Abstract
Deep learning (DL) is a powerful tool to accelerate topology optimization towards a wide range of engineering applications that demand instantaneous conceptual design with high accuracy and precision. However, many existing DL-based topology optimization methods predict structures that have low image quality with significant blur and distortions, obstructing direct manufacturing of the designed parts. To address the technical challenge, this study proposes a DL model based on the deep Residual U-net (ResUnet) architecture, a convolutional neural network (CNN) that is efficient and accurate even without a large amount of data. Combining the complementary distance-based and similarity-based loss functions, a new loss function is proposed for DL-based topology optimization. It has two parameters that are optimized to achieve the best performance considering four criteria, i.e., maximum image quality, minimum compliance error, minimum volume fraction error, and minimum structural discontinuity. Trained with the optimal structures under a variety of loading and boundary conditions, the present DL model can predict optimized structures almost instantaneously, with high image quality readily for manufacturing. The image quality improvement, along with the other performance improvements, is shown to persist regardless of the training image quality or the resolution of the problem. The highly universal loss function is expected to provide an inherent approach to improve the manufacturability of DL-predicted structures and extend the application of DL-based topology optimization methods.
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Acknowledgements
This work was financially supported by the startup fund provided to L.L. by Temple University, the U.S. DOE’s ARPA-E under the Award Number DE-AR0001576, and the U.S. DOE’s Office of Energy Efficiency and Renewable Energy (EERE) under the AMO Award Number DE-EE0010205. M.M.I. and L.L. are also grateful to the support by the Temple University Library through the Loretta C. Duckworth Scholars Studio (LCDSS) graduate extern and faculty fellowship programs.
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In this work, training and testing data were generated by the SIMP method implemented in FEniCSx, an open-source computing platform for solving partial differential equations. However, any computational codes that implement SIMP for topology optimization (e.g., MATLAB code (Andreassen et al. 2011), PolyTop++, and TopOpt) are expected to generate similar data. The DL model is based on the ResUnet architecture, which is available in multiple public domains, e.g., the TensorFlow implementation of Residual U-Net (David 2022). Our development on top of ResUnet is available upon reasonable request.
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Islam, M.M., Liu, L. Deep learning accelerated topology optimization with inherent control of image quality. Struct Multidisc Optim 65, 325 (2022). https://doi.org/10.1007/s00158-022-03433-4
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DOI: https://doi.org/10.1007/s00158-022-03433-4