基于响应面和空间映射技术的模面设计优化

阐述了响应面近似模型和空间映射技术用于快速模面设计优化的基本原理．为避免数值噪声干扰和求解隐函数敏度，提出通过多项式响应面方法构造真实目标和约束的逼近曲面，以光滑响应进行全局最优；并利用空间映射技术的代理模型确定新的响应面及其梯度，经精细模型修正优化方向和设计子域，使计算成本降低．算法结合有限元模拟实施，通过对金钣拉延成形和回弹补偿的分析证明，该算法具有很高的效率和鲁棒性，适用于模面设计优化．

Die-Face Design Optimization Using Response Surface Method with Space Mapping Technique

Conventional optimization algorithms are effective in solving general engineering problems, but lose their power in highly non-linear metal forming process. Our approach shows that a polynomial based on response surface method can be successfully utilized to eliminate computational noise and help to converge to a global optimum. Surrogate models in space mapping are used to determine response surfaces with their associated gradients, and then a fine model is applied to correct the design point for the next iteration. Thus space mapping makes it possible to reduce the total computation time to reach optimum solution. The proposed methodology has been realized with FE simulations, and examples demonstrate that it is efficient, accurate and robust for metal forming die-face design optimization.