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In practice, inverse problems related to explicit interface detection rely on scarcely available information of the background continuous spatial fields. To accurately carry on inversion in such cases, a method called Hamiltonian Monte Carlo for Simultaneous Interface and Spatial Field Detection (HMCSISFD) is developed. Update of the interface parameters is done in a reversible mesh moving framework leading to a change in domain geometry which forces a recomputation of the spatial field covariance function as it is domain dependent. The eigenvalue problem and its derivatives w.r.t. the parameters are solved again on the updated domain to enable dimensionality reduction of the spatial field parameters through the use of the truncated Karhunen‐Loève expansion. This simultaneous parameter update procedure is applied to the detection of the interface and spatial field properties of a piping zone. Inversion is done considering hydraulic head and discharge rate data, with a priori known observation noise, from a carefully designed laboratory seepage flow experiment in a domain consisting a predefined piping zone. The static pipe in the experiment is representative of a pipe in equilibrium beneath an embankment/levee where the current hydraulic gradient isn't sufficient to cause further pipe progression. Markov chains obtained from the HMCSISFD method show convergence and the true interface and spatial field parameters are found to lie well within the 95% high probability density regions and the 0.05 and 0.95 quantiles, respectively, provided a proper choice for the observation noise is made. [ABSTRACT FROM AUTHOR]

Summary: A numerical technique for detecting the number and shape of subsurface cavities is presented, applying the particle filter and the parametric level set method to elastic wave propagation under the ground. When subsurface cavities exist, the elastic wave propagating in the ground is reflected at the boundary faces of the cavities. Observing the velocity of the reflection wave at the surface of a ground that includes multiple cavities and parameterizing the shape of the cavities by the parametric level function, both the number and the shape of the cavities can be identified by the particle filter. Numerical experimentation for detecting multiple cavities is conducted with synthetic observation data. The results show that the proposed technique enables the number of cavities to be identified by the number of peaks in the posterior probabilistic distribution function and solves geometric inverse problems by estimating the shape of the cavities through the parameter identification of the level set function. [ABSTRACT FROM AUTHOR]

SUMMARY A computational method, incorporating the finite element model (FEM) into data assimilation using the particle filter, is presented for identifying elasto-plastic material properties based on sequential measurements under the known changing traction boundary conditions to overcome some difficulties in identifying the parameters for elasto-plastic problems from which the existing inverse analysis strategies have suffered. A soil-water coupled problem, which uses the elasto-plastic constitutive model, is dealt with as the geotechnical application. Measured data on the settlement and the pore pressure are obtained from a synthetic FEM computation as the forward problem under the known parameters to be identified for both the element tests and the ground behavior during the embankment construction sequence. Parameter identification for elasto-plastic problems, such as soil behavior, should be made by considering the measurements of deformation and/or pore pressure step by step from the initial stage of construction and throughout the deformation history under the changing traction boundary conditions because of the embankment or the excavation because the ground behavior is highly dependent on the loading history. Thus, it appears that sequential data assimilation techniques, such as the particle filter, are the preferable tools that can provide estimates of the state variables, that is, deformation, pore pressure, and unknown parameters, for the constitutive model in geotechnical practice. The present paper discusses the priority of the particle filter in its application to initial/boundary value problems for elasto-plastic materials and demonstrates a couple of numerical examples. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A method is developed for the explicit identification of solid-void interfaces in a Bayesian framework using a statistically efficient gradient based Markov Chain Monte Carlo (MCMC) algorithm called Hamiltonian Monte Carlo (HMC). The elastodynamic inversion is carried out in a Finite Element discretized domain considering parameterized representations of the actual interface between the elastic solid and void embedded in the solid itself. Using a reference configuration, a parameter update procedure is designed, to ensure reversibility of the HMC algorithm, thereby satisfying the detailed balance condition. The quality of mesh at every parameter update is maintained through a simple mesh moving strategy that introduces volume scaled Elastic modulus in the mesh moving stage. HMC gradient computation procedure is detailed for a general parameterization of the interface. Integration of these techniques with the HMC algorithm enables the continuous variation of parameters and maintains continuity of the Hamiltonian. The performance of the proposed method is investigated with respect to two solid-void interface identification problems, one of well-defined and the other of arbitrary geometry. Results show that the proposed method performs well, maintaining a good mesh quality after each parameter update. The Markov chains converge and statistical descriptions of the inferred parameters are obtained. [ABSTRACT FROM AUTHOR]