Input Estimation in Structural Dynamics
Abstract: Knowledge of time-varying excitation is of importance in the design of a wide range of engineering applications, from spacecraft and processing plants to electronic circuits. Regardless of the actual application or underlying physics, the expected input will play a key role in the determination of adequate system properties and parameters. This thesis is concerned with computational methods and aspects of input estimation for systems described by differential equations in time. Emphasis is put on indirect force measurement in structural dynamics, where the task is to establish the time variation of unknown excitation forces from given measurements of structural response. The main field of application is measurement of forces and moments acting at locations inaccessible for direct measurement, e.g. contact forces between rails and wheels of running trains. The present work includes a survey of different approaches for input estimation in structural dynamics. A comparison of time domain methods is given and some issues related to ill-posedness are investigated. Furthermore, a non-iterative recursive algorithm for estimation of input on generally time-variant linear systems is developed. Excellent estimation results for a numerical example based on a moving force problem show the potential of the proposed algorithm. Finally, a general approach for estimation of unknown input and initial conditions for linear and nonlinear systems is suggested. The framework allows for incorporation of a priori knowledge of the physics of the input and includes a strategy for assessment of solution sensitivity with respect to measurement noise. In cases where regularization is used to diminish noise effects, upper and lower bounds for efficient values of the regularization parameter may be readily obtained with little additional computational effort. The potential of the suggested approach is illustrated by numerical examples.
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