Assessing seismic risks for new and existing buildings using performance-based earthquake engineering (PBEE) methodology - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 312

Loss curve (mean cumulative annual total repair cost = $ 3.13e + 004)

0.045

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

0 0

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

10 6

$C ×

12.5 Example of loss curve (Yang et al. 2009).

such as this can be used by building owners/stakeholders to make a rational
decision regarding building insurance.
The procedures in Step 3 through Step 5 have been implemented in a
computer program and thus automated (Yang 2009). Input to the program
requires the user to defi ne the performance groups, the repair quantity
tables, the repair cost functions, the EDP matrices obtained by running a
limited number of nonlinear dynamic analyses, and the total number of
repair cost simulations required to compute the loss function. Given these
input quantities, the program generates loss functions in a variety of differ-
ent formats, including those described above.

12.2.4 Generating correlated EDP vectors

To generate correlated EDP vectors, the peak quantities of the EDP s
recorded from sets of dynamic analysis are tabulated into matrix X , as
shown in Table 12.2. Each column of X represents an EDP , while each row
of X represents different EDP recorded for the same ground motion.
Because the entries of the EDP matrix X are obtained from the maximum
of the absolute value of the EDP response, X is assumed to be lognormal
distribution. X is then transformed to a normal distribution Y by taking the
natural log of X . The mean vector M Y , the diagonal standard deviation
matrix D Y , and the correlation coeffi cient matrix R YY are then calculated
using Eq. [12.15] through Eq. [12.18].