A robust approach for iterative contaminant source location and release history recovery

Contamination source identification is a crucial step in environmental remediation. The exact contaminant source locations and release histories are often unknown due to lack of records and therefore must be identified through inversion. Coupled source location and release history identification is a complex nonlinear optimization problem. Existing strategies for contaminant source identification have important practical limitations. In many studies, analytical solutions for point sources are used; the problem is often formulated and solved via nonlinear optimization; and model uncertainty is seldom considered. In practice, model uncertainty can be significant because of the uncertainty in model structure and parameters, and the error in numerical solutions. An inaccurate model can lead to erroneous inversion of contaminant sources. In this work, a constrained robust least squares (CRLS) estimator is combined with a branch-and-bound global optimization solver for iteratively identifying source release histories and source locations. CRLS is used for source release history recovery and the global optimization solver is used for location search. CRLS is a robust estimator that was developed to incorporate directly a modeler's prior knowledge of model uncertainty and measurement error. The robustness of CRLS is essential for systems that are ill-conditioned. Because of this decoupling, the total solution time can be reduced significantly. Our numerical experiments show that the combination of CRLS with the global optimization solver achieved better performance than the combination of a non-robust estimator, i.e., the nonnegative least squares (NNLS) method, with the same solver.