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Deep Learning Architecture for Topological Optimized Mechanical Design Generation with Complex Shape Criterion

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Advances and Trends in Artificial Intelligence. Artificial Intelligence Practices (IEA/AIE 2021)

Abstract

Topology optimization is a powerful tool for producing an optimal free-form design from input mechanical constraints. However, in its traditional-density-based approach, it does not feature a proper definition for the external boundary. Therefore, the integration of shape-related constraints remains hard. It requires the experts’ intervention to interpret the generated designs into parametric shapes; thus, making the design process time-consuming. With the growing role of additive manufacturing in the industry, developing a design approach considering mechanical and geometrical constraints simultaneously becomes an interesting way to integrate manufacturing and aesthetics constraints into mechanical design. In this paper, we propose to generate mechanically and geometrically valid designs using a deep-learning solution trained via a dual-discriminator Generative Adversarial Network (GAN) framework. This Deep-learning-geometrical-driven solution generates designs very similar to traditional topology optimization’s outputs in a fraction of time.

Moreover, it allows an easy shape fine-tuning by a simple increase/decrease of the input geometrical condition (here the total-bar-count), a task that a traditional topology optimization cannot achieve.

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Notes

  1. 1.

    The architecture of the residual unit block used in this work is detailed in [32].

  2. 2.

    The stem and inception/reduction blocks used defers from the original paper [27] only by the number of input/output feature maps.

  3. 3.

    This code is available on the GitHub repository: https://github.com/dbetteb/TOP_OPT.git.

  4. 4.

    A loaded node \(n_e\) located at line \(i\) and column \(j\) tilted \(\theta \) degrees has \(F_x(i,j) = cos(\theta )\) and \(F_y(i,j) = sin(\theta )\); the magnitude of the loads were set to \(1.0\) \(N\).

  5. 5.

    A fixed bar is a bar where boundary conditions are applied. A loaded bar is a bar where a load is applied.

References

  1. Abueidda, D.W., Koric, S., Sobh, N.A.: Topology optimization of 2D structures with nonlinearities using deep learning. Comput. Struct. 237, 106283 (2020)

    Google Scholar 

  2. Adam, G.A., Zimmer, D.: Design for additive manufacturing–element transitions and aggregated structures. CIRP J. Manuf. Sci. Technol. 7(1), 20–28 (2014)

    Article  Google Scholar 

  3. Allaire, G., Jouve, F., Toader, A.M.: A level-set method for shape optimization. Comput. R. Math. 334(12), 1125–1130 (2002)

    MathSciNet  MATH  Google Scholar 

  4. Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. optim. 1(4), 193–202 (1989)

    Article  Google Scholar 

  5. Bendsøe, M.P., Sigmund, O.: Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69(9–10), 635–654 (1999)

    MATH  Google Scholar 

  6. Bi, S., Zhang, J., Zhang, G.: Scalable deep-learning-accelerated topology optimization for additively manufactured materials. arXiv preprint arXiv:2011.14177 (2020)

  7. Goodfellow, I., et al.: Generative adversarial nets. In: Advances in Neural Information Processing Systems, pp. 2672–2680 (2014)

    Google Scholar 

  8. Guo, Y., Liu, Y., Oerlemans, A., Lao, S., Wu, S., Lew, M.S.: Deep learning for visual understanding: a review. Neurocomputing 187, 27–48 (2016)

    Article  Google Scholar 

  9. He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778 (2016)

    Google Scholar 

  10. Hoyer, S., Sohl-Dickstein, J., Greydanus, S.: Neural reparameterization improves structural optimization. arXiv preprint arXiv:1909.04240 (2019)

  11. Kallioras, N.A., Kazakis, G., Lagaros, N.D.: Accelerated topology optimization by means of deep learning. Struct. Multi. Optim. 62(3), 1185–1212 (2020)

    Google Scholar 

  12. Leary, M., Merli, L., Torti, F., Mazur, M., Brandt, M.: Optimal topology for additive manufacture: a method for enabling additive manufacture of support-free optimal structures. Mater. Des. 63, 678–690 (2014)

    Article  Google Scholar 

  13. Li, S., Yuan, S., Zhu, J., Wang, C., Li, J., Zhang, W.: Additive manufacturing-driven design optimization: building direction and structural topology. Add. Manuf. 36, 101406 (2020)

    Google Scholar 

  14. Malviya, M.: A systematic study of deep generative models for rapid topology optimization (2020)

    Google Scholar 

  15. Mass, Y., Amir, O.: Topology optimization for additive manufacturing: accounting for overhang limitations using a virtual skeleton. Add. Manuf. 18, 58–73 (2017)

    Google Scholar 

  16. Mirza, M., Osindero, S.: Conditional generative adversarial nets. arXiv preprint arXiv:1411.1784 (2014)

  17. Nie, Z., Lin, T., Jiang, H., Kara, L.B.: Topologygan: topology optimization using generative adversarial networks based on physical fields over the initial domain. arXiv preprint arXiv:2003.04685 (2020)

  18. Radford, A., Metz, L., Chintala, S.: Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434 (2015)

  19. Rawat, S., Shen, M.H.H.: A novel topology optimization approach using conditional deep learning. arXiv preprint arXiv:1901.04859 (2019)

  20. Rawat, W., Wang, Z.: Deep convolutional neural networks for image classification: a comprehensive review. Neural Comput. 29(9), 2352–2449 (2017)

    Google Scholar 

  21. Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28

    Chapter  Google Scholar 

  22. Sharpe, C., Seepersad, C.C.: Topology design with conditional generative adversarial networks. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 59186, p. V02AT03A062. American Society of Mechanical Engineers (2019)

    Google Scholar 

  23. Sigmund, O.: A 99 line topology optimization code written in matlab. Struct. Mult. Optim. 21(2), 120–127 (2001)

    Article  Google Scholar 

  24. Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Optim. 16(1), 68–75 (1998)

    Article  Google Scholar 

  25. Sosnovik, I., Oseledets, I.: Neural networks for topology optimization. Russ. J. Numer. Anal. Math. Modell. 34(4), 215–223 (2019)

    Article  MathSciNet  Google Scholar 

  26. Subedi, S.C., Verma, C.S., Suresh, K.: A review of methods for the geometric post-processing of topology optimized models. Journal of Computing and Information Science in Engineering, vol. 20, no. 6 (2020)

    Google Scholar 

  27. Szegedy, C., Ioffe, S., Vanhoucke, V., Alemi, A.A.: Inception-v4, inception-resnet and the impact of residual connections on learning. In: Thirty-First AAAI Conference on Artificial Intelligence (2017)

    Google Scholar 

  28. Ulu, E., Zhang, R., Kara, L.B.: A data-driven investigation and estimation of optimal topologies under variable loading configurations. Comput. Methods Biomech. Biomed. Eng. Imaging Vis. 4(2), 61–72 (2016)

    Article  Google Scholar 

  29. Wang, C., Qian, X.: Simultaneous optimization of build orientation and topology for additive manufacturing. Add. Manuf. 34, 101246 (2020)

    Google Scholar 

  30. Yu, Y., Hur, T., Jung, J., Jang, I.G.: Deep learning for determining a near-optimal topological design without any iteration. Struct. Multi. Optim. 59(3), 787–799 (2018). https://doi.org/10.1007/s00158-018-2101-5

    Article  Google Scholar 

  31. Zhang, W., Zhou, L.: Topology optimization of self-supporting structures with polygon features for additive manufacturing. Comput. Methods Appl. Mech. Eng. 334, 56–78 (2018)

    Article  MathSciNet  Google Scholar 

  32. Zhang, Z., Liu, Q., Wang, Y.: Road extraction by deep residual u-net. IEEE Geosci. Remote Sens. Lett. 15(5), 749–753 (2018)

    Article  Google Scholar 

  33. Zhao, Z.Q., Zheng, P., Xu, S.T., Wu, X.: Object detection with deep learning: a review. IEEE Trans. Neural Netw. Learn. Syst. 30(11), 3212–3232 (2019)

    Google Scholar 

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Acknowledgement

This work was supported by Expleo France.

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Correspondence to Waad Almasri .

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Almasri, W., Bettebghor, D., Ababsa, F., Danglade, F., Adjed, F. (2021). Deep Learning Architecture for Topological Optimized Mechanical Design Generation with Complex Shape Criterion. In: Fujita, H., Selamat, A., Lin, J.CW., Ali, M. (eds) Advances and Trends in Artificial Intelligence. Artificial Intelligence Practices. IEA/AIE 2021. Lecture Notes in Computer Science(), vol 12798. Springer, Cham. https://doi.org/10.1007/978-3-030-79457-6_19

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  • DOI: https://doi.org/10.1007/978-3-030-79457-6_19

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