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Stochastic data assimilation of the random shallow water model loads with uncertain experimental measurements. (English) Zbl 1398.76188
Summary: 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.
MSC:
76M35 Stochastic analysis applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
93E12 Identification in stochastic control theory
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
65Y05 Parallel numerical computation
65C30 Numerical solutions to stochastic differential and integral equations
74S05 Finite element methods applied to problems in solid mechanics
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