Uncertainty quantification (UQ) within topology optimization (TO) is a growing trend, with designers recognizing that deterministic analysis does not reflect the natural variabilities found in real-world structural performance. Thus far the majority of works have dealt with uncertain loading and material properties; however, minimal research has considered uncertain boundary conditions (BCs), which play a vital role for static and dynamic analysis involving compliance and natural frequency objectives and/or constraints. BCs uncertainty is studied in this paper by assuming a random percentage of a cantilever can be freed to rotate and/or translate in space. This is firstly demonstrated through a case study on a flat plate wing where the frequency gap between two modes is maximized, and secondly through optimizing the wing of a sensorcraft where compliance is minimized. A robust objective is formulated via a weighted sum of the mean and standard deviation, which is approximated efficiently using a Non-Intrusive Polynomial Chaos Expansion (NIPC). Both studies demonstrate the pitfalls of a deterministic optimum in dealing with uncertain BCs, and how using Robust TO (RTO) can effectively reduce the variance and worst-case performance of the objective. Experimental validation for the flat plate wing is also undertaken to ensure practical feasibility of the RTO topologies and to provide motivation to study BCs uncertainty further.

拓扑优化（TO）中的不确定性量化（UQ）是一个不断发展的趋势，设计人员意识到确定性分析不能反映实际结构性能中的自然变化。到目前为止，大多数工作都涉及不确定的载荷和材料特性。然而，极少的研究考虑了不确定的边界条件（BCs），这对于涉及顺应性和固有频率目标和/或约束的静态和动态分析起着至关重要的作用。通过假设随机百分比的悬臂可以在空间中自由旋转和/或平移，对BC的不确定性进行了研究。首先通过在平板机翼上的案例研究证明了这一点，在该机翼上，两种模式之间的频率间隙最大，其次是通过优化顺应性最小的传感器飞行器的机翼。通过均值和标准差的加权总和来制定鲁棒的目标，使用非侵入式多项式混沌扩展（NIPC）可以有效地近似该目标。两项研究均表明，在处理不确定的BC时，确定性最优方案存在陷阱，以及使用稳健TO（RTO）如何有效地减少物镜的方差和最坏情况的性能。还对平板机翼进行了实验验证，以确保RTO拓扑的实际可行性，并为进一步研究BC的不确定性提供了动力。两项研究均表明，在处理不确定的BC时，确定性最佳方案存在陷阱，以及如何使用稳健的TO（RTO）可以有效减少目标的方差和最坏情况的性能。还对平板机翼进行了实验验证，以确保RTO拓扑的实际可行性，并为进一步研究BC的不确定性提供了动力。两项研究均表明，在处理不确定的BC时，确定性最佳方案存在陷阱，以及如何使用稳健的TO（RTO）可以有效减少目标的方差和最坏情况的性能。还对平板机翼进行了实验验证，以确保RTO拓扑的实际可行性，并为进一步研究BC的不确定性提供了动力。