Abstract

A recent design paradigm seeks to overcome the challenges associated with broadly exploring a design space requiring computationally expensive model evaluations by formally viewing design as a sequential decision process (SDP). With the SDP, a set of computational models of increasing fidelity are used to sequentially evaluate and systematically eliminate inefficient design alternatives from further consideration. Key to the SDP are concept models that are of lower fidelity than the true function and are constructed in such a way that when used to evaluate a given design, they return two-sided limits that bound the precise value of the decision criteria, hence referred to as bounding models. Efficiency in the SDP is achieved by using such low-fidelity, inexpensive models, early in the design process to eliminate inefficient design alternatives from consideration after which a higher fidelity, more computationally expensive model, is executed, but only on those design alternatives that appear promising. In general, low-fidelity models trade off discriminatory power for computational complexity; however, it can be demonstrated that knowledge of the underlying physics and/or mathematics can be used to increase the discriminatory power of the lower fidelity models for a given computational cost. Increasing the discriminatory power of the bounding models directly translates into an increase in the efficiency of the SDP. This paper discusses and demonstrates how knowledge of the underlying physics and/or mathematics, otherwise referred to as “problem-specific knowledge,” such as monotonicity and concavity can be used to increase the discriminatory power of the bounding models in the context of the SDP and for engineering designs characterized by demand and capacity relationships. Furthermore, the concept of constructing the bounding models to systematically defer decisions on a subset of design variables, for example for a subsystem, is demonstrated, while retaining the desirable convergence guarantees to the optimal set. The utility of leveraging knowledge to increase discriminatory power and systematically deferring decisions through bounding models in the context of the SDP is demonstrated through two design problems: (1) the notional design of an engine-propeller combination to minimize takeoff distance for a light civil aircraft, and (2) the design of a building’s seismic force resisting structural-foundation system where the performance is evaluated on the basis of minimizing drift and total system cost.

中文翻译：

---

将设计视为顺序决策过程时，使用特定于问题的知识来增加边界模型的区分能力

摘要

最近的设计范例试图通过将设计正式视为顺序决策过程（SDP）来克服与广泛探索需要计算量大的模型评估的设计空间相关的挑战。借助SDP，可以使用一组保真度更高的计算模型来顺序评估并系统地消除效率低下的设计选择，以免进一步考虑。SDP的关键是保真度低于真实功能的概念模型，其构造方式使得当用于评估给定设计时，它们返回限制决策标准的精确值的双向限制，因此称为作为边界模型。通过使用此类低保真，廉价的模型，可以实现SDP的效率，在设计过程的早期，从考虑中消除低效的设计替代方案，然后再执行更高保真度，计算成本更高的模型，但仅限于那些看起来很有希望的设计替代方案。通常，低保真模型会在区分能力上权衡计算复杂性。但是，可以证明，对于给定的计算成本，可以使用有关基础物理和/或数学的知识来提高较低保真度模型的判别能力。增加边界模型的区分能力直接转化为SDP效率的提高。本文讨论并演示了有关基础物理和/或数学的知识如何被称为“特定于问题的知识”，“单调性和凹度”可用于在SDP的上下文中以及以需求和容量关系为特征的工程设计中增加边界模型的区分能力。此外，展示了构造边界模型以系统地推迟对设计变量的子集（例如子系统）的决策的概念，同时将理想的收敛性保证保持在最佳集合上。通过两个设计问题证明了利用知识来提高歧视能力并通过SDP范围内的边界模型系统地推迟决策的实用性，它通过以下两个设计问题得到了证明：（1）发动机-螺旋桨组合的概念设计，以最小化轻型民用飞机的起飞距离，