Authors: Mariusz Bujny1, Tim Grasser2, Daniel Weber2, Markus Olhofer1, Stefan Menzel1
1Honda Research Institute Europe GmbH; 2Fraunhofer-Institut für Graphische Datenverarbeitung IGD
Building upon research experience in simulation and optimization, scientists from Honda Research Institute Europe (HRI-EU) and Fraunhofer IGD worked together on development of interactive engineering systems to shape the future of the industrial design process. This fruitful collaboration was established in 2019 and resulted in a CAE tool, taking advantage of Fraunhofer’s computationally-efficient GPU-based interactive simulation software, RISTRA (Rapid Interactive Structural Analysis), to effectively utilize innovative preference-based optimization technologies from HRI-EU. We strongly believe that such systems will be an essential part of the future development process in industry, allowing for a seamless human-machine collaboration. The current project developments open the perspective for a joint future research, which can potentially involve utilization of Fraunhofer’s advanced visualization, nonlinear simulation, and multi-material 3D-printing technologies, as well as geometric deep learning methods from HRI-EU, to bring the CAE systems to the new levels of creativity.
Structural Topology Optimization (TO) [1] is a very powerful engineering design tool which can be used to automatically generate large sets of creative and unintuitive design concepts that engineers never thought about before (Figure 1). In the most popular TO approaches, a computer program redistributes the material in a design space defined by the user by adjusting densities of a large number of pixels/voxels, based on formal numerical optimization methods. Typically, the optimizer aims maximizing one or more performance metrics, like structural stiffness, while respecting constraints imposed by the user, for instance volume or the total mass of the structure. During the last 30 years, TO methods have been used in a wide range of structural optimization problems [1,3,4], leading to large weight savings or performance improvements. However, TO approaches are still used to a limited extent in industry, mainly due to the high complexity of the overall design process, where multiple additional criteria, often difficult to quantify and predefine, have to be taken into account. As a result, conventional TO results are usually far away from the designs viable from engineering as well as economic point of view, and a cumbersome manual interpretation of the complex topologies is necessary. The designs resulting from the interpretation of the topologically-optimized structures offer only moderate improvements compared to the existing solutions, indicating the need for alternative TO approaches which would allow for integrating designer’s preferences directly in the optimization process.
Cooperative Topology Optimization
At the Honda Research Institute Europe (HRI-EU), we conduct research in the domain of Cooperative Intelligence (CI), being Artificial Intelligence (AI) embedded in a social context. Instead of replacing humans, CI targets empowering them to solve problems in complex environments by enhancing collaboration between humans and machines. In the context of TO, one could realize this concept by replacing fully automated, black-box systems with a cooperative tool, allowing designers to express their preferences about the final design in a fully interactive fashion, to guide the optimization towards feasible solutions. As a result, such a “human in the loop” system could effectively address the main shortcomings of the standard TO systems. Figure 2 compares the standard TO with a conceptual cooperative TO system, integrating different types of user preferences.
To efficiently conduct research in Cooperative TO, fast simulation tools, allowing for real-time, interactive TO, are necessary. At HRI-EU, we build interactive TO systems based on Fraunhofer IGD’s GPU-accelerated finite element solver, RISTRA.
GPU-based Finite Element Simulation
Unlike conventional solvers, RISTRA is designed for highly parallel GPUs (Graphics Processing Units). This includes not just linear solvers, but also other computation intensive tasks like matrix assembly. Beside the FE-solver, RISTRA also includes a pre- and post-processor. Figure 3 presents a result of a GPU-accelerated simulation with the RISTRA solver.
Interactive GPU-accelerated Topology Optimization
RISTRA enables considerably faster simulations compared to the standard finite element
simulation software. As a result, for finite element models of moderate size, e.g. 100k elements, the optimization process can be monitored in real time, with each iteration of the algorithm taking a couple of seconds. A considerable speedup is obtained thanks to the efficient implementation of the finite element simulations on GPU as well as an improved communication between TO codes and the solver, which is typically purely file-based for the commercial, black-box simulation software.
RISTRA can be operated as a console application for servers or as a UI application. In the latter case, used for coupling with the TO code, RISTRA is addressed using a TCP/IP connection, only communicating the changes compared to previous simulation steps. This enables interactive inspection of intermediate results during the optimization process and might help to identify problems even before the convergence of the optimization algorithms.
To fully demonstrate the benefits coming from using RISTRA as the solver for TO, a large-scale optimization problem based on the model shown in Figure 4 was considered. This size of models is considered frequently in industrial applications of TO. The optimization targets minimization of compliance (maximization of stiffness) by adjusting the densities of the elements within the design space, while respecting a 30% mass constraint. The convergence of compliance over the optimization iterations is shown in Figure 5. Although the optimization converges already within the first 10 iterations, a fixed budget of 50 simulations was considered in the study, to let the optimizer fine-tune the design. The final, optimized structure is depicted in Figure 6.
In Table 1, a comparison of the optimization times for TO based on LS-Dyna and RISTRA is presented. In both cases, a Python implementation of the SIMP method [1] by HRI-EU was used as the optimization algorithm. The total optimization time with RISTRA is over 11 times shorter than with LS-Dyna. This is both due to the more efficient, GPU-based finite element simulations, as well as thanks to the utilization of TCP/IP communication between the optimizer and RISTRA, which is used instead of file saving/loading as done for the commercial software. However, even when neglecting the time required for saving and loading the output files, the RISTRA-based TO is almost 8 times faster, with each iteration requiring on average ca. 50 seconds. As a result, with RISTRA-based TO, it becomes feasible to control the optimization process in an online fashion, even for large-scale industrial problems. Additionally, due to the high efficiency of the finite element simulations, even higher speedups w.r.t. commercial solvers could be potentially observed for multi-load-case, multi-objective optimization problems, crucial from the point of view of industrial applications.
Table 1. Comparison of the hardware and optimization times for TO with LS-Dyna and RISTRA finite element solvers.
| CPU-based TO using LS-Dyna | GPU-based TO using RISTRA | |
| Simulation software | LS-Dyna SMP R7.1.1 DBL * | RISTRA |
| CPU | Intel(R) Xeon(R) CPU E5-2697 v3 @ 2.60GHz | Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz |
| GPU | – | NVIDIA GeForce GTX 1650, 4096 MB, 896 CUDA cores |
| RAM | 64 GB | 16 GB |
| Total optimization time | 500 min | 44 min |
| Optimization time excluding file saving | 343 min | 44 min |
* LS-Dyna simulations were run using single core only, since no speedup was obtained when increasing the number of cores for the SMP version of the software.
Multi-objective Topology Optimization
As shown in the previous sections, RISTRA allows for considerable shortening of the simulation time. As a result, addressing complex multi-load-case optimization problems becomes considerably easier. In the industrial setting, TO problems with more than 10 load cases are not uncommon, showing the importance of this aspect. In multi-load-case scenarios, the user has to specify relative importance of each of the load cases, expressed with the weights, or alternatively, preference factors [5] of the objective function (e.g. stiffness) related to each of the cases. This task is not trivial and represents a multi-objective optimization problem [6]. The load case weights can be adjusted exclusively based on the preferences of the designer, to direct the optimization towards designs satisfying all the requirements.
Multi-objective TO can be conducted now with RISTRA, considerably shortening the overall optimization time. A set of RISTRA topologically-optimized designs obtained for different values of the preference factors for the load cases depicted in Figure 7, yielding different performance values for both of the considered load cases, is shown in Figure 8. Please note that all those designs are equal from the optimality point of view, composing so-called Pareto front, and the selection of particular designs can be based only on a subjective judgment of the designer. Each of the points in the plot represents a separate topology optimization run. With RISTRA-based TO, the user can interact with the tool by adjusting the load case weights and run TO to get the an optimized design in a very short time, which allows for a smooth, collaborative work of a human and machine.
Multi-material Topology Optimization
In order to meet stringent requirements concerning vehicle safety, costs, and weight, vehicle structures composed of multiple material types become a standard in the automotive industry. However, standard TO methods search for an optimal material distribution using a single material type only. To allow for a multi-material TO, we employ so-called ordered SIMP (Solid Isotropic Material with Penalization) approach [7,8], which encodes material types at different density levels and penalizes stiffness values in between to eliminate intermediate densities (Figure 9). As a result, additional preferences regarding material types can be embedded in the formulation of the optimization problem and the TO tool can find both the optimal material distribution and the material type.
Similarity-based Topology Optimization
Many of the user preferences regarding the final result of topology optimization are difficult to express in from of a formal mathematical description such as additional optimization constraints. In fact, considering even established manufacturing techniques and standard TO problems, the methods to incorporate additional constraints are still under active development. In many cases, however, the requirements on the final material layout might be far more complex and be influenced by such factors as commonality, assembly process, or the ability to re-integrate the optimized part into an existing system.
Thus, it becomes essential to define constraints on material layout in a more intuitive way, while allowing for incorporation of all of the necessary design requirements. This can be achieved by specifying appropriate reference structure and flexibly adjusting the similarity level of the part being optimized to that design in a similarity-based TO [9] as illustrated in Figure 11.
Similarity-based TO can be now realized with RISTRA based on HRI’s TO framework. Figure 12 presents a result of a similarity-based TO using RISTRA, with a reference structure being a hollow beam, which is demonstrating how an important and so far unresolved problem of using TO to create tubular structures can be addressed with this approach.
Design Clustering and Prototype Identification
Given a large set of topologically-optimized design concepts that can be potentially generated using multi-objective, multi-material, and similarity-based TO, it becomes prohibitive for the designer to manually review and compare all of them. In general, one would have to consider both the performance and geometric differences among all the designs. In particular, considering geometric differences is very difficult in case of the designs optimized using TO techniques, being often highly complex, bionic-like structures (Figure 1). To address this problem, at HRI-EU, we develop techniques for automatic processing of big data sets of topologically-optimized designs, with the help of modern AI tools. For instance, we use so-called point could autoencoders, being deep neural networks which can be used to automatically learn low-dimensional representations of complex topologies. Based on that, we can perform automatic clustering of hundreds of designs obtained via TO and identify a limited set of representative design prototypes [10,11], which can be easily reviewed by a human designer to select the most interesting design concepts (Figure 13).
After selecting the most interesting design prototypes, the designer can further guide the optimization using load case preferences and similarity-based TO towards structures combining the features of the selected designs, in a cooperative TO process. The human-machine collaboration in this context is an active research at HRI-EU and can be now carried out much more efficiently using the GPU-accelerated RISTRA finite element solver.
Summary
With the rising requirements concerning vehicle safety and emissions, topology optimization will play more and more important role in the automotive industry. Although those tools are predominantly used to identify interesting concepts in early design phases, the recent advances in manufacturing technologies as well as optimization algorithms allow for a direct application of these techniques for the part design. In both cases, however, the key to success is to use this technology to empower the human designers to develop better structures and not to replace them by a fully automatic system. This can be achieved by realizing the concept of Cooperative Intelligence in the context of topology optimization, to “keep the human designer in the optimization loop”. Such a cooperative topology optimization system can be realized by including engineer’s preferences regarding the final design, which requires an interactive optimization environment, providing real-time feedback to a human. Thanks to the efficient implementation of GPU-accelerated RISTRA finite element solver, an interactive topology optimization of industrial-scale models becomes feasible and allows for a smooth interaction with human designers. As a result, with limited computational resources, a wide range of creative concepts can be studied to select the structures meeting all design requirements, including subjective preferences of human designers, which are difficult to quantify and define prior to the optimization.
Acknowledgements
The authors would like to thank Nivesh Dommaraju (Technical University of Munich, Germany) for the help in evaluating the performance of TO using LS-Dyna solver.
References
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