Description of constrained responses based on correction approaches of physical parameters

Physical parameters to be estimated based on measured data from dynamic or static tests of systems do not coincide with analytical parameters due to measurement noise, model inadequacies, and structural damages. Measured data can be regarded as constraints to explain the behavior of the dynamic or static systems. The existence of constraints requires the additional forces to satisfy the measured data. The variation in the responses by constraints is expressed by the changes of physical parameters. Minimizing a square function of the difference between the analytical and corrected parameter matrices, this study derives the analytical equations to describe the constrained static and dynamic responses and the corrected forms of physical parameter matrices. It is shown that the derived equations coincide with the equations provided by Udwadia and Kalaba for dynamic systems and by Eun et al. for static systems. The validity of the proposed method is illustrated in applications.