Project Title/ID Number  Methodology for Selection of Input Ground Motions for PBEE and Propagation of Uncertainty—3172002 
Start/End Dates  10/1/02—9/30/03 
Project Leader  C. Allin Cornell (Stanford/Faculty) 
Team Members  Fatemeh Jalayer (Stanford/Grad Student) & Jack Baker (Stanford/Grad Student) 
Project goals and objectives  
This project is designed to continue and bring to a level of completion the main issues of the Year 5 work statement: uncertainty propagation, IM sufficiency and efficiency investigations, and record selection/processing. We find it novel to view the last two subjects as being strongly interrelated. Uncertainty propagation: IM efficiency and sufficiency: Record
selection/processing: 

Role of this project in supporting PEER’s vision  
Introduction and development of probabilistic methods in seismic PBEE. 

Methodology employed  
Analytical development of uncertainty propagation by FOSM; design of record sets and oscillator/structural analyses and statistical analysis to study IM and record selection. 
Brief description of past year’s accomplishments and more detail on expected Year 6 accomplishments  
1. In year 5 and 6 we have developed and documented a comparatively simple firstorder, secondmoment scheme for conducting the (aleatory and epistemic) uncertainty propagation through the several, long correlated random vectors of EDPs and DMs to the DVs in the PEER framing equation. The results are the first and second moments of the DVs given IM = x. These can be used with the IM hazard curve to produce mean and variance of each DV, and, with an appropriate distribution assignment, the DV “hazard curve”, i.e., the annual probability of exceeding DV level y vs. y. It is presumed that this scheme will be adequately accurate for treatment of these intermediate variables given the comparative uncertainty dominance of the IM variable. The report includes a discussion and examples of estimating the second moments in the case of EDPIM 2. As described
last year in Year 5 we developed and documented further methods for
estimating the conditional probability distribution of EDP given IM
= x as a function of x for nonlinear structures based on suites of
nonlinear dynamic analyses. 

3. In Year 6 we have worked further on the question of the “sufficiency” of Sa (at the firstmode period) as this issue is closely related to the problem of record selection. We demonstrated that even the two extreme cases (a very HF oscillator) and a longperiod, multimodedominated 20story structure no statistically significant dependence on magnitude, distance or epsilon remains once one conditions on Sa (the definition of “sufficiency”) implying that the records used in the nonlinear dynamic analyses need not be selected with great care with respect to these features of the threatening seismicity. For a model of the Van Nuys Testbed structure we have demonstrated using a very large suite of records designed to accentuate the problem, we have demonstrated that Sa is a sufficient IM with respect to M, R and “epsilon” for this structure. The figure here shows this (with respect to the most difficult parameter, magnitude) by the mild and statistically insignificant slope of the residuals of max interstory drift (regressed on Sa) versus those of magnitude. 4. More directly, we have selected records at random from a catalog covering a broad magnitude distance range and showed that scaled to the same Sa level, they produced the same (statistically) speaking displacements as a set taken from a set representing the “strongest” records in the range (i.e., those from a large magnitude, close distance range). Further studies along these lines are continuing with the focus shifting to consider nearsource records as well. 

Other similar work being conducted within and outside PEER and how this project differs  
S. Kramer looking at IMs for soil problems.  
Plans for Year 7 if this project is expected to be continued  
Describe any instances where you are aware that your results have been used in industry  
Expected milestones  
Completion of uncertainty propagation work; interacting IM and record selection subjects advanced.  
Deliverables  
Two technical papers on IM estimation; report/paper on record selection; report on uncertainty propagation (in press). 