Optimal configuration for the self-identification of a two-dimensional variable geometry truss

Abstract

This study addresses the optimal changes in geometry of a two-dimensional variable geometry truss (VGT) to identify the stiffness matrix of the truss using the concept of self-identification. The optimization of the geometry changing of the VGT is a problem of selecting the optimal combination of multiple design variables from a large number of candidate sets. This study proposes a simple optimization method for determining a set of optimal geometric parameters; in this method, the approximated mode shape matrix obtained using spline interpolation techniques is used to calculate the objective function for self-identification. The objective function used in this paper is a function of the condition number of the coefficient matrix of a linear matrix equation and a criterion for self-identification. The proposed algorithm can be used to reduce the number of actual vibration tests required for measuring the mode shapes and modal frequency while it maximizes the objective function. Numerical experiments are conducted to investigate the relationship between the convergence characteristics of the optimization and the target vibration modes. The effectiveness of the optimized geometry changing is verified by comparing the identification error for the uniform geometry changing, the optimized one for the three lower modes of the VGT, and the one found by a classical QR decomposition. Furthermore, the numerical results show that the identification sensitivity with respect to noisy data is reduced by the optimization.