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Automatic concept model generation for
Advances in Engineering Software Article in Press, Corrected Proof
Automatic concept model generation for optimization and robust design of passenger cars
J. Hilmanna,, M. Paasb, A. Haenschkeb and T. VietoraFord Werke GmbH – Cologne, Pre Program and Concept Engineering, ML/PPC1, D-50725 Cologne, GermanybFord Werke GmbH – Cologne, Body Core Engineering – Safety, ME2/J2, D-50725 Cologne, Germany Received 23 June 2005; accepted 14 August 2006. Available online 31 January 2007. Abstract
A fully automated method of structural optimization for the body in white structure is presented. The body in white is a technical term for the car body without windows and closures. The iterations in the optimization loop comprise the following steps: fully parameterized design creation, automated meshing and model assembly, parallel computation and evaluation. For this purpose several free and commercially available software applications were combined, including: SFE concept, Hyper mesh, Perl, Matlab, and Radioss. The optimisation was conducted using Genetic Algorithms (GA), which are ideally suited to solve problems with solution spaces that are too large to be exhaustively searched. The viability of the method is demonstrated for a vehicle component model of a front bumper system utilizing both material and geometry related properties as design variables.
Keywords: Vehicle engineering; Structural optimisation; SFE concept; Genetic algorithms; Finite element method; Parametric modelling; Sensitivity analysis Article Outline
1. Introduction
2. Tools and methods
2.1. Finite element model generation
2.2. Simulation processing
2.3. Evaluation
2.4. Genetic algorithms
3. Structural optimisation of demonstrator model
3.1. Fitness function
3.2. Sensitivity analysis
3.3. Optimisation results
4. Discussion and conclusions
References
1. Introduction
Passenger car development is a multi-disciplinary task. The vehicle has to fulfil demands out of different attributes like safety, dynamics, statics, NVH (Noise, Vibration, and Harshness). For these attributes various numerical tools are established. The importance of these tools is continuously increasing due to shortening of product cycle times and competitive pressure. Because of the massive reduction of physical prototypes the development process is guided by numerical methods. A huge amount of work and time for model generation is required. Furthermore, the attributes are highly sensitive against variation of design parameters, like material grades, material gauges, assembly processes and spot weld properties.
Research efforts in the field of vehicle engineering are focussing on proper deployment of numerical optimization techniques, involving parameter, shape and topology optimisation [1], [2], [3], [4] and [5]. Here finite element models are adopted for generating modified meshes based on scaling and/or morphing algorithms. Stochastic simulation in combination with non-linear optimisation to support vehicle design process is addressed in [1], [2] and [3].
For the next years the optimisation tasks will be extended to the following activities: shape and topology optimisation with arbitrary geometrical adaptations, and multi-disciplinary optimisation (for different vehicle attributes [1], [2], [3] and [4]).
Topology optimisation, which is based on capturing the design space in volume elements, may produce infeasible solutions for sheet metal parts as used in typical body in white structures.
In [6] the idea to combine parametric SFE/Concept models with optimisation tools was discussed as prospect for future work.
In this paper a method for automated model generation is discussed, which allows for effective model generation in automotive engineering applications. In conjunction with model generation an optimisation procedure is adopted, which is capable of structural optimisation, involving both material and geometry related properties. In addition, the system is capable of conducting robustness and sensitivity analyses.
Key in the above mentioned approach is the automated creation of complex finite element models based on a parametric design as provided by the batch mode of SFE concept [7], which is prerequisite for the extension to multi-disciplinary optimisation of full scale vehicle models [11] and [12]. The optimisation process is based on genetic algorithms, which apply the principle of survival of the fittest to produce optimal solutions to problems.
In Chapter 2 of this paper, the toolset and methods for model creation, assembly, computation, evaluation and optimization are discussed. A finite element model of a bumper/crash box/side rail system is presented. In Chapter 3, plastic side rail deformation of this system is minimized. Finally, in Chapter 4 conclusions are drawn and future work is discussed.
2. Tools and methods
Pre-requisite for a structural shape and topology optimisation is the ability to automatically generate calculation models based on various designs. A schematic process chain is shown in Fig. 1. The left hand side statements in Fig. 1 list the subsequent tasks for each generation (iteration), the right hand side displays the process flow. In the optimisation process several free and commercially available software products are utilized. Major component in the simulation loop is SFE concept which is a parametric tool supporting fast geometry modelling for body in whites combined with a powerful auto meshing functionality [7].
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Fig. 1. Process flow of structural optimisation method.
The result is a high-quality finite element mesh as shown in Fig. 2. Flange and connectivity information as spot welds are included as well. In order to assess safety attribute performance, it is required to add boundary and initial conditions, contacts, and material properties. Although the process chain presented is focussing on safety, it can be rephrased to other applications.
Fig. 2. SFE concept model (left) and automatically generated mesh (right).
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2.1. Finite element model generation
In order to demonstrate the viability of the process flow and to limit simulation times a component model was created as demonstrator. The model comprises two crash cans, the bumper beam and parts of the side rails, as shown in Fig. 3. The side rails are split behind the engine mounts and are part of the original finite element base model; the bumper beam and the crash boxes are part of the SFE concept geometrical model. The overall masses and moments of inertia of the vehicle are represented by a rigid body formulation. The optimisation task is limited to the bumper/crash box sub system. Fig. 4 shows design variables of the bumper beam/crash box system. The design vector includes: material gauge and grade, cross-section dimensions geometrical dimensions as trigger or closing plate positions. In the SFE concept model creation process it is important to comply with package limitations as ramp angles or opening areas for the cooling pack. As mentioned previously, the bumper beam/crash box parts of the optimisation example are totally parametric geometry created with the SFE concept design tool.
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Fig. 3. Finite element model for optimization, side rails, crash boxes and bumper beam.
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Fig. 4. Design variables of bumper beam/crash box example.
The geometry is updated for each member of the optimisation generation and is translated to new finite element meshes for the bumper/crash can system. Then, the new finite element meshes are combined with the existing side rail elements to form new designs for all optimisation loops.
2.2. Simulation processing
The simulations are distributed to multiple workstations. This parallel calculation method uses one workstation as master for the model preparation and control functions. On a set of workstations a program called “worker” is started. That worker looks up whether the master initiated a task in a queued folder, which will then be marked as running and the worker starts to calculate the model. If finished the task is put into a finished folder. This approach is very suited for combination with genetic algorithm optimization, which will be discussed in Section 2.4. It basically enables us to reduce the calculation time for one generation (iteration) to the calculation time of one member. Thus is reducing the turn around times dramatically. After having calculated all members, the master starts the evaluation of all members and the optimisation interface is tasked. A brief overview of the pros and cons of the computing alternatives is given in Table 1. It is noted that the assessment is based on the company specific infrastructure.
Table 1.
Comparison of calculation alternatives
Parallel/sequential process Sequential single workstation
Multi-workstation Sequential
Multi-workstation
Dedicated Linux cluster
Cray super-computers
Parallel/non-parallel computing Non-parallel Non-parallel Parallel Parallel Parallel Parallel
Calculation time Hours/generation 8 member/generation 15 2 7 1 1 if no jam 1 if no jam
Process robustness +++ ++ O − +++ +++
Demand for workstations Process 1 1 1 1 1
Total 8 3 24
For calculation 1 workstation per calculation 3 workstations per calculation 8*(3 workstations per calculation) 12*(6 CPUs per calculation) 12*(6 CPUs per calculation)
Implementation Done Done Tested but not preferred Not implemented not planned Implemented for large models Tested but not preferred
Cost for CPU time + + + + O −
Comment Positive Very robust easy implementation no costs Good robustness good calculation power no costs Better calculation power no costs Good calculation power no costs Highest performance Robust process High performance Robust process
Negative Low calculation power Calculation power limited to component models Non dedicated cluster not robust enough Huge amount of WS required Hardware cost are calculated based on used CPU time CPU time expensive
2.3. Evaluation
The evaluation of crash results is realized with Ford standard software Envision and TH++, both applications support macro scripts for automated model evaluation.
So far, only plastic strains in side rails, resistant wall forces and bumper system weight are stored (in ASCII format). The evaluation tools can be customized and additional outputs can be extracted for improved system knowledge.
2.4. Genetic algorithms
Genetic algorithms (GA) are stochastic iterative search methods that mimic natural biological evolution [13] and [14]. GAs have been applied successfully to numerous problems from different domains, including optimisation, machine learning, operations research, social systems etc. GAs operate on a population of potential solutions applying the principle of survival of the fittest to obtain best solutions. For each generation, its members representing feasible solutions in the search space, are encoded and evaluated according to some predefined quality criterion, referred to as fitness. Genetic algorithms are capable of solving difficult problems with objective functions that do not possess continuity and differentiability. GAs work in many situations because solutions with above-average fitness receive exponentially increasing trials in subsequent generations. The population members or chromosomes should contain information about the solution that is represented. A number of coding schemes exist, such as binary coding and real value coding. In what follows the real value coded GAs have been adopted, since these generally converge more rapidly and are more efficient, because there is no need for encoding and decoding.
The basic GA algorithm is outlined below:
(1) [Start] Generate initial population of random chromosomes (population members) representing suitable solutions to the problem.
(2) [Fitness] Evaluate the fitness f(x) of each chromosome (member) x in the population.
(3) [New population] Generate a new population based on the following steps:
(a) [Selection] With probabilities proportional to their fitness, parent chromosomes of the population are selected.
(b) [Crossover] Based on crossover probability parents exchange genetic material (bits in chromosomes). This produces two new chromosomes, called offspring or children, which replace the parents.
(c) [Mutation] Randomly chosen bits in the offspring chromosomes are flipped based on mutation probability.
(d) [Accepting] Place new offspring in the new population.
(4) [Replace] Use new population for next step.
(5) [Test] The algorithm repeats for some specified number of additional generations or until a convergence criterion is reached, such as no significant further increase in the average population fitness. If the termination condition is satisfied, stop, and return the best solution in current population.
(6) [Loop] Go to step 2.
Key parameters of GA involve crossover probability, mutation probability, and population size.
Crossover probability denotes how often crossover will be performed. If crossover probability is 100%, then all offspring are made by crossover. If it is 0%, a next generation is made from exact copies of chromosomes from the old population. Typically, crossover probability should be high (larger than 50%).
Mutation probability: denotes how often parts of chromosomes will be mutated. If mutation probability is 100%, the whole chromosome is changed, if it is 0%, nothing is changed. Mutation generally prevents the GA from falling into local extremes. Mutation rate should be low generally (typically less than 5%).
Population size: denotes how many chromosomes are in population. If there are too few chromosomes, GAs have few possibilities to perform crossover and only a small part of search space is explored. On the other hand, if there are too many chromosomes, GA slows down. In the current example the population size was set to eight members.
Advantages of using GAs
• Ideally suited for problems with solution spaces that are too large to be extensively searched.
• No limitations regarding continuity or differentiability of design variables: discrete variables, such as sheet metal thickness, can be introduced flawlessly.
• GAs tend to explore a wider variety of potential solutions, which can lead to solutions that would otherwise not be considered.
• Easy to implement.
• Unlike gradient methods capable of dealing with large set of design variables.
• Ideally suited to implementation on parallel computers.
• Easy restart based on best population.
Disadvantages
• Computational efficiency can be lower than in other methods.
• GAs do not provide general system knowledge.
3. Structural optimisation of demonstrator model
Next the optimisation results of the demonstrator model are discussed.
3.1. Fitness function
Typically, the proper choice of a fitness function is not trivial. For the optimisation of the energy absorbing capacity of the bumper/crash box/side rail system impacting a rigid wall, the objective function was initially targeting at a constant force level during impact so as to maximize the energy absorption efficiency [8]. Hence, the fitness function was expressed as
with FT the target force vector which must be achieved by the wall force vector F.
A drawback of this approach is the underlying assumption of an a priori known optimal force level. In a second step plastic strains of side rails were minimised in order to limit repair and insurance costs in low speed impacts. The associated fitness function was defined as
with the maximum plastic strain in the side rails and K a suitable scaling factor, whose value was selected as 20. The fitness function expresses that the maximum plastic strain in the side rails may not exceed a threshold level of 0.015 in order to avoid visible residual deformations. The best fitness values were normalized to enables comparison with potential additional fitness criteria.
3.2. Sensitivity analysis
GA provide no detailed information on the system characteristics. In order to gain some a priori system knowledge on the effects of the design parameters on the fitness function, Monte Carlo simulations (100 runs) were conducted.
All design parameters were varied under the assumption of uniform statistical distributions. Fig. 5 shows the sensitivity of the design variables in terms of linear correlation coefficients. It can be easily seen that parameters 5 and 7, referring to crash can inner and outer panel thicknesses, have the biggest influence on the fitness function. Also, it can be observed that parameters 0–4 and parameters 8 and 10 exhibit only a small linear correlation with fitness. Based on these results one could decide to either omit these parameters from the optimisation or to adjust the associated interval sizes. Next, adaptive fuzzy logic modelling was adopted to establish the relationship between design variables and fitness. Using a given input/output data set the Matlab toolbox function ANFIS (Adaptive Neuro Fuzzy Inference System) was utilised to construct a fuzzy inference system whose membership function parameters were tuned to optimally represent the system’s behaviour. ANFIS models are multi-input single-output models, the inputs being the design variables and the output being the fitness. A major advantage of ANFIS modeling over other methods is, that no a priori model knowledge is required. To select the best ANFIS model the design variables that have the strongest influence on the fitness are determined by checking the root mean square errors for all permutations of the design variables. (35K)
Fig. 5. Sensitivity chart for the design variables.
Given the number of runs that have been performed, a maximum of two selected design variables is most convenient. The design variables yielding the best ANFIS model are par5 and par7. This result is consistent with the linear correlation coefficients results depicted in Fig. 5.
Fig. 6 shows the associated response surface, which gives a three-dimensional representation of the relationship between two design variables and the normalised fitness. It can be seen that the best fitness values are obtained on the plateau with par5 values in the vicinity of 1.7 and par7 values in the vicinity of 1.4. Also, it can be observed that the plateau warrants robustness with respect to perturbations of the design variables. (44K)
Fig. 6. Response surface fitness function versus two design variables. 3.3. Optimisation results
The mean population fitness versus the number of generations is shown in Fig. 7. It is remarked that the termination condition was fulfilled after 20 generations (Schwarz inequality).
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Fig. 7. Mean fitness of bumper systems versus generation. In Fig. 8 a sample of four different designs is shown at 60ms simulation time. In the initial generation mainly bending modes of the crash box can be observed. The crash can consist of two parts where both material thicknesses and material grades are included in the design vector. (91K)
Fig. 8. Sample of four population members after 60 ms for generation 1 (left) and generation 16 (right). In the initial population inner and outer crash can parts were selected with different panel thicknesses. This initiated a bending mode in the crash can and side rail. By varying material thickness, material grade and shape of the crash can and its crash initiators (triggers) an axial bending mode of the crash box was found to have a high fitness. Then, a dramatic reduction of the plastic deformation of the side rails was obtained. The best design solutions withstood the impact without visible damage after 20 generations. Since the design target of minimal plastic strain in the side rails had been achieved, the structural optimisation was terminated after 20 generations.
The optimisation resulted in a significant weight reduction of 30%, it is noted that this was not the dominating design objective.
4. Discussion and conclusions
The viability of a structural optimisation process was demonstrated. The importance of achieving optimal system performance in conjunction with robustness was emphasised. System noise due to statistical variations in the design parameters was addressed. Combined application of optimisation methods and sensitivity analysis based on Monte Carlo simulations enables optimal numerical efficiency by reducing total number of design variables and selecting initial population of fit members. Genetic Algorithms offer distinct benefits like: problem solving for large solution spaces, no limitations on maximum number of design variables, avoidance of premature convergence to local optima, no limitations on continuity or differentiability and numerical efficiency through parallel computing.
SFE concept delivers high quality meshes based on parameterised models thus providing high flexibility for investigating design alternatives.
Parallel computing gives the opportunity to extend the size of the models and to include additional components like the engine.
It is noted that the application of evolution strategies based on deterministic selection and self-adaptation of strategy parameters may result in less function evaluations and hence improved computational efficiency. This will be topic of future research. In addition, future work is targeting at the application of the optimisation process to large component models and to multi-disciplinary optimisation involving adjacent attributes, such as stiffness analyses.
References
[1] Streilein T, Hillmann J. Stochastische Simulation und Optimierung am Beispiel VW Phaeton. VDI-Bericht Nr. 1701, 2002.
[2] Höfer C, Sakaryali C. Method for Automated Geometry Modification in Stochastic Analyses. In: 4th European LS-DYNA Conference, May 2003, Ulm, Germany.
[3] Will J, Bucher C, Riedel J, Akguen T. Stochastik und Optimierung: Anwendung genetischer und stochastischer Verfahren zur multidisziplinären Optimierung in der Fahrzeugentwicklung. VDI-Bericht Nr. 1701, 2002.
[4] Meyerwerk M. Optimierung in der Fahrzeugindustrie, Methoden und Anwendungen. VDI-Bericht 1701, 2002.
[5] C. Reed, Applications of Optistruct Optimisation to Body in White Design, Altair Engineering Ltd, Jaguar (2002).
[6] Hilmann J, Hänschke, A. Use of simplified models for the improved vehicle lay out with regards the vehicle Safety 10. Aachen Colloquium: Automobile and Engine Technology; 2001.
[7] Zimmer H, Hövelmann A, Schmidt H, Umlauf U, Frodl B, Hänle U. Entwurfstool zur Generierung parametrischer, virtueller Prototypen im Fahrzeugbau. VDI-Bericht Nr. 1559, 2000.
[8] Paas M, Ippen H, Schilling R. Structural Component Optimisation and Material Model Identification based on Generic Algorithms. VDI-11. Internationaler Kongreß Numerical analysis and simulation in Vehicle engineering, 01.–02. Oktober 2rzburg. |
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