A tandem trust-region optimization approach for ill-posed falling weight deflectometer backcalculation

Abstract

Falling weight deflectometer backcalculation is a structural health monitoring approach for estimating the dynamic modulus of flexible pavements. It consists of two key aspects: a computational pavement model and an optimization routine. When using gradient-based methods, the optimization problem is commonly ill-posed, whereby a unique solution does not necessarily exist. In this paper, a new tandem trust-region optimization algorithm is proposed for ill-posed falling weight deflectometer backcalculation. The algorithm’s performance is tested against existing optimization methods in the context of dynamic modulus estimation for flexible pavements, and the performance tests are simulated computationally using practical values for material properties and geometry. The tandem trust-region algorithm combines the relative strengths of the subspace trust-region interior reflective method with those of the Levenberg–Marquardt algorithm. The increased computational expense of executing these two methods in parallel is negligible compared to the expense of other essential steps in backcalculation. For ill-posed problems, the performance tests indicate the tandem trust region algorithm has an overall reliability that is 33.9% higher than using only the subspace trust-region interior reflective method, and 56.9% higher than using only the Levenberg–Marquardt algorithm. Further, the new optimizer is 13.5% more reliable than a robust commercial option.