Improved Dynamic Mode Decomposition and Its Application to Fault Diagnosis of Rolling Bearing

Abstract

To solve the intractable problems of optimal rank truncation threshold and dominant modes selection strategy of the standard dynamic mode decomposition (DMD), an improved DMD algorithm is introduced in this paper. Distinct from the conventional methods, a convex optimization framework is introduced by applying a parameterized non-convex penalty function to obtain the optimal rank truncation number. This method is inspirited by the performance that it is more perfectible than other rank truncation methods in inhibiting noise disturbance. A hierarchical and multiresolution application similar to the process of wavelet packet decomposition in modes selection is presented so as to improve the algorithm’s performance. With the modes selection strategy, the frequency spectrum of the reconstruction signal is more readable and interference-free. The improved DMD algorithm successfully extracts the fault characteristics of rolling bearing fault signals when it is utilized for mechanical signal feature extraction. Results demonstrated that the proposed method has good application prospects in denoising and fault feature extraction for mechanical signals.

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

“…Essentially, it is a kind of order reduction methods based on the theory of singular value decomposition (SVD) and mode decomposition. e detailed algorithm process of sDMD is described in [23,24].…”

“…In 2009, Schmid [23] firstly proposed the standard DMD (sDMD) method, which can extract the spatiotemporal coherent characteristics by decomposing the complex flow field signal into a series of simple expressions. DMD can decompose the time series into a series of single-frequency modal components [24], avoiding the modal aliasing problem in EMD and LMD. At the same time, because of its nature of being equation-free and data-driven [25], DMD has strict mathematical and theoretical foundation, avoiding the drawbacks of EMD.…”

“…erefore, DMD avoids the FT's drawbacks in characterizing the system by harmonic signals. With the advantage of describing the dynamic characteristics in a series of single nonorthogonal frequency modes [24], DMD maximizes the complexity of the original system, while POD decomposes data into a series of multiple orthogonal modal components, lacking the variability in structure and the concept of freedom in signal expression. As a whole, DMD has certain advantages compared with the traditional fault signal diagnosis method.…”

Theoretical Analysis of Empirical Mode Decomposition

“…The fault signal of the inner ring of the drive end is selected to analyze the feature of the EMD method, and compared with the application effect of the wavelet method. Specific experimental procedures are detailed in References [26][27][28]. The experimental conditions are as follows: the drive end bearing adopts 6205-2RS JEM SKF deep groove ball bearing, EDM bearing single point damage, the damage diameter is 0.1778 mm, the motor speed is 1748 r/min, the sampling frequency is 12 KHz, the sampling time is 0.25 s (107.dat).…”

Intelligent Ball Bearing Fault Diagnosis Using Fractional Lorenz Chaos Extension Detection

“…The ability to accurately monitor the state of wear and performance of ball bearings [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ] in machine tools is important for several reasons. The most serious being that an unexpected breakdown can cause irreparable damage to other parts of the machine.…”