Estimation of modal loads using structural response

In this study an analytical procedure is developed based on the Kalman filtering approach to estimate modal loads applied on a structure using limited measured response of the structure. The effect of various variables such as the type of response, the noise level, and the level of uncertainty in dynamic properties of the structure, on the modal load estimation is evaluated in the frequency domain through numerical analysis for a single-degree-of-freedom (SDOF) and a multi-degree-of-freedom (MDOF) system. It is observed that the acceleration response is relatively more stable and robust in external load estimation than other response components. The noise is amplified at the high frequency range for the displacement or velocity response whereas in the case of acceleration response the noise is not amplified in the estimated external load. It is also found that the discrepancy between dynamic characteristics derived for an analytical model and the actual structure causes the transfer function from the actual load to the estimated load to distort near and below the structural natural frequency. The estimation of external loads is extended to a MDOF system. The results show that the modal loads can be estimated accurately from limited measurements of acceleration response on the basis of the assumption that the measured response can be transformed to the modal response by a proper orthogonal decomposition and the corresponding modal properties used for the transformation can be obtained by a system identification technique.