OPTIMIZATION OF MORLET WAVELET FOR MECHANICAL FAULT DIAGNOSIS

Condition monitoring of rotating machines is commonly based on analysis of machine vibrations. In the presence of a mechanical fault, vibration signals comprise periodic impulses with a characteristic frequency corresponding to a particular defect. However, due to a heavy noise in the industrial applications, vibration signals have very low signal-to-noise ratio, thus requiring the extraction of impulses by an appropriate technique. Therefore, a novel denoising method based on the Morlet wavelet with adaptive time-frequency resolution has recently been proposed. However, this adaptation may under certain conditions violate the admissibility condition on mother wavelets, resulting in severe distortion of the wavelet scalogram. This paper presents a modification of the Morlet wavelet, restricting the adaptive parameter to a specific allowable range. As a result, undesired scalogram distortion is avoided, thus guaranteeing stable performance of the de-noising algorithm. Consequently, the improved method provides more reliable fault diagnosis, as well as higher computational efficiency, suitable for industrial production applications. INTRODUCTION Rolling bearings are essential mechanical parts of various rotating machines, such as universal motors for electric household appliances. Therefore, detection and identification of bearing faults has been the subject of extensive research [1,2], in order to guarantee high standards of quality control on prod uction lines. Vibration analysis is the most common tool for diagnosis of m anufacturing defects, although vibration signals have a low signal-to-noi se ratio (SNR), caused by large noise from electric brushes and windings of motors [3]. For t his reason, it is desirable to suppress the noise by an appropriate pre-processing, pri or to classification of faults. Since it is well known that periodic impulses correspond to t he repetition frequency of bearing defects [1], a novel wavelet-based denoising metho d has been proposed [4,5], employing the similarity between the impulse signal and the Morlet wavelet. Furthermore, the extraction of impulses with variable decay is prov ided by an adaptive parameterβ controlling the time-frequency resolution of the Morlet wa velet. However, our study reveals that the parameter β must be adapted only within a limited range in order to meet mathematical requirements on wavelet functions. This paper hence proposes a modification of the Morlet wavelet, de fining the solution to avoid possible adaptation problems. THEORY OF THE WAVELET TRANSFORM The continuous wavelet transform (CWT) of a finite energy signa l x(t) with an analyzing waveletψ(t) is the convolution ofx(t) with a scaled and conjugated mother wavelet: