Optimal extraction of structural characteristics from response measurements

Abstract

When random input data are not or cannot be measured, then only the available output data can be fitted to a time domain autoregressive moving-average (ARMA) model. This estimation process always produces a minimum phase system. This means that only the natural frequency and damping ratio of the system can be identified. The mode shape cannot be determined uniquely. A new approach has been introduced in this paper to overcome these problems when a structure is randomly excited. The selection of the sampling interval for estimating the modal parameters from a randomly excited structure subjected to unmeasurable inputs is also considered. The theoretical basis of the procedure is presented together with simulation results. I. Introduction E XPERIMENTAL modal analysis has become an increasingly important engineering tool during the past 40 years in the aerospace, automotive, and machine tool industries. Modal parameters estimates obtained from experimental modal analysis are being used in the direct solution of vibration and/or acoustic problems, for correlation with output from finite-element programs, and for prediction of changes in system dynamics due to structural changes. In all cases, the quality of the modal parameter estimates is of major concern. Time series methods have been applied to the synthesis of structural systems excited by random forcing functions as well as to the identification of the natural frequencies and the damping ratio. Autoregressive moving-average (ARMA) models have been used to estimate the characteristics of buildings being excited by wind force and the characteristics of the cutting process that participated with random cutting forces.1'2 Recently, there has been a great deal of interest in determining modal parameters from measured response data taken on operating systems (e.g., turbulent flow over an airfoil; road inputs to automobiles, and environmental inputs to proposed large space structures). When random input data are not or cannot be measured, then only the available output data can be fitted to a time domain ARMA model. This estimation process always produces a minimum-phase system. The transfer functions defined this way by the ARMA model are successful in the estimation of magnitudes of the true transfer functions but do not give the correct phase information3'4 except when the true system is minimum phase. In other words, the mode shape cannot be determined uniquely. The objective of this paper is to solve the aforementioned problem and estimate the modal parameters when the input force is an unmeasured white noise sequence. The selection of the sampling interval for estimating the modal parameters is also considered. Emphasis is placed on the optimum design of uniform data sampling intervals when experimental constraints allow only a limited number of discrete time measurements of the output from the continuous system and the parameters of interest are natural frequencies, damping ratio, and time constant of the continuous system.