Frequency warped cross-wavelet multiresolution analysis of guided waves for impact localization

Passive source localization in dispersive systems with sparse sensors array represent a fundamental issue in applications such as seismic, radar, underwater acoustics, wireless transmission. This paper presents a new in situ Structural Health Monitoring (SHM) system based on wave propagation approach able to assess damages and to identify the location of acoustic emission (AE) sources due to impacts. When we deal with such channels, it is necessary to compensate the frequency dependent propagation and then the localization is achieved from time-difference-of-arrival (TDOA) between sensor outputs. In this paper a novel impact localization algorithm based on the frequency warping unitary operator applied to E-spline wavelet multiresolution analysis is presented. Unitary frequency warped representation is important to analyze class of signal covariant to group delay shift as those propagating through frequency-dependent channels. The innovative key points behind the developed framework are: (i) to perform a nonstationary wavelet multiresolution analysis on the acquired signals; (ii) to design a proper scaling wavelet through the frequency warping operator; (iii) application of the frequency warped wavelet multiresolution on the cross-correlated signal to achieve an accurate time difference of arrival (TDOA) estimation. Finally, the TDOA data are exploited to locate the acoustic emission source through hyperbolic positioning. The Cramèr–Rao lower bound (CRLB) is derived and the performance of the proposed algorithm is analyzed. It is found that the theoretical variances of the estimates are unbiased and approach the CRLB at high signal-to-noise ratio (SNR). In order to demonstrate the effectiveness of the proposed framework, we have investigated lamb wave transmission over aluminum plate that suffers from severe multi modal frequency dispersions and multipath reflections.