Multi-objective optimization for the probabilistic seismic performance based design of an example moment frame steel structure is presented. Direct economic and social losses associated with seismic events, which are of interest in the current recommended frameworks for the performance based design of structures, are considered in the optimization problem defined. Three optimization objectives are selected: the initial construction cost, modeled as the weight of the structural system; expected annual economic loss associated with damage resulting from seismic hazard; and expected annual social loss resulting from seismic hazard induced damage. Hazus recommended procedures are applied in the economic and social loss calculations which include the fragility functions used in the damage analyses and injury event models implemented in the social loss calculations. The multiobjective optimization method uses a non-dominated sorting genetic algorithm strategy. The optimization results for the multiple objectives are presented and discussed in the form of Pareto fronts. Engineering demand parameters implemented for the seismic loss analysis are inter-story drifts and peak floor accelerations and are obtained using inelastic time history analysis for the ground motions associated with various seismic hazard levels. To illustrate the design procedure, loss parameters are calculated for an example steel structure located in Los Angeles, CA.

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Sanaz Saadat, Ph.D. - Gilsanz Murray Steficek LLP
Charles Camp, Ph.D. - University of Memphis
Shahram Pezshk, Ph.D. - University of Memphis
Christopher Foley, Ph.D. - Marquette University
April 2015

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• Performance-based Design and Seismic
Loss Evaluation
• Multi-Objective Optimization Problem
• Example Design Problem
• Summary and Conclusions

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Fragility curves for structural and non-structural
members for different damage measures → based
on parameters given in Hazus technical manual

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• Expected direct economic losses for each
component (SS, NSD, NSA) are calculated:
• Expected loss is calculated as the sum of
losses for structural and nonstructural
components.
Repair
Costs
&

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• Hazus recommendations for social loss
calculation→ event tree of consequent
casualty levels for different damage levels
• Social loss is the aggregation different
possible scenarios
• Weights assigned to different casualty
severity levels using National Safety
Council (NSC) suggestions

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Building
Damage State 1
CSL1
CSL2
CSL3
CSL4
Damage State 2
CSL1
CSL2
CSL3
CSL4
Damage State 3
CSL1
CSL2
CSL3
CSL4
Damage State 4
No Collapse
CSL1
CSL2
CSL3
CSL4
With Collapse
CSL1
CSL2
CSL3
CSL4

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• Seismic loss parameters are the
optimization objectives
• Two types of seismic losses considered:
economic and social
• Loss parameter is the expected annual
loss value

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Multi-objective Optimization Procedure:
Non-Dominated Sorting Genetic Algorithm NSGA-II
(Deb et al. 2002)

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Multi-objective optimization problem
)3,1(:
),,(
 ilctoSubjected
EASLEALWMinimize
ii
ppp
EALEALp 
EASLEASLp 
min,1 : CPCP CLCLc 
min,2 : IOIO CLCLc 
0.1: *
*
3 


pb
pc
M
M
c






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iii
ii
i
ii
i
i
i
lcif
lcif
c
cl
0.1
where
3
1


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The penalty function φ is defined as
Constraints
WWp 

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PERFORMANCE
OBJECTIVES
Collapse Prevention for hazard level
of 2% POE in 50 years
Immediate Occupancy for hazard
level of 50% POE in 50 years

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The acceptable confidence levels (CL) for meeting
these performance objectives are:
• CLCP = 90%
• CLIO = 50%
Meeting these performance objectives are set as
the acceptance criteria for the feasibility of the
designs in the multi-objective optimization
problem.

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• Seismic loss values as objectives in optimized
probabilistic performance-based design
• Different types of seismic losses considered:
economic and social
• Multi-objective optimization results in the form of
Pareto fronts
• Pareto front: provide decision makers with useful
comparison tool for optimized design considering
different objectives

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For the example structure considered:
• Reduction in both economic and social losses in the
obtained results with increase in the weight of the
structural system
• Minimum weight design: drift-sensitive non-structural
components have a more significant contribution to the
calculated economic loss
• Minimum loss designs: acceleration-sensitive non-
structural components have a larger contribution to the
calculated economic loss

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