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202 I.-M.LEE AND D.-H.KIM
conventional Bayesian approach, the objective function is composed of two
components:
(7.1)
where J (θ) and J (θ) are the observed and predicted objective functions,
0
p
respectively. A significant drawback of the Bayesian method is the
incommensurate matching between the two components, since the objective
function is equally divided between them. To overcome this, Neuman and
Yakowitz (1979) introduced the adjusting positive scalar β term, which adjusts
the weights of J (θ) and J (θ):
0
p
(7.2)
where J (θ) and J (θ) are objective functions of the observed and predicted
p
0
parameters, respectively. This concept is called the extended Bayesian method or
EBM (Honjo, Wen-Tsung and Sakajo 1994:5; Honjo, Wen-Tsung and Guha
1994: 709).
Model identification is the procedure to select the best model describing the
problem. Complex models may reduce possible model errors, but may increase
uncertainties of parameters, and vice versa. Therefore, the choice of the most
appropriate model should be based not only on the accuracy of a model but also
on the quantity of available information. A methodology of model identification
utilizing the EBM is also proposed herein to identify the geometrical and
geotechnical parameters that are the most influential in assessing the ground
motions caused by underground excavation. To select the best model in the
Bayesian method, the Akaike Information Criterion is proposed (Akaike 1973:
267).
Background of the extended Bayesian method
Model identification
The techniques proposed so far for parameter estimation focus only on the
estimation of model parameters for a given model, and they do not provide any
information regarding the selection of the most appropriate model among
alternative models. To make possible the selection of the best model for the
Bayesian approach, the Akaike Information Criterion (AIC) will be introduced
(Akaike 1973:267). The AIC for the kth alternative model is expressed as:
(7.3)
