用高斯过程生成复杂形状的梯度材料分布，实现平滑设计与优化。
FGM optimization in complex domains using Gaussian process regression based profile generation algorithm
- 基于高斯过程回归生成任意形状的梯度材料分布。
- 可控制分布平滑度与设计空间大小，支持多方案探索。
- 结合遗传算法优化，适合结构功能一体化设计场景。
本文针对任意形状域的功能梯度材料（FGM）设计挑战，提出一种基于高斯过程回归（GPR）的通用体积分数分布生成算法。该算法可处理复杂几何形状，在满足边界/部分边界指定体积分数条件下生成平滑的FGM分布。由GPR构建的设计空间包含多样化配置，提升发现最优结构的潜力。通过长度尺度参数可调控分布平滑性及设计空间规模。进一步将该分布生成方法与遗传算法结合，以求解特定应用下的最优FGM分布。为使遗传算法与GPR生成机制一致，对标准模拟二进制交叉算子进行了改进，引入投影操作。通过多个热弹性优化案例验证了所提算法与优化框架的有效性。
原文摘要 · Abstract (English)
This manuscript addresses the challenge of designing functionally graded materials (FGMs) for arbitrary-shaped domains. Towards this goal, the present work proposes a generic volume fraction profile generation algorithm based on Gaussian Process Regression (GPR). The proposed algorithm can handle complex-shaped domains and generate smooth FGM profiles while adhering to the specified volume fraction values at boundaries/part of boundaries. The resulting design space from GPR comprises diverse profiles, enhancing the potential for discovering optimal configurations. Further, the algorithm allows the user to control the smoothness of the underlying profiles and the size of the design space through a length scale parameter. Further, the proposed profile generation scheme is coupled with the genetic algorithm to find the optimum FGM profiles for a given application. To make the genetic algorithm consistent with the GPR profile generation scheme, the standard simulated binary crossover operator in the genetic algorithm has been modified with a projection operator. We present numerous thermoelastic optimization examples to demonstrate the efficacy of the proposed profile generation algorithm and optimization framework.
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