Damage detection using multivariate recurrence quantification analysis

Abstract Recurrence-quantification analysis (RQA) has emerged as a useful tool for detecting subtle non-stationarities and/or changes in time-series data. Here, we extend the RQA analysis methods to multivariate observations and present a method by which the “length scale” parameter e (the only parameter required for RQA) may be selected. We then apply the technique to the difficult engineering problem of damage detection. The structure considered is a finite element model of a rectangular steel plate where damage is represented as a cut in the plate, starting at one edge and extending from 0% to 25% of the plate width in 5% increments. Time series, recorded at nine separate locations on the structure, are used to reconstruct the phase space of the system's dynamics and subsequently generate the multivariate recurrence (and cross-recurrence) plots. Multivariate RQA is then used to detect damage-induced changes to the structural dynamics. These results are then compared with shifts in the plate's natural frequencies. Two of the RQA-based features are found to be more sensitive to damage than are the plate's frequencies.