A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. © 2013 Elsevier B.V.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors thank the two anonymous reviewers for their insightful and constructive comments. We are particularly indebted to one of the reviewers for his/her extensive and insightful comments which resulted in considerable improvements to this manuscript. A.H. Elsheikh performed initial investigation of this research as part of the activities of the Qatar Carbonates and Carbon Storage Research Centre (QCCSRC) at Imperial College London. He gratefully acknowledges the funding of QCCSRC provided jointly by Qatar Petroleum, Shell and the Qatar Science and Technology Park.
ASJC Scopus subject areas
- Water Science and Technology