Why determining the number of code spectrum matched records based on usual statistics is an ill-posed problem

The most advanced analytical tool in earthquake engineering is non-linear dynamic analysis, which typically entails a computer model of a structure subjected to a set of real recorded accelerograms. Although computationally demanding, this type of analysis is gradually becoming the norm in seismic design and assessment applications. Seismic reliability calculations according to the paradigm of performance-based earthquake engineering (PBEE) use dynamic analysis results to estimate the probabilistic distribution of structural response. In this context, the uncertainty in estimation of structural seismic risk depends, among other things, on the number of records used. On the other hand, modern seismic codes that espouse PBEE principles, but do not incorporate its probabilistic framework, do not require explicit estimates of structural seismic risk and acquiesce to the use of dynamic analysis for the purpose of pass/fail verifications of a single performance level, based on comparing average response vs fixed thresholds. While structural seismic reliability studies use a few tens of records, codes often require no more than seven to eleven records for obtaining an estimate of mean response, mandating that these records be selected based on criteria of compatibility with the design spectrum. The present study addresses this issue by investigating the effect of spectrum-compatible acceleration records' sample size on estimating average single-stripe inelastic structural response. To this end, multiple record sets are assembled, with a fixed number of records that are all selected to match-on-average the same target design spectrum, without repeating any record among sets. This exercise of obtaining multitudes of spectrum-compatible sets is repeated for various record sample sizes. The record sets are subsequently used for response-history analysis of a code-conforming inelastic frame. Examination of the results reveals that the spectral compatibility condition leads to response statistics that do not exhibit the trends expected in the case of simple random samples of various sizes. In fact, the responses obtained by using the selected spectrum-compatible records cannot be considered neither independent nor identically distributed. Thus, such statistics do not provide estimates of the intended characteristics of the underlying distribution. In other words, looking at the estimation uncertainty in the response distribution's parameters, by using statistics only suitable for cases of simple random sampling, is an ill-posed problem, since the sampled distribution may be very different from the one implicitly assumed by this approach. In conclusion, when code-based record selection is of concern, using tools of statistical inference such as the assessment of estimation uncertainty, suitable in cases of simple random sampling, to determine the necessary number of spectrum-compatible records, may be conceptually inappropriate.