Uncertainty is ubiquitous in engineering design. The past decade has seen a significant growth of research developments in design under uncertainty, and a wide range of applications from designing simple product components to designing complex and emerging engineered systems. While methods like “robust design” and “reliability-based design optimization” have become mature and widely adopted in computational design software, it has become evident that these techniques are mostly limited to handling parametric uncertainty. New methods and strategies for uncertainty characterization, problem formulation, preference elicitation, and risk mitigation are needed for managing many other sources of uncertainty in design such as those associated with modeling and prediction, the design process itself, the product use environment, emergent system behavior, and the changing market.
To address the aforementioned aspects of design under uncertainty, both theoretical and computational challenges need to be overcome. While various approaches exist, some are ad hoc in nature. It is therefore imperative to develop theoretically sound, self-consistent, and computationally efficient methods to support design under uncertainty. With this in mind, we organized this Special Issue to gather the state-of-the-art research in design under uncertainty, which we hope will help identify new research frontiers in this area. Over 60 technical papers were submitted for review to the Special Issue. All papers went through a rigorous peer-review process with quality standards set by the Journal of Mechanical Design. While the three of us served as associate editors for most of these manuscripts, we would like to thank Dr. Jonathan Cagan, Dr. David Gorsich, Dr. Michael Kokkolaras, Dr. Zissimos Mourelatos, Dr. Karthik Ramani, Dr. Olivier de Weck, and Dr. Bernard Yannou for their assistance coordinating the reviews of some of the papers. We are also very grateful to all reviewers who helped review these papers.
This Special Issue collects 14 papers including one technical brief. These papers are organized into four groups based on common themes: (1) New Problem Formulations for Design under Uncertainty, (2) Strategies for Design under Uncertainty, (3) Methods for Uncertainty Characterization, and (4) Methods for Uncertainty Computing. The following summaries provide brief snapshots of these papers and the relationships between them.
New Problem Formulations for Design Under Uncertainty
In design research, the importance of explicitly considering uncertainty in the formulation of design problems is increasingly being recognized. In this Special Issue, four papers focus on advancing the state of the art in such problem formulation under uncertainty. First, Resende et al. introduce a problem formulation for robust optimal product design based on profit maximization at a firm-specified level of risk tolerance. The formulation is based on an α-profit metric, which allows a designer to manage expected profitability versus downside risk due to uncertainty in market share predictions. In the second paper (a technical brief) in this category, Behdad et al. formulate a design and remanufacturing problem in which end-of-life electronic waste issues are explicitly modeled under uncertainty—uncertainty of quantity, timing of arrival, and quality of the returned products. Considering this variability in the stream of returned end-of-life products facilitates the planning for remanufacturing facility materials, equipment and human resource requirements. The last two papers in this category add to the problem formulation the consideration of uncertainty over time—over the lifetime of the system as its state changes, or even over multiple generations of a product platform. First, Agte et al. present an integrated multistate method for the early-phase design of inherently robust systems. The method predicts probabilistic metrics such as reliability and availability through behavioral-Markov analysis methods. Finally, in the last paper in this category, Arendt et al. formulate a problem in which the technologies being considered for the design of a system evolve over time. Before committing to a particular technology, this problem formulation enables the consideration of the long-term, uncertain impact of such a choice.
Strategies for Design Under Uncertainty
A second issue of great significance in design under uncertainty relates to the strategies used for accounting for various uncertainties in design, such as those associated with design process, analysis model, and changing market. In this special issue, three technical papers tackle this challenging problem and propose solutions to advance the state of the art. First, Hamraz et al. address uncertainty that is introduced due to design changes, and propose a new engineering change propagation model based on a function–behavior–structure linkage model represented as a network combined with a change propagation method based on graph theory applied to the network. These models are used to help control and counteract change propagation and ultimately reduce uncertainty (hence risk) during design. The paper by Allaire et al. addresses uncertainty due to model inadequacy. The authors propose a method to incorporate model inadequacy to ensure that complexity due to using low-fidelity models can be accounted for, and to incorporate code uncertainty to ensure that uncertainty associated with inexpensive surrogate models can be accounted for in the design. Uncertainty in this work is directly related to complexity, which is defined as the potential of a system to exhibit unexpected behavior in the quantities that characterize the performance, cost, and other attributes of the system. Finally, Withnage et al. propose a dynamic partial least squares path model for customer-driven product design and development with the goal of receding market uncertainty by formulating specific preference models that reflect market dynamics. The model is presented as a tool to evaluate design alternatives during the concept-screening stage.
Methods for Uncertainty Characterization
Uncertainty characterization and representation are challenging topics in design under uncertainty due to the lack of data and knowledge about the system. In this special issue, three papers address the quantification of model uncertainty, which is often overlooked in model-based or simulation-based design. The first two papers by Arendt et al. are companion papers on quantification of model uncertainty by combining the information from both computer simulations and physical experiments. The first paper by Arendt et al. presents a Bayesian inference framework for quantifying model uncertainty and brings up the challenge in distinguishing between the effects of calibration parameters versus model discrepancy, the so-called identifiability issue. The second paper by Arendt et al. provides a solution to the identifiability issue by using multiple responses that share a mutual dependence on a common set of calibration parameters. Finally, the paper by Drignei et al. offers a different approach from the Bayesian techniques presented in the first two papers by using the statistical techniques (parametric and nonparametric bootstrapping approaches) for model calibration. A combined model-calibration and design-optimization approach in engineering design is also presented.
Methods for Uncertainty Computing
Developing computationally efficient methods for uncertainty propagation and optimization under uncertainty is critical for engineering applications that involve expensive simulations. Four papers address this problem. The paper by Anderson and Mattson illustrates that design-performance outputs under uncertainty are seldom Gaussian for nonlinear functions. They then present an uncertainty-propagation approach based on second-order Taylor series for assessing high-order statistics of performance with minimal additional computational cost. The paper by Lee et al. proposes a novel second-order reliability method (SORM) using noncentral or general chi-squared distribution to improve the accuracy of reliability analysis in existing SORM without sacrificing efficiency. Zhou et al. present a sequential quadratic programing approach to robust design optimization to solve single-objective continuous nonlinear optimization problems with interval uncertainty in parameters and design variables. Finally, the paper by Gogu et al. presents an approach for calculating belief and plausibility measures for propagating epistemic uncertainty under the framework of evidence theory through multidimensional outputs by formulating the problem as a one-dimensional optimization problem.
Although the above contributions collect several important efforts on design under uncertainty in the community, the set is far from complete. In particular, we have not received or accepted any papers that address some of the solicited topics, including theoretical foundations and frameworks for design under uncertainty, multifidelity and surrogate modeling for design under uncertainty, stochastic methods for designing multiscale engineering systems, information systems for supporting design under uncertainty, communication of uncertainty analysis results, and teaching design under uncertainty.
We should also point out that the papers collected do not necessarily provide a unified theoretical view of design under uncertainty. Although most of the papers adopt a probabilistic perspective, a few papers build on nonprobabilistic representations of uncertainty. Given that these different representations are inconsistent with each other, the question is: Which theoretical foundation is “right?” For example, it has been a philosophical debate as to whether interval-based methods or evidence theory provide a rigorous treatment of uncertainty in design. Many believe that the probabilistic methods provide the only rigorous treatment of uncertainty due to the axiomatic consistency between probability theory and decision theory. It is our hope that this Special Issue will stimulate further research and discussion on this topic, thus helping the community make new, rigorous advances in design under uncertainty.
|Wei Chen Northwestern University e-mail: email@example.com||Chris Paredis Georgia Tech e-mail: firstname.lastname@example.org||Irem Y. Tumer Oregon State University e-mail: email@example.com|