On the wavelet–fractal nonlinear damage diagnosis of mechanical systems

Nonlinear damage is a common occurrence for mechanical systems in service, whereas the studies concerning the diagnosis of nonlinear damage are often limited due to the intensive complexity. Wavelets and fractals are versatile mathematical tools suitable for nonlinear problems, and they have emerged recently in nonlinear damage diagnosis. Generally, the wavelet transform is carried out on a contaminated testing response to reveal damage information, while the fractal analysis is implemented on a unitary signal to generate a fractal dimension as a damage indicator. Of the existing work, wavelets and fractals have always been used separately in damage diagnosis. Different from existing studies, the present study aims to develop a synergistic wavelet–fractal nonlinear damage diagnosis (WFNDD) algorithm considering the complementary merits of wavelets and fractals. The proposed WFNDD algorithm leads to development of two new techniques: the wavelet packet component signal assurance criterion (WPAC) and correlation-integral-based damage indicator (CIDI). The WPAC is originated from the conventional mode assurance criterion (MAC), and it is capable of extracting slight damage information from dynamic responses, while the CIDI is derived from the correlation integrals of the WPAC-extracted slight damage information, and it gets rid of the errors in correlation dimension estimation and reflects damage from the statistical–physical characteristics of the responses analyzed. The progressive implementations of the WPAC and the CIDI constitute the basic procedures of the WFNDD for nonlinear damage diagnosis. Compared to the separate wavelet or fractal methods available, the WFNDD has a more advanced capability of characterizing nonlinear damage due to the intrinsic consolidation of wavelets and fractals. The great potentials of combined wavelets and fractals in nonlinear damage diagnosis of mechanical systems are demonstrated in this study