Application of the Variable Projection Method for Updating Models of Mechanical Systems

U Prells & MI Friswell (University of Wales Swansea)

Journal of Sound and Vibration, Vol. 225, No. 2, August 1999, pp. 307-325


To update the parameters of a mathematical model of a mechanical system usually a cost function is minimised which consists of the difference between calculated and measured quantities. This paper deals with the special case that the forces are unknown. Instead of following the usual way of handling this type of updating problem by assuming a model for the forces, in this paper the Variable Projection Method is applied to estimate the unknown forces in addition to the model parameters. Under certain conditions this two-fold inverse problem can be solved by eliminating the force from the parameter estimation process. The remaining equation to estimate the model parameters consists of the projection of the response data, where the associated projector depends on the model parameters. This application of the Variable Projection Method is essentially an extension of the Output Residual Method and leads to an estimation equation which is nonlinear with respect to the model parameters. The Variable Projection Method is introduced and investigated for two general types of unknown forces. Two theoretical examples, wind excitation of a tower and a rotary machine under unknown unbalance configuration, and the experimental case of a free-free steel beam tested by hammer excitation, are presented and discussed.

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Link to paper using doi:10.1006/jsvi.1999.2272

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