ABSTRACT:

In Risk Analysis decisions have to be made, which are based on uncertain information. Most of the existent risk analysis systems deal only with the effect of random ("common") geological and construction uncertainties on time and cost of construction, not specific geotechnical risks. In order to be able to consider these risks a system needs to be able to capture expert knowledge. This can be done using a knowledge based system (KBS). The traditional knowledge based systems, the so-called ruled based systems suffer from significant deficiencies handling decision making under uncertainty. Bayesian networks are more suitable to handle uncertainty in this context. They were developed as a decision support tool originally used for purposes of artificial intelligence engineering. They have been replacing the traditional "rule based" systems when dealing with uncertainties. Bayesian networks are so-called normative systems that model the domain of uncertainty using classical probability calculus and decision theory. The goal of this paper is to present the potential of the application of Bayesian Networks to Risk Analysis for tunneling projects. A numerical example of this methodology applied to the situation of excessive deformation at the surface is presented.

1 RISK ANALYSIS USING BAYESIAN NETWORKS
1.1 Introduction

In Risk Analysis decisions have to be made under uncertainty. The existing systems do not deal with the specific geotechnical risks, such as heading failure, excessive deformations or rock falls. In order to consider these risks it is necessary to capture expert knowledge. Bayesian Networks are a technique that models the domain of uncertainty using classical probability calculus and decision theory (Faber, 2006). This paper will focus on the description of the Bayesian Network technique and its principles. A numerical example of this methodology applied to the domain of tunneling will be presented.

1.2 Bayesian Network

Over the last decade, Bayesian networks have become a popular representation for encoding uncertain expert knowledge in expert systems (Heckerman et al., 1995). Bayesian networks can be used at any stage of a risk analysis, and may substitute both fault trees and event trees in logical tree analysis. While common cause or more general dependency phenomena pose significant complications in classical fault tree analysis, this is not the case with Bayesian networks.They are in fact designed to facilitate the modeling of such dependencies. Because of what has been stated, Bayesian networks provide a strong tool for decision analysis, including prior analysis, posterior analysis and pre-posterior analysis. Furthermore they can be extended to influence diagrams, including decision and utility nodes in order to explicitly model a decision problem (Faber, 2006). A Bayesian network is a graphical representation of knowledge for reasoning under uncertainty. Figure 1 is an illustration of a simple Bayesian network.The arrows going from one variable to another reflect the relations between variables. In this example the arrow from C to B1 means that C has a direct influence on B1.

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