COMPARISON OF VARIOUS TECHNIQUES USED FOR ESTIMATION OF INPUT FORCE AND COMPUTATION OF FREQUENCY RESPONSE FUNCTION (FRF) FROM MEASURED RESPONSE DATA

Inverse problems such as input force estimation from the response (acceleration/velocity/displacement) of structures play a vital role in applications where the input forces acting on structures cannot be measured directly, e.g., the wind excitation load acting on a bridge or on a multi-storey building and also in estimation of modal parameters of a system from FRFs. Hence in this paper various force estimation techniques have been compared through studies on a mild steel cantilever beam using approaches such as (i) Sum of weighted acceleration technique (SWAT), (ii) Pseudo inverse method, (iii) Kalman filter and (iv) Empirical approach for system identification. The last method has been carried out for the first time in solving inverse problems. SWAT involves estimation of input forces in time domain using weights which are computed based on a reference input force, whereas pseudo inverse technique is carried out in frequency domain by computing FRFs. In Kalman filter technique, the system is modelled in terms of state space equations and system parameters are necessary for estimating input force. The empirical method for system identification involves obtaining the empirical relationship between the response data and input force, using which the latter can be estimated. Studies have been carried out on a mild steel cantilever beam. An electrodynamic shaker has been used for imparting the required input load on the beam and piezoelectric accelerometers for sensing the responses. In each method, estimated forces are compared with the measured forces and the computed FRFs are compared with those obtained through modal analysis. Percentage errors are then calculated, based on which the best approach for force identification is obtained. Comparisons are also carried out based on the complexity in modelling, computation efficiency based on time required for estimation, transducer requirement,