Inverse Methods for Load Identification Augmented By Optimal Sensor Placement and Model Order Reduction

Abstract

Design problems require accurate characterization of loads acting on a structure. One way to estimate the loads is through experimentally measured structural response. This is known as the "inverse problem." The instrumented structure essentially acts as its own transducer. It is well known that the inverse problems tend to be highly ill-conditioned. This dissertation proposes several novel time domain and modal domain algorithms for estimating multiple dynamic loads exciting a structure from structural response measured at a finite number of optimally placed non-collocated sensors on the structure. The optimal placement of sensors is necessary to counter the inherent limitation of such inverse problems - ill-conditioning. Solution procedures based on construction of D-optimal design as well as sparse nature of mass, damping and stiffness matrices are proposed and implemented to determine the optimum locations of sensors that will provide the most precise load estimates. Both strain measurements using strain gages and acceleration measurements using accelerometers have been given due attention. Improvements in the load identification algorithms, based on model order reduction and reduced modal parameters, are further proposed to reconstruct the input forces accurately. Load identification techniques based on dynamic programming and Markov parameters have also been studied in this work. Several limitations to these existing techniques have been identified. An attempt has been made in this dissertation to address the identified shortcomings based on D-optimal design for obtaining optimal sensor locations on the structure and model order reduction for computational cost reduction. Both experimental measurements as well as numerical simulations have been performed in order to validate the proposed techniques. The experimental validation is done using a simple beam clamped at the base and attached to a shaker head. The focus of this example is to reconstruct the input forces exciting the structure through the shaker head. Numerical simulations are performed on the computational models developed in finite element tool ANSYS that works in close conjunction with MATLAB. Numerical sensitivity analyses are further performed to study the effect of uncertainties (noise) in experimental data as well as in the model; the techniques are validated to be robust - even with the presence of noise, the applied loads are recovered accurately.