Adaptive Redundant Lifting Wavelet Transform Based on Fitting for Fault Feature Extraction of Roller Bearings

A least square method based on data fitting is proposed to construct a new lifting wavelet, together with the nonlinear idea and redundant algorithm, the adaptive redundant lifting transform based on fitting is firstly stated in this paper. By variable combination selections of basis function, sample number and dimension of basis function, a total of nine wavelets with different characteristics are constructed, which are respectively adopted to perform redundant lifting wavelet transforms on low-frequency approximate signals at each layer. Then the normalized lP norms of the new node-signal obtained through decomposition are calculated to adaptively determine the optimal wavelet for the decomposed approximate signal. Next, the original signal is taken for subsection power spectrum analysis to choose the node-signal for single branch reconstruction and demodulation. Experiment signals and engineering signals are respectively used to verify the above method and the results show that bearing faults can be diagnosed more effectively by the method presented here than by both spectrum analysis and demodulation analysis. Meanwhile, compared with the symmetrical wavelets constructed with Lagrange interpolation algorithm, the asymmetrical wavelets constructed based on data fitting are more suitable in feature extraction of fault signal of roller bearings

Distortion estimates for adaptive lifting transforms with noise

Multimedia analysis, enhancement and coding methods often resort to adaptive transforms that exploit local characteristics of the input source. Following the signal decomposition stage, the produced transform coefficients and the adaptive transform parameters can be subject to quantization and/or data corruption (e.g. due to transmission or storage limitations). As a result, mismatches between the analysis- and synthesis-side transform coefficients and adaptive parameters may occur, severely impacting the reconstructed signal and therefore affecting the quality of the subsequent analysis, processing and display task. Hence, a thorough understanding of the quality degradation ensuing from such mismatches is essential for multimedia applications that rely on adaptive signal decompositions. This paper focuses on lifting-based adaptive transforms that represent a broad class of adaptive decompositions. By viewing the mismatches in the transform coefficients and the adaptive parameters as perturbations in the synthesis system, we derive analytic expressions for the expected reconstruction distortion. Our theoretical results are experimentally assessed using 1D adaptive decompositions and motion-adaptive temporal decompositions of video signals