Abstract Heterogeneous uncertainties due to model imperfection, lack of training data, and input variations coexist in simulation-based design optimization. In this work, a Bayesian-enhanced meta-model is developed to handle heterogeneous uncertainties concurrently in reliability-based design optimization. To account for model form uncertainty, a Bayesian model inference approach is first employed to calibrate unknown parameters of simulation models. Then a hybrid GP model is constructed based on a set of simulation data and experimental observations to predict the response of the actual physical system. By using Monte Carlo simulation (MCS), the resultant hybrid GP model predictions are utilized to form a Gaussian mixture model (GMM) for propagating heterogeneous uncertainties in system reliability analysis. An aggregative reliability index (ARI) is then defined based on GMM to approximate the probability of failure under heterogeneous uncertainties. The proposed approach is further integrated with the RBDO framework to search for optimal system designs. The effectiveness of the proposed approach is demonstrated through three case studies.

中文翻译：

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使用贝叶斯推理进行基于仿真的设计优化的异构不确定性量化

摘要 在基于仿真的设计优化中，由于模型不完善、缺乏训练数据和输入变化而导致的异构不确定性并存。在这项工作中，开发了贝叶斯增强元模型，以在基于可靠性的设计优化中同时处理异构不确定性。为了解决模型形式的不确定性，首先采用贝叶斯模型推理方法来校准模拟模型的未知参数。然后基于一组仿真数据和实验观察构建混合GP模型，以预测实际物理系统的响应。通过使用蒙特卡罗模拟 (MCS)，所得到的混合 GP 模型预测用于形成高斯混合模型 (GMM)，用于传播系统可靠性分析中的异构不确定性。然后基于 GMM 定义聚合可靠性指数 (ARI)，以近似异构不确定性下的故障概率。所提出的方法进一步与 RBDO 框架集成，以搜索最佳系统设计。通过三个案例研究证明了所提出方法的有效性。