Seismic risk analysis using Bayesian belief networks - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 188

where X

ij and X ij are the scaled and unscaled values for indicator i and
region j , respectively. Furthermore, for input parameters that are inversely
related to disaster risk, the transformation function is:

′

( )

−++ XXs

s

2

ij , i i

X ′ = [7.9]

ij ,

i

A salient feature of this transformation method is that the transformed
values are in a relative scale and comparisons can be made quite easily.

Input parameters

In order to show utility of the proposed model, 11 Canadian cities were
considered (see Cockburn and Tesfamariam 2012). These cities are Victoria,
Vancouver, Edmonton, Calgary, Saskatoon, Winnipeg, Toronto, Ottawa,
Quebec, Montreal, and Halifax. The basic input parameters (Table 7.6) are
obtained from different Canadian sources (see footnote of Table 7.6). Sub-
sequently, the values are transformed (see Equations (7.8) and (7.9)) into
commensurable units and plotted in Fig. 7.9. Subsequently, the transformed
input parameters are used in the proposed BBN model, and the corre-
sponding EDRI values are computed.

Results and discussion

Using the BBN of the hierarchical structure depicted in Fig. 7.8 and input
parameters described in Table 7.6, the EDRI model is developed. The
transformed input parameters shown in Fig. 7.9 are used as input parame-
ters to the BBN model. The results of the EDRI obtained through the BBN
model are depicted in Fig. 7.10, which shows that, as expected, cities located
in high seismic hazard zones (e.g. Vancouver and Montreal) show higher
EDRI values, as compared with cities in moderate and low seismicity (e.g.
Calgary and Halifax). Furthermore, for similar magnitude of seismicity, the
consequence of failure dictates the EDRI values. Vancouver has the highest
EDRI value, followed by Victoria and Montreal.
To compare the BBN results with WAM method results (Davidson and
Shah 1997), states of EDRI values (EDRI VL , EDRI L , EDRI M , EDRI H ,
EDRI VH ; superscripts stand for very low, low, medium, high and very high)
are transformed into a single index. This is done by multiplying each state,
EDRI VL , EDRI L , EDRI M , EDRI H , and EDRI VH , respectively, by the follow-
ing weights, 0, 0.25, 0.50, 0.75 and 1. Subsequently, the EDRI results of the
BBN and WAM are normalized by their corresponding maximum values
and the results are depicted in Fig. 7.11. The BBN results show that the two
cities located in high seismic hazard, Vancouver and Montreal, have the
highest EDRI values, whereas, the WAM showed Toronto has the highest