System identification of dynamic structures

Abstract

A method is developed for determining the mass and the nonlinear stiffness and damping characteristics of structures subjected to crash-loading environments. The system identification is accomplished using adaptive time domain, constrained minimization techniques. The underlying assumptions are that the stiffness and damping characteristics of a structural element are separable and that characteristics can be idealized with piecewise linear segments. Incremental equations of motion, including error terms, are formulated and solved for nonnegative parameters using linear and quadratic programming algorithms. The parameters are estimated using three formulations: minimizing the sum of the absolute errors ( L 1 error norm), minimizing the sum of the squared errors ( L 2 error norm), and minimizing the maxium absolute error ( L ∞ error norm). Adaptivity is incorporated into the formulation for identifying discontinuities in the structural characteristics and for improving the parameter estimation. Finally, the methodology allows for the specification of upper and lower bounds for the damping forces. The motivation for this research is toward identifying the structural characteristics and developing lumped mass models of automobiles from acceleration and barrier load data collected during frontal barrier crash testing.