Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy

Abstract

Dynamic mode decomposition (DMD) is essentially a hybrid algorithm based on mode decomposition and singular value decomposition, and it inevitably inherits the drawbacks of these two algorithms, including the selection strategy of truncated rank order and wanted mode components. A novel denoising and feature extraction algorithm for multi-component coupled noisy mechanical signals is proposed based on the standard DMD algorithm, which provides a new method solving the two intractable problems above. Firstly, a sparse optimization method of non-convex penalty function is adopted to determine the optimal dimensionality reduction space in the process of DMD, obtaining a series of optimal DMD modes. Then, multiscale permutation entropy calculation is performed to calculate the complexity of each DMD mode. Modes corresponding to the noise components are discarded by threshold technology, and we reconstruct the modes whose entropies are smaller than a threshold to recover the signal. By applying the algorithm to rolling bearing simulation signals and comparing with the result of wavelet transform, the effectiveness of the proposed method can be verified. Finally, the proposed method is applied to the experimental rolling bearing signals. Results demonstrated that the proposed approach has a good application prospect in noise reduction and fault feature extraction.

A Fault Diagnosis Method for One‐Dimensional Vibration Signal Based on Multiresolution tlsDMD and Approximate Entropy

“…In the past, many researchers have done a lot of work in the field of truncation criteria. e proposed methods include hard threshold [45], soft threshold [46], and the nonconvex optimization algorithm [47]. e above methods either need to know the SNR in advance or add additional parameters.…”

A data driven method applied on nonlinear vibration of flexible rotor supported on centralized squeeze film damper

“…This method removes the mode related to noise and evolve rest mode within the present sample in flow space. Dang et al 32 proposed a novel method for sorting the problems of rank truncation and dominant mode selection by DMD algorithm. A sparse optimization method is used for finding the optimal DMD modes.…”

Parametric Dynamic Mode Decomposition for Reduced Order Modeling

“…DMD aims at finding a reduced representation Koopman operator [41], which allow us to naturally represent the dynamic evolution of the system on the selected POD modes via a transient, mode-decaying algebraic equation based on the modes and frequencies of this operator [42]. Although Mezic [43] was the first one to use DMD as a ROM method, many variants have later appeared to improve DMD performance on large-stream datasets [44], prediction boundness [45], ability to capture multiple scales [46,47], and reduce sensitivity to noise [48], between others. The reader is referred to the review by Kutz et al for details about these methods [40].…”