Adaptive Ensemble Surrogate Modelling with Local Error Measures for Reliability-Based Design Optimization

  • Vásquez Estepan, Luis José (INSA ROUEN NORMANDIE)
  • Aoues, Younes (INSA ROUEN NORMANDIE)
  • Sánchez Jimenez, Oscar (INSA ROUEN NORMANDIE)
  • Pagnacco, Emmanuel (INSA ROUEN NORMANDIE)

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Structural Optimization frequently aims to find optimal designs of structures while minimizing manufacturing costs and maintaining an adequate safety level. However, structural performances are affected by various sources of uncertainty, including material properties, external loads, and environmental conditions. Reliability-Based Design Optimization (RBDO) provides an effective framework for addressing these uncertainties by enforcing target failure probability constraints in the optimization procedure. A major challenge in RBDO lies in the high computational cost associated with repeated evaluations of mechanical models, typically based on the finite element method, required for failure probability estimation within an optimization loop. To alleviate this computational burden, surrogate models are commonly employed to approximate expensive numerical simulations. Nevertheless, selecting a single surrogate model that is both accurate and robust for a given problem remains difficult, and assessing its predictive accuracy a priori is often unreliable. Ensemble surrogate modelling addresses this issue by combining multiple surrogate models to exploit their complementary strengths, thereby improving prediction robustness. In particular, ensemble approaches based on local error measures are well suited for adaptive surrogate modelling strategies. This paper proposes an RBDO framework that integrates adaptive ensembles of surrogate models guided by local error measures and active learning techniques. The ensemble combines Kriging with machine learning models such as Artificial Neural Networks (ANN) and Support Vector Regression (SVR), while local error estimates are obtained through resampling-based techniques. Failure probabilities are evaluated using Monte Carlo simulation, and their sensitivities with respect to the design variables are computed via an efficient stochastic sensitivity analysis. The proposed approach is validated against benchmark problems from the literature and subsequently applied to a finite element–based structural optimization problem. The results demonstrate that the proposed ensemble approach enhances robustness and accelerates convergence in reliability-based structural optimization by leveraging consensus among the models.