VMD Time-Frequency Analysis And Its Application In Machinery Fault Diagnosis

The collected vibration signals in actual working conditions are mostly non-stationary and non-linear multi-component time-varying signals.How to accurately extract features from the signals is still a difficult and hot topic in mechanical fault diagnosis.Time-frequency analysis technology can reveal the characteristics of frequency and time variation simultaneously,it has been thus widely used in the fault diagnosis of machinery.At present,short-time Fourier transform,Wigner-Ville distribution,wavelet transform and other time-frequency methods have their own limitations,so new time-frequency analysis methods and corresponding feature extraction techniques need to be studied.This paper synthetically used modern signal processing method and proposed new construction method for the time-frequency diagram of VMD.We then studied its time-frequency concentration and the instantaneous feature extraction technology and finally applied it to the mechanical fault diagnosis under variable speed conditions.The main contents of this article are as follows:(1)The N-order complex time-frequency analysis method was introduced and then the calculation method of its instantaneous frequency was proposed.Through simulated signal analysis,it was shown that the aggregation of the time-frequency spectrum will be better when the order of time-frequency method is higher.Moreover,cross terms will be also less and the instantaneous frequency can be obtained accurately.However,this method needs a large amount of computation,and the existing complex delay time-frequency method cannot handle signals with too many data points,which greatly limits its application.The principle of VMD algorithm and its implementation process have been introduced briefly.At the same time,the time-frequency plot of VMD was constructed via Hilbert transform.The Gini index and the time-frequency kurtosis were utilized to quantitatively analyze the time-frequency concentration of the VMD time-frequency spectrum.Result of simulated analysis has demonstrated that the proposed VMD-based time-frequency representation has better time-frequency aggregation and less mode aliasing compared with other time-frequency methods such as EEMD.(2)A parameter optimization method used in VMD was proposed based on bat algorithm.The bat algorithm has advantages of good global search capability and fast convergence,which was applied to the VMD algorithm to automatically determine key parameters mentioned in VMD algorithm.This proposed method improves the adaptability of the VMD algorithm for the practical applications.The effectiveness of the proposed method was verified by numerical simulation and experimental analysis.The resultsdemonstrated the robustness and the accuracy of the parametric optimization method.(3)The basic principle of generalized Warblet Transform(GWT)was discussed.Considering the disadvantages of GWT in analyzing multi-component modulated signals and the advantages of VMD in analysis of multi-component signals,VMD was taken as the pre-processing of GWT.The effectiveness of the method was verified by gear fault diagnosis.(4)A fault diagnosis method based on angular domain order spectrum has been proposed for rolling bearing diagnosis in variable condition environments,which combines VMD method and computed order tracking(COT).The non-stationary signal in the time domain was firstly transformed into a stationary signal in the angular domain using COT,and then fault diagnosis of the rolling bearing in time-varying conditions was conducted through the reconstructed angular domain-order spectrum.The effectiveness of the method was verified in the fault identification of bearing with defects on the inner ring and outer ring.