<p>Reliability-based robust design optimization (RBRDO) is a powerful tool for achieving optimal, robust, and reliable products. However, most existing approaches focus only on design specification limits at the design stage and are not applicable to products whose performance degrades over time. In addition, the high computational cost of nested double-loop optimization, especially when finite-element (FE) or computer-aided design models are required to evaluate nonlinear performance functions, limits their use in realistic engineering applications. To overcome these challenges, this paper proposes a machine learning-driven time-dependent RBRDO framework. The design problem is reformulated as a time-independent optimization with two objectives and a probabilistic constraint to account for optimality, reliability, and robustness simultaneously. A multilayer perceptron surrogate model is trained on FE data to approximate performance degradation, significantly reducing the computational burden of repeated reliability evaluations. The surrogate is integrated with Monte Carlo Simulation for reliability assessment, and an evolutionary algorithm is employed for optimization. The framework is demonstrated on two widely used nickel-based superalloy springs, Nimonic 90 and alloy X-750, showing its ability to maintain reliability under stress relaxation while drastically reducing computational cost. The results highlight the potential of the proposed method as a general and efficient tool for designing reliable, degradation-resistant components in high-temperature and safety–critical applications.</p>

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Reliability-based robust design considering performance degradation: a machine learning-driven approach for high-temperature helical springs

  • Hossein Hassani,
  • Saeed Khodaygan

摘要

Reliability-based robust design optimization (RBRDO) is a powerful tool for achieving optimal, robust, and reliable products. However, most existing approaches focus only on design specification limits at the design stage and are not applicable to products whose performance degrades over time. In addition, the high computational cost of nested double-loop optimization, especially when finite-element (FE) or computer-aided design models are required to evaluate nonlinear performance functions, limits their use in realistic engineering applications. To overcome these challenges, this paper proposes a machine learning-driven time-dependent RBRDO framework. The design problem is reformulated as a time-independent optimization with two objectives and a probabilistic constraint to account for optimality, reliability, and robustness simultaneously. A multilayer perceptron surrogate model is trained on FE data to approximate performance degradation, significantly reducing the computational burden of repeated reliability evaluations. The surrogate is integrated with Monte Carlo Simulation for reliability assessment, and an evolutionary algorithm is employed for optimization. The framework is demonstrated on two widely used nickel-based superalloy springs, Nimonic 90 and alloy X-750, showing its ability to maintain reliability under stress relaxation while drastically reducing computational cost. The results highlight the potential of the proposed method as a general and efficient tool for designing reliable, degradation-resistant components in high-temperature and safety–critical applications.