Application of advanced data-driven parametric models to load reconstruction in mechanical structures and systems

This paper considers a method for reconstructing sine-wave excitation using an inverse, parametric data-driven model developed to monitor the magnitude and frequency of the load to which a structure is exposed. The main goal of the paper is to discuss, and experimentally verify, the applicability of different SISO and MIMO structures of parametric models, such as the ARX, ARARX, OE, BJ, and PEM models described by the linear system identification theory. Experimental validation tests were conducted on a set-up consisting of a metal frame equipped with two electrodynamic exciters, several acceleration transducers and a data-acquisition system. The fidelity and adequacy of various model structures was judged in time and frequency domains based on stability diagrams, FPE and AIC criteria, as well as on the magnitude of the relative error between the measured and reconstructed load. The experimental test results showed that, in the case of measurement data moderately corrupted by noise, the ARX and OE models provide better accuracy of inversion than advanced models, such as ARARAX, BJ or PEM. This leads to the conclusion that increasing the complexity of a model structure does not result in better reconstruction of the load. Therefore, less complicated structures are acceptable for practical applications and, in fact, should be favored.