Anatomy of design space exploration

Design space exploration is both a class of quantitative methods and a category of software tools for systematically and automatically exploring very large numbers of design alternatives and identifying those with the most optimal performance parameters. The mathematical techniques that underpin design space exploration have been long known—and sometimes applied, in cases where the attendant costs in expertise, time and labor could be justified. What’s changing now is the way fresh software technologies are at last converting these powerful but formerly difficult-to-use methods into practical everyday engineering aids.

Core capabilities of today’s commercial software suites for design space exploration typically include:

  • Design of experiments (DOE)
  • Multidisciplinary optimization (MDO)
  • Multi-objective or Pareto optimization
  • Stochastic simulations for robustness and reliability optimization
  • Process automation
  • Multi-tool integration

Design of experiments (DOE)—DOE studies are used to predict design sensitivities and/or gain a better understanding of the design space. Their aim is to extract the maximum amount of information quickly with the least computational or experimental effort. In a DOE study, an analysis model is automatically evaluated multiple times, with the design variables set to different values in each iteration. The results identify which variable(s) affect the design the most, and which least. This allows variables that are not important to be ignored subsequently, or set to values that are most convenient or least costly.

DOE study of electronics heat-sink design reveals which design variables have greatest impact on performance
Source: CD-adapco

The results of a DOE sampling process can be used to generate an approximate model of the system being studied, generally called a response surface model (RSM). The RSM is generated by interpolating between the discrete DOE results to create a continuous surface map or model. These models are very convenient for visualizing the design space, examining relationships among variables and their effects on key responses, and rapidly evaluating design alternatives without performing additional expensive CAE evaluations or experiments.

Response surface model
Source: Noesis Solutions

Multidisciplinary optimization (MDO)—Incorporates all relevant disciplines—structural (linear or nonlinear, static or dynamic, bulk materials or composites), fluid, thermal, acoustic, NVH, multibody dynamics, or any combination—simultaneously in an optimization problem. See Optimization fundamentals for more detail; see also Design exploration vs. design optimization.

Multi-objective or Pareto optimization—Identifying the set of tradeoff designs that cannot be improved on according to one design criterion without harming another criterion. See Optimization fundamentals for more detail.

Stochastic simulations—Product designs are nominal, while manufacturing and operating conditions are real-world. Finite geometric tolerances, variations in material properties, uncertainty in loading conditions and other variances encountered by a manufactured product in service can cause it to perform slightly differently from its nominal as-designed values. For this reason, robustness and reliability as design objectives beyond the nominal design are desirable in many cases. Performance of robust and reliable designs is less affected by these expected variations, and remains at or above specified acceptable levels in all conditions.

Robust design
Source: OptiY

To evaluate the robustness and reliability of a design during simulation, its variables and system inputs are made stochastic—that is, defined in terms of both mean value and a statistical distribution function. The resulting system performance characteristics are then measured in terms of a mean value and its variance.

Robustness and reliability optimization
Source: Vanderplaats Research & Development

RobustnessIn robustness-based design optimization, a measure of the robustness of the system or component is used as an optimization constraint or objective. The aim is to obtain not the best performance possible, but the best robust performance possible. Such a design is robust to small design changes, so that if small perturbations of the design parameters happen, the performance of the system or component does not decrease below the desired quality level.

ReliabilityIn reliability-based design optimization, the mean values of the random system parameters are used as design variables, and the cost or objective function is optimized subject to prescribed probabilistic constraints such as probabilities of failure or reliability indexes, through solution of a mathematically nonlinear programming problem. Thus, reliability-based design produces not only an improved design, but also a higher degree of confidence in the design.

Design process layout and corresponding software workflow
Source: Phoenix Integration

Process automation and multi-tool integration—The power of design space exploration is grounded in chained simulation process flows in which parameters and results from one software tool are automatically provided as inputs to another. Beyond eliminating the time and error penalties of manual data extraction and reentry, automating the manipulation and mapping of data between process steps makes it feasible to combine simulation models and applications from multiple disciplines and physical domains into a holistic model of product performance, then automate their execution across a range of values hundreds or thousands of times to explore and map the potential design space.

Isight process flow diagram for optimization of aircraft composite panels
Source: Grupo TAM

Industry veteran Dr. Dennis Nagy tells us that simulation process automation and integration were in fact the original objectives of Engineous Software founder Siu Tong, but the company discovered it needed to add applications such as DOE and optimization to make the software more attractive to buyers. Engineous, founded in 1996, was one of the pioneering developers of design exploration software; Nagy served as CEO some years before its 2008 acquisition by Dassault Systèmes, where its Isight and SEE (formerly FIPER) products are today part of the DS SIMULIA brand.

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For a roundup of commercially available design space exploration software, see Design exploration vs. design optimization.