A new gradient based step size controlled inverse eigen sensitivity algorithm for identification of material and boundary parameters of plates

Abstract

The dynamic performance of any structure is function of existing material properties and boundary stiffness parameters which may deteriorate or become more flexible due to prolonged use. These parameters are estimated inversely through optimization of a suitable objective function. The gradient based optimization methods are preferred due to their faster convergence from a set of initial guess points, but suffers mostly from lack of reliable methodology to select appropriate step sizes. Arbitrary selection of step sizes may sometimes work well, depending upon the judgment of the user, but is case specific. The present work describes the estimation of existing material properties and boundary stiffness of isotropic and orthotropic plates from measured frequencies and mode shapes using a new gradient based step size controlled inverse eigensensitivity algorithm. The method takes a strategy that the step sizes automatically become smaller when the change in gradient of objective function is having a high value and similarly, takes larger steps when the gradient is remaining fairly constants in subsequent iterations. The results obtained from the investigations are encouraging, as some convergences could be achieved by this new adaptive step size control only, whereas methods adopting arbitrary or no step size control diverged.