International Journal of Wavelets, Multiresolution and Information Processing

Complex Shifted Morlet Wavelets (CSMW) present a number of advantages when used for the demodulation of the vibration response of defective rolling element bearings: (A) They present the optimally located window simultaneously in the time and in the frequency domains; (B) They allow for the maximal time-frequency resolution; (C) The magnitudes of the complex wavelet coefficients in the time domain lead directly to the required envelope; (D) They allow for the optimal selection of both the center frequency and the bandwidth of the requested filter. A Peak Energy criterion (P. E.) is proposed in this paper for the simultaneous automatic selection of both the center frequency and the bandwidth of the relevant wavelet window to be used. As shown in a number of application cases, this criterion presents a more effective behavior than other criteria used (Crest Factor, Kurtosis, Smoothness Index, Number of Peaks), since it combines the advantages of energy based criteria, with criteria characterizing the spikiness of the response.

A critical issue to ensuring the effectiveness of wavelet transform in machine condition monitoring and health diagnosis is the choice of the most suited base wavelet for signal decomposition and feature extraction. This paper addresses this issue by introducing a quantitative measure to select an appropriate base wavelet for analyzing vibration signals measured on rotary mechanical systems. Specifically, the measure based on energy-to-Shannon entropy ratio has been investigated. Both the simulated Gaussian-modulated sinusoidal signal and an actual ball bearing vibration signal have been used to evaluate the effectiveness of the developed measure on base wavelet selection. Experimental results demonstrate that the wavelet selected using the developed measure is better suited than other wavelets in diagnosing structural defects in the bearing. The method developed provides systematic guidance in wavelet selection.

A periodic transient detection and representation method, termed synchronous enhancement of periodic feature (SEPF), based on the Continuous Wavelet Transform (CWT) is proposed. This method first represents a given signal in the time-scale domain through CWT and then maps the resulted wavelet coefficients into the polar diagram using the given potential periods. Transient features would thus be synchronously enhanced at a certain area if the mapping time period matches that of the transient vibrations. The simulation study and the applications in the gearbox and bearing fault diagnosis verify the effectiveness of the proposed method in detecting the periodical transient vibrations.

Based on finite element of B-spline wavelet on the interval (BSWI), the quantitative identification method of transverse crack for rotor systems was studied. The new model of BSWI Rayleigh–Euler rotary beam element considering gyroscopic effect and rotational inertia was constructed to solve the first three natural frequencies of the cracked rotor with high precision, and the first three frequencies solution surfaces of normalized crack location and size were obtained by using surface-fitting technique. Then the first three metrical natural frequencies were employed as inputs of the solution curve surfaces. The intersection of the three frequencies contour lines predicted the normalized crack location and size. The numerical and experimental examples were given to verify the validity of the beam element for crack quantitative identification in rotor systems. The new method can be applied to prognosis and quantitative diagnosis of cracks in the rotor system.

A new technique for sound loudness evaluation, the so-called antinoise wavelet pre-processing neural network (ANWT-NN) model, is presented in this paper. Based on passing vehicle noise, the ANWT-NN loudness model combines the techniques of wavelet analysis and neural network regression and classification. A wavelet-based, 21-point model for vehicle noise feature extraction is established. Verification shows that the trained ANWT-NN models are more accurate and effective than the WT-NN models for sound quality evaluation of nonstationary vehicle noises. The newly proposed ANWT-NN model can be applied to both the stationary and nonstationary sound signals and even to the transient ones. The ANWT-NN technique is suggested not only for the prediction, classification, and comparison of the sound quality of passing vehicle noise, but also for applications in other sound-related engineering fields, in place of the conventional psychoacoustical models.

This paper is concerned with the spectral decomposition and the adaptive analysis of data coming from car crash simulations. The mathematical ingredient of the proposed signal processing technique is the flexible Gabor-wavelet transform or the α-transform that reliably detects both high and low frequency components of such complicated short-time signals. We go from the functional treatment of this wavelet-type transform to its numerical implementation and we show how it can be used as an improved tool for spectral investigations compared to the short-time Fourier transform or the classical wavelet transform.

The acoustic signal of mechanical watch is a distinct multi-component signal. It contains many frequency components corresponding to specific escapement motion sources with a very wide frequency range. Therefore, it is challenging for signature analysis of mechanical watch by the acoustic signal. This paper studies the time-frequency signatures of the mechanical watch based on wavelet decomposition. Two methods are proposed to improve the frequency resolution of traditional wavelet techniques by combining other beneficial techniques in the sense of decomposing specific mono- or independent components. The empirical mode decomposition (EMD) is presented to advance the wavelet packet decomposition (WPD) to decompose the mono-component signals. And the blind source separation (BSS) makes the redundancy of continuous wavelet transform (CWT) further gain good frequency resolution in the independent meaning. The decomposed signals by the two methods reveal the insight of mechanical watch movement and can contribute much simpler and clearer time-frequency signatures. Experimental results indicated the effectiveness of the two methods and the value of the time-frequency signatures in analyzing and diagnosing mechanical watch movements.

Corrosion causes a degradation of the structural integrity of petrochemical plants, nuclear power plants, ships, bridges and other constructions containing steel with the consequence that people and the environment may be exposed to dangerous situations. The detection of corrosion and the prediction of the type of corrosion are studied in this article by means of the acoustic emission technique. We use a wavelet packet decomposition to compute features from the acoustic emission signals. The basis functions with the highest discriminative power are selected according to the highest pair-wise Kullback–Leibler divergence between distributions of wavelet coefficients. It is proven that the pair-wise Kullback–Leibler divergence used in the local discriminant basis algorithm requires class conditional independence of the wavelet coefficients. Several classification algorithms using the most discriminative wavelet coefficients are compared for the prediction of three types of corrosion and the absence of corrosion.