A signal-adapted wavelet design method for acoustic emission signals of rail cracks

Though multiresolution analysis has found successful applications on Acoustic emission (AE) signals, existing wavelets suffer from the problem of expressing AE signals in many applications. In the field of rail defect detection, complicated AE signals emitted from rail crack growth cannot be described properly by commonly used wavelets. In order to give better expressions of these signals, this paper proposes a design approach for signal-adapted wavelet in the frame of a two-band analysis/synthesis system, in which the problem of wavelet design is converted into a constrained optimization problem. For perfect reconstruction of the system, necessary and sufficient conditions, as well as orthogonality and normalization of the wavelet, are considered as constraints of the optimization problem. In order to preserve more information of crack growth AE signals, Euclid norm of the error between the approximation signal and the input signal is minimized in the cost function. AE signals of crack growths from a tensile test of a steel specimen are acquired for experimental verification. By comparing with the commonly used wavelets, it is demonstrated that the wavelet designed by the proposed method has superior performance in expressing the crack AE signal, and can outperform the most suitable existing wavelet due to its adaptivity. Moreover, the designed wavelet shows good robustness against noise, which has profound meaning for rail crack detection in practical applications.