Maximizing Flexibility for Complex Systems Design to Compensate Lack-of-Knowledge Uncertainty

Abstract The consideration of uncertainty is especially important for the design of complex systems. Because of high complexity, the total system is normally divided into subsystems, which are treated in a hierarchical and ideally independent manner. In recent publications, e.g., (Zimmermann, M., and von Hoessle, J. E., 2013, “Computing Solution Spaces for Robust Design,” Int. J. Numer. Methods Eng., 94(3), pp. 290–307; Fender, J., Duddeck, F., and Zimmermann, M., 2017, “Direct Computation of Solution Spaces,” Struct. Multidiscip. Optim., 55(5), pp. 1787–1796), a decoupling strategy is realized via first the identification of the complete solution space (solutions not violating any design constraints) and second via derivation of a subset, a so-called box-shaped solution space, which allows for decoupling and therefore independent development of subsystems. By analyzing types of uncertainties occurring in early design stages, it becomes clear that especially lack-of-knowledge uncertainty dominates. Often, there is missing knowledge about overall manufacturing tolerances like limitations in production or subsystems are not even completely defined. Furthermore, flexibility is required to handle new requirements and shifting preferences concerning single subsystems arising later in the development. Hence, a set-based approach using intervals for design variables (i.e., interaction quantities between subsystems and the total system) is useful. Because in the published approaches, no uncertainty consideration was taken into account for the computation of these intervals, they can possibly have inappropriate size, i.e., being too narrow. The work presented here proposes to include these uncertainties related to design variables. This allows now to consider lack-of-knowledge uncertainty specific for early phase developments in the framework of complex systems design. An example taken from a standard crash load case (frontal impact against a rigid wall) illustrates the proposed methodology.

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A decoupled design approach for complex systems under lack-of-knowledge uncertainty

International Journal of Approximate Reasoning ◽

10.1016/j.ijar.2020.01.006 ◽

2020 ◽

Vol 119 ◽

pp. 408-420

Author(s):

Marco Daub ◽

Fabian Duddeck

Keyword(s):

Complex Systems ◽

Design Approach ◽

Knowledge Uncertainty ◽

Lack Of Knowledge

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On the Optimal Decomposition of High-Dimensional Solution Spaces of Complex Systems

ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg ◽

10.1115/1.4037485 ◽

2017 ◽

Vol 4 (2) ◽

Cited By ~ 3

Author(s):

Stefan Erschen ◽

Fabian Duddeck ◽

Matthias Gerdts ◽

Markus Zimmermann

Keyword(s):

Complete Solution ◽

Cartesian Product ◽

Solution Space ◽

Linear Functions ◽

High Dimensional ◽

Development Work ◽

Interior Point Algorithm ◽

Dimensional Solution ◽

Design Work ◽

Design Variables

In the early development phase of complex technical systems, uncertainties caused by unknown design restrictions must be considered. In order to avoid premature design decisions, sets of good designs, i.e., designs which satisfy all design goals, are sought rather than one optimal design that may later turn out to be infeasible. A set of good designs is called a solution space and serves as target region for design variables, including those that quantify properties of components or subsystems. Often, the solution space is approximated, e.g., to enable independent development work. Algorithms that approximate the solution space as high-dimensional boxes are available, in which edges represent permissible intervals for single design variables. The box size is maximized to provide large target regions and facilitate design work. As a result of geometrical mismatch, however, boxes typically capture only a small portion of the complete solution space. To reduce this loss of solution space while still enabling independent development work, this paper presents a new approach that optimizes a set of permissible two-dimensional (2D) regions for pairs of design variables, so-called 2D-spaces. Each 2D-space is confined by polygons. The Cartesian product of all 2D-spaces forms a solution space for all design variables. An optimization problem is formulated that maximizes the size of the solution space, and is solved using an interior-point algorithm. The approach is applicable to arbitrary systems with performance measures that can be expressed or approximated as linear functions of their design variables. Its effectiveness is demonstrated in a chassis design problem.

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Modeling multidisciplinary design with multiagent learning

Artificial intelligence for engineering design analysis and manufacturing ◽

10.1017/s0890060418000161 ◽

2018 ◽

Vol 33 (1) ◽

pp. 85-99 ◽

Cited By ~ 2

Author(s):

Daniel Hulse ◽

Kagan Tumer ◽

Christopher Hoyle ◽

Irem Tumer

Keyword(s):

Complex Systems ◽

Multiagent System ◽

Systems Design ◽

Organizational Outcomes ◽

Learning System ◽

Multidisciplinary Teams ◽

Design Teams ◽

Multiagent Learning ◽

Complex Engineered Systems ◽

Design Variables

AbstractComplex engineered systems design is a collaborative activity. To design a system, experts from the relevant disciplines must work together to create the best overall system from their individual components. This situation is analogous to a multiagent system in which agents solve individual parts of a larger problem in a coordinated way. Current multiagent models of design teams, however, do not capture this distributed aspect of design teams – instead either representing designers as agents which control all variables, measuring organizational outcomes instead of design outcomes, or representing different aspects of distributed design, such as negotiation. This paper presents a new model which captures the distributed nature of complex systems design by decomposing the ability to control design variables to individual computational designers acting on a problem with shared constraints. These designers are represented as a multiagent learning system which is shown to perform similarly to a centralized optimization algorithm on the same domain. When used as a model, this multiagent system is shown to perform better when the level of designer exploration is not decayed but is instead controlled based on the increase of design knowledge, suggesting that designers in multidisciplinary teams should not simply reduce the scope of design exploration over time, but should adapt based on changes in their collective knowledge of the design space. This multiagent system is further shown to produce better-performing designs when computational designers design collaboratively as opposed to independently, confirming the importance of collaboration in complex systems design.

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A Distributed Pool Architecture for Highly Constrained Optimization Problems in Complex Systems Design

Volume 9: 23rd International Conference on Design Theory and Methodology; 16th Design for Manufacturing and the Life Cycle Conference ◽

10.1115/detc2011-48620 ◽

2011 ◽

Author(s):

Vijitashwa Pandey ◽

Zissimos P. Mourelatos

Keyword(s):

Complex Systems ◽

Optimization Problems ◽

Mechanical Design ◽

Systems Design ◽

Optimization Approach ◽

Dynamic Changes ◽

Design Problems ◽

Complete Knowledge ◽

Design Variables ◽

Design Requirements

The design of complex systems design is challenging because of the presence of numerous design variables and constraints. Dynamic changes in design requirements and lack of complete knowledge of subsystem requirements add to the complexity. A recently proposed pool architecture has been shown to aide distributed solving of optimization problems. The approach not only saves solution time but also has other benefits like resiliency against failures of some processors. We apply this approach in this paper, to highly constrained design problems, with dynamically changing constraints, where finding a feasible solution is challenging. This task is distributed between the processors in the methodology we propose. We demonstrate the efficacy of our method using an MINLP-class of mechanical design optimization problem. We demonstrate the computational savings and the resistance to partial failures in the processors. In addition, we show how the optimization approach can adapt to dynamic changes in design constraints.

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Approximating solution spaces as a product of polygons

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-021-02979-z ◽

2021 ◽

Author(s):

Helmut Harbrecht ◽

Dennis Tröndle ◽

Markus Zimmermann

Keyword(s):

Design Space ◽

Complete Solution ◽

Cartesian Product ◽

Solution Space ◽

Monte Carlo Sampling ◽

High Dimensional ◽

Two Dimensional ◽

Design Work ◽

Design Variables ◽

Linear Problems

AbstractSolution spaces are regions of good designs in a potentially high-dimensional design space. Good designs satisfy by definition all requirements that are imposed on them as mathematical constraints. In previous work, the complete solution space was approximated by a hyper-rectangle, i.e., the Cartesian product of permissible intervals for design variables. These intervals serve as independent target regions for distributed and separated design work. For a better approximation, i.e., a larger resulting solution space, this article proposes to compute the Cartesian product of two-dimensional regions, so-called 2d-spaces, that are enclosed by polygons. 2d-spaces serve as target regions for pairs of variables and are independent of other 2d-spaces. A numerical algorithm for non-linear problems is presented that is based on iterative Monte Carlo sampling.

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Value-Driven Modeling of Tactical and Operational Decisions in Support of Aerospace Product-Service Systems Design

Volume 2B: 41st Design Automation Conference ◽

10.1115/detc2015-46965 ◽

2015 ◽

Cited By ~ 1

Author(s):

Cassio D. Goncalves ◽

Michael Kokkolaras

Keyword(s):

Quality Function Deployment ◽

Systems Design ◽

Service Systems ◽

Business Strategies ◽

Functional Requirements ◽

Operational Decisions ◽

Design Engineers ◽

Design Variables ◽

Product Service ◽

Product Service Systems

Competitive markets and complex business-to-business environments compel manufacturers to provide innovative service offerings along with their products. This necessitates effective methodologires for developing and implementing sucessful new business strategies. This article presents an approach to model tactical and operational decisions to support the design and development of Product-Service Systems (PSSs). A combination of Quality Function Deployment and Design-to-Cost techniques is proposed as the first step of a PSS design framework that aids design engineers to determine the relations among value to customer, functional requirements, design variables and cost. The objective is to identify PSS design alternatives that deliver value to customer while respecting cost targets. An aerospace software case study is conducted to demonstrate the proposed approach.

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