Identification of Unknown, Time-Varying Forces/Moments in Dynamics and Vibration Problems Using a New Approach To Deconvolution

C.D Johnson

doi:10.1155/1998/415028

Abstract

In this paper an alternative approach to the classical deconvolution idea is used to obtain a new and practical method for real-time identification of unknown, time-varying forces/moments in a general class of linear (linearized) dynamics and vibration problems with multiple-inputs and multiple-measurements. This new method for force/moment identification is unique in the respect that the uncertainty in the force/moment time-variations is not characterized by random-process methods, but rather by a generalized spline-model with totally unknown weighting coefficients and completely known basis-functions. The basis-functions are custom chosen in each application to reflect, qualitatively, the known characteristics of the force/moment time-variations to be identified. The method does not involve explicit identification of the unknown weighting coefficients. General-purpose identification algorithms for both continuous-time and discrete-time measurements are developed, and a worked example including computer simulation results is presented.

Highlights

The problem of identifying or estimating the forces/ moments that acted on a dynamic system to produce an observed system response is of interest in many areas of dynamics and vibrations and has become an active research topic in recent years [5,27, 29]
The unknown force/moment variations of interest in “input-identification” problems in dynamics and vibrations are typically not totally random or “arbitrary” functions of time but rather, in each application, belong to some restricted class of time-functions that are related to an underlying physical process and have distinguishable patterns of characteristic waveform behavior, at least over short intervals of time
To illustrate the effectiveness of the unknown force/ moment identification technique presented in this paper, consider the generic one degree of freedom, damped spring–mass system modeled by

Summary

Introduction

The problem of identifying or estimating the forces/ moments that acted on a dynamic system to produce an observed system response is of interest in many areas of dynamics and vibrations and has become an active research topic in recent years [5,27, 29]. Between successive jumps of the associated Cij in Eq (3), the vector of unknown force/moment variations f (t) in Eq (7) is identifiable, from the vector of response measurements y(t), by the (n + R − m)-th order deconvolution algorithm provided the (n + R − m) × m matrix Σ in Eqs (18a), (18b), (18d) can be designed to make all eigenvalues λi of (D+ΣH) have sufficiently “large” negative realparts. The latter is possible if rank HT|DTHT| · · · |DT(n+R−m−1)HT. In the absence of any reliable information about the true value of f (0) in Eq (7), the “best” choice for the initial-condition value ξ(0) in Eq (18b) is zero [17, p. 864]

Solution and simulation of a numerical example

Other generalizations