Particle filter based matching pursuit; decomposition for damage quantification in composite structures

In structural health monitoring, the fundamental goal is to address the problem of damage identification, localization and quantification. Using the wave based approach, the presence of damage is visualized in terms of the changes in the signature of the resultant wave that propagates through the structure. Surface mounted piezoelectric transducers have been used for monitoring. The voltage output of each sensor is used for signature characterization. Due to the time-varying nature of these signals, performance of some existing analyzing tools may not be satisfactory. The present research demonstrates the use of the matching pursuit decomposition as a signal processing technique to compare signals from healthy and damaged structures. The developed methodology is based on the localized analysis of waveforms obtained from damaged structures using "matching pursuit decomposition (MPD)" technique and time-frequency representations (TFR), with a broader view of damage quantification. However the matching pursuit method uses a dictionary that is large enough to decompose the signal. The major drawback of using such a large dictionary is the computational expense that limits the use of matching pursuits in real applications. Therefore, the availability of a smaller dictionary, able to adapt to the specific signal to be decomposed, would combine the generality of the original matching pursuit with execution speed. In this paper, we use the particle filter matching pursuit decomposition (PFMPD) algorithm to estimate the matching pursuit dictionary that is suited to the structure of the waveform to be decomposed. The proposed algorithm, sequentially estimates a dictionary that contains only those components that match the waveform structure, uses the matching pursuits for the decomposition of the signal and, if necessary, adapts the dictionary to the structure of the resulting residues for further decomposition. Finally we demonstrate using real life data that the particle filtering matching pursuit retains the ability of the matching pursuit to decompose waveforms and quantify them accurately while reducing computational expense.