Experimental embedded sensitivity functions for use in mechanical system identification

Chulho Yang, Purdue University

Abstract

In applications involving manufactured mechanical vibrating systems such as vehicle components and systems, an experimental technique for determining the forced response sensitivity to changes in mass, damping or stiffness parameters is needed. In order to distinguish physical changes in the system from nonlinear input-output distortion, an experimental sensitivity technique for identifying nonlinear input-output models in mechanical systems is also needed. An experimental sensitivity method for analyzing forced vibration data is developed and applied in this research. It is shown that if a subset of measured mechanical system input-output functions is available in vibrating systems, an appropriate analytical linear parameterization of these functions leads to algebraic relationships between the measured data in the form of so called ‘embedded sensitivity functions.’ These functions are solely a function of experimental frequency response function data and determine the linear forced response sensitivity to physical perturbations in the system mechanical properties. Applications in three key areas of mechanical dynamic systems are examined to verify and further study the requirements of the embedded sensitivity function approach in experimental sensitivity analysis. First, the embedded sensitivity approach is used to examine the ‘forward problem’ of identifying optimal design modifications for reducing linear vibration resonance problems. Second, embedded sensitivity functions are applied to characterize nonlinear mechanical systems and identify nonlinear input-output models for those systems. Using embedded sensitivity analysis, frequency response functions are measured at multiple input amplitudes and combined to extract spectral patterns for characterizing stiffness and damping nonlinearities. Expressions for estimating nonlinear parameters are derived using Taylor series expansions of frequency response functions. Third, embedded sensitivity functions are applied to examine the ‘inverse problem’ of identifying structural perturbations, which might occur at various stages throughout the development and operation of mechanical systems. By comparing the embedded sensitivity functions with finite difference functions using baseline and modified frequency response functions, perturbations are shown to be properly detected, located and quantified in theory and practice assuming that structures of interest are only perturbed in one location. Demonstrations on the bench top system and exhaust system indicate that the technique is most effective for identifying perturbations when certain frequency ranges in the data are analyzed to avoid low signal-to-noise ratios and distortions in the resulting estimated stiffness reductions.

Degree

Ph.D.

Advisors

Adams, Purdue University.

Subject Area

Mechanical engineering

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