Parametric vs. non-parametric optimization

Parametric shape optimization “searches the space spanned by the design variables to minimize or maximize some externally defined objective function” (Jiaqin Chen, Vadim Shapiro, Krishnan Suresh and Igor Tsukanov, Spatial Automation Laboratory, University of Wisconsin–Madison, “Parametric and Topological Control in Shape Optimization,” Proceedings of ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference). “In other words, parametric shape optimization is essentially a sizing problem that is a natural extension of parametric computer-aided design.

“The downside of parametric shapes is that they do not provide any explicit information about the geometry or topology of the shape’s boundaries. This, in turn, leads to at least two widely acknowledged difficulties: boundary evaluation may fail, and topological changes in the boundaries may invalidate boundary conditions or the solution procedure.”

Non-parametric optimization, by contrast, operates at the node/element level to derive an optimal structure. It can offer greater design freedom, and can make use of existing CAE models without the need for parameterization. “The main advantage of non-parametric shape optimization is the ease of setup, avoiding tedious parameterization that may be too restrictive with respect to design freedom” (Michael Böhm and Peter Clausen, FE-DESIGN GmbH, “Non-Parametric Shape Optimization in Industrial Context,” PICOF (Problèmes Inverses, Contrôle et Optimisation de Formes) ’12). “One of the major disadvantages on the other hand is that the CAD interpretation of the shape optimization result is not trivial.”

Non-parametric optimization made some news when Dassault Systèmes last year acquired FE-DESIGN, developer of the respected TOSCA Fluid software for topology optimization of channel flow problems and TOSCA Structure for topology, shape and bead optimization of structures. Remarking on the move during Dassault Systèmes’ quarterly earnings call April 25, 2013, CEO Bernard Charlès said, “In our opinion [FE-DESIGN] is the technology leader for non-parametric optimization [and is] complementary to our parametric optimization capabilities”—the size, parametric shape and geometric parameter optimization of DS SIMULIA’s Isight.

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Shape optimization of a connecting rod with TOSCA Structure
Source: DS SIMULIA & Ford Werke AG

In a subsequent call for North American investors the same day, Charlès sought to underscore how pervasive are technological acumen and discernment throughout the DS organization by playfully calling not on a technology executive but instead on the company’s chief financial officer, Thibault de Tersant, for color on the technical rationale. “Now, a very techie acquisition,” said Charlès. “And because, believe it or not, Thibault was the one who convinced me we should acquire this very scientific acquisition, I will let him comment to you why we bought this company.”

de Tersant was more than game. “Okay, why not! So the interest of non-parametric optimization is the topic here. Optimization—design optimization—is about designing for a certain targeted robustness of the product such that you can optimize your design and remove material until you have removed all material necessary for the targeted robustness of the car’s chassis, or whatever part you are doing.

“You have two methods to do that. One is parametric optimization; the other one is non-parametric optimization. And, believe it or not, the words here are confusing because the one which is more automated is the non-parametric optimization method, and [the other] one, the opposite. So this is the interest of this acquisition—it’s frankly the best technology for non-parametric optimization. And this does drive a lot of savings in time in order to run this optimization process.”

Charlès termed the FE-DESIGN deal “a very interesting acquisition with a company we already have an OEM relationship with, as we embedded some of their technology in SIMULIA,” specifically ATOM (Abaqus Topology Optimization Module), based on a subset of TOSCA Structure. FE-DESIGN became part of DS SIMULIA when the transaction closed April 23, 2013. Terms were not disclosed; DS reported FE-DESIGN had 50 employees and more than 200 customers at the time of acquisition.

Future posts will examine more of the techniques and algorithmic methods used in optimization software.

Challenge of multifidelity, multiphysics modeling

In conceptual and preliminary design, many aspects of mechanical products are most efficiently modeled for simulation using 0D/1D/rigid entities. In vehicle drivelines, for example, these include beams, bushings, bearings, point masses and the like. Combining these models with other product components best represented by 2D/3D CAE models can yield systems models that are highly revealing in design exploration activities such as parameter studies, design of experiments and optimization runs. But bringing multiple levels of fidelity together in a single model has conventionally been a labor-intensive manual process, severely limiting the number of design variants able to be studied this way when not precluding the practice altogether.

While mainstream CAE vendors are beginning to progress on this front, breakthrough technologies addressing the problem are available today that work with the industry’s leading solvers. Continue reading

From PIDO to design space exploration

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Design space exploration as an engineering formalism originated in the embedded-systems industry as a set of methodologies for hardware/software co-design, configuration of software product lines, and real-time software synthesis. “The set of all possible design alternatives for a system is referred to as a design-space, and design-space exploration (DSE) is the systematic exploration of the elements in a design-space” (Saxena and Karsai, “Towards a Generic Design Space Exploration Framework,” Proceedings of 2010 IEEE 10th International Conference on Computer and Information Technology).

In mechanical engineering, design space exploration is rooted in the technological domain often referred to as process integration and design optimization, or PIDO, first identified and defined (Jenkins, Daratech, 2001) as software and methods to help:

  • Automate and manage the setup and execution of digital simulation and analysis;
  • Integrate/coordinate analysis results from multiple disciplines and domains to produce a more holistic model of product performance; and
  • Optimize one or more aspects of a design by iterating analyses across a range of parameter values toward specified target conditions.

Continue reading

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. Continue reading

Optimization fundamentals

Design optimization is the search for a structural design that is optimal in one or more respects. In all the various methods available for optimization, the design is guided to satisfy operating limits imposed on the response of the structure, and by further limits on the values that the structural parameters can assume. The power of numerical optimization is its ability to rationally and rapidly search through alternatives for the best possible design(s). Continue reading

Design exploration vs. design optimization

Automating the search for solutions to engineering problems can take either of two broad approaches: design exploration or design optimization. Practitioners making technology choices need to understand which tools do one, which do the other, and which approach best fits their needs. Continue reading