Robust inversion method for jointly estimating parameters and variance components from heterogeneous monitoring data

Abstract

In this paper, a novel inversion method is proposed for jointly robust estimation of parameters and variance components from disjunctive groups of observations affected by outliers. This method, named robust non-negative variance component estimation (RVCE), is a coupling of variance component estimation (VCE) technique with a robust estimation method, developed to cope with outliers and to avoid negative variance, leading thus, to an estimation reliable enough. The principle of RVCE method is based on the refinement of the stochastic model via an equivalent weight matrix established from the original measurement weight matrix and an adapted full weight matrix with hard rejection to outliers. This last one is derived from the robust standardized residuals, using a highly robust estimator, as an initial solution of the inverse problem, and a cut-off value adapted to sort out the good observations from the bad ones. Furthermore, because the original weight matrix is partly known, the integration of the VCE technique plays a key role to reach an optimal solution and to provide valuable information on the precision of the estimates. The performance of the proposed method is demonstrated by considering a rockfill dam as an example, where the material parameters and variance components are jointly estimated from geotechnical and geodetic measurements. The results of comparison study between RVCE method with other methods such as the classical NN-VCE, RIMCO, least squares and the combined Huber’s M-estimator with VCE (HVCE) for various configuration options have highlighted the pertinence of the proposed method.