Nonparametric Identification of Nearly Arbitrary Nonlinear Systems

A nonparametric identification technique is presented for use with discrete multidegree-of-freedom nonlinear dynamic systems. The method requires information regarding the system response and estimates of its pertinent “mode shapes” to determine, by means of regression techniques involving the use of two-dimensional orthogonal functions, an approximate expression for the system generalized restoring forces in terms of the corresponding generalized system state variables. The technique is applied to several example systems. The method can be used with deterministic or random excitation to identify dynamic systems with arbitrary nonlinearities, incuding those with hysteretic characteristics. It is also shown that the method is easy to implement and needs much less computer time and storage requirements compared to the Wiener-kernel approach.