An Inverse Approach on Load Identification From Optimally Placed Accelerometers

Abstract

This paper presents an inverse approach for estimating dynamic loads acting on a structure from acceleration time response measured experimentally at finite number of optimally placed accelerometers on the structure. The structure acts as its own load transducer. The approach is based on the standard equilibrium equation of motion in modal coordinates. Modal model of a system is defined by its modal parameters — natural frequencies, corresponding mode shapes and modal damping factors. These parameters can be estimated experimentally from measured data, analytically for simple problems, or from finite element method. For measurement of the acceleration response, there can be a large number of combinations of locations on the structure where the accelerometers can be mounted and the results may be quite sensitive to the locations selected for accelerometer placements. In fact, the precision with which the applied loads are estimated from measured acceleration response depends on the number of accelerometers utilized and their location on the component. Implementation of a methodology to determine the optimum set of accelerometer locations, based on the construction of D-optimal design, is presented to guide the selection of number and locations of accelerometers that will provide the most precise load estimates. A technique based on model reduction is proposed to reconstruct the input forces accurately. A numerical validation that helps to understand the main characteristics of the proposed approach is also presented. The numerical results reveal the effectiveness and utility of the technique.