A Genetic Algorithm Solution for the Problem of Selection and

Scaling of Ground Motion Records

Arzhang Alimoradi and Farzad NaeimJohn A. Martin & Associates

First PEER Workshop on Ground Motion Selection and Modification for Nonlinear Analysis

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

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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

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

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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)

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

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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 effects6. Soil-foundation-structure interaction 7. … ?!?!?!

6 DOF Time Series of Point Displacement

Earthquake Ground Motion Process (Complex System)

Genetic Algorithms

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

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Chromosomes

Nucleus

Optimization through adaptation!

Genetic algorithms: what does biology have to do with ground

motion selection?

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

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(Genotype) (Phenotype)

(Structure) (Solution Alternative)

(Environment)

(Problem)

[0110100101][1110101101][0000110011] {Optimal Variables}

Adaptation through generations

(Genotype) (Phenotype)

(Structure) (Solution Alternative)

(Environment)

(Problem)

[0110100101][1110101101][0000110011] {Optimal Variables}

Adaptation through generations

GA BasicsN

atur

al S

yste

mA

rtif

icia

l Sys

tem

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

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A population of five chromosomes:

10111001100010100110111010011000101001110010101110

01100111011101001000111100101111010111000111000101

00101001100010100110001010011000101001100000100110

00101001110010110111001010011100101101101010110110

10111101100010100110001111111000101001100110100010

00100001110010100000001110011000101001100000010110

11101001100010100110001010011001101001100010110000

00100111011101000010110001110101000111001110100111

00101001110010100111001010101000101001100110101111

00100111011101001000111001110101010111010010100100

Gene 1: Gene 1: record 1 record 1 and the and the scalingscaling

Gene 2: scaling set 2Gene 2: scaling set 2Gene 3-5: …Gene 3-5: …

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

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211080.3

Total number of different combinations =

8010

The number of stable particles in the universe =

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

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Example I: SAC-20 LA

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

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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

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

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Comparison of Modal Properties

Krawinkler’s M2 Perform-3D

T1, sec. 3.65 3.64

T2, sec. 1.26 1.28

T3, sec. 0.72 0.74

Effective Modal Mass 1 80.1 78.2

Effective Modal Mass 2 11.8 11.3

Effective Modal Mass 3 3.1 3.9

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

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Denali Pump Station #10 -051 Denali Pump Station #10 -321

Imperial Valley El Centro Array Station 6 -140

Imperial Valley El Centro Array Station 6 -230

Landers Yermo EW Landers Yermo NS

Loma Prieta Anderson Dam 270 Loma Prieta 360

Loma Prieta Hollister EW Loma Prieta Hollister EW

Northridge Newhall EW Northridge Newhall NS

Northridge Sylmar County Hospital Parking Lot 360

Northridge Sylmar County Hospital Parking Lot 90

Selected Bin

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

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

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Example II: PEER GMSM Study

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

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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)

n

i

t

trecord etT

record dttSa

tSaZ

27

1 arg

1min

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

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Estimate I

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

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Estimate II

• Median of maximum interstory drift ratio (To be used only for the evaluation of the arithmetic mean of response)

n

i

t

tetT

recordrecord

dttSa

tSa

Z 17

minarg

7

1

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

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Estimate II

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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.

It is a scale of proportions which makes the It is a scale of proportions which makes the bad difficult and the good easybad difficult and the good easy

Albert EinsteinAlbert Einstein