# Solution of bound constrained nonlinear least squares problems with ap- plication to backcalculation of asphalt pavements

## Palavras-chave:

Nonlinear Least Squares, Bound Constraints, Backcalculation, Asphalt Pavements## Resumo

Backcalculation is a procedure used to estimate the material properties of pavement layers from results of non destructive tests, as the Falling Weight Deflectometer. It is important to assess the quality of a pavement construction and/or to monitor its condition during its lifespan. The Finite Element Method can be used to evaluate pavement deflections, provided that the loading and the properties of each layer are known. Assuming linear elastic behavior and known Poisson’s ratios, the backcalculation procedure consists in the determination of the elastic moduli that minimize the differences between the simulated and measured deflections. Thus, pavement backcalculation corresponds to the solution of a Nonlinear Least Squares problem, where the unknown parameters (elastic moduli) are strictly positive. This paper presents a simply approach to include bound constraints in the Gauss-Newton and the Levenberg–Marquardt methods to ensure convergence to physically meaningful solutions. The accuracy, robustness, and computational efficiency of the modified algorithms are compared in the backcalculation of asphalt pavements.