Mutual Residual Energy Method for Parameter Estimation in Structures

In this work we describe an approach to parameter estimation of complex linear structures that we call the mutual residual energy approach. We have endeavored to develop a unified approach to the discrete inverse problems describing static equilibrium and free, undamped vibration, with a particular view toward evolving methods that are amenable to large‐scale computation. The mutual residual energy method is based on the assumption that the topology and geometry of the structure are known, and that the system matrices can be linearly parameterized in terms of kernel matrices that have a solid physical basis and are easy to assemble. Measured motions of the structure and used (in conjunction with measured loads for the static case) to make estimates of the constitutive parameters. The method is based on a particular statement of the principle of virtual work and yields equations for estimating stiffness and mass parameters of linear structures. A condensation procedure is presented to deal with the case of incompletely measured systems. The quantity and quality of response measurements required, the consequences of noisy data, and the choice of load form are among the issues important to the success of our parameter estimation scheme. A numerical simulation is presented to demonstrate the features of the method.