Parameter reconstruction based on sensitivity vector fields

A novel approach to determine very accurately multiple parameter variations by exploiting the geometric shape of dynamic attractors in state space is presented. The approach is based on the analysis of sensitivity, vector fields. These sensitivity vector fields describe changes in the state space attractor of the dynamics and system behavior when parameter variations occur. Distributed throughout the attractor in state space, these fields form a collection of snapshots for known parameter changes. Proper orthogonal decomposition of the parameter space is then employed to distinguish multiple simultaneous parametric variations. The parametric changes are reconstructed by analyzing the deformation of attractors which are characterized by means of the sensitivity vector fields. A set of basis functions in the vector space formed by the sensitivity fields is obtained and is used to successfully identify test cases involving multiple simultaneous parametric variations. The method presented is shown to be robust over a wide range of parameter variations and to perform well in the presence of noise. One of the main applications of the proposed technique is detecting multiple simultaneous damage in vibration-based structural health monitoring.