Integrated mathematical forms for update of physical parameter matrices of damped dynamic system

Mathematical modelling and updating of damped dynamic systems that involve some modelling errors and subsequent analysis based on those errors will lead to inaccuracy in the results. Because measured and analytical data are unlikely to be identical due to measurement noise and model inadequacies, it is necessary to estimate more accurate parameter matrices for design and analysis. By minimizing a cost function expressed as the sum of the norms of the difference between analytical and experimental parameter matrices, this study directly derives the integrated mathematical expressions for updated physical parameter matrices. In the derivation process, the eigenfunction of a damped dynamic system is utilized as a constraint equation for the updating. It is illustrated that the proposed methods take more explicit forms and can be widely utilized in the damped and undamped systems. Based on the comparison with other methods, the validity of the proposed methods is demonstrated in numerical applications.