Proposed Method for Estimating pdf of Structural Response

1
Proposed Method for Estimating pdf of Structural
Response

• 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 will be 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.)
  will be developed.

2
Model of EDP

• Distribution
• Find best normalizing transform for EDP using
  Maximum Likelihood
• May not be log-normal
• EDP Model
• Median F(x1,x2, xn)
• Sigma (may not be constant)
• PDF of EDP (for limited M,R range)

3
Proposed Method for Estimating pdf of Structural
Response

• The EDP model will be 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 will be developed using the full PEER
  database.
• - Dependent on MR
• Fx1(M,R), Fx2(M,R), Fxn(M,R)
• - Dependent on M, R, Sa(T1)
• Fx1(M,R,Sa(T1)), Fx2(M,R Sa(T1)), Fxn(M,R
  Sa(T1))

4
Proposed Method for Estimating pdf of Structural
Response

• 6. Evaluate the correlations of the residuals of
  the record properties for both models
• COV(x1,x2), COV(x1,x3), COV(x2,x3),
• Combining steps 5 6 will give the joint pdf of
  record properties
• fx(x1,x2,xn,M,R)
• fx(x1,x2,xn,M,R,Sa(T1))

5
Proposed Method for Estimating pdf of Structural
Response

• 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, Rrup10km earthquake will be calculated.

6
pdf of Response Not
Conditioned on Sa
7
pdf of Response Conditioned on Sa
8
Point of Comparison Option 1

• P(EDPgtX1M,R)Z1

9
Point of Comparison Option 2

• P(EDPgtX2M,R,Sa)Z2