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Data-driven reduced order model and simplicial homology global optimization for reliability analysis and application.

Hongbo Zhao1, Meng Wang1, Xu Chang2

  • 1School of Civil and Architectural Engineering, Shandong University of Technology, Zibo, 255000, People's Republic of China.

Heliyon
|October 24, 2022
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Summary

This study introduces a new reliability analysis framework for geotechnical engineering, combining reduced-order models (ROM) with optimization. The method accurately assesses risks in complex geological conditions, offering an efficient alternative to traditional simulations.

Keywords:
First-order reliability methodGeomechanicsMonte Carlo simulationReduced-order modelUncertainty

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Area of Science:

  • Geotechnical Engineering
  • Reliability Analysis
  • Computational Mechanics

Background:

  • Geotechnical and geological engineering problems often involve complex uncertainties in materials and conditions.
  • Traditional numerical models for reliability analysis can be computationally intensive and time-consuming.
  • Existing methods may struggle with complex, nonlinear, and implicit limit state functions.

Purpose of the Study:

  • To develop a novel framework for reliability analysis that incorporates uncertainties in geomaterials and geological conditions.
  • To combine reduced-order modeling (ROM), reliability analysis, and numerical modeling for enhanced accuracy and efficiency.
  • To provide an effective and accurate method for assessing the reliability of geotechnical and geological engineering systems.

Main Methods:

  • Developed a novel framework integrating reduced-order models (ROM), reliability analysis, and numerical models.
  • Employed the simplicial homology global optimization (SHGO) method based on ROM to determine the reliability index.
  • Verified the developed method using three numerical examples and a simple slope analysis.

Main Results:

  • The limit state curves generated by the ROM method showed excellent agreement with actual curves in all numerical examples.
  • Reliability indices and failure probabilities closely matched results from the first-order reliability method (FORM) and Monte Carlo simulations.
  • The ROM method effectively approximates complex limit state functions, demonstrating feasibility and efficiency.

Conclusions:

  • The developed framework is feasible and effective for reliability analysis in geotechnical and geological engineering, especially for complex problems.
  • The method is efficient and accurate, providing a valuable alternative to time-consuming numerical models in practical engineering.
  • This approach offers an excellent way to approximate limit state functions, improving the practicality of reliability analysis.