Designing civil structures such as bridges, dams or buildings is a complex task requiring many synergies from several experts. Each is responsible for different parts of the process. This is often done in a sequential manner, e.g. the structural engineer makes a design under the assumption of certain material properties (e.g. the strength class of the concrete), and then the material engineer optimizes the material with these restrictions. This paper proposes a holistic optimization procedure, which combines the concrete mixture design and structural simulations in a joint, forward workflow that we ultimately seek to invert. In this manner, new mixtures beyond standard ranges can be considered. Any design effort should account for the presence of uncertainties which can be aleatoric or epistemic as when data is used to calibrate physical models or identify models that fill missing links in the workflow. Inverting the causal relations established poses several challenges especially when these involve physics-based models which most often than not do not provide derivatives/sensitivities or when design constraints are present. To this end, we advocate Variational Optimization, with proposed extensions and appropriately chosen heuristics to overcome the aforementioned challenges. The proposed methodology is illustrated using the design of a precast concrete beam with the objective to minimize the global warming potential while satisfying a number of constraints associated with its load-bearing capacity after 28days according to the Eurocode, the demoulding time as computed by a complex nonlinear Finite Element model, and the maximum temperature during the hydration.

翻译：设计桥梁、水坝或建筑物等土木结构是一项复杂任务，需要多位专家的协同配合。每位专家负责流程的不同环节，且通常按顺序进行，例如：结构工程师在假定特定材料属性（如混凝土强度等级）的基础上进行设计，随后材料工程师在此限制条件下优化材料。本文提出了一种整体优化流程，将混凝土配比设计与结构模拟整合至一个联合的正向工作流中，最终目标是实现该流程的逆向求解。通过这种方式，可考虑超出标准范围的新型配比方案。任何设计工作都需考虑不确定性的存在（包括偶然不确定性及认知不确定性），例如当使用数据校准物理模型或识别模型中缺失的关联环节时。逆向求解已建立的因果关联面临诸多挑战，尤其是当涉及基于物理的模型时——这类模型通常无法提供导数/灵敏度，或存在设计约束条件。为此，我们采用变分优化方法，并通过提出的扩展方案及合理选择的启发式策略来克服上述挑战。本文以预制混凝土梁的设计为例验证所提方法，目标是在满足以下约束条件的前提下最小化全球变暖潜能值：①基于欧盟规范的28天承载能力；②由复杂非线性有限元模型计算的脱模时间；③水化过程中的最高温度。