1897
Data assimilation strategies for parameter identification of elasto-plastic
geomaterials and its application to geotechnical practice
Stratégie d'assimilation de données pour l'identification des paramètres de géomatériaux
élastoplastiques et son applications à la pratique géotechnique
Shuku T., Nishimura S.
Graduate School of Environmental and Life Science, Okayama University, Okayama 700-8530, Japan
Murakami A., Fujisawa K.
Graduate School of Agriculture, Kyoto University, Kyoto 606-8502, Japan
ABSTRACT: The objective of this study is to demonstrate the numerical and the practical applicability of the particle filter (PF) to
some geotechnical problems, i.e., the parameter identification of elasto-plastic geomaterials and the prediction of the deformation
behavior of soil deposits and geotechnical structures, by applying the methodology to hypothetical experiments and an actual
construction project. The results of the hypothetical experiments reveal that the parameters identified by the PF, based on the
sequential importance sampling (SIS) algorithm, have converged into their true values, and that the approach presented herein can
provide a highly accurate parameter identification strategy for elasto-plastic geomaterials. Moreover, the simulation results using the
identified parameters are close to the actual observation data, and the ensemble-based approach produces more information about the
parameters of interest than simple estimated values obtained from optimization methods. In other words, the identification comes in
the form of a probability density function.
RÉSUMÉ : L'objet de cette étude est de démontrer l'applicabilité numérique et pratique du filtrage des particules (FP) pour certains
problèmes géotechniques, à savoir, l'identification des paramètres de géomatériaux élastoplastiques et la prédiction du comportement
en déformation de dépôts de sol et de structures géotechniques, en appliquant la méthodologie à des expériences hypothétiques et à
des projets de construction existants. Les résultats des expériences à partir d'hypothèses montrent que les paramètres identifiés par le
FP, basé sur l'algorithme d'échantillonnage d'importance séquentiel (SIS), ont convergé vers leurs valeurs réelles, et que l'approche
présentée ici peut fournir une stratégie d'identification paramétrique très précise pour les géomatériaux élastoplastiques. En outre, les
résultats de la simulation utilisant les paramètres identifiés sont proches des données d'observation réelles, et l'approche groupée
produit plus d'informations sur les paramètres d'intérêt que de simples valeurs estimées obtenues à partir des méthodes d'optimisation.
En d'autres termes, l'identification se présente sous la forme d'une fonction de densité de probabilité.
KEYWORDS: data assimilation, particle filter, parameter identification
1 INTRODUCTION
Inverse analyses have been successfully applied to linear elastic
problems in which the deformation to be addressed is linear and
depends only on the model parameters and the applied load; it
does not depend on the loading history. However, the
mechanical behavior of geomaterials is commonly described by
an elasto-plastic model, and the deformation behavior displays
strong nonlinearity and depends not only on the values of the
parameters, but also to a great extent on the stress state and the
history, whereby the identification of elasto-plastic parameters
still remains a major challenge.
Data assimilation (DA) is available as a methodology to
tackle the above difficulties (Nakamura
et al
. 2005). The
estimation of the interest dynamic system via DA involves a
combination of observation data and the underlying dynamical
principles governing the system. The melding of data and
dynamics is a powerful methodology, which makes efficient
and realistic estimations possible. This approach has recently
proven fruitful in earth science, e.g., geophysics, meteorology,
and oceanography (e.g., Awaji
et al
. 2009).
Several kinds of powerful DA methods have been proposed.
Among the existing strategies, this study focuses on the filtering
techniques referred to as the particle filter (PF, Gordon
et al
.
1993), because it can be applied to nonlinear and non-Gaussian
problems and can provide a simple conceptual formulation and
ease of implementation.
Herein numerical and practical effectiveness of the DA
strategies using the PF are examined for geotechnical problems
through their applications to the numerical experiments and an
actual construction project. For this purpose, first, we outline
the concepts and methods of DA and refer to the PF. Second,
we deal with the parameter identification of elasto-plastic
parameters for geomaterials applying the PF to initial and
boundary value problems in geomechanics. Finally, we
investigate the applicability of the PF to a practical settlement
prediction of a well-documented construction project, Kobe
Airport Island, comparing the obtained simulation with the
observation data, and the practical effectiveness of the DA
based on the PF is discussed.
2 DA: CONCEPTS AND METHODS
DA is a versatile methodology for estimating the state of a
dynamic system of interest by merging sparse observation data
into a numerical model for the system. The state of the system is
usually estimated with deterministic simulation models, which
are subject to the uncertainty that arises due to a lack of
knowledge and a poor understanding of the physical
phenomena. Meanwhile, observation data, which represent the
true state, but are subject to stochastic uncertainty and
randomness, may occasionally be available as a function of a
subset of the system variables. Based upon a prognostic model
and a limited number of observations, DA attempts to provide a
more comprehensive system analysis which may lead to more
accurate predictions. This approach has recently proven useful
in earth science (Awaji
et al
. 2009).
Novel sequential data assimilation methods include the
Ensemble Kalman Filter (EnKF, Evensen 1994) and the PF
which are categorized into nonlinear Kalman filtering. Although
the EnKF can be applied to nonlinear systems, it basically
assumes a linear relationship between a state and the
observation data in calculating a Kalman gain. Therefore, the
