A noise reduction method of symplectic singular mode decomposition based on Lagrange multiplier

Time series analyses still play a crucial role in industrial applications; further, highlighting or extracting useful state characteristics under the process of mechanical state monitoring is also crucial. However, owing to the background noise in acquired signals, it is impossible to identify faulty states at all times. Therefore, it is essential to implement noise reduction processes. In this paper, a new noise reduction method based on symplectic singular mode decomposition (SSMD) and Lagrange multiplier v, called v-SSMD noise reduction method, is proposed. First, this method uses the symplectic geometry similarity transformation for the constructed trajectory matrix to obtain the characteristics and eigenvectors of useful components and noise. Linear estimation is then used to approximate the pure signal, and a Lagrange multiplier is used to enhance the useful component and restrain the residual signal expressed as noise. Finally, the desired dominant characteristics and eigenvectors are obtained to reconstruct the signal without noise. The simulation and gear fault signals are used to demonstrate the effectiveness of the v-SSMD noise reduction method. The analysis results indicate that the proposed method exhibits good performance in eliminating noise from practical data. (C) 2019 Elsevier Ltd. All rights reserved.