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Inverse input estimation problems, in which a set of inputs are estimated from sparse, noisy system-response measurements, are common in engineering practice. In structural engineering applications, input estimation problems manifest when the forces on a structure are estimated from measurements of structural motion. Structural inverse problems are almost always ill-conditioned, and naïve system inversion yields unacceptable force estimates that amplify noise in the response data. While input force estimation techniques have been well-studied for cases where discrete forces act at known locations, little work has been done about how these techniques can be extended to cases where the force locations are unknown or the forces are distributed over the domain.
This dissertation presents three methods of solving distributed and moving force estimation problems for each of the three types of temporal loading: static, harmonic, and general dynamic. The techniques presented here supplement common techniques for estimating concentrated loads at known locations with additional techniques that enable distributed and moving load estimation. First, a method of estimating distributed static loads is presented along with a method for intelligently placing strain sensors. Second, a method for estimating distributed harmonic forces using a novel form of Tikhonov regularization is described. Lastly, we outline a Kalman filter-based method for estimating moving loads. Because these techniques are all extensions of standard methods, they should be immediately applicable to a wide variety of engineering problems. Additionally, this manuscript can be viewed as a tutorial that describes the state-of-the-art of structural input estimation techniques.
