Identification of linear mechanical systems by deconvolution techniques

This paper describes how the impulse response function of a linear and time invariant dynamic system can be computed numerically by deconvolution techniques, starting from its input and output time histories. The integral equation governing the problem is transformed into a severely ill-conditioned set of linear equations whose approximate solution is obtained through regularisation methods. A proposal, with the aim of taking into account the possible non-null initial conditions of the physical system, is suggested together with an algorithm that allows the definition of long impulse responses with limited computing effort. The implementation developed can deal with single input single output, single input multiple output and multiple input multiple output systems and has been tested both numerically and on two simple real structures. The advantages and disadvantages of these time domain techniques are discussed in comparison with the widely used frequency methods.