first a digression The POC Ranking the Methods

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first a digression The POC Ranking the Methods. Jennie Watson-Lamprey October 29, 2007. A Digression. Top 20 MIDR Values. 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.

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### first a digressionThe 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
• A suite of records from Mw6.75-7.25, Rrup 0-20km events was developed. A total of 98 records were distributed to the group June 26th.
• The suite is run through each model using scale factors of 1, 2, 4 and 8.
• A model of the desired structural response parameter using properties of the input time series (e.g. Sa(T1), Sa(2T1), duration, etc.) is developed.
Method for Estimating Point of Comparison
• 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

• Models for the record properties that affect response are developed using the full PEER database and correlations between properties.
• Combining the models in step 5 gives the joint pdf of record properties
• 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, Rrup=10km earthquake is calculated.
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.

### 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
Ranking Statistic
• Goal: Accurate estimate of MIDR | M, R, Sa
• Statistic: P ( -0.1 < X < 0.1)
Ranking Statistic
• Goal: Minimize under-estimation of MIDR | M, R, Sa
• Statistic: P ( X > 0 )
Ranking of Methods
• Ranking is dependent on analysis goal.