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Application of High Performance Computing and Visualization to Crashworthiness Design Optimization
R. J. Yang*, G. Li, L. Gu, Ciro A. Soto
Ford Motor Company, Dearborn, Michigan 48124, USA
Srinivas Kodiyalam† Silicon Graphics, Inc., Mountain View, California 94043-1351, USA
Visualization based design steering facilitates expert-in-the-loop optimization and enhances efficiency of the Multidisciplinary Design Optimization (MDO) process. The use of high performance computing for rapid visualization of design alternatives and the subsequent use of such visualization for design steering during the design optimization process are beneficial and critical for quick decision-making. In this study, response surfaces based surrogate models and Message Passing Interface based parallel programming models are used for approximation and rapid visualization of design responses. Application of the proposed procedure for vehicle impact design optimization is investigated through a full vehicle example. The design variables include size and shape design variables, which are parameterized using state-of-the-art morphing technology.
Nomenclature CAD = Computer-Aided Design DOE = Design of Experiments DV = Design Variable FMVSS = Federal Motor Vehicle Safety Standards FE = Finite Element HPC = High Performance Computing MPI = Message Passing Interface MDO = Multidisciplinary design optimization NVH = Noise, Vibration, and Harshness
I. Introduction he automotive industry today is facing a number of complex and often conflicting requirements and challenges for improving product performance, safety, quality, and reliability. The industry is beginning to use more formal
and structured approaches to design, analysis and optimization. In particular, the vehicle design process has always involved intensive collaboration among teams with specialized disciplines, such as safety, Noise, Vibration, and Harshness (NVH), durability and vehicle dynamics. Like practically all engineered and manufactured systems, vehicle systems experience interactions among the various physical phenomena and between different parts of the full system. Current processes require a trade-off between the disciplines to develop the final design. Traditionally, this is accomplished by passing the designs back and forth between the teams working within these disciplines until the differences are minimized and a mutually acceptable solution is found.
Today, this approach is too sequential and time consuming. The need to reduce time to market for new vehicles coupled with the increased availability of affordable High Performance Computing (HPC) systems that can process hundreds of simulations concurrently has led to the increased adoption of collaborative design methods including Multidisciplinary Design Optimization (MDO) [1, 2].
Kodiyalam et al. [3] showed the usefulness of a proposed rapid visualization methodology and the engineer-in-the-loop steering the design to an “acceptable” optimal solution, specifically, for the compute intensive vehicle impact design. The focus of this work is on the application of HPC for rapid visualization of design alternatives and
* Technical Leader, Passive Safety Research and Advanced Engineering, MD2115-SRL, ASME Fellow. † HPC Applications Business Development Manager, MS 405, Associate Fellow AIAA.
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10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference30 August - 1 September 2004, Albany, New York
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the subsequent use of such visualization for design steering with the MDO process [3]. The primary intent of this work is to utilize the proposed procedure [3] for rapidly updating and visualizing the behavior responses of a structure, for example, a car body structure under impact loads, for changes in design variables. Specifically, rapid visualization of impact mode deformations of a full vehicle corresponding to changes in design variables is enabled using MPI (Message Passing Interface) based parallel programming model and surrogate modeling methods. This near real time updates of impact mode deformations corresponding to change in design variables provides a powerful visual tool for engineers to understand the behavior of the vehicle under impact and make appropriate changes to the design model. The changes to the design model can be as part of a MDO process or simply design trades conducted by the engineer with the aid of this visual tool. Details of the method and its application to vehicle design are in [3]. In addition size design variables used in [3], shape design variables using morphing technology are investigated in this study.
II. Morphing Technology Traditionally, when a vehicle model was changed, such as change to new body profile, a new CAD model had to
be created and then finite element meshes were generated. This process usually took long time and lots of efforts. A new FE model can be built directly from the old one by modifying meshes to fit new profile, when using morphing technique. Morphing transforms an existing design into a new design by using new engineering criteria and existing design information. For example, if a new product, such as a door from a newly developed theme, is to be designed, morphing will aid in transforming the styled door into a fully engineered, production ready door. Morphing also allows engineers to quickly parameterize models and stretch finite element meshes when the geometry of the structure is changed. It has potential to reduce design and engineering cycle time as existing meshes can be quickly morphed to hypothetical design considerations - without remeshing - for evaluation while preserving the model integrity and connectivity. This eliminates the need to continuously work back through the CAD system to evaluate design considerations and automatically creates design variables for optimization studies.
Morphing can be used in two important areas: shape optimization and preliminary simulation after model change. For shape optimization, feasible shapes need to be characterized by parameters, such as length, height, width, angle and profile curves. The specific shape can be easily created by morphing tool with a set of parameter data. When the morphing process is embedded into optimization loop, the optimal shape can be achieved after certain iterations. Those shape variables or parameters can be either vehicle level or component level parameters.
III. Visual Design Steering with Rapid Visualization of Design Alternatives Visual design steering, in general, refers to the use of visualization to steer the design process and in this work,
specifically refers to the use of visualization within the MDO process to facilitate domain knowledge capture and steer the solution towards an improved design. Visual design steering involves a sequence of steps including: • Allow users to walk through the design space and locate key areas to explore • Request an enhanced rendering from the server of behavior responses at the design point of interest. This is
accomplished either through the use of surrogate models for compute intensive analysis or playback of large stores of pre-computed data.
• Recommend changes in configuration and design optimization model based on disciplines’ data visualization and expert’s domain knowledge.
• Perform full analyses of the design with recommended changes. Based on the analysis solution, accept or reject the changes and proceed with MDO.
The MDO process with visual design steering is shown in Figure 1. The process is generic. The figure shows a
specific example of an automotive vehicle MDO for crashworthiness, noise-vibration-harshness (NVH), and weight requirements.
Quick visualization of simulations for different impact modes is important. It allows engineers to evaluate and confirm the design concept for occupant protection. However, real-time visualization for actual impact simulations is often impossible, as it has to be re-analyzed and then post-processed using vehicle impact responses corresponding to design perturbations. To aid design, the approximation methods for simulation results must be used [3].
Consider a relatively small model of about 100,000 FE nodes and a simulation time interval of t = 0 to 100 msec, with animation time step of every 10 msec. This would result in construction of over 3 million surrogate models for each of the nodal displacements (x, y, z direction) as a function of the design variables.
100000 nodes * 3 (x, y, z) degrees-of-freedom=300000;
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10 animation files over the simulation time interval; Total number of displacement responses to be approximated, as a function of the design variables equals 300000*10 = 3,000,000
While this is a computationally intensive task, the process of generating these surrogate models for each nodal degree-of-freedom is completely independent of the other degrees-of-freedom and hence is highly parallel. The MPI parallel programming model is used to utilize all the processors in a multiprocessor server with hundreds of processors to minimize the elapsed time of constructing these surrogate models and update the impact deformation modes for changes in design variables.
A flowchart of the conventional and the new process are provided in Figures 2 and 3. To visualize in real-time (or, near real-time) impact mode deformations for changes in design variables in a conventional process is very time consuming for large models. It often requires more than 10 hours using an 8-processor high performance computer. Figure 3 shows the proposed MPI programming model and surrogate models based approach to performance response visualization. This study uses a polynomial-based subset selection regression model for vehicle impact performance responses [5, 6]
IV. Crashworthiness Design Optimization Example A 50% offset frontal impact is considered to demonstrate the MPI process. The optimization process is identical
to that of gauge optimization, as shown in Figure 1. The finite element model used in this study contains about 100,000 elements. In this model, the vehicle crashes into a 90 degree fixed rigid wall with 50% offset (Figure 4). The impact velocity is 40 mph. One of the key outputs from the 50% frontal offset impact is the toeboard intrusion. The design target for toeboard intrusion is set to be less than 6 inches or 152.4 mm.
In [3], the design optimization for three gauges of the parts was conducted for minimizing the toe-board intrusion with a weight constraint. The maximum intrusion was then successfully reduced by 25% without increasing the vehicle weight.
In this study, the same FE analysis model is used for both size and shape optimization. The shape design variables are parameterized using morphing techniques in HyperMesh [7]. Two shape parameters and two more gauges are added to the original three gauge variables as design variables (Figure 6). One of the shape variables is the length between the bumper and the A-pillar (DV6 in Figure 6). This variable is a vehicle level parameter and three levels are used in DOE for DV6. When applying a shape change, all nodes in that region are displaced accordingly. The other shape variable is the height of the rail (DV7). Two levels are defined in DOE for this component level parameter. For rail height change, only nodes of rail components are moved while the rest of the structure is fixed. The five size design variables include rail inner and outer, shot gun and sub frame (see Figure 6). The objective is to minimize vehicle weight while satisfying intrusion requirements, as shown in the following:
x6: Shape design variable (length of the front end) x7: Shape variable (height of the rail)
The explicit finite element analysis software RADIOSS [8] was used for the crashworthiness analysis. A Latin Hypercube sampling with a uniform distribution is used to generate 24 designs for constructing the response surfaces for the nodal displacements. A total of 25 finite element simulations are performed to build the response surface as a function of the seven sizing and shape design variables. Each RADIOSS simulation requires about 6 hours 20 minutes of elapsed time on a SGI Origin 3800 HPC server using 8 processors. Using the rapid visualization process discussed in the earlier section, the rail deformation for a new design can be updated and displayed on the screen in a few minutes.
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Optimization results are summarized in Table 1. The weight-intrusion trade-off is given in Figure 7, which provides engineers trade-off information between intrusion and weight. Compared to the baseline design, the average intrusion at the optimal design, shown in Figure 7, is reduced by 11 %, while vehicle weight is reduced by 4.11 kg. The maximum intrusion is reduced about 15%.
Due to the limitations of the printed media, a dynamic simulation of a vehicle impact using the response surface generated using the MPI approach cannot be showed. Figure 8 attempts to describe the process and explain how MPI is used.
Table 1: Gauge/Shape Optimization Results
Baseline Optimal Design
Change
DV1 Gauge 1 1.9 1.33
DV2 Gauge 2 1.9 2.19
DV3 Gauge 3 2.4 2.76
DV4 Gauge 4 1.2 1.38
DV5 Gauge 5 2.5 1.75
DV6 Front Extension (mm) 0 +13.00
DV7 Rail height (mm) 0 +30.00
Maximum Intrusion (mm) 170.20 143.97 -15.4%
Average Intrusion (mm) 148.4 131.9 -11.1%
Mass (kg) 1749.8 1745.7 -4.11
V. Summary This paper applied a novel methodology for automotive impact design optimization and rapid visualization by
coupling a response surface algorithm with crashworthiness analysis. The main purpose of creating such large number of response surfaces is to enable the design engineer to quickly visualize the entire impact deformation of the vehicle as a function of time without re-analysis of the perturbed design. The method can be used for both gauge/material and shape optimization with real time or near-real time visualization. Results from the example have yielded the following conclusions:
• An approximation concept based on a response surface method is effective in reducing time for visualization of the optimal design or any predicted design. It can be a useful tool for engineers to make design decisions.
• The example shows that the structural performances are more influential for the shape than the gauge/material changes.
• As the key idea in morphing is the manipulation of FE meshes, improvements in the efficiency, flexibility, and robustness of the morphing process are still required. Some limitations and challenges of current morphing technology are listed as follows:
− Definition of shape variables is time-consuming when the component shape is complicated. In addition, the design variables are not physical or engineering dimensions, with which engineers are familiar.
− For component level morphing, local mesh smoothing may be required to maintain model quality. − In addition to mesh distortion as in the component level, how to separate components for morphing and
isolate hard points are still difficult to perform. − Morphing results need to pass back to CAD system.
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References
1. J. S. Sobieski, “Optimization by Decomposition: A Step from Hierarchic to Non-hierarchic Systems,” Proceedings, 2nd NASA/USAF Symposium on Recent Advances in Multidisciplinary Analysis and Optimization, Hampton, Virginia, 1988. NASA CP-3031. Also, NASA TM-101494, 1988.
2. J. S. Sobieski and R. T. Haftka, “Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments,” Structural Optimization, pp. 1-23, Vol. 14, No. 1, August 1997.
3. S. Kodiyalam, R. J. Yang, and L. Gu, "High Performance Computing and Rapid Visualization for Design Steering In MDO," AIAA-2003-1528, In Proceedings of 44th AIAA SDM Conference, Norfolk, Virginia, 2003.
4. S. Kodiyalam, R. J. Yang, L. Gu and C. H. Tho, “Multidisciplinary Optimization of a Vehicle System in a Scalable, High Performance Computing Environment”, To be published in Structural and Multidisciplinary Optimization, Special Edition, 2003.
5. L. Gu, "A Comparison of Polynomial Based Regression Models in Vehicle Safety Analysis," DETC2001/DAC-21063, Proceedings, ASME Design Engineering Technical Conferences, Pittsburgh, Pennsylvania, September 2001.
6. J. Miller, Subset Selection in Regression, Chapman & Hall, London, 1990. 7. HyperMesh, http://www.altair.com, Altair Engineering, Detroit, Michigan, USA. 8. RADIOSS, http://www.radioss.com, Mecalog, France.
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