Comparison and investigation of inverse identification techniques for the material properties of a brake disc through experimental and numerical modal analysis

In the present study, a fast and accurate procedure for the inverse identification of material properties of a brake disc is proposed through the results of numerical and experimental modal analyses, where a particular attention is given to different objective functions and weighting. First, experimental and numerical modal analyses are conducted to obtain the natural frequencies and corresponding mode shapes. Second, design of experiment (DoE) methods are utilized to generate the meta-model of natural frequency results that are calculated numerically through finite element methods (FEMs). Several FEM simulations are run by altering critical material properties (density, Young’s modulus, and Poisson’s ratio) as independent variables according to the determined sample points by DoEs. Third, a second-degree response surface model is built by using linear regressions of simulation results. Predictive accuracies of two DoEs are investigated by the analysis of the residuals between FEM and meta-model results. Fourth, three different objective functions are adopted and used with 10 and 16 natural frequencies, with and without weighting, and compared with each other to investigate the effectiveness of functions and weighting for the particular problem. The sequential quadratic programming method is preferred for the minimization of the objective functions. As opposed to the related literature, weights of the objective functions are determined by variances of natural frequencies measured at different locations of the disc which are already required to obtain mode shapes. Therefore, a computationally and experimentally low-cost and fast identification process is attained. The results showed that the use of weights usually improves the accuracy of identification. Changing the number of included natural frequencies in the optimization process, where the third objective function is used, has a significant effect, especially on the identification of the Poisson’s ratio. Finally, a good correlation is achieved between experimental and computational frequencies updated by the optimum properties.