Case Study Investigating Probabilistic and Deterministic Sampling Methods for Developing In-Structure Response Spectra of a Fixed Base Structure Model

August 20, 2017

This study compares probabilistic and deterministic seismic structural responses for a relatively simple, fixed base steel structure founded on rock. The scope of the investigation is limited to assessing the validity of the simplified deterministic sampling method that is used in practice to estimate the distribution of seismic structural responses associated with uncertainty in structure frequency.

Structural response analysis is a critical step in seismic fragility evaluation of structures, systems, and components for Seismic Probabilistic Risk Analyses (SPRAs) of nuclear power plants (NPPs). Response analyses for SPRAs typically aim to reasonably estimate median structural response quantities and associated variability. The median response quantities and variabilities are then used to develop realistic fragility curves for NPP equipment. A realistic estimate of the median seismic response and associated variability is therefore essential to realistic risk predictions in SPRAs.

Two alternative approaches are commonly considered for calculating seismic structural responses for SPRAs: a probabilistic, sampling-based approach, and a more simplified and approximate deterministic approach. Probabilistic methods consider a number of different randomized combinations of input ground motions, soil properties, and structure properties.  In probabilistic analyses, a sufficient number of randomized samples are needed to achieve stable statistical results.  Conversely, as a simplifying approximation, deterministic methods include fewer sample combinations of ground motions with soil and structure properties; and rather than being randomly selected, soil and structure properties are targeted at expected median and plus-and-minus one standard deviation values to estimate median and 84% non-exceedance probability (NEP) response quantities. Because deterministic results are developed from fewer statistical samples, they are less rigorous, yet they are commonly judged to reasonably approximate probabilistic results.

In this paper, probabilistic and deterministic seismic response estimates of a simple structure are compared in terms of median and 84% NEP in-structure response spectra (ISRS). The objective of this investigation is to test the validity of the more approximate deterministic sampling approach that is used in practice to estimate the distribution of structure response associated with uncertainty in structure frequency. As such, a simplified comparison of the two approaches is performed by including only structure frequency uncertainty; other sources of structure response variability (soil properties, horizontal direction peak response, structure damping, etc.) are omitted accordingly.

Based on the results, an epistemic variability related to time history sampling bias is derived to characterize the additional uncertainty associated with using the more approximate deterministic analyses in-lieu of more rigorous probabilistic methods.  This unintentional uncertainty and the time history randomness are identified as causes of deterministic underpredictions.  A methodology to correct deterministic estimates and remove underpredictions is investigated, and results are shown to better match probabilistic results.

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24th International Conference on Structural Mechanics in Reactor Technology: Transactions, SMiRT-24, BEXCO, Busan, Korea

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