Stochastic data assimilation of the random shallow water model loads with uncertain experimental measurements

• Published in: Computational mechanics Vol. 47; no. 6; pp. 603 - 616
• Main Authors: Mathelin, Lionel, Desceliers, Christophe, Hussaini, M. Yousuff
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-06-2011; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Analysis; Classical and Continuum Physics; Computational Science and Engineering; Constraint modelling; Earthquakes; Engineering; Engineering Sciences; Estimates; Fields (mathematics); Fluid Dynamics; Fluid mechanics; Fluids mechanics; Inverse method; Mathematical analysis; Mathematical models; Mathematical optimization; Mechanics; Optimization; Optimization techniques; Original Paper; Parameter uncertainty; Physical simulation; Physics; Physiological aspects; Polynomials; Probabilistic models; Representations; Shallow water; Statistical analysis; Stochastic processes; Stochasticity; Theoretical and Applied Mechanics; Uncertainty; Vectors (mathematics); Stochastic inverse method; Polynomial chaos; Maximum likelihood; Parametric estimation; Data assimilation; inverse problems; Chaos representations
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-010-0560-7

This paper is concerned with the estimation of a parametric probabilistic model of the random displacement source field at the origin of seaquakes in a given region. The observation of the physical effects induced by statistically independent realizations of the seaquake random process is inherent with uncertainty in the measurements and a stochastic inverse method is proposed to identify each realization of the source field. A statistical reduction is performed to drastically lower the dimension of the space in which the random field is sought and one is left with a random vector to identify. An approximation of the vector components is determined using a polynomial chaos decomposition, solution of an optimality system to identify an optimal representation. A second order gradient-based optimization technique is used to efficiently estimate this statistical representation of the unknown source while accounting for the non-linear constraints in the model parameters. This methodology allows the uncertainty associated with the estimates to be quantified and avoids the need for repeatedly solving the forward model.