Seismic Assessment using a Bayesian Network

This paper presents a framework for seismic vulnerability assessment based on Bayesian Networks. This framework incorporates the HAZUS model, the demand model and the capacity model, which are used to calculate the probabilities of earthquake-induced bridge damage. The framework is here applied to ‘twin’ bridges that are correlated with the demand model and the capacity model. The paper investigates how the observation of the damage occurred on one bridge affects the estimate of the reliability of the other. Generally the framework can be used to update the seismic risk of bridges in post-earthquake scenarios with a limited number of observations. the variables. The BN originates from the field of artificial intelligence and incorporates graph theory and probability theory. It is a useful tool that helps perform uncertainty analysis in complex systems. For an extensive explanation of BN, see Jensen & Nielsen (2007). Due to their generality, such as incorporation of graph theory and probabilistic inference, accounting for the evolving nature of available information, BNs have been widely used in many areas in the last two decades. However, the general BN algorithm can only effectively handle discrete variables, while most variables in civil engineering areas are continuous; therefore the application of BN to civil engineering is still at a preliminary stage. Friis-Hansen (2000) is one of the first publications that applied BN to engineering risk related issues: by solving decision problems in marine engineering, the potential of BNs in risk analysis was investigated and their advantages such as flexibility and compatibility were demonstrated; Nishijima et al. (2009) modelled a transportation system with BN which related the reliabilities of individual system components to overall performance: given an acceptance criteria, it proposed finding target reliabilities for components in a complex engineering system. Daniel Straub has done much work in applying BN to civil engineering risk assessment: first he proposed a framework for the earthquake hazard through a ground motion attenuation law, and then applied this model to a transportation system (Straub et al. 2008, Bensi et al. 2009). In addition, he also proposed some models to calculate the risks of rock-falls and avalanches, based on Bayesian updating (Straub 2005, Straub & Grêt 2006, Straub & Schubert 2008). Most of the above research used discretization to approximate continuous variables when dealing with hybrid BNs, which contain both continuous and discrete variables. The continuous variables are replaced by discrete variables with a sufficient number of stages. However, this would add to the computation burden when high accuracy is to be achieved. Fortunately, when the continuous variables have conditional linear Gaussian distributions, and the discrete nodes do not have continuous parents, there exists exact inference in hybrid BNs (Lauritzen & Jensen 2001). In this paper, in order to avoid approximating continuous variables, all the variables in BN are assumed to follow Gaussian distributions, so the exact inference methods can be performed on the framework. The remainder of the paper is as follows. In section 2, the HAUZUS, demand and capacity models are described. In section 3, the general computation scheme which includes construction of a junction tree, initialization and propagation, is introduced and performed on a case study. Last, the results are given and analyzed. 2 MODEL DESCRIPTION 2.1 Descriptions of the DSS Bensi et al. (2009) modelled seismic demands of an infrastructure system by constructing a BN model of ground motion intensity. In that BN model, the seismic intensities (Si), normally characterized as peak ground accelerations (PGA) at different sites across a spatially distributed infrastructure system following an earthquake, are expressed as a function of the magnitude (M), site-to-source distance (Ri), and other characteristics of the source and site (Xi), such as the type of faulting mechanism and the site shear-wave velocity; the source-to-site distance is a function of the earthquake location and magnitude. Given the distribution of ground motion intensity at the site, the performance of infrastructure system components is modelled using fragility functions which provide the probability of exceeding some specific damage state. Then the system performance is modelled based on the performance of its components. Figure 1 gives the conceptual framework, taken from that paper. In this paper, we apply this DSS to two twin bridges in APT-BMS. In order to facilitate computations, some simplifications and modifications are made to the framework in Bensi et al. (2009). Below we introduce the demand model, capacity model and fragility function in the application framework. 2.2 Bridges descriptions The Fersina-Canezza (A) and Avisio (B) are ‘twin’ bridges in APT-BMS. Both are 3 span prestressed concrete bridges with wall piers, non monolithic abutments, built in year 1967. The lengths of the two bridges are 58.3m and 57.5m respectively. In figure 2 and figure 3 we can see overviews and cross sections of these structures.