1. A Genetic Algorithm Solution for the Problem of Selection and Scaling of Ground Motion Records Arzhang Alimoradi and Farzad Naeim John A. Martin & Associates First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis

2. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 2 Agenda Why Genetic Algorithms? –Formulation of an optimal search and scaling method (minimal or no scaling) Example I: SAC-20 LA Example II: PEER-GMSM Concluding remarks

3. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 3 Why GA? Different philosophies with the analysis of complex systems: 1.Stochastic analysis, non-stationary indeterministic processes, applied with ‘reductionism’ 2.Analysis of complex systems (critical, chaotic)  Evidence for deterministic process (Olson and Allen, Nature, Vol. 438, pp. 212-215, November 2005)  Physically critical systems (Corral, Physical Review Letters, Vol. 92, No. 10, March 2004)

4. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 4 1.Fault location, type, size and activity, strain rate 2.Rupture dynamics (slip rate, seismic moment, stress drop, directivity, mechanism,…) 3.Path (Q, topology, distances, refraction and reflection,…) 4.Local site effects (amplification, filtering, nonlinear soil deformations,…) 5.Basin effects 6.Soil-foundation-structure interaction 7.… ?!?!?! 6 DOF Time Series of Point Displacement Earthquake Ground Motion Process (Complex System)

5. Genetic Algorithms

6. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 6 Chromosomes Nucleus Optimization through adaptation! Genetic algorithms: what does biology have to do with ground motion selection?

7. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 7 GA Basics Natural System Artificial System

8. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 8 A population of five chromosomes: Gene 1: record 1 and the scaling Gene 2: scaling set 2 Gene 3-5: …

9. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 9 Total number of different combinations = The number of stable particles in the universe =

10. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 10

11. Example I: SAC-20 LA

12. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 12 SAC-20 LA, Post-Northridge 3 Dimensional inelastic model in CSi-Perform Prof. Krawinkler’s M2 Model (with panel zone distortions are modeled) Gravity beam-to-column connections are pinned

13. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 13 Comparison of Modal Properties Krawinkler’s M2Perform-3D T 1, sec.3.653.64 T 2, sec.1.261.28 T 3, sec.0.720.74 Effective Modal Mass 180.178.2 Effective Modal Mass 211.811.3 Effective Modal Mass 33.13.9

14. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 14 Denali Pump Station #10 -051Denali Pump Station #10 -321 Imperial Valley El Centro Array Station 6 -140 Imperial Valley El Centro Array Station 6 -230 Landers Yermo EWLanders Yermo NS Loma Prieta Anderson Dam 270Loma Prieta 360 Loma Prieta Hollister EW Northridge Newhall EWNorthridge Newhall NS Northridge Sylmar County Hospital Parking Lot 360 Northridge Sylmar County Hospital Parking Lot 90 Selected Bin

15. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 15

16. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 16

17. Example II: PEER GMSM Study

18. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 18 Estimate I Cumulative distribution function of maximum interstory drift ratio conditioned on a given earthquake event on a site with a given 30m soil shear-wave velocity. (To be used for distribution and mean evaluations)

19. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 19 Estimate I

20. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 20 Estimate II Median of maximum interstory drift ratio (To be used only for the evaluation of the arithmetic mean of response)

21. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 21 Estimate II

22. Oct. 27, 2006First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis 22 Conclusions Need for a consistent theory with regards to selection and scaling, Scaling scheme shall not distort the spatial distribution of response when compared to ‘conforming records,’ A computational tool was presented for efficient search and scaling of ground motion records in a database.

23. It is a scale of proportions which makes the bad difficult and the good easy Albert Einstein