A probabilistic method for dynamic force identification of uncertain structures

Abstract

To address the dynamic force identification problem of uncertain structures with random parameters, this study proposes a novel approach to describe the probabilistic properties of the identified forces. First, the integral equation for the force probability density function (PDF) is derived from the mathematical mapping relationship between the identified force and random structural parameters. Next, the sample space of the random parameters is partitioned into non-overlapping subdomains using a point selection technique based on the generalized F-discrepancy. Meanwhile, the function fitting technique and Tikhonov regularization method are applied to identify the force samples under the corresponding partitioned subdomains. Thus, the integral equation of the force PDF is transformed into a summation of the force probabilities for all the subdomains. Subsequently, a smoothing technique is introduced to obtain the expression of the identified force PDF. Finally, the confidence interval over the entire time domain is constructed from the force cumulative distribution function, which effectively quantifies the influence of random structural parameters on the identified results. The efficiency and superiority of the proposed method are verified using an example of a plane truss structure with multiple random structural parameters, and force identification for a simplified launch vehicle model with connection uncertainties is discussed.