PERFORMANCE-BASED EARTHQUAKE ENGINEERING DESIGN OPTIMIZATION OF BUILDINGS

Principal Investigator: Khalid M. Mosalam, UC BerkeleyStudent Investigators: Euihyun Choi, UC Berkeley

Seismic building design is a complex procedure requiringsophisticated structural analysis (e.g. nonlinear time-historyanalysis) and has various sources of uncertainties. In addition,engineers should consider not only damages in structuralelements of buildings, but also other sources of economic loss(e.g. repair cost and downtime). From the above reason,various design tools and frameworks for supporting engineer’sdecision making are developed within the earthquakeengineering community. The Pacific Earthquake EngineeringResearch (PEER) Center developed the Performance-BasedEarthquake Engineering (PBEE) methodology which is arobust framework for evaluating a system performancemeasures in the interest of various stakeholders, such asmonetary losses, downtime, or casualties.

The engineer’s goal in design is to solve optimizationproblem and find the “best” design. The PEER PBEEmethodology is a robust method to determine the model’sutility, which is a good metric to decide the best design amongthe design alternative sets. Proper optimization algorithmneeds to be developed for extension of the PEER PBEEmethodology into the design space. In this study, GeneticAlgorithm (GA) is adopted for design optimization framework.

INTRODUCTION OPTIMIZATION ALGORITHM

In this study, an optimization framework for the PBEEmethodology using a genetic algorithm is developed andperformed with the steel-MRF. Two common methods in thegenetic algorithm, crossover and random mutations, are usedin difference phases of the optimization process in theapplication. Design alternatives converges well with thecrossover operator. In the application, the solution convergeswith a few generations (10 generations).

The PBE approaches are powerful tools for multi-objectivedesigning and also hugely effective for multi-hazard design. Inthis application, only repair and construction cost are used asutility, and only single hazard (earthquake) is considered.However, in further study of PBE approaches, the optimaldesign frameworks for various performances (not just cost,e.g. CO2 emission, energy efficiency) considering multi-hazard (e.g. fire, tsunami) are expected to be developed.

CONCLUSION

PBEE METHODOLOGY

Phase 1: Crossover

Phase 2: Random Mutation

In this study, the genetic algorithm is performed with twophases. In this first phase, the algorithm begins with 50randomly generated design alternatives. For the nextgeneration, 10 design alternatives who have better utility thanthe others are selected, and 10 offspring are generated fromthem with crossover. In this second phase, the first generationconsists of the top 10 design alternatives from the lastgeneration of phase 1 and 20 randomly generated designalternatives. In this phase, the top 10 design alternatives arealso selected for the next generation, but 10 offspring aregenerated by the random mutation

RESULTS

[Optimization results for columns and beams, black lineindicates the design of the best alternatives in each generation]

[Best design from phase 2: Random Mutation]

APPLICATIONModel ConfigurationA hypothetical three-bay, five-story

steel-Moment Resisting Frame (MRF)building located in Berkeley, CA (2150Shattuck Ave. 37.87 ° , -122.27 ° ) isused as an application example.

All elements of the steel-MRF arewide flange steel beams meetingASTM standard A36 with a yieldstress of 36 ksi. The sectionproperties of the beams and columnsfor each story are chosen fromamong 203 wide beam sections.

Phase 1: Crossover

Phase 2: Random Mutation

The PEER PBEE methodology is used as the mainframework for evaluating the seismic performances ofstructures or facilities. In the framework of PEER PBEE, thereare four consecutive steps: hazard analysis, structuralanalysis, damage analysis, and loss analysis. The final goalfor this process is to obtain the utility of each designalternative which will be the objective function of designoptimization.

The Hayward Fault is located about 3 km east of the site,the San Andreas Fault is located about 30 km west of this site.Soil condition is assumed as stiff soil corresponding to ASCE7 Site Class D. The above figure is USGS hazard curves anduniform hazard response spectra obtained by USGS UnifiedHazard Tool.

Artificial ground motions conforming the response spectraare generated for structural analysis.

We obtain repair and construction cost as utility of designalternative