ASCE Structures Congress 2015

Probabilistic Performance-Based Design of Steel Structures –Multi-Objective Optimization

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

ASCE Structures Congress 2015

OUTLINES

• Performance-based Design and Seismic Loss Evaluation

• Multi-Objective Optimization Problem• Example Design Problem• Summary and Conclusions

ASCE Structures Congress 2015

Performance-Based Design

ASCE Structures Congress 2015

Seismic Loss Evaluation

ASCE Structures Congress 2015

Probabilistic Damage Analysis

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

ASCE Structures Congress 2015

Probabilistic Loss Analysis

• 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 &

ASCE Structures Congress 2015

Probabilistic Loss Analysis

• 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

ASCE Structures Congress 2015

Probabilistic Loss Analysis

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

ASCE Structures Congress 2015

Seismic Loss Evaluation

•Seismic loss parameters are the optimization objectives

•Two types of seismic losses considered: economic and social

•Loss parameter is the expected annual loss value

ASCE Structures Congress 2015

Multi-objective Optimization

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

ASCE Structures Congress 2015

Optimization Problem

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

Mc

iii

iii

iii

ii

lcif

lcifc

cl

0.1

where

3

1

The penalty function φ is defined as

Constraints WWp

ASCE Structures Congress 2015

Performance Objectives

PERFORMANCE OBJECTIVES

Collapse Prevention for hazard level of 2% POE in 50 years

Immediate Occupancy for hazard level of 50% POE in 50 years

ASCE Structures Congress 2015

Performance Objectives

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.

ASCE Structures Congress 2015

Example Structure

ASCE Structures Congress 2015

Multi-objective Optimization Results

ASCE Structures Congress 2015

Multi-objective Optimization Results

ASCE Structures Congress 2015

Distribution of Losses

ASCE Structures Congress 2015

Distribution of Losses

ASCE Structures Congress 2015

Summary and Conclusions

• 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

ASCE Structures Congress 2015

Summary and Conclusions

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

ASCE Structures Congress 2015

Thank You!