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Gaussian Process Surrogate Models for Efficient Estimation of Structural Response Distributions and Order Statistics

Vegard Flovik, Sebastian Winter, Christian Agrell

TL;DR

Problem: long-term estimation of extreme structural responses under stochastic weather is computationally expensive with full physics-based simulations. Approach: employ Gaussian Process (GP) surrogates to map weather inputs to distribution parameters of the structural response, then sample from predicted distributions to compute order statistics such as $Y_{100}$, avoiding extensive simulations. Contributions: a proof-of-concept for 25-year $Y_{100}$ estimation using Gumbel, Rayleigh, and Weibull fits; results show GP-based sampling can match brute-force outputs at a fraction of the cost, with Weibull and Rayleigh offering favorable performance. Significance: enables efficient, probabilistic Serviceability Limit State assessments and more informed design under weather variability.

Abstract

Engineering disciplines often rely on extensive simulations to ensure that structures are designed to withstand harsh conditions while avoiding over-engineering for unlikely scenarios. Assessments such as Serviceability Limit State (SLS) involve evaluating weather events, including estimating loads not expected to be exceeded more than a specified number of times (e.g., 100) throughout the structure's design lifetime. Although physics-based simulations provide robust and detailed insights, they are computationally expensive, making it challenging to generate statistically valid representations of a wide range of weather conditions. To address these challenges, we propose an approach using Gaussian Process (GP) surrogate models trained on a limited set of simulation outputs to directly generate the structural response distribution. We apply this method to an SLS assessment for estimating the order statistics \(Y_{100}\), representing the 100th highest response, of a structure exposed to 25 years of historical weather observations. Our results indicate that the GP surrogate models provide comparable results to full simulations but at a fraction of the computational cost.

Gaussian Process Surrogate Models for Efficient Estimation of Structural Response Distributions and Order Statistics

TL;DR

Problem: long-term estimation of extreme structural responses under stochastic weather is computationally expensive with full physics-based simulations. Approach: employ Gaussian Process (GP) surrogates to map weather inputs to distribution parameters of the structural response, then sample from predicted distributions to compute order statistics such as , avoiding extensive simulations. Contributions: a proof-of-concept for 25-year estimation using Gumbel, Rayleigh, and Weibull fits; results show GP-based sampling can match brute-force outputs at a fraction of the cost, with Weibull and Rayleigh offering favorable performance. Significance: enables efficient, probabilistic Serviceability Limit State assessments and more informed design under weather variability.

Abstract

Engineering disciplines often rely on extensive simulations to ensure that structures are designed to withstand harsh conditions while avoiding over-engineering for unlikely scenarios. Assessments such as Serviceability Limit State (SLS) involve evaluating weather events, including estimating loads not expected to be exceeded more than a specified number of times (e.g., 100) throughout the structure's design lifetime. Although physics-based simulations provide robust and detailed insights, they are computationally expensive, making it challenging to generate statistically valid representations of a wide range of weather conditions. To address these challenges, we propose an approach using Gaussian Process (GP) surrogate models trained on a limited set of simulation outputs to directly generate the structural response distribution. We apply this method to an SLS assessment for estimating the order statistics , representing the 100th highest response, of a structure exposed to 25 years of historical weather observations. Our results indicate that the GP surrogate models provide comparable results to full simulations but at a fraction of the computational cost.

Paper Structure

This paper contains 13 sections, 2 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Statement and Approach
  3. Methods
  4. Simulation model overview
  5. From weather data to structural responses and simulator output
  6. Calculating order statistics
  7. Generating training data for the surrogate model
  8. Generating the structural response spectrum using GP models
  9. Training the models
  10. Generating the predicted response distribution
  11. Results and Discussion
  12. Estimation of $Y_{100}$ over a 25 year period
  13. Conclusions

Figures (8)

  • Figure 1: Example output from simulation model: array of $L$ peak values, $y_{out}$
  • Figure 2: Estimating the expectation value of $Y_{100}$ as the Q.O.I
  • Figure 3: Fitting the output from the simulation model to a Gumbel distribution.
  • Figure 4: From point predictions to multiple realizations. a) Single prediction and the corresponding generated data. b) Sampling multiple realizations from the GP's predictive distribution. c) Generating data using multiple realizations to estimate the uncertainty in the predicted responses.
  • Figure 5: Generating structural response data from predicted distribution.
  • ...and 3 more figures