Model Construction and Physical Parameter Identification from Spectral Data

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Yitshak M. Ram, Louisiana State University,Proposal Number: 9978786Model Construction and Physical Parameter Identification from Spectral DataProposal Abstract. The inverse problem of reconstructing a model based on spectral data is investigated, and methods for constructing low order models for vibrating systems are developed. The physical parameters of the systems are determined by the derived model. The main difficulty in addressing this problem is that vibrating structures are distributed parameter systems, whereas the descriptive analytical models are finite dimensional. The spectrum of a continuous system is inconsistent with that of the associated finite dimensional model. In order to overcome the difficulty associated with the inconsistency of the spectral data, the distributed parameter system with continuous variables is approximated by a continuous system with a finite number of physical parameters. As a result a new non-linear eigenvalue problem, with transcendental matrix elements, is introduced. The inverse problem is approached by iterative gradient and Newton's methods, and from a wave propagation standpoint. The results are validated by laboratory experiments where the density and rigidity functions of non-uniform vibrating rods are determined by using data from modal tests. The fundamental problem of identifying the physical parameters of a system from spectral data has theoretical importance and practical applications in many areas of science and engineering, e.g. dynamic system control, and sonar and radar detection. The new transcendental inverse problem introduced has the potential of bridging the gap between the infinite spectrum of distributed parameter systems and the finite spectrum of their discrete representative models. Characterization of the properties of this eigenvalue problem is thus of great theoretical and practical importance.