Monte Carlo Matching Pursuit Decomposition Method for Damage Quantification in Composite Structures

In 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. In structural health monitoring, the fundamental goal is to detect, localize, and quantify these damage signatures. The current approach uses matching pursuit decomposition (MPD) to compare signals from healthy and damaged structures. However, the major drawback of the MPD is that, in the decomposition process, it performs an exhaustive search over a large dictionary of elementary functions. Therefore, this method of decomposition is associated with a large computational expense. In this research, the Monte Carlo matching pursuit decomposition (MCMPD) is proposed, that adapts a smaller dictionary to the signal structure, thus avoiding the exhaustive search over the time-frequency plane. 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 residues for further decomposition. Finally, we demonstrate using real life data that the MCMPD retains the ability of the matching pursuit to decompose waveforms and quantify them accurately while reducing computational expense.