Ground motion selection is a crucial step in probabilistic seismic performance assessment of structural systems. Particularly, identifying ground motion records compatible with a specific hazard level has been the major focus of past studies. We propose a multivariate return period (MRP)‐based record selection methodology to further improve the multivariate hazard consistency over a vector of intensity measures (IMs). Unlike the traditional univariate return period anchored on a scalar IM, MRP generalizes the return period concept by accommodating the joint rate of exceedance of a vector of IMs, thereby providing more holistic seismic hazard characterization. By leveraging MRP in linking the seismic hazard to a vector IMs, the proposed MRP‐based ground motion selection methodology for the first time offers a mathematically rigorous yet practical solution for multivariate hazard consistency in ground motion selection. The merit of the MRP‐based ground motion selection is demonstrated by comparing the resulting target spectra and seismic demand estimates for several case‐study structures with other state‐of‐the‐art ground motion selection alternatives. From the results, the MRP‐based ground motion selection employing Kendall's distribution function turns out to be a promising alternative, offering favorable new features including (a) moderate target spectra intensity and moderately low target spectra standard deviation; (b) superior convergence with the increase of the conditioning IM dimension and ability to approximate higher‐dimensional multivariate hazard consistency with lower dimensional conditioning IMs; and (c) capability to realistically capture the multimodal spectral shape owing to the incorporation of multivariate Gaussian mixture distribution in generating target spectra.
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher dimension than the parameter. Here we show that features of the auxiliary variable are often fully observed and, in such cases, a simultaneous dimension reduction and information aggregation can be achieved by conditioning. This proposed conditioning strategy leads to efficient IM inference and casts new light on Fisher's notions of sufficiency, conditioning and also Bayesian inference. A differential-equation-driven selection of a conditional association is developed, and validity of the conditional IM is proved under some conditions. For problems that do not admit a conditional IM of the standard form, we propose a more flexible class of conditional IMs based on localization. Examples of local conditional IMs in a bivariate normal model and a normal variance components model are also given.
more » « less- NSF-PAR ID:
- 10397809
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Volume:
- 77
- Issue:
- 1
- ISSN:
- 1369-7412
- Page Range / eLocation ID:
- p. 195-217
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Summary Intensity measure (IM) selection is a critical step in probabilistic seismic risk assessment (PSRA). In many past studies, the efficiency of an IM, which quantifies its explanatory power within a probabilistic seismic demand model, has been a predominant IM evaluation criterion. However, because PSRA requires convolution of the conditional demand model and the probabilistic seismic hazard, IM selection solely based on efficiency ignores the influence of uncertainty contribution particularly from the ground motion prediction equations (GMPEs), which is also dependent on the IMs, and may lead to biased IM selection. In the present study, the concept of joint entropy from information theory is introduced to quantify the uncertainty of unconditional multivariate seismic demands for general multiresponse structural systems, offering a holistic consideration of different sources of uncertainties. We propose a novel entropy‐based IM evaluation criterion that can serve as the basis for IM selection and develop a practical framework to facilitate the implementation of the entropy‐based IM selection in site‐specific PSRA. Based on two case‐study highway bridges, the merit of the proposed IM selection methodology is demonstrated, and the influence of IM selection on demand entropy and loss estimation in PSRA is evaluated. From the results, the proposed entropy‐based IM selection manifests improved capability in considering different sources of uncertainties and is found to deliver much more consistent and confident seismic risk estimates.
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