Applied Acoustics 139 (2018) 251–258 Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust A signal-adapted wavelet design method for acoustic emission signals of rail cracks Qiushi Hao, Xin Zhang , Kangwei Wang, Yi Shen, Yan Wang Department of Control Science and Engineering, Harbin Institute of Technology, 150001, PR China ARTIC L E I NF O ABSTRAC T Keywords: Though multiresolution analysis has found successful applications on Acoustic emission (AE) signals, existing Rail crack detection wavelets suﬀer from the problem of expressing AE signals in many applications. In the ﬁeld of rail defect de- Acoustic emission signal tection, complicated AE signals emitted from rail crack growth cannot be described properly by commonly used Wavelet design wavelets. In order to give better expressions of these signals, this paper proposes a design approach for signal- Constrained optimization 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
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