Mixed Integer Nonlinear Least-Squares Problem for Damage Detection in Truss Structures

Abstract

We present a mixed integer nonlinear least-squares problem for identifying damage in truss structures from their measured response. In detecting damage based on parameter estimation, the number of unknown parameters is often less than that of measurements, which gives rise to nonunique solutions. To overcome the difficulty, we formulate damage detection as a mixed integer nonlinear least-squares problem, where the subset of unknown parameters is sought that best represents damaged sites. To solve the problem, we present four heuristic algorithms based on the greedy algorithm. One is its direct application. The other three select the near-optimal subsets more efficiently by linearizing the error function, by applying the line search, and by grouping unknown parameters. We assess the performance of these algorithms along with conventional regularization methods through numerical experiments, where many synthetic damage cases are tested. The effect of modeling and measurement errors on the estimate is also studied. We found from the numerical experiments that the linearization-based approach was more efficient than the direct application while the two methods gave reasonably accurate estimates.