Tunable Q-factor wavelet transform denoising with neighboring coefficients and its application to rotating machinery fault diagnosis

Fault diagnosis of rotating machinery is of great importance to the high quality products and long-term safe operation.However,the useful weak features are usually corrupted by strong background noise,thus increasing the difficulty of the feature extraction.Thereby,a novel denoising method based on the tunable Q-factor wavelet transform(TQWT)using neighboring coefficients is proposed in this article.The emerging TQWT possesses excellent properties compared with the conventional constant-Q wavelet transforms,which can tune Q-factor according to the oscillatory behavior of the signal.Meanwhile,neighboring coefficients denoising is adopted to avoid the overkill of conventional term-by-term thresholding techniques.Because of having the combined advantages of the two methods,the presented denoising method is more practical and effective than other methods.The proposed method is applied to a simulated signal,a rolling element bearing with an outer race defect from antenna transmission chain and a gearbox fault detection case.The processing results demonstrate that the proposed method can successfully identify the fault features,showing that this method is more effective than the conventional wavelet thresholding denoising methods,term-by-term TQWT denoising schemes and spectral kurtosis.

基于可调Q因子小波变换的海杂波抑制算法

针对海杂波背景下弱目标检测中存在的信杂比低的问题,提出了改进的基于可调Q因子小波变换的海杂波抑制算法。由于海杂波能量远大于目标信号能量,提出选取与海杂波振荡特性相匹配的参数进行可调Q因子小波变换,得到各小波子带的系数,并对小波系数进行稀疏优化后重构海杂波信号。为了判断弱目标信号是否存在,提出一种自适应的阈值检测方法,将原始回波信号与海杂波重构信号的差作为检测样本,实现对弱目标信号的检测。该算法不依赖海杂波具体模型。最后对某实测海杂波数据集进行实验,验证了所提算法的正确性。

Improved TQWT for marine moving target detection

Under the conditions of strong sea clutter and complex moving targets,it is extremely difficult to detect moving targets in the maritime surface.This paper proposes a new algorithm named improved tunable Q-factor wavelet transform(TQWT)for moving target detection.Firstly,this paper establishes a moving target model and sparsely compensates the Doppler migration of the moving target in the fractional Fourier transform(FRFT)domain.Then,TQWT is adopted to decompose the signal based on the discrimination between the sea clutter and the target’s oscillation characteristics,using the basis pursuit denoising(BPDN)algorithm to get the wavelet coefficients.Furthermore,an energy selection method based on the optimal distribution of sub-bands energy is proposed to sparse the coefficients and reconstruct the target.Finally,experiments on the Council for Scientific and Industrial Research(CSIR)dataset indicate the performance of the proposed method and provide the basis for subsequent target detection.

Oscillatory-Plus-Transient Signal Decomposition Using TQWT and MCA

This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is modeled as a signal that can be sparsely denoted by high Q-factor TQWT;similarly, the transient component is modeled as a piecewise smooth signal that can be sparsely denoted using low Q-factor TQWT. Since the low and high Q-factor TQWT has low coherence, the morphological component analysis (MCA) can effectively decompose the signal into oscillatory and transient components. The corresponding optimization problem of MCA is resolved by the split augmented Lagrangian shrinkage algorithm (SALSA). The applications of the proposed method to speech, electroencephalo-graph (EEG), and electrocardiograph (ECG) signals are included.

Adaptive TQWT filter based feature extraction method and its application to detection of repetitive transients

The local defect in rotating machine always gives rise to repetitive transients in the collected vibration signal. However, the transient signature is prone to be contaminated by strong background noises, thus it is a challenging task to detect the weak transients for machine fault diagnosis. In this paper, a novel adaptive tunable Q-factor wavelet transform(TQWT) filter based feature extraction method is proposed to detect repetitive transients. The emerging TQWT possesses distinct advantages over the classical constant-Q wavelet transforms, whose Q-factor can be tuned to match the oscillatory behavior of different signals, but the parameter selection for TQWT heavily relies on prior knowledge. Within our adaptive TQWT filter algorithm, the automatic optimization techniques for three TQWT parameters are implemented to achieve an optimal TQWT basis that matches the transient components. Specifically, the decomposition level is selected according to a center frequency ratio based stopping criterion, and the Q-factor and redundancy are optimized based on the minimum energy-weighted normalized wavelet entropy.Then, the adaptive TQWT decomposition can be achieved in a sparse way and result in subband signals at various wavelet scales.Further, the optimum subband signal which carries transient feature information, is identified using a normalized energy to bandwidth ratio index. Finally, the single branch reconstruction signal from the optimum subband is obtained with transient signatures via inverse TQWT, and the frequency of repetitive transients is detected using Hilbert envelope demodulation. It has been verified via numerical simulation that the proposed adaptive TQWT filter based feature extraction method can adaptively select TQWT parameters and the optimum subband for repetitive transient detection without prior knowledge. The proposed method is also applied to faulty bearing vibration signals and its effectiveness is validated.