly and accurately identify the current operation mode of the distribution network online based on the real-time measurement data of smart meters in the distribution network, and can be applied to new power systems with frequent changes in operation mode.

[0006] The method for identifying the operation mode of a distribution network based on big data analysis of measurements, as described in this invention, comprises the following steps:

[0007] Step 1: Preprocess the voltage measurement data of the smart meter and calculate the three-phase voltage amplitude difference between distribution network nodes;

[0008] Step 2: Take the voltage and power measurement data at each sampling time as a sample, and use the improved t-distribution random nearest neighbor embedding algorithm to reduce the dimensionality of each sample;

[0009] Step 3: For each distribution network operation mode, select one sample under that operation mode from all samples, manually label the distribution network operation mode corresponding to these selected samples, and then automatically label the distribution network operation mode corresponding to the remaining samples that were not selected through semi-supervised learning.

[0010] Step 4: Reduce the dimensionality of the real-time measurement data and identify the real-time operation mode of the distribution network based on the known correspondence between the measurement data and the operation mode of the distribution network.

[0011] Furthermore, in step 1, based on the three-phase voltage amplitude measurements from the smart meters, the three-phase voltage amplitude difference between distribution network nodes is calculated using the following formula:

[0012]

[0013] Among them, U i,A U i,B and U i,C For the measurement of the three-phase voltage amplitude of the smart meter installed at node i of the distribution network, U j,A U j,B and U j,C For measuring the three-phase voltage amplitude of a smart meter installed at node j in the distribution network, N is the set of all nodes in the distribution network that are equipped with smart meters.

[0014] Furthermore, in step 2, each sample consists of the three-phase voltage amplitude difference between distribution network nodes at a historical sampling time and the three-phase active and reactive power injected into the distribution network at each node except the slack node. That is, the pre-processed smart meter voltage measurement data and power measurement data, as shown in the following formula:

[0015]

[0016] Where t is the sampling time number, x t Let U be the sample at time t, N be the set of all nodes in the distribution network equipped with smart meters, and U be the sample at time t. t,i,j Let be the difference in three-phase voltage amplitude between node i and node j in the distribution network at time t. and Let k be the distribution network node at time t. The active and reactive power injected into the phase.

[0017] Furthermore, the improved t-distribution random nearest neighbor embedding algorithm is used to reduce the dimensionality of the samples. The JS divergence is used as a quantitative indicator to measure the similarity between two probability distributions in the high-dimensional and low-dimensional spaces. When the JS divergence value is minimized, the probability distribution of the data point location in the high-dimensional space is closest to that in the low-dimensional space. At this point, the data point in the low-dimensional space is a mapping of the data point in the high-dimensional space, and the probability distribution p of the data point in the high-dimensional space... ij The probability distribution q of low-dimensional space data points ij The formula for calculating the JS divergence is as follows:

[0018]

[0019] Construct a minimization optimization problem, using the JS divergence as the objective function and the data points in the low-dimensional space as the decision variables. Solve this minimization problem using gradient descent, where the gradient of the objective function is:

[0020]

[0021] in, This represents the partial derivative of "JS divergence" with respect to "coordinates of the i-th data point in the low-dimensional space", where n is the number of data points, and y is the partial derivative of "JS divergence" with respect to "coordinates of the i-th data point in the low-dimensional space". i and y j Let w be the coordinates of the i-th and j-th data points in the low-dimensional space. ij and w ji Here, represents the weight value, used to measure the similarity between two data points. It can be calculated using the Gaussian kernel function, as shown in the following formula:

[0022]

[0023] Where exp() is the exponential function. It is a constant, and its value can be determined based on the degree of dispersion of the data point distribution.

[0024] The optimal solution obtained by solving the minimization problem is the dimensionality reduction result of the high-dimensional data points.

[0025] Furthermore, in step 3, for each distribution network operation mode, the earliest sampling time in which the distribution network is in that operation mode is found, and the sample at that sampling time is manually labeled with the corresponding operation mode. Next, based on semi-supervised learning technology, the K-Medoids clustering algorithm is used to analyze all samples. The initial cluster centers are the sample points manually labeled with the corresponding operation modes, and each cluster center corresponds to a cluster. The specific steps of the K-Medoids clustering algorithm are as follows:

[0026] Step a: Calculate the distance from each sample point (excluding the initial cluster centers) to each initial cluster center, and assign the sample point to the cluster corresponding to the nearest initial cluster center;

[0027] Step b: In each cluster, calculate the intra-cluster distance criterion function for each sample point belonging to that cluster, and select the sample point with the smallest intra-cluster distance criterion as the new cluster center; the intra-cluster distance criterion function is:

[0028]

[0029] Among them, J i For sample x i intra-cluster distance, M i For sample x i The set of all samples in the cluster; x j ∈M i Indicates sample x i With sample x j Belonging to the same cluster; ||x i -x j || 2 Indicates sample x i With sample x j The square of the Euclidean distance between them.

[0030] Step c: Repeat steps a and b until the cluster centers of each cluster no longer change. At this point, all samples in each cluster correspond to the same power distribution network operation mode. Based on the sample points that have been manually marked with the corresponding operation mode, the operation mode corresponding to other samples in the same cluster can be obtained.

[0031] Furthermore, in step 4, the same preprocessing and dimensionality reduction methods as the historical measurement data are used to preprocess and reduce the dimensionality of the real-time measurement data. Then, the distances from the sample points of the real-time measurement data obtained after preprocessing and dimensionality reduction to the cluster centers of each cluster are compared to find the nearest cluster center. The distribution network operation mode corresponding to the sample in the cluster is the identification result of the distribution network operation mode at the current moment.

[0032] The formula for calculating the distance from real-time measurement data sample points to the cluster centers of each cluster is as follows:

[0033] d t,i =||x t -x c(i) || 2

[0034] Where, d t,i Let x be the distance from the real-time measurement data sample point at time t to the cluster center of cluster i. t Let x be the real-time measurement data sample point at time t. c(i) Let i be the cluster center of cluster i.

[0035] The beneficial effects of this invention are as follows: The dimensionality reduction method for smart meter measurement data in distribution networks proposed in this invention can reduce the high-dimensional measurement data at each sampling moment to two dimensions, while maintaining the probability distribution between data points at each sampling moment, thus realizing the visualization of measurement data characteristics; the proposed clustering analysis method for the dimensionality-reduced measurement data can establish the correspondence between measurement data and distribution network operation modes using only a small number of labeled samples and a large number of unlabeled samples, reducing the workload of adding labels to samples; the proposed method for inferring the distribution network operation mode based on the cluster to which the dimensionality-reduced real-time measurement data belongs is time-efficient and can achieve online identification of operation modes. The online identification method provided by this invention can quickly and accurately identify the current operation mode of the distribution network based on the real-time measurement data of smart meters in the distribution network, effectively breaking down industry barriers, making up for the deficiencies of current distribution network automation systems, and providing a guarantee for the real-time observability of the operation mode of active distribution networks containing a large number of distributed renewable energy sources. Attached Figure Description

[0036] Figure 1 This is a schematic diagram illustrating the acquisition, preprocessing, and dimensionality reduction of measurement data according to the present invention;

[0037] Figure 2 It is the result of preprocessing, dimensionality reduction, and semi-supervised learning of historical measurement data;

[0038] Figure 3 It is a 33-node distribution network case study that includes multiple sectionalizing switches and tie switches;

[0039] Figure 4 This is a schematic diagram of various operating modes of a power distribution network example;

[0040] Figure 5 These are five power distribution network operation modes used for testing;

[0041] Figure 6 These are sample points obtained after preprocessing and dimensionality reduction of real-time measurement data;

[0042] Figure 7 It is the Euclidean distance from each real-time measurement sample point to the cluster center of each cluster;

[0043] Figure 8 It is the online identification result of the power distribution network operation mode;

[0044] Figure 9 It is the recognition accuracy of the proposed method after adding different levels of measurement error;

[0045] Figure 10 This is a flowchart of the method described in this invention. Detailed Implementation

[0046] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0047] like Figure 10 As shown, the present invention provides a method for identifying the operation mode of a distribution network based on big data analysis of measurement data. First, the voltage measurement data from smart meters is preprocessed. Based on the three-phase voltage amplitude measurements from the smart meters, the three-phase voltage amplitude difference between distribution network nodes is calculated using the following formula:

[0048]

[0049] Among them, U i,A U i,B and U i,C For measuring the three-phase voltage amplitude of a smart meter installed at node i in the distribution network, N is the set of all nodes in the distribution network that are equipped with smart meters.

[0050] This invention uses an improved t-distributed random nearest neighbor embedding algorithm to reduce the dimensionality of samples at each sampling time. For example... Figure 1 As shown, each sample consists of the three-phase voltage amplitude difference between distribution network nodes at a historical sampling time and the three-phase active and reactive power injected into the distribution network at each node except the slack node. That is, the pre-processed smart meter voltage measurement data and power measurement data, as shown in the following formula:

[0051]

[0052] Where t is the sampling time number, x t Let U be the sample at time t, N be the set of all nodes in the distribution network equipped with smart meters, and U be the sample at time t. t,i,j Let be the difference in three-phase voltage amplitude between node i and node j in the distribution network at time t. and Let k be the distribution network node at time t. The active and reactive power injected into the phase.

[0053] An improvement to the t-distribution random nearest neighbor embedding dimensionality reduction algorithm is made by replacing KL divergence with JS divergence. This solves the asymmetry problem of KL divergence, and JS divergence is smoother than KL divergence, better preserving the global structural information between data points. JS divergence is used as a quantitative indicator to measure the similarity between two probability distributions in high-dimensional and low-dimensional spaces. When the JS divergence value is minimized, the probability distribution of data point positions in the high-dimensional space is closest to that in the low-dimensional space. At this point, the data points in the low-dimensional space are essentially a mapping of the data points in the high-dimensional space, and the probability distribution p of the data points in the high-dimensional space... ij The probability distribution q of low-dimensional space data points ij The formula for calculating the JS divergence is as follows:

[0054]

[0055] Construct a minimization optimization problem, using the JS divergence as the objective function and the data points in the low-dimensional space as the decision variables. Solve this minimization problem using gradient descent, where the gradient of the objective function is:

[0056]

[0057] in, This represents the partial derivative of "JS divergence" with respect to "coordinates of the i-th data point in the low-dimensional space", where n is the number of data points, and y is the partial derivative of "JS divergence" with respect to "coordinates of the i-th data point in the low-dimensional space". i and y j Let w be the coordinates of the i-th and j-th data points in the low-dimensional space. ij and w ji Here, represents the weight value, used to measure the similarity between two data points. It can be calculated using the Gaussian kernel function, as shown in the following formula:

[0058]

[0059] Where exp() is the exponential function. It is a constant, and its value can be determined based on the degree of dispersion of the data point distribution.

[0060] The optimal solution obtained by solving the minimization problem is the dimensionality reduction result of the high-dimensional data points.

[0061] Then, as Figure 2As shown, semi-supervised learning is used to obtain the correspondence between each sample and the distribution network operation mode. For each distribution network operation mode, the earliest sampling time in which the distribution network is in that operation mode is found. The sample at that sampling time is manually labeled with the corresponding operation mode. Then, based on semi-supervised learning technology, the K-Medoids clustering algorithm is used to analyze all samples to obtain the distribution network operation mode corresponding to all samples.

[0062] The K-Medoids clustering algorithm was used to analyze all samples. The initial cluster centers were the labeled sample points, and each cluster center corresponded to a cluster. The specific steps of the clustering analysis are as follows:

[0063] Step a: Calculate the distance from each sample point (excluding the initial cluster centers) to each initial cluster center, and assign the sample point to the cluster corresponding to the nearest initial cluster center;

[0064] Step b: In each cluster, calculate the intra-cluster distance criterion function for each sample point belonging to that cluster, and select the sample point with the smallest intra-cluster distance criterion as the new cluster center; the intra-cluster distance criterion function is:

[0065]

[0066] Among them, J i For sample x i intra-cluster distance, M i For sample x i The set of all samples in the cluster; x j ∈M i Indicates sample x i With sample x j Belonging to the same cluster; ||x i -x j || 2 Indicates sample x i With sample x j The square of the Euclidean distance between them.

[0067] Step c: Repeat steps a and b until the cluster centers of each cluster no longer change. At this point, all samples in each cluster correspond to the same power distribution network operation mode. Based on the sample points that have been manually marked with the corresponding operation mode, the operation mode corresponding to other samples in the same cluster can be obtained.

[0068] Finally, in the online identification of distribution network operation mode, the same preprocessing and dimensionality reduction methods as historical measurement data are used to preprocess and reduce the dimensionality of real-time measurement data; then, the distances from the sample points of the real-time measurement data obtained after preprocessing and dimensionality reduction to the cluster centers of each cluster are compared, and the nearest cluster center is found. The distribution network operation mode corresponding to the sample in the cluster is the identification result of the distribution network operation mode at the current moment.

[0069] The formula for calculating the distance from real-time measurement data sample points to the cluster centers of each cluster is as follows:

[0070] d t,i =||x t -x c(i) || 2

[0071] Where, d t,i Let x be the distance from the real-time measurement data sample point at time t to the cluster center of cluster i. t Let x be the real-time measurement data sample point at time t. c(i) Let i be the cluster center of cluster i.

[0072] (1) Simulation verification model designed by the invention

[0073] To verify the feasibility and effectiveness of the online identification method for distribution network operation modes based on measurement data dimensionality reduction and semi-supervised learning proposed in this invention, simulation analysis was conducted based on an improved IEEE-33 node power network. The system includes multiple sectional switches and tie switches, and the topology diagram is shown below. Figure 3 As shown, S1, S2, ... S6 are sectionalizing switches, and TS1, TS2, ... TS5 are tie switches. By changing the opening and closing states of the sectionalizing switches and tie switches, the operation mode of the distribution network can be changed. Figure 4 Two possible distribution network operation modes are demonstrated. Five distribution network operation modes were designed to test the accuracy of identification, such as... Figure 5 As shown.

[0074] Furthermore, to enhance the robustness of the proposed operating mode identification method to measurement data errors, different levels of normally distributed random errors were incorporated into the voltage and power measurement data:

[0075]

[0076] Among them, v i,j p i,j q i,j and v′ i,j p′ i,j ,q′ i,j The voltage, active power, and reactive power measurement data of node i at the j-th sampling time point before and after adding random errors. σ is the standard deviation of the normal distribution, representing the level of measurement error. The maximum range of error can be expressed as ±3σ.

[0077] The definition of recognition accuracy is

[0078]

[0079] Where N is the number of operating modes, and M is the number of test samples for each operating mode, M = 100. i The goal is to identify the number of correctly identified test samples after performing online identification on each of the M test samples for the i-th operating mode.

[0080] (2) Identification results and accuracy

[0081] For the aforementioned test system, there are smart meter measurement data at 48 sampling time points for each operating mode. Only one of these is tagged (marking the distribution network operating mode), while the other 47 are untagged. All historical measurement data consists of 5 tagged sample points and 235 untagged sample points. Each sample point contains the three-phase voltage amplitude differences between each pair of 33 nodes and the three-phase active and reactive power of 32 nodes excluding power supply nodes. Therefore, the dimension of each sample point is 33×32 / 2×3+32×6=1776. Using the algorithm proposed in this invention, dimensionality reduction and cluster analysis are performed on these 240 sample points to obtain the distribution network operating mode corresponding to each cluster. Then, dimensionality reduction is performed on the real-time measurement data, and the results are as follows: Figure 6 As shown, the distances from the dimensionality-reduced data points to each cluster center are obtained, such as... Figure 7 As shown in the figure. Based on this, the cluster to which the real-time measurement data belongs is determined, and the operating mode corresponding to the cluster is the identification result of the current power distribution network operating mode. Figure 6 The identification results of the dimensionality-reduced coordinates, clusters, and operating modes of the five real-time measurement points are as follows: Figure 8 As shown.

[0082] After introducing different levels of measurement error, 100 real-time measurement data points were selected for each operating mode to test the recognition accuracy. The results are as follows: Figure 9 As shown in the figure. The results show that the proposed online identification method for distribution network operation modes can maintain an identification accuracy of over 90% when the accuracy of the measuring device is not lower than 0.2.

[0083] The above description is merely a preferred embodiment of the present invention and is not intended to further limit the present invention. All equivalent changes made based on the description and drawings of the present invention are within the protection scope of the present invention.

Claims

1. A method for identifying the operation mode of a distribution network based on big data analysis of measurements, characterized in that, The method steps are as follows: Step 1: Preprocess the voltage measurement data of the smart meter and calculate the three-phase voltage amplitude difference between distribution network nodes; Step 2: Take the voltage and power measurement data at each sampling time as a sample, and use the improved t-distribution random nearest neighbor embedding algorithm to reduce the dimensionality of each sample; Step 3: For each distribution network operation mode, select one sample under that operation mode from all samples, manually label the distribution network operation mode corresponding to these selected samples, and then automatically label the distribution network operation mode corresponding to the remaining samples that were not selected through semi-supervised learning. Step 4: Reduce the dimensionality of the real-time measurement data and identify the real-time operation mode of the distribution network based on the known correspondence between the measurement data and the operation mode of the distribution network. In step 2, the improved t-distribution random nearest neighbor embedding algorithm is used to reduce the dimensionality of the samples, specifically as follows: Using JS divergence as a quantitative indicator to measure the similarity between two probability distributions in high-dimensional and low-dimensional spaces, the probability distribution of data point locations in the high-dimensional space is closest to that in the low-dimensional space when the JS divergence value is minimum. In this case, the data points in the low-dimensional space are essentially a mapping of the data points in the high-dimensional space, and the probability distribution of the data points in the high-dimensional space... Probability distribution of low-dimensional spatial data points The formula for calculating the JS divergence is as follows: ； Construct a minimization optimization problem, using the JS divergence as the objective function and the data points in the low-dimensional space as the decision variables. Solve this minimization problem using gradient descent, where the gradient of the objective function is: ， in, Let represent the partial derivative of "JS divergence" with respect to "coordinates of the i-th data point in the low-dimensional space", where n is the number of data points. and Let i and j be the coordinates of the i-th and j-th data points in the low-dimensional space. and Here, represents the weight value, used to measure the similarity between two data points. It is calculated using the Gaussian kernel function, as shown in the following formula: ， Where exp() is the exponential function. It is a constant, and its value can be determined based on the degree of dispersion of the data point distribution; The optimal solution obtained by solving the minimization problem is the dimensionality reduction result of the high-dimensional data points.

2. The method for identifying the operation mode of a distribution network based on big data measurement analysis according to claim 1, characterized in that, In step 1, based on the three-phase voltage amplitude measurements from the smart meters, the three-phase voltage amplitude difference between distribution network nodes is calculated using the following formula: ； in, , and For measuring the three-phase voltage amplitude of a smart meter installed at node i of the distribution network, , and For measuring the three-phase voltage amplitude of the smart meter installed at node j of the distribution network, It is the set of all nodes in the distribution network that are equipped with smart meters.

3. The method for identifying the operation mode of a distribution network based on big data measurement analysis according to claim 1, characterized in that, In step 2, each sample consists of the three-phase voltage amplitude difference between distribution network nodes at a historical sampling time and the three-phase active and reactive power injected into the distribution network at each node except the slack node. That is, the pre-processed smart meter voltage measurement data and power measurement data, as shown in the following formula: ， Where t is the sampling time number, Let be the sample at time t, and N be the set of all nodes in the distribution network equipped with smart meters. Let be the difference in three-phase voltage amplitude between node i and node j in the distribution network at time t. and Let k be the distribution network node at time t. The active and reactive power injected into the phase.

4. The method for identifying the operation mode of a distribution network based on big data measurement analysis according to claim 1, characterized in that, In step 3, for each distribution network operation mode, find the earliest sampling time when the distribution network is in that operation mode, and manually label the sample at that sampling time with the corresponding operation mode.

5. The method for identifying the operation mode of a distribution network based on big data measurement analysis according to claim 4, characterized in that, In step 3, based on semi-supervised learning techniques, the K-Medoids clustering algorithm is used to analyze all samples. The initial cluster centers are sample points manually labeled with corresponding operating modes. Each cluster center corresponds to a cluster. The specific steps of the K-Medoids clustering algorithm are as follows: Step a: Calculate the distance from each sample point (excluding the initial cluster centers) to each initial cluster center, and assign the sample point to the cluster corresponding to the nearest initial cluster center; Step b: In each cluster, calculate the intra-cluster distance criterion function for each sample point belonging to that cluster, and select the sample point with the smallest intra-cluster distance criterion as the new cluster center; the intra-cluster distance criterion function is: ， in, For the sample intra-cluster distance, For the sample The set of all samples in the cluster; Indicates sample With sample They belong to the same cluster; Indicates sample With sample The square of the Euclidean distance between them; Step c: Repeat steps a and b until the cluster centers of each cluster no longer change. At this point, all samples in each cluster correspond to the same power distribution network operation mode. Based on the sample points that have been manually marked with the corresponding operation mode, the operation mode corresponding to other samples in the same cluster can be obtained.

6. The method for identifying the operation mode of a distribution network based on big data measurement analysis according to claim 1, characterized in that, In step 4, the same preprocessing and dimensionality reduction methods as those used for historical measurement data are used to preprocess and reduce the dimensionality of real-time measurement data. Then, the distances from the sample points of the real-time measurement data obtained after preprocessing and dimensionality reduction to the cluster centers of each cluster are compared, and the nearest cluster center is found. The distribution network operation mode corresponding to the sample in the cluster is the identification result of the distribution network operation mode at the current moment. The formula for calculating the distance from real-time measurement data sample points to the cluster centers of each cluster is as follows: ， in, Let be the distance from the real-time measurement data sample point at time t to the cluster center of cluster i. Let be the real-time measurement data sample points at time t. Let i be the cluster center of cluster i.

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