Abstract

Effective processing and compact representation of signals from manufacturing processes is necessary for sensor-based modeling (Venuvinod 98), and real-time diagnosis and control purposes. However, the processing and the representation of signals emerging from nonlinear processes remains largely ignored. This article focuses on the compact representation of near-periodic signals (signals containing a dominant period), emerging from nonlinear dynamical systems with known initial conditions. Such signals commonly occur in machine tool operations. We propose the concept of pseudoprobability space and provide an approach based on lifting scheme to customize wavelet filters to compactly represent near-periodic signals, and validate the approach for acoustic emission signals emanating from machine tool operations. Here, we focus on the concentration of the reconstructed signal using the coefficients from lifting on a single scale. We provide a detailed assessment of our approach, including a detailed study of the relationship between the discrete wavelet transform (DWT) and the discrete-time wavelet transform (DTWT). We derive the pyramid algorithm for DTWT with non-biorthogonal wavelets, which is necessary for our assessment. Our numerical experiments establish the viability of our approach.

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