first a digression The POC Ranking the Methods Jennie Watson-Lamprey October 29, 2007

A Digression

Top 20 MIDR Values

Not a lot of overlap. We don’t know going into the problem which ground motions are high and which are low.

Top 20 MIDR Values If we’re after the median EDP, we use a GMSM method to get rid of the outliers If we’re after the distribution of EDP, we don’t want to throw away the outliers.

Top 20 MIDR Values The point isn’t to identify the outliers. The point is to figure out which GMSM method does it for you.

The POC

Calculating the Point of Comparison Time series from a bin of M, R –Should work for a median –Too much variability! Time series from a bin of M, R corrected for the difference between the recorded event and the design event –Not enough records to push the structure into the nonlinear range -> not a good estimator of rare response values

Calculating the Point of Comparison Current Method: –Run scaled and unscaled time series through a structural model –Perform a regression on a response parameter using time series properties (spectral acceleration) –Use predictive equations to define the joint distribution of the time series properties –Integrate the regression over the joint distribution –This gives a distribution of a response parameter

Method for Estimating Point of Comparison 1.A suite of records from Mw , Rrup 0-20km events was developed. A total of 98 records were distributed to the group June 26th. 2.The suite is run through each model using scale factors of 1, 2, 4 and 8. 3.A model of the desired structural response parameter using properties of the input time series (e.g. Sa(T 1 ), Sa(2T 1 ), duration, etc.) is developed.

Method for Estimating Point of Comparison 4.The EDP model is checked to ensure that there is no bias with scale factor. -This is only a test for the limited M,R range represented by the 98 selected recordings 5.Models for the record properties that affect response are developed using the full PEER database and correlations between properties. 6.Combining the models in step 5 gives the joint pdf of record properties 7.Using the joint pdf of record properties and the model for building response based on those record properties, the pdf of structural response for a M7, R rup =10km earthquake is calculated.

Building A - Results from 98

Building A - Regression Perform a regression to determine probability of collapse - Here it’s 0. Perform a regression to determine median and variability of MIDR. Regression is based on spectral values at a number of periods.

Building A - Residuals

Building A - Integration

Building A - Integration Really

Building A - CDF

Building A - POC

POC Questions?

Ranking the Methods

Ranking of Methods Focus on suites of 7-ground motions 10 contributors provided 4 suites of 7 ground motions for buildings A, C & D. Develop an estimated distribution of predictions Use the estimated distribution and the goal of the analysis to develop a statistic for ranking

GMSM Methods

Compiling Results for Each Method and Building

Compiling All Results by Method and Building

Consolidating Results for Each Method

Distribution of Predictions

Ranking Statistic Goal: Accurate estimate of MIDR | M, R, Sa Statistic: P ( -0.1 < X < 0.1)

Accurate Estimate

Accurate Estimate Ranking

Ranking Statistic Goal: Minimize under-estimation of MIDR | M, R, Sa Statistic: P ( X > 0 )

Minimize Under-Estimation

Ranking of Methods Ranking is dependent on analysis goal.

CMS Thoughts