# Stochastic Emulation using Generalized Stratified Sampling for Performance-Based Risk Optimization of Structures

arXiv: https://arxiv.org/abs/2608.05006 · HTML: https://mlsanity.com/paper/2608.05006/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 65 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 7 of 7)

- [Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions](https://mlsanity.com/paper/1911.09067/) (2019)
- [Emulation of stochastic simulators using generalized lambda models](https://mlsanity.com/paper/2007.00996/) (2020)
- [Seismic fragility analysis using stochastic polynomial chaos expansions](https://mlsanity.com/paper/2208.07747/) (2022)
- [Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models](https://mlsanity.com/paper/2005.01309/) (2020)
- [Generalized Stratified Sampling for Efficient Reliability Assessment of Structures Against Natural Hazards](https://mlsanity.com/paper/2305.06338/) (2023)
- [Reliability analysis for data-driven noisy models using active learning](https://mlsanity.com/paper/2401.10796/) (2024)
- [High-dimensional reliability-based design optimization using stochastic emulators](https://mlsanity.com/paper/2604.05759/) (2026)

## Abstract (arXiv)

Metamodels are instrumental in reducing the computational burden associated with nested reliability analyses and optimization loops in Performance-Based Risk Optimization (PBRO) of structures under stochastic loads. In this context, stochastic emulators are particularly useful because they approximate response distributions while accounting for the intrinsic stochasticity of the simulator. Among these methods, Stochastic Polynomial Chaos Expansion (SPCE) is especially attractive because it does not require replications of nonlinear analyses at fixed input conditions. However, SPCE may present limitations in accurately representing extreme responses in the tails of structural response distributions. To address this limitation, this study proposes a framework that combines Generalized Stratified Sampling (GSS) with SPCE. The GSS scheme partitions the input space into strata according to the intensity of the hazard, improving the representation of extreme responses, while independent SPCE emulators are trained within each stratum. The conditional exceedance probabilities estimated in each stratum are then recombined using the total probability theorem to evaluate the probabilistic constraints. The proposed GSS-SPCE framework is applied to the optimal design of buckling-restrained brace cross-sectional areas in a two-story steel building. The objective is to minimize the initial construction cost while satisfying prescribed probabilistic performance constraints. Results show that the proposed framework accurately estimates structural response distributions, including their tail regions, while substantially reducing the number of nonlinear model evaluations required for PBRO.