Force State Maps Using Reproducing Kernel Particle Method and Kriging Based Functional Representations

The problem of identification of nonlinear system parameters from measured time histories of response under known excitations is considered. Solutions to this problem are obtained by using the force state mapping technique with two alternative functional representation schemes. These schemes are based on the application of reproducing kernel particle method (RKPM) and kriging techniques to fit the force state map. The RKPM has the capability to reproduce exactly polynomials of specified order at any point in a given domain. The kriging based methods represent the function under study as a random field and the parameters describing this field are optimally determined based on available observations. The present study investigates the performance of RKPM and kriging based fits to the force state maps for a variety of nonlinear dynamical systems. The study also examines the application of force state maps in (a) determining the fixed points limit cycles of the system and their stability, (b) determining the properties of the linear system which would result if nonlinearity were to be absent, and (c) dealing with nonlinearities that are continuous but not differentiable and nonlineatities that are discontinuous at a set of points within the domain of interest. Illustrative examples on single and multi-degrees of freedom nonlinear systems are presented to demonstrate the scope of the proposed procedures.