Advances in Explicit Design Space Decomposition for Computational Design

该奖项的研究目标是为复杂系统的计算设计开发一种新的范例。这项研究将帮助工程师找到最优的设计方案，将性能目标最小化，同时满足不确定性存在下的要求。这可以通过明确定义与特定系统行为相对应的设计空间区域的边界来实现。这种使用支持向量机实现的显式设计空间分解（EDSD）已被证明是有前途的，特别是对于不连续或二元问题以及涉及昂贵的计算机模拟的问题。该研究通过三个主要途径扩展了EDSD方法。首先，将开发一个多保真度方案，使设计师能够利用来自各种来源的丰富信息（分析模型，工程师经验，模拟和物理实验）。通过自适应采样，多保真度方法可以大大减少对昂贵的计算机模拟的调用次数。其次，新方法将量化显式边界的不准确性，并将此信息纳入故障概率的评估中。最后，本工作提出将EDSD方法与基于响应近似（如Kriging）的现有方法统一起来。如果成功，这些方法将导致更灵活的计算设计框架，特别是对于复杂的系统。事实上，EDSD和提出的进展能够处理具有非光滑行为的问题，减少计算时间，传播不确定性，并结合大量不同的信息源。相关的好处，如成本最小化、设计周期缩短和可靠性提高，将为公司提供竞争优势。这些技术适用于许多工程学科，在使用临床数据和计算模型（例如髋部骨折预测）的生物医学领域尤其有用。这些方法将通过桑迪亚国家实验室的自由DAKOTA软件包的实现，传播到工程和研究社区。

The research objective of this award is to develop a new paradigm for the computational design of complex systems. This research will aid engineers to find optimal design solutions that will minimize performance objectives while satisfying requirements under the presence of uncertainties. This is made possible by defining explicitly the boundaries of the regions of the design space corresponding to specific system behaviors. This Explicit Design Space Decomposition (EDSD), which is achieved using support vector machines, has been shown to be promising and particularly useful for problems that are discontinuous or binary and involve costly computer simulations. The research extends the EDSD approach following three main avenues. First, a multifidelity scheme will be developed that will enable the designers to exploit the wealth of information coming from various sources (analytical models, engineer experience, simulations, and physical experiments). Through adaptive sampling, the multifidelity approach can lead to a drastic reduction in the number of calls to expensive computer simulations. Second, the new approach will quantify the inaccuracy of the explicit boundaries and incorporate this information in the assessment of probabilities of failure. Finally, this work proposes to unify the EDSD approach with existing approaches based on response approximations such as Kriging.If successful, these methods will lead to a more flexible computational design framework, particularly for complex systems. In fact, EDSD and the proposed advances are able to handle problems with non-smooth behaviors, reduce computational time, propagate uncertainties, and combine vastly different sources of information. The associated benefits such as cost minimization, design cycle time reduction, and improved reliability, will provide a competitive advantage to companies. The techniques are applicable to many engineering disciplines and are particularly useful in the biomedical field where both clinical data and computational models are used (e.g., for hip fracture prediction). The methods will be disseminated to the engineering and research community through their implementation in the free DAKOTA software package from Sandia National Laboratory.