A detection algorithm of maximum and minimum eigenvalues based on random matrix theory is proposed for the problem of abnormal detection of customer electricity consumption. Firstly, the data source matrix is constructed by time alignment and superimposed Gaussian white noise, and the sliding window method is used to obtain the window data indicating the operation status at each moment; secondly, the window data are standardized, feature extraction and other operations are performed, and the difference and the sum of the maximum and minimum eigenvalues are compared to construct the feature detection indexes and thresholds; finally, the algorithm is studied and verified by simulation. The results show that the algorithm does not depend on any model, can analyze the operation status of the system more comprehensively and adequately, and realizes the effective detection of abnormal data
Using QR decomposition of a matrix, the inverse quadratic eigenvalue problem is transformed into an equivalent system of equations, the expressions of the general solution and the Necessity and sufficiency solution of the symmetric Orthogonal symmetric Matrix for the inverse Matrix problem are obtained. Furthermore, the optimal approximation problem for any given Matrix is considered and the optimal approximation symmetric orthogonal symmetric solution is obtained.
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