Optimization driven design/Optimeringsdriven design

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PhD project 1: Multilevel and collaborative optimization

Intended supervisor: Prof. Larsgunnar Nilsson, Division of Solid Mechanics, Linköping university

In a large scale industrial product development process many design teams are concurrently developing different parts of the product (system) considering objectives and constraints from different disciplines. It is infeasible to directly integrate all involved multidisciplinary analyses from all different teams into one optimizer. It is more feasible to use a multilevel optimization strategy where subspace optimizations are used for the different parts and different disciplines. In such an optimization procedure different software in heterogeneous computing environments can be used to solve the subspace optimization problems. The decomposition keeps domain-specific constraint information in the subdomain. In addition, this approach leaves most of the design decisions to the disciplinary design teams.

Our approach to solve the complete system optimization is to use a multilevel collaborative optimization technique based on metamodels (surrogate response surfaces) and space-mapping. By using the metamodel concept it is also possible to include variations and uncertainties in selected model parameters, i.e. robustness analysis and robustness optimization are parts of our development. To be more specific, it is our objective to develop a system-level coordination method and to further refine the metamodel concept to enlarge the region of interest in each subdomain.

PhD project 2: Optimization driven design of machine components

Intended supervisor: Assoc. Prof. Niclas Strömberg, School of Engineering, Jönköping university

The development of machine components in automotive industry is an important challenge in order to meet the demands on lighter vehicles for tomorrow. Machine components in engines, gear boxes and brakes are crucial for the performance of a vehicle. These systems must be robust, long-life, efficient, silent and economic and fulfill regulations. Therefore, in the development process, accurate simulations and optimizations of these machine elements are of great interest. In this project we will investigate the possibility to introduce optimization driven design of machine elements following the principle sketch below:

The process is initiated by generating concepts using topology optimization. Objectives and constraints are then evaluated for the concepts by FEA. This is automated by using successive response surface optimization. Finally, a new physical prototype is tested. This process will decrease lead times, decrease the number of physical prototypes and also generate new innovative designs. In particular we will improve methodology for topology optimization of mechanical systems with contact constraints, topology optimization of thermo-mechanical systems as well as response surface optimization of these systems. In the latter different choices of surrogate models will be developed and investigated (e.g. Neural networks, Kriging, radial basis functions and space mapping). We are also most interested in improving methodology for including manufacturing constraints like e.g. residual stresses from solidification of castings.

PhD project 3: Cost, manufacturability and game theory for multi-physics optimization

Intended supervisor: Prof. Anders Klarbring, Division of Mechanics, Linköping university

Multi-objective optimization problems have almost exclusively been treated by the concept of Pareto optimality. There are some well known disadvantages related to such a notion of optimality, the main one being that it generates (after a huge amount of calculations) a so-called Pareto front of solutions and a second decision step has to be performed when deciding on the final design. In some situations when the objectives and the design variables are somewhat separated, as is the case in many multiphysics problems, the notion of game theory is an alternative option which does not share this disadvantage. In particularly, we think of non-cooperative or Nash games, which were applied to a heat transfer – thermoelastic design problem in a pioneering work from Linköping University.

As another example of a design case where Nash equilibrium applies, consider aircraft wing design with respect to both aerodynamic and structural properties: aerodynamic properties are mainly related to one set of design variables - the outer shape of the wing – while structural properties are mainly related the inner frame structure – parameterized by, e.g., topologogical variables.

Yet another natural situation for Nash equilibrium is when different design groups of the same company works on the same product but with somewhat different design goals, an all but too common situation. Seeking an equilibrium solution from the point of view of game theory may be the proper compromise

Cost is always an important factor in product design, but it has, nevertheless, been sparsely studied in structural optimization. As a first approximation for cost one has used weight, but it becomes obvious that this is not good when material selection is introduced as a design criterion. Moreover, the complexity of a structure (how many parts, and so on) will obviously have great impact on manufacturability costs. An important direction of the research in this application is to attempt to include considerations such as these as early as possible in the design process in order to reduce the number of costly redesigns.

Overall plan of intent

We claim that an increased product quality can be achieved and that the mechanical engineering design process can be made significantly more efficient. The optimization driven design process is the next step for industry and the quick adoption of it is a key to increased competitiveness and success.

The engineering process of designing products or systems can roughly be broken down into three distinct phases:

Conceptual design: Basic requirements (functionality) are met and realized in rough choices of topology, geometry and material, as well as a preliminary plan of the manufacturing techniques.

Preliminary design: More precise requirements such as stiffness and strength result in preliminary sizing and material selection (or design).

Detailed design: The final geometry and material selection is based on all criteria considered in previous phases together with additional concerns such as cost of manufacturing, life cycle costs, etc.

Several different concepts may be developed in parallel during the Conceptual and Preliminary design phases, see the figure below. The concept(s) that will be further developed is the concept that best fulfil the overall objectives, requirements and constraints. Topology optimization is taking place in a multi-disciplinary fashion within the design of each concept. Within the Detailed design, optimizations are carried out by different teams, each one considering its special discipline. Overall coordination and global optimization are carried out on a regular basis. Many products are developed as a family of products (platform), and it is important to consider that many components or modules are shared by other family members. The goal of a developed optimization driven design process is to eliminate costly testing, i.e. the virtual product design will be validated on the first serial product.

Decisions in all phases need to be based on models of the product or process. In mechanical engineering these models are most frequently based on Finite Element Analysis (FEA). Moreover, an iterative procedure is required: Design modifications need to be tested virtually (by FEA) or by using prototypes. If, when tested in this way, a design does not satisfy requirements a re-design is needed. The traditional design process can be termed iterative-intuitive: while new designs are analysed at high precision by advanced FEA, the re-design is made manually (intuitively) without computational indications of trends and consequences. In contrast, when using Optimization Driven Design (ODD), the re-designs are found as solutions or outcomes from precisely formulated optimization problems. This makes it possible to find the best re-design within the currently considered requirements. The use of ODD has several consequences, such as the possibility to consider manufacturing and life cycle costs at early design stages.

As evident by several commercial computer systems, the move from intuitive-iterative design to ODD has started: Continuum topology optimization, as found in OptiStruct (Altair), TOSCA (FE-Design), Ansys and Nastran, has shown to be most useful in the conceptual design phase. Multi-objective optimization methods, mostly useful in the detailed design phase, are found in iSIGHT, modeFRONTIER and LS-OPT. However, to fully make ODD into the next generation virtual prototyping both methods and general design procedures need to be further de

Our goal is to develop methods and processes of ODD that are needed to make it widely applicable in Swedish mechanical, automotive and aerospace industry. To do this we have identified a number of critical areas were industrial demonstrators are intended to drive our research efforts. These areas can also be considered as cutting each academic research in structural and multidisciplinary optimization.

With an optimization driven design process we aim at addressing problems in:

Concurrent engineering. Each step of the manufacturing process can be simulated and optimized. The mechanical properties developed during the manufacturing process will be intrinsic to the final model and, thus, represented in the predicted functional response

Multi-stage optimization. Many different tasks are solved by different design teams. Each design team attempt to finds its optimal solution. The optimal properties of the final product will be the result of many successive stages of optimal solutions of substructures or components.

Multi-physics optimization. The optimal solution needs to consider constraints from different fields of physics, e.g. heat conduction, fluid flow, etc

Multi-objective optimization. Classical mathematical optimization requires one objective, but in real life many objectives exist, and these objectives are sometimes contradicting each other. By using Nash game theory or Pareto optimization, we can address some of these problems.

Product family optimization. A common industrial design process involves the design of a family (or platform) of products, where several members of the family may have common components or substructures. Thus, it is impossible to optimize one family member without considering the other members of the family. We are currently developing optimization techniques to address this type of problems.

Below we describe three specific PhD projects that will be part of ProOpt.