prony_JASA

Prony_JASA - DeterminatiOn of structural modes via the Prony model System order and noise induced poles S Brauna and Y M Ram Technion-Israel

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DeterminatiOn of structural modes via the Prony model: System order and noise induced poles S. Braun a) and Y. M. Ram Technion--Israel Institute of Technology, Faculty of Mechanical Engineering, Haifa, Israel (Received 2 November 1985; accepted for publication 13 November 1986) The parameters of multiple degree of freedom structural systems can be identified from their impulse response via the Prony method. Overdetermining the system's order is shown to improve the identification accuracy in noisy situations, but introduces additional mathematical poles. Described are methods to determine the necessary overdetermination and the true system poles. A novel, efficient perturbation method, based on the singular value decomposition, is shown to be effective under noisy situations. PACS numbers: 43.60. Gk INTRODUCTION The identification of structural systems consists of ob- taining estimates of natural frequencies and damping factors (global parameters of system eigenvalues) as well as modal constants (local parameters or system eigenvectors). From a system point of view, this is equivalent to identifying poles and residues for the partially fractioned transfer functions which describe input/output relationships between struc- ture points. Dedicated instrumentation systems for structural test- ing (with FFT based computations) compute transfer func- tions in the frequency domain, but time domain impulse re- spunsos are also readily available via an inverse Fourier transform. Time domain identification methods, using the said impulse response, have thus become popular in the last decade. One such approach is based on the Prony method, whereby the impulse response is approximated as a set of complex exponential functions. A major problem associated with the identification of system parameters is caused by a need to set a priori the (unknown) model order. It has been noted •'2 that, using an overdetermined system improves the accuracy of identifica- tion, and many researchers advocate the use of said overdo- termination. Various problems are associated with such an approach. One concerns the existence of the additional poles (or pa- rameters), artificially induced by the overdetermination. The necessary extent of overdetermination has often to be set by an "educated guess." Appropriate computational meth- ods may be called for, as the overdetermination can cause the system equation to become ill-conditioned. A further prob- lem is that of separating between system poles and those due to the overdetermination or the unavoidable existing noises. The Prony decomposition is known to be noise sensitive TM and the identification of extraneous system parameters is a phenomenon well known to practitioners in the field of dy- namic structural testing. In this article, we present a theoretical basis
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This note was uploaded on 12/02/2011 for the course ME 7533 taught by Professor Staff during the Summer '11 term at LSU.

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Prony_JASA - DeterminatiOn of structural modes via the Prony model System order and noise induced poles S Brauna and Y M Ram Technion-Israel

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