Hybrid Power Quality Disturbance Recognition Method Based on Multi-Core Support Vector Machine

Abstract

The present invention proposes a hybrid power quality disturbance identification method based on a multi-core support vector machine. First, the improved maximum relevance minimum redundancy criterion is used to select key features effective for classification, taking into account the influence of the joint action of features on the maximum relevance of categories and the comparability of different features. Secondly, in order to reduce the influence of different kernel functions and feature distributions on the performance of the classifier, a multi-core support vector machine introducing radius information is used to carry out disturbance identification. The simulation results show that the proposed identification algorithm of the present invention can effectively identify various disturbances under different noise intensities, demonstrating the effectiveness and feasibility of the proposed identification algorithm of the present invention. This method overcomes the influence of the fuzzy feature space of hybrid power quality disturbances on the identification accuracy, is less affected by noise, and has good stability.

Description

Technical Field

[0001] The present invention relates to the technical field of power quality disturbance type identification, and in particular to a hybrid power quality disturbance identification method based on a multi-core support vector machine. Background Art

[0002] In recent years, the continuous commissioning of nonlinear, impulsive and unbalanced loads has led to many power quality problems such as waveform distortion, three-phase imbalance, and power grid resonance, seriously affecting industrial production and user life. At the same time, more and more sensitive loads such as power electronic devices are put into operation, putting forward higher requirements for power quality. Different types of power quality disturbances have different degrees of impact on users. How to correctly and quickly identify various power quality disturbances from a large amount of power quality monitoring data is of great significance for the analysis of power quality disturbances and the selection of suppression measures.

[0003] Remarkable research achievements have been made in power quality disturbance identification algorithms. In reference [1] (Qin Sishi, Liu Qianjin. Power quality disturbance identification based on STFT transform and DAGSVMs [J]. Power System Protection and Control, 2011, 39(1): 83-86.), the time-frequency maximum amplitude vector extracted by the short-time Fourier transform is input into the support vector machine with a directed acyclic graph to realize the identification of power quality disturbances. In reference [2] (Xu Yonghai, Zhao Yan. Power quality disturbance identification based on short-time Fourier transform and disturbance time location using singular value decomposition [J]. Power Grid Technology, 2011, 35(8): 174-180.), six characteristic quantities are extracted by the short-time Fourier transform, and a decision tree is used to identify single and composite disturbances. In references [3-4] (Yao Jiangang, Guo Zhifei, Chen Jinpan. A new method for power disturbance classification based on wavelet and BP neural network [J]. Power Grid Technology, 2012, 36(5): 139-144.; Wu Zhaogang, Li Tangbing, Yao Jiangang, et al. Power quality disturbance classification based on wavelet and improved neural tree [J]. Power System Protection and Control, 2014, 42(24): 86-92.), the statistical characteristics and wavelet energy of the wavelet coefficients of each layer of the disturbance are extracted and input into a neural network to identify various disturbances. In reference [5] (He Julong, Wang Genping, Liu Dan, et al. Power quality disturbance location and identification in distribution network systems based on lifting wavelet and improved BP neural network [J]. Power System Protection and Control, 2017, 45(10): 69-76.), the wavelet coefficients of each layer extracted by the lifting wavelet transform are used to train the improved BP neural network for identification. In reference [6] (Huang Nantian, Xu Dianguo, Liu Xiaosheng. Power quality composite disturbance identification based on S transform and SVM [J]. Transactions of China Electrotechnical Society, 2011, 26(10): 23-30.), the two optimal features extracted by the S transform are determined by statistical methods, and a support vector machine with a binary tree structure is used to identify various disturbances. In reference [7] (Huang Nantian, Zhang Weihui, Cai Guowei, et al. Power quality disturbance identification using improved multi-resolution fast S transform [J]. Power Grid Technology, 2015, 39(5): 1412-1418.), five features are extracted by the fast S transform and a decision tree is established to identify various power quality disturbances containing noise. In reference [8] (Qin Xingfu, Gong Renxi. Power quality disturbance identification based on generalized S transform and PSO-PNN [J]. Power System Protection and Control, 2016, 44(15): 10-17.), six-dimensional characteristic quantities are extracted by the generalized S transform and input into the PSO-PNN to classify and identify various disturbances.

[0004] These algorithms are all aimed at single power quality disturbances or include a small number of mixed power quality disturbances.

[0005] In recent years, more attention has been focused on single power quality disturbances. However, various power quality disturbances often occur simultaneously on-site, resulting in blurred boundaries between features and affecting the accuracy of identifying hybrid power quality disturbances [9] (Yin Zhiyong, Chen Yongguang, et al. Research on the identification method of composite power quality disturbances in the equipped power system [J]. High Voltage Apparatus, 2017, 53(12): 195-201.). To address this problem, there are currently two main solutions. One is to introduce a window width adjustment factor to optimize the feature extraction method. In Refs. [10-11] (Yang Jianfeng, Jiang Shuang, et al. Identification of composite power quality disturbances based on segmented improved S-transform [J]. Power System Protection and Control, 2019, 47(9): 64-71.; Xu Liwu, Li Kaicheng, et al. Identification of composite power quality disturbances based on incomplete S-transform and gradient boosting tree [J]. Power System Protection and Control, 2019, 47(6): 24-31.), the window width adjustment factor of the S-transform is segmented according to the frequency level to take into account the characteristic differences between high-frequency and low-frequency disturbances. In Ref.

[12] (Li Jianmin, Lin Haijun, Liang Chengbin, et al. A power quality disturbance detection method based on double-resolution S-transform and learning vector quantization neural network [J]. Transactions of China Electrotechnical Society, 2019(16)), the size of the window width adjustment factor is changed according to the number of main frequencies of the signal to improve the time-frequency resolution of the S-transform. However, this method determines the size of the window width adjustment factor based on experience, and when the number of disturbance types increases, it will be difficult to meet the resolution requirements of different frequency disturbances by simply dividing into two segments according to frequency or changing the window width adjustment factor. The other method is to use a hierarchical structure combined with different feature extraction methods for classification. The accuracy of this method is easily affected by the rationality of the hierarchical structure. In Ref.

[13] (Wang Yang, Xiao Xianyong, et al. Feature selection and Mahalanobis distance classification method for short-term composite power quality disturbances [J]. Power System Technology, 2014, 38(4): 1064-1069.), a three-layer selection strategy is adopted. Two types of disturbances distinguished by the FFT transform are respectively used to extract disturbance features by the S-transform and the Hilbert transform, and the Mahalanobis distance is used for classification. This literature focuses on the mixed signal of single high-frequency section disturbance and low-frequency section disturbance, but this scheme will fail when high-frequency section disturbances are combined. In Ref.

[14] (Yang Zhigang, Chen Huafeng, Liu Shuanglin. Identification of composite power quality disturbances based on S-transform and rule base [C] / / Electrical Measurement & Instrumentation, 2015.), the FFT transform is combined with the dynamic measurement method to extract 6 features and the S-transform is used to extract 5 features, and then the types of power quality disturbances are hierarchically identified based on a rule-based classifier. However, this literature does not fully consider the influence of the interaction between disturbances on the effectiveness of feature classification, and there is a large redundancy between the selected features. Summary of the Invention

[0006] Aiming at the defects and deficiencies existing in the prior art, the present invention proposes a hybrid power quality disturbance identification method based on a multi-core support vector machine. To give full play to the advantages of different feature extraction methods and reduce the impact of the application scenario on the recognition accuracy rate, the present invention proposes a new method for identifying various disturbances. First, the improved maximum correlation and minimum redundancy criterion is used to select key features effective for classification. This step takes into account the influence of the combined action of features on the maximum correlation degree of categories and the comparability of different features. Secondly, to reduce the influence of different kernel functions and feature distributions on the performance of the classifier, a multi-core support vector machine introducing radius information is used to carry out disturbance identification.

[0007] The present invention specifically adopts the following technical solutions:

[0008] A hybrid power quality disturbance identification method based on a multi-core support vector machine, characterized in that: various feature extraction methods are used to identify the disturbance type, and the improved maximum correlation and minimum redundancy criterion is used to select key features effective for classification; the improved maximum correlation and minimum redundancy criterion introduces mutual information to take into account the influence of the simultaneous action of newly added features and existing features on the classification contribution degree, and introduces symmetric uncertainty to normalize the mutual information.

[0009] Furthermore, the incremental strategy method in the forward search method is adopted for feature selection based on the improved maximum correlation and minimum redundancy criterion.

[0010] Furthermore, a multi-core SVM considering radius information is used to identify hybrid power quality disturbances. The trace of the sample divergence matrix is introduced into the multi-core support vector machine, and the model is transformed into two convex optimization problems for solution.

[0011] Specifically, in the present invention, the specific meaning of the improved maximum correlation and minimum redundancy criterion includes:

[0012] Based on the definition of mutual information: the mutual information of random variables X, Y, and T is:

[0013] MI(X; Y; T) = MI(X,Y; T) - MI(X; T) - MI(Y; T) (1)

[0014] Mutual information is introduced in the maximum correlation and minimum redundancy criterion to consider the high-order correlation between features and the target category, and the expression of the maximum correlation and minimum redundancy criterion is modified to:

[0015]

[0016] MI(f i ,f j ; T) in the above formula can be expressed as:

[0017] MI(f i ,f j; T) = MI(f i ; T|f j )+MI(f j ; T)

[0018] =H(f i |f j )-H(f i |T,f j )+H(T)-H(T|f j )

[0019] =H(f i ,f j )-H(f i ,f j ,T)+H(T) (3)

[0020] Using symmetrical uncertainty to normalize MI yields:

[0021]

[0022]

[0023] Through normalization, the value range of the normalized mutual information SU is limited to the interval [0,1];

[0024] The improved maximum correlation and minimum redundancy criterion expression under interaction is equivalent to:

[0025]

[0026] Among them, the original given feature set is TF, the target category is T, and there are m-1 key feature subsets F m-1 ;

[0027] The selection of the mth feature in this criterion takes into account its redundancy, interaction with the first m-1 features, and the impact of its correlation with the target category.

[0028] Specifically, in the present invention, the multi-core SVM taking into account the radius information is specifically:

[0029] Assume that there are n samples in total, which are divided into {x j,s ; j = 1, 2…, k; s = 1, 2… n j}, where k is the number of target categories, n j is the number of samples in the jth class, is the mean of the samples of the jth class mapped to the samples in the mth feature space, and M is the mean of the samples of all samples mapped to the samples in the mth feature space;

[0030] When the mth kernel function maps the sample to the mth feature space, the trace of the divergence within the sample class is:

[0031]

[0032] The trace of the between-class divergence is:

[0033]

[0034] Then, for the m-th feature space, the trace of the total scatter matrix of the samples is:

[0035]

[0036] Then, after the samples are mapped by the multi-kernel function, the trace of their total scatter matrix is:

[0037]

[0038] Using the trace-margin bound of the total scatter matrix to optimize the base kernel weights, the multi-kernel SVM model considering the radius information is:

[0039]

[0040] where C is the penalty parameter, ξ i is the slack variable.

[0041] K m (x, xi) is the m-th single kernel function of the kernel SVM, and d m is the weight corresponding to the m-th single kernel function of the multi-kernel SVM. M is the number of kernel functions and the number of data sources. The objective value of the multi-kernel support vector machine is J(d).

[0042] Furthermore, the process of solving the multi-kernel SVM considering the radius information is as follows:

[0043] First, solve the optimal value of the objective value J(·) of the multi-kernel support vector machine. In this step, it is considered that the weights of the kernel functions are unchanged, solve the parameters of the multi-kernel SVM, then calculate the gradient of J(·), and solve the weights of the kernel functions. The two steps are iterated repeatedly until the optimal solution is found.

[0044] Furthermore, the process of solving the multi-kernel SVM considering the radius information is specifically as follows:

[0045] (1) Solve the optimal solution of the multi-kernel SVM

[0046] The Lagrangian equation of the multi-kernel SVM model (11) considering the radius information is:

[0047]

[0048] where α i 、v iis the Lagrange multiplier; and the weights of the kernel functions in this step are invariant. Let:

[0049]

[0050] Then equation (12) is equivalent to:

[0051]

[0052] Similar to the Lagrange equation when tr(S T ) is not introduced; taking the extreme value of J with respect to the original variables and further solving, we can obtain:

[0053]

[0054] Furthermore, the optimal solution of the multi-kernel SVM model is obtained

[0055] (2) Solving the weights of the kernel functions

[0056] Let d m / tr(S T ) = ρ m , then according to equation (10), it can be deduced that:

[0057]

[0058] Combining equation (15) and equation (16), the problem is transformed into:

[0059]

[0060] And since is a fixed value, the problem of solving the weights of the kernel functions is transformed into the problem of solving ρ m ; taking the gradient of equation (17) with respect to gives:

[0061]

[0062] To satisfy the equality and non-negativity on , the gradient update direction is:

[0063]

[0064] where μ is the coefficient with the largest component in, then The update equation of is:

[0065]

[0066] where γ is the update step size, and the optimal step size is obtained by searching with the golden section method; after obtaining the optimal solution , according to dm / tr(S T ) = ρ m Since the sum of dm is 1, the kernel function weight dm and the SVM parameter α can be further obtained.

[0067] The kernel function weight dm and the SVM parameter α i Iterate alternately until the stopping conditions are met; the stopping conditions are the KKT conditions and the maximum number of iterations to ensure convergence.

[0068] After the stopping conditions are met, the optimal solution is obtained. b * , and then the decision function is obtained as:

[0069]

[0070] Furthermore, comprehensively utilize five analysis methods including time-domain extraction, Fourier transform, short-time Fourier transform, wavelet transform, and S transform to extract the characteristics of the disturbance to be identified, and then construct the original feature space.

[0071] Furthermore, adopt the improved maximum correlation and minimum redundancy criterion to select the key feature subset with the largest correlation with the target category and the smallest mutual redundancy from the original feature space.

[0072] Furthermore, before adopting the improved maximum correlation and minimum redundancy criterion to select the key feature subset with the largest correlation with the target category and the smallest mutual redundancy from the original feature space, first normalize the features.

[0073] And, an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that when the processor executes the program, it implements the steps of the above-mentioned hybrid power quality disturbance recognition method based on a multi-core support vector machine.

[0074] And, a non-transitory computer-readable storage medium, on which a computer program is stored, characterized in that when the computer program is executed by a processor, it implements the steps of the above-mentioned hybrid power quality disturbance recognition method based on a multi-core support vector machine.

[0075] The present invention and its preferred solutions have the following advantages or beneficial effects:

[0076] (1) The features obtained by integrating different feature extraction means help to improve the identification accuracy.

[0077] (2) A feature selection algorithm based on the improved mRAR under interaction is proposed, which effectively removes useless redundant information, improves the operation speed of the classifier, and ensures a high identification accuracy in the case of a small number of features.

[0078] (3) The multi - core SVM algorithm integrating radius information adopted not only avoids the subjectivity in the selection of the number of base kernels and parameters, but also describes the features from different sources more comprehensively and accurately, improving the identification accuracy and stability.

[0079] (4) The proposed identification method has a high classification accuracy in various situations, is less affected by noise and interference between disturbances, and has strong recognition robustness and anti - noise ability.

[0080] (5) The proposed method still obtains good classification results in the case of fewer samples. Description of the Drawings

[0081] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments:

[0082] Figure 1 It is a schematic diagram of the voltage sag plus harmonic characteristic curve of an embodiment of the present invention.

[0083] Figure 2 It is a schematic diagram of the flicker plus transient oscillation characteristic curve of an embodiment of the present invention.

[0084] Figure 3 It is a schematic diagram of the flow of the feature selection algorithm of an embodiment of the present invention.

[0085] Figure 4 It is a schematic diagram for comparing the SVM identification results corresponding to different feature groups of an embodiment of the present invention.

[0086] Figure 5 It is a schematic diagram for comparing the SVM identification results under different dimensions of an embodiment of the present invention.

[0087] Figure 6 It is a schematic diagram of the multi - core SVM identification results under different sample sizes of an embodiment of the present invention. Detailed Embodiments

[0088] In the following, specific embodiments of the present application will be described in detail with reference to the drawings. According to these detailed descriptions, those skilled in the art can clearly understand the present application and can implement the present application. Without departing from the principle of the present application, the features in different embodiments can be combined to obtain new embodiments, or some features in certain embodiments can be replaced to obtain other preferred embodiments.

[0089] To solve the problem of overlapping edges among the typical classification features of hybrid power quality disturbances, this embodiment proposes a new method for identifying disturbance types by using multiple feature extraction means. First, the analysis of different characteristic curves is carried out to illustrate the effectiveness of comprehensively using multiple feature extraction means for hybrid disturbance identification. Secondly, to consider the correlation between high-dimensional features and target categories and the normalization of measurement scales, an improved maximum correlation minimum redundancy criterion is used to optimize the key feature subset effective for identification, and then a multi-kernel SVM considering radius information is used to identify hybrid power quality disturbances. Finally, the simulation results show that the proposed identification algorithm in this embodiment can effectively identify various disturbances under different noise intensities, demonstrating the effectiveness and feasibility of the proposed identification algorithm in this embodiment. This method overcomes the influence of the fuzzy feature space of hybrid power quality disturbances on the identification accuracy, is less affected by noise, and has good stability.

[0090] To make the features and advantages of this patent more obvious and understandable, specific embodiments are given below and described in detail in conjunction with the accompanying drawings as follows:

[0091] 1 Multi-kernel Identification Strategy for Hybrid Power Quality Disturbances

[0092] 1.1 Feature Algorithms and Adaptability Analysis of Different Means

[0093] According to the IEEE standard and references [6],

[15] (Huang Nantian, Xu Dianguo, Liu Xiaosheng. Identification of Composite Power Quality Disturbances Based on S-Transform and SVM [J]. Transactions of China Electrotechnical Society, 2011, 26(10): 23-30.; Youssef A M, Abdel-Galil T K, El-Saadany E F, et al. Disturbance Classification Utilizing Dynamic Timewarping Classifier [J]. IEEE Transactions on Power Delivery, 2004, 19(1): 272-278.), eight types of typical single PQD signals and 12 kinds of hybrid disturbances are established. Taking voltage sag plus harmonics and flicker plus transient oscillation as examples, the typical characteristic curves obtained by using different feature extraction means are shown as Figure 1 - Figure 2 shown.

[0094] As can be seen therein:

[0095] 1) From Figure 2 (a) figure, it can be seen that the high-frequency component of 500HZ of flicker plus transient oscillation is submerged, and it is difficult for Fourier transform to identify the flicker plus transient oscillation disturbance.

[0096] 2) From Figure 2 (a) figure, it can be seen that wavelet transform is difficult to distinguish composite disturbances related to the middle frequency band and high frequency band.

[0097] 3) By Figure 1 Comparing the curves of the two figures, it can be found that the short-time Fourier transform has a relatively narrow frequency band near the characteristic frequencies in the middle and high frequency bands of each disturbance, while the S transform has a relatively narrow frequency band near the characteristic frequencies in the low frequency band of each disturbance, indicating that neither of them can achieve high resolution in both the low frequency band and the middle and high frequency bands simultaneously.

[0098] From the above analysis, it can be seen that using different feature extraction methods to identify disturbances all have their applicability. Therefore, in this embodiment, five analysis methods including time-domain extraction, Fourier transform, short-time Fourier transform, wavelet transform, and S transform are comprehensively used to extract the features of the disturbances to be identified [2], [6],

[16] -

[21] (Xu Yonghai, Zhao Yan. Power Quality Disturbance Recognition Based on Short-Time Fourier Transform and Disturbance Time Location Using Singular Value Decomposition [J]. Power System Technology, 2011, 35(8): 174-180.; Huang Nantian, Xu Dianguo, Liu Xiaosheng. Power Quality Composite Disturbance Recognition Based on S Transform and SVM [J]. Transactions of China Electrotechnical Society, 2011, 26(10): 23-30.; Chen Xiaoguang. Research on Harmonic Detection Method Based on Wavelet Transform and Fourier Analysis [D]. Harbin Institute of Technology, 2009.; Huang Jianming, Qu Hezuo, et al. Power Quality Mixed Disturbance Classification Based on Short-Time Fourier Transform and Its Spectral Kurtosis [J]. Power System Technology, 2016, 40(10): 3184-3191.; Wu Zhaogang, Li Tangbing, Yao Jiangang, et al. Power Quality Disturbance Classification Based on Wavelet and Improved Neural Tree [J]. Power System Protection and Control, 2014(24): 95-101.; Zhu T X, Tso S K, Lo K L. Wavelet-Based Fuzzy Reasoning Approach to Power-Quality Disturbance Recognition [J]. IEEE Transactions on Power Delivery, 2004, 19(4): 1928-1935.; W. Kanitpanyacharoean, S. Premrudeepreechacharn. Power Quality Problem Classification Using Wavelet Transformation and Artificial Neural Networks [C]. IEEE PES Power Systems Conference and Exposition, 2004, 1185-1190.; Chen Yongyan. Research on Power System Power Quality Disturbance Recognition Method [D]. Zhejiang University, 20108.). As shown in Table 1, and then the original feature space is constructed.

[0099] Table 1 Original feature space of various disturbances

[0100]

[0101] 1.2 Improved mRAR algorithm under interaction

[0102] The original feature space provides data support for accurately identifying hybrid power quality disturbances, but there is a lot of redundant and noisy information, which leads to complex classifier structure and low classification efficiency. Therefore, it is necessary to select key feature subsets from it to improve the calculation speed while retaining the classification information as much as possible.

[0103] The maximum relevance and minimum redundancy criterion (mRMR) is a classic feature selection algorithm. Its essence is to select a subset of key features with the greatest relevance to the target category and the least redundancy with each other from the original typical feature set. Mutual information is often used to measure the contribution of features to class relevance. However, in this method, the features are measured as independent individuals to measure their relevance to the target category, and the mutual information is biased towards features with a large number of possible values, making it difficult to compare features of different types. Therefore, in order to improve the mRMR algorithm, this embodiment first introduces mutual information to take into account the impact of the simultaneous action of newly added features and existing features on the classification contribution, and then introduces symmetric uncertainty to normalize the mutual information.

[0104] The mRMR standard is defined as follows:

[0105]

[0106] If we use incremental search methods, we can write this as an optimization problem:

[0107]

[0108] That is, based on the selected features, find the feature that can maximize the above formula in the remaining feature space.

[0109] Mutual information is information that is not in any feature subset but is shared by all feature subsets.

[22] The mutual information among the random variables X, Y, and T is

[0110] MI(X;Y;T)=MI(X,Y;T)-MI(X;T)-MI(Y;T) (1)

[0111] First, mutual information is introduced into the maximum relevance and minimum redundancy criterion to consider the high-order correlation between features and target categories, and the expression of the maximum relevance and minimum redundancy criterion is modified as follows:

[0112]

[0113] MI(f in the above formula i , f j ; T) can be expressed as:

[0114] MI(f i , f j ; T) = MI(f i ; T|f j ) + MI(f j ; T)

[0115] = H(f i |f j ) - H(f i |T, f j ) + H(T) - H(T|f j )

[0116] = H(f i , f j ) - H(f i , f j , T) + H(T) (3)

[0117] Next, to compensate for the bias of features with a relatively large number of possible values of information gain and to make the feature values with different measurement units comparable, the symmetric uncertainty

[23] (W. Press, B. Flannery, S. Teukolsky, et al. Numerical Recipes in C: The Art of Scientific Computing [J]. Cambridge University Press, 1998.) is used to normalize MI, and we can get:

[0118]

[0119]

[0120] Through normalization, the value range of the normalized mutual information SU is limited to the interval [0, 1]. If the value of the normalized mutual information SU is larger, it indicates a greater correlation between variables and also a greater overlap in the information provided between the two.

[0121] Finally, combining equations (2) - (5), the expression of the improved mRAR algorithm under interaction is equivalent to

[0122]

[0123] The selection of the m-th feature in this criterion simultaneously considers its redundancy with the previous m - 1 features, the interaction, and the influence of the correlation with the target class.

[0124] The feature selection algorithm based on the improved maximum correlation and minimum redundancy criterion adopts the incremental strategy method in the forward search method. The flow chart is as Figure 3 shown.

[0125] 1.3 Multi-core SVM algorithm integrating radius information

[0126] Currently, there is a lack of a complete theory to select an appropriate kernel function, thereby ensuring the recognition performance under different given input samples. Moreover, due to the diverse and irregular feature distributions obtained by using various feature extraction methods, in this embodiment, a multi-core support vector machine is adopted, and different kernel functions are used to map features with different distributions respectively, thereby improving the identification accuracy of hybrid power quality disturbances.

[0127] Since the default feature sample space is fixed, most existing multi-core support vector machines determine model parameters based on the maximum classification margin. However, in this embodiment, the feature distribution is diverse, and at this time, the influence of the minimum hyper-sphere radius of the feature on the loss function cannot be ignored. Moreover, the trace tr(S T ) of the training sample scatter matrix can be regarded as an approximation of the square of the minimum hyper-sphere radius

[24] (Liu X, Wang L, Yin J, et al. An Efficient Approach to Integrating Radius Information into Multiple Kernel Learning [J]. IEEE transactions on systems, 2012, 43(2): 557-569.). Therefore, in this embodiment, the trace of the sample scatter matrix is introduced into the multi-core support vector machine, and the model is transformed into two convex optimization problems, thereby reducing the number of algorithm iterations and improving the anti-noise performance.

[0128] Suppose there are n samples in total, which are divided into {x j,s ; j = 1, 2…, k; s = 1, 2…n j} according to different categories, where k is the number of target categories, and n j is the number of samples in the j-th category, is the mean of the samples in the j-th category mapped to the m-th feature space, and M is the mean of all samples mapped to the m-th feature space.

[0129] When the m-th kernel function maps the samples to the m-th feature space, the trace of the within-class scatter of the samples is:

[0130]

[0131] The trace of the between-class scatter is:

[0132]

[0133] Then, corresponding to the m-th feature space, the trace of the total scatter matrix of the samples is:

[0134]

[0135] Then, after the samples are mapped by the multiple kernel function, the trace of its total scatter matrix is:

[0136]

[0137] The multiple kernel support vector machine model is to optimize the base kernel weights by minimizing the trace-margin bound of the total scatter matrix:

[0138]

[0139] where C is the penalty parameter, and ξ i is the slack variable. Since the constraint in (11) that the sum of the weights of the kernel functions is 1 makes it difficult to optimize the dual problem obtained from this problem. If the problem in (11) is directly solved by the Lagrange multiplier method, this equality constraint condition may be transferred to the objective function, thus making the objective function may become non-differentiable, resulting in new difficulties in solving.

[0140] Therefore, this problem is completed in two steps. First, the optimal value of the objective value J(·) of the multiple kernel support vector machine is solved. In this step, it is considered that the weights of the kernel functions are invariant, and the parameters of the multiple kernel SVM are solved. Then, the gradient of J(·) is calculated to solve the weights of the kernel functions. The two steps are iterated repeatedly until the optimal solution is found.

[0141] (1) Solve the optimal solution of the multiple kernel SVM

[0142] The accuracy of the solution obtained under this framework is monitored by the duality gap and is approximated to the original solution

[25] (SONNENBURG S, G, C, et al. Large scale multiple kernel learning[J]. Journal of Machine Learning Research, 2006, 7(2): 1531-1565.). The Lagrangian equation of problem (11) is:

[0143]

[0144] where α i , v i are the Lagrange multipliers. And the weights of the kernel functions are invariant in this step. Let:

[0145]

[0146] Then equation (12) is equivalent to:

[0147]

[0148] Similar to the Lagrangian equation when tr(S T ) is not introduced. Taking the extreme value of J with respect to the original variables and further solving, we can obtain:

[0149]

[0150] Furthermore, the optimal solution of the multi-kernel SVM model is obtained

[0151] (2) Solving the weights of the kernel function

[0152] Let d m / tr(S T ) = ρ m , then according to equation (10), we can deduce:

[0153]

[0154] Combining equation (15) and equation (16), the problem is transformed into:

[0155]

[0156] And since is a fixed value, the problem of solving the weights of the kernel function is transformed into the problem of solving ρ m . Taking the gradient of equation (17) with respect to , we can obtain:

[0157]

[0158] To satisfy the equality and non-negativity on , the gradient update direction is:

[0159]

[0160] where μ is the coefficient with the largest component in , then the update equation of is:

[0161]

[0162] where γ is the update step size, and the optimal step size is obtained by searching with the golden section method. After obtaining the optimal solution , according to d m / tr(S T ) = ρ m and dm and is 1, we can further calculate

[0163] Kernel function weight dm and SVM parameter α i Iterate alternately and repeatedly until the stopping condition is satisfied. The stopping conditions are the KKT condition and the maximum number of iterations to ensure convergence.

[0164] After the stopping condition is satisfied, the optimal solution is obtained b * , and then the decision function is obtained as

[0165]

[0166] 2 Simulation experiments

[0167] In this embodiment, simulation is used to generate eight types of typical single PQD signals and 12 types of mixed disturbances. The 12 typical disturbances are respectively harmonic plus voltage sag R1, harmonic plus voltage swell R2, harmonic plus voltage interruption R3, harmonic plus flicker R4, transient oscillation + flicker R5, voltage sag plus flicker R6, voltage swell plus flicker R7, voltage interruption plus flicker R8, voltage swell plus transient oscillation R9, voltage interruption plus transient oscillation R 10 , voltage sag plus transient oscillation R 11 , harmonic + flicker + voltage sag R 12 , and a total of 2400 disturbances are generated. The sampling frequency of the signal is 3200HZ, and Gaussian white noise of 50dB / 30dB / 20dB is respectively superimposed on the signal. Five power quality analysis methods, namely time-domain extraction, Fourier transform, short-time Fourier transform, wavelet transform, and S transform algorithm, are respectively used to extract the features in Table 1, and the above features are normalized. The expression is as follows:

[0168]

[0169] where Emax and Emin are the original maximum and minimum data respectively, and E i is the data to be processed.

[0170] SVM is trained using polynomial kernel, exponential power, and Gaussian radial basis kernel functions respectively. The order of the linear kernel is 1-4 respectively, the kernel parameter σ in the rbf kernel function is 1, 1 / 2, 1 / 3, 1 / 4, 1 / 5, 1 / 7 respectively, and the kernel parameter σ in the power exponential kernel function is 1, 1 / 2, 1 / 3, 1 / 4, 1 / 5, 1 / 7 respectively. Since the number of disturbance types is large, multi-class SVM is implemented in a one-against-all manner, and the identification model uses the 5-fold cross-validation method.

[0171] A Evaluation of the selection results based on the improved mRAR algorithm under interaction

[0172] To illustrate the performance of the feature selection algorithm based on the improved maximum correlation and minimum redundancy criterion, the first 40 key features are taken and evenly divided into the 1st - 8th groups in the order of sorting. The 8 groups of features are tested using SVM(rbf), and the results are as Figure 4 shown.

[0173] It can be seen through Figure 4 that when the sorting of the feature selection results is more forward, the classification result of SVM is higher, and when only the first 5 features are input, the recognition accuracy of the classifier is also greater than 80%, indicating that the feature selection algorithm based on the improved mRAR criterion under interaction is effective.

[0174] B Construction of the key feature subset

[0175] The dimension of the features is gradually increased successively according to the order of the selection results, and the support vector machine (rbf kernel) is used for recognition. The obtained results are as Figure 5 shown.

[0176] It can be seen from Figure 5 that as the feature dimension increases, the classification results of both types of classifiers first gradually increase and then fluctuate within a small range after reaching the peak. This indicates that the features added after the peak not only do not improve the recognition accuracy of the classifier but may also have an unnecessary impact on classification. At the same time, considering the recognition accuracy and computational cost of the classifier, it is easy to obtain that the optimal dimension of SVM is 10.

[0177] The key feature subset of the hybrid power quality disturbance is given in Table 2 as follows.

[0178] Table 2 Key feature subset

[0179]

[0180]

[0181] As can be seen from Table 2, the key feature subset comes from the features obtained by different feature extraction methods, indicating that combining features from different sources is beneficial to improving the recognition accuracy.

[0182] C Weight distribution of the kernel functions

[0183] The weights of each base kernel when the multi - kernel SVM algorithm recognizes different hybrid power quality disturbances are given (only the weights of the base kernels that are not all 0 are given), as shown in Table 3.

[0184] Table 3 Weight distribution of each base kernel

[0185]

[0186] It can be seen from the analysis in Table 3 that most of the weights are zero and only a small part of the kernel weights are non-zero. This is because during the training process, most of the redundant features are deleted, and only a small part of the useful features are retained during the classification process. At the same time, the entire weight determination process is automatically completed, avoiding the influence of human subjectivity on the identification accuracy.

[0187] Comparison of single-core and multi-core SVMs with integrated radius information

[0188] To illustrate the superiority of the multi-core SVM, the identification results of the single-core SVM and the multi-core SVM based on the key feature subspace under different noise intensities are given in Table 4.

[0189] Table 4 Comparison of identification results of single-core and multi-core SVMs

[0190]

[0191] It can be seen from Table 4 that the multi-core SVM algorithm with integrated radius information has a higher classification accuracy than the single-core SVM classification method under different noise environments, and the accuracy of various classifiers has increased after feature selection, indicating that the improved mRAR algorithm under the interaction can not only reduce the feature calculation amount and classifier complexity, but also effectively improve the classification accuracy.

[0192] To illustrate the adaptability of the multi-core SVM algorithm with integrated radius information to samples, the identification results of the algorithm under different sample sizes are given respectively as Figure 6 shown.

[0193] By Figure 6 it can be seen that near a sample size of 500, the identification accuracy of the multi-core SVM with integrated radius information is basically stable. This is because the SVM itself has relatively superior identification accuracy for small samples, and combined with multiple kernel functions to map multi-source data, it can better identify multi-source data in the case of small samples.

[0194] E Comparison with other identification methods

[0195] To verify the effectiveness of the identification strategy in this embodiment, a comparison is made with the methods in references [10-11],

[13] (Yang Jianfeng, Jiang Shuang, et al. Identification of composite power quality disturbances based on piecewise improved S-transform [J]. Power System Protection and Control, 2019, 47(9): 64-71.; Xu Liwu, Li Kaicheng, et al. Identification of composite power quality disturbances based on incomplete S-transform and gradient boosting tree [J]. Power System Protection and Control, 2019, 47(6): 24-31.; Wang Yang, Xiao Xianyong, et al. Selection of classification features for short-term composite power quality disturbances and Mahalanobis distance classification method [J]. Power Grid Technology, 2014, 38(4): 1064-1069.). The comparison results are shown in Table 5. In the simulation model, the high-frequency and low-frequency window width coefficients of reference

[10] (Yang Jianfeng, Jiang Shuang, et al. Identification of composite power quality disturbances based on piecewise improved S-transform [J]. Power System Protection and Control, 2019, 47(9): 64-71.) are set to 0.15 and 10, the high-frequency and low-frequency window width coefficients of reference

[11] (Xu Liwu, Li Kaicheng, et al. Identification of composite power quality disturbances based on incomplete S-transform and gradient boosting tree [J]. Power System Protection and Control, 2019, 47(6): 24-31.) are set to 0.2 and 5, and reference

[13] (Wang Yang, Xiao Xianyong, et al. Selection of classification features for short-term composite power quality disturbances and Mahalanobis distance classification method [J]. Power Grid Technology, 2014, 38(4): 1064-1069.) adopts the corresponding hierarchical classification structure.

[0196] Table 5 Comparison of classifier results

[0197]

[0198] As can be seen from Table 5, in different noise environments, the classification accuracy of the method proposed in this embodiment is relatively high, indicating that the method has strong classification ability and anti-interference ability.

[0199] 3 Conclusions

[0200] To reduce the influence of the blurred edges of typical features obtained by a single feature extraction method on the identification accuracy, this embodiment proposes to identify disturbances by integrating multi-source features. On the basis of screening out the key feature subsets in each source feature, a multi-kernel SVM integrated with radius information is used to achieve accurate identification. The conclusions are as follows:

[0201] (1) Through the analysis of different characteristic curves, it shows that different feature extraction methods have their own applicability, and fusing the features obtained by different feature extraction methods helps to improve the identification accuracy.

[0202] (2) An improved mRAR-based feature selection algorithm under interaction is proposed, which effectively removes useless redundant information, improves the operation speed of the classifier, and ensures a high identification accuracy with a small number of features.

[0203] (3) By comparing the identification results of multi-kernel SVMs with different kernel function weight distributions, as well as single-kernel and integrated radius information, it shows that the multi-kernel SVM algorithm with integrated radius information not only avoids the subjectivity of the number of base kernels and parameter selection, but also more comprehensively and accurately describes features from different sources, improving the identification accuracy and stability.

[0204] (4) Through the analysis of the identification results under different noise intensities, it is verified that the identification method proposed in this embodiment has a high classification accuracy in various situations, is less affected by noise and interference between disturbances, and has strong recognition robustness and anti-noise performance.

[0205] (5) By comparing the identification results under different training sample sizes, it is proved that the method proposed in this embodiment still obtains good classification results with a small number of samples.

[0206] The above method provided in this embodiment can be stored in a computer-readable storage medium in a codified form, implemented in the form of a computer program, and input the basic parameter information required for calculation through computer hardware and output the calculation results.

[0207] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, devices, or computer program products. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0208] The present invention is described with reference to the flowcharts of methods, devices (apparatuses), and computer program products according to the embodiments of the present invention. It should be understood that each process in the flowchart and the combination of processes in the flowchart can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in Figure 1 one process or multiple processes.

[0209] These computer program instructions can also be stored in a computer-readable memory capable of guiding a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including an instruction device that implements the functions specified in one process Figure 1 or in multiple flowcharts.

[0210] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one process Figure 1 or in multiple processes.

[0211] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific embodiments of the present invention. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

[0212] This patent is not limited to the above best embodiments. Anyone inspired by this patent can obtain various other forms of hybrid power quality disturbance identification methods based on multi-core support vector machines. All equal changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope covered by this patent.

Claims

1. A hybrid power quality disturbance recognition method based on a multi-core support vector machine, characterized in that: Identify the disturbance type by using a variety of feature extraction methods, and select the key features effective for classification by using the improved maximum correlation and minimum redundancy criterion; the improved maximum correlation and minimum redundancy criterion introduces the mutual information to account for the influence of the simultaneous action of the newly added features and the existing features on the classification contribution, and introduces the symmetric uncertainty to normalize the mutual information; The expression of the improved maximum correlation and minimum redundancy criterion is equivalent to: Among them, TF is the original given complete set of features, T is the target category, F n-1 is the existing n- 1 key feature subset; Identify the hybrid power quality disturbance by using the multi-kernel SVM considering the radius information. Introduce the trace of the sample divergence matrix into the multi-kernel support vector machine, and transform the model into two convex optimization problems for solution: The multi-kernel SVM model considering the radius information is: Among them, C is the penalty parameter, is the slack variable; d m is the weight corresponding to the m-th single-core function of the multi-core SVM, M is the number of kernel functions and the number of data sources, and the objective value of the multi-core support vector machine is J(d); tr(S T m ) is the trace of the total scatter matrix of the samples corresponding to the m-th feature space.

2. The hybrid power quality disturbance identification method based on a multi-core support vector machine according to claim 1, wherein: Adopt the incremental strategy method in the forward search method for feature selection based on the improved maximum correlation and minimum redundancy criterion.

3. The hybrid power quality disturbance identification method based on a multi-core support vector machine according to claim 1, characterized in that: Comprehensively use five analysis methods including time-domain extraction, Fourier transform, short-time Fourier transform, wavelet transform, and S transform to extract the features of the disturbance to be identified, and then construct the original feature space.

4. The hybrid power quality disturbance identification method based on a multi-core support vector machine according to claim 3, characterized in that: Adopt the improved maximum correlation and minimum redundancy criterion to select the key feature subset with the largest correlation with the target category and the smallest mutual redundancy from the original feature space.

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