Selection of the number of effective singular values for noise reduction

As for noise reduction adopting singular value decomposition (SVD) algorithm, it is important that how to choose the number of effective singular values. This paper improves SVD algorithm. The improved algorithm can automatically calculate the number of effective singular values of the signal with noise, avoiding the misjudgment caused by artificial selection of the number of effective singular values. The relationship between effective singular values of a signal and the dimension of Hankel matrix is confirmed. The relationship of the singular values between the signal with noise, the original signal and the noise signal, as well as the relationship between the magnitude of singular values and the signal energy, are clarified. A hyperparameter ACC to control two data obtained by processing singular values is proposed, so that the number of effective singular values can be identified more accurately. Finally, this algorithm is adopted to process noise successfully in vibration signal of a rotor.