Measuring Bias in Incremental Dynamic Analysis Using Bootstrap

Abstract eng:
We present a methodology for the evaluation of the effect of scaling when Incremental Dynamic Analysis (IDA) is performed. The median capacity curve of IDA is compared to the capacity curve obtained using cloud analysis. Cloud analysis data contain results obtained using unscaled natural and synthetic ground motion records. Synthetic records were used due to the lack of a statistically significant number of natural records for large intensities. Nonlinear regression is performed with the aid of the Local Regression Smoothing Algorithm (LOESS) in order to post-process the results of cloud analysis. The primary difference between the two methods is that cloud analysis allows obtaining capacity curves without scaling the ground motion records, as opposed to the IDA algorithm. To investigate the statistical significance of this comparison, the bootstrap method is used. The bootstrap method is a powerful and easy-to-implement tool that allows calculating confidence intervals. Using bootstrap we are able to measure the bias introduced by record scaling when IDA is adopted. Thus, the bias is examined quantitatively and qualitatively for the full range of limit-states, yielding useful conclusions regarding scaling and its legitimacy in the context of IDA. A three-storey and a nine-storey steel moment resisting frames are used as testbeds for our investigations.

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