AI 中文总结
研究旋节状超材料结构-性能映射，提出基于异方差高斯过程回归的不确定性感知框架，能从稀疏数据推断预测不确定性，应用于可靠性设计优化，揭示刚度散射特性及不同公式表现，强调该建模对可靠性感知逆设计的重要性。
AI 中文摘要
旋节状超材料为各向异性机械性能提供了广阔的可调设计空间，但其结构-性能关系通常被视为从锥角描述符到单一有效刚度值的代表性映射。这种确定性观点忽略了基于高斯随机场（GRF）拓扑生成的随机性，相同的锥角描述符可能产生不同的形态实现和性能散射。本文提出了一个不确定性感知结构-性能映射框架，将锥角描述符重新解释为与输入相关的性能分布的随机描述符。使用异方差高斯过程回归（GPR），该框架从每个点仅有一个实现的稀疏数据中推断出与输入相关的预测不确定性，而无需在每个设计点都有经验方差标签。结果表明，刚度散射根据张量分量的机械活动方向而有所不同，并且产生相同平均刚度的参数集可能具有不同的偶然不确定性。将这种不确定性应用于基于可靠性的设计优化（RBDO），结果表明，一旦考虑形态诱导的变异性，确定性最优解极易违反约束，并且同方差RBDO公式无法满足规定的可靠性目标——只有异方差公式在异方差不确定性评估下满足可靠性目标。这表明不确定性感知代理建模对于旋节状超材料的可靠性感知逆设计至关重要；将该框架扩展到非线性响应仍有待未来研究。
英文摘要
Spinodoid metamaterials offer a broad, tunable design space for anisotropic mechanical properties, yet their structure-property relationships are commonly treated as representative mappings from cone-angle descriptors to single effective stiffness values. This deterministic view overlooks the stochastic nature of Gaussian random field (GRF)-based topology generation, where identical cone-angle descriptors can produce different morphology realizations and property scatter. Here, we present an uncertainty-aware structure-property mapping framework that reinterprets cone-angle descriptors as stochastic descriptors associated with input-dependent property distributions. Using heteroscedastic Gaussian process regression (GPR), the framework infers input-dependent predictive uncertainty from sparse one-realization-per-point data without requiring empirical variance labels at every design point. The results show that stiffness scatter differs across tensor components according to each component's mechanically active directions, and that parameter sets yielding identical mean stiffness can carry different aleatoric uncertainty. Applying this uncertainty to reliability-based design optimization (RBDO), we show that a deterministic optimum is highly susceptible to constraint violation once morphology-induced variability is considered, and that a homoscedastic RBDO formulation fails to meet the prescribed reliability target - only the heteroscedastic formulation satisfies the reliability target under the heteroscedastic uncertainty evaluation. This establishes uncertainty-aware surrogate modeling as essential for reliability-aware inverse design of spinodoid metamaterials; extending the framework to nonlinear responses remains for future work.
Comments52 pages, 13 figures
