In this paper, a mechanistic data-driven approach is proposed to accelerate structural topology optimization, employing an in-house developed finite element convolutional neural network (FE-CNN). Our approach can be divided into two stages: offline training, and online optimization. During offline training, a mapping function is built between high and low resolution representations of a given design domain. The mapping is expressed by a FE-CNN, which targets a common objective function value (e.g., structural compliance) across design domains of differing resolutions. During online optimization, an arbitrary design domain of high resolution is reduced to low resolution through the trained mapping function. The original high-resolution domain is thus designed by computations performed on only the low-resolution version, followed by an inverse mapping back to the high-resolution domain. Numerical examples demonstrate that this approach can accelerate optimization by up to an order of magnitude in computational time. Our proposed approach therefore shows great potential to overcome the curse-of-dimensionality incurred by density-based structural topology optimization. The limitation of our present approach is also discussed.
翻译:本文建议采用机械数据驱动方法,以加速结构地形优化,采用内部开发的有限元素进化神经网络(FE-CNN)。我们的方法可以分为两个阶段:离线培训和在线优化。在离线培训期间,在一个特定设计域的高分辨率和低分辨率表示之间构建了绘图功能。绘图由FE-CNN表示,该方法针对不同分辨率设计领域的共同客观功能价值(如结构合规性);在网上优化过程中,高分辨率的任意设计领域通过训练有素的绘图功能降低到低分辨率。因此,最初的高分辨率域的设计只能以低分辨率版本进行计算,然后逆向绘图回溯至高分辨率域。数字实例表明,这一方法可以加速优化,在计算时达到一个数量级。因此,我们提出的方法显示出克服基于密度的结构表层优化造成的极限的巨大潜力。我们目前方法的局限性也得到了讨论。