复杂产品基于非自适应压缩采样的响应面仿真优化方法

In order to resolve the emerging efficiency problem in the simulation optimization of complex products design, a non-adaptive and compressive sampling response surface based simulation optimization approach is presented. The core idea includes 1) a higher sparse representation matching the intrinsic distribution characteristics is built so as to maximally reduce the required samples to be planned, and improve the efficiency of simulation optimization; 2) a unified, non-adaptive and compressive sampling method is proposed, which is incoherent to the shape variation of the response surface, and is very beneficial to multi-objective optimization based on simulation as there is no needs on multiple times of sampling on the design space, and additionaly promote the efficiency of simulation optimization; 3)an accurate response surface represented with a few sparse coefficients is robustly reconstructed based on 1-norm optimization from compressive samplings, and dynamically updated based on the Kalman filter, and then used to efficiently find the global optimal point through parallel optimization and elaborately design space shrinking.Finally, a prototype system of response surface based simulation optimization is to be developed on the above algorithms, and is validated with the servo control parameters optimization of a feeding system on the NC machines. Such approach is very meaningful on theory and engineering applications as it can relieve the technique bottleneck, and enables the problems of efficiency, adaptivity and robustness can be solved in simulation optimization, and then efficiently supports the optimal design of complex products.

针对复杂产品仿真优化效率等瓶颈问题，拟提出基于非自适应压缩采样的响应面仿真优化方法，通过对响应值固有分布特征的学习与匹配，建立与其相适应的响应面高稀疏性表示，以减少计算机试验设计采样，提高仿真优化效率；采用与响应面形状无关的统一非自适应压缩采样规划方法，突破现有方法与响应面形状相关的局限性，使其支持多目标（或约束）仿真优化，避免多次重复采样，进一步提高仿真优化效率；通过1范数响应面逼近及基于卡尔曼滤波的动态更新，从压缩采样中优化恢复更加稀少的表示系数，以及时稳定地获取精确响应面，并通过并行寻优与有效设计空间缩减，高效获取全局优化设计点。以此为基础，研制响应面仿真优化原型系统，并通过数控机床进给系统伺服控制参数优化整定进行应用验证。本项目研究有望突破现有方法所面临的技术瓶颈，解决仿真优化效率、适应性及稳定性等问题，为复杂产品优化设计提供理论方法及支撑软件，具有重要理论研究及工程应用意义。

项目针对复杂产品仿真优化中的效率、稳定性和适应性等瓶颈问题，提出了基于非自适应压缩采样的稀疏响应面仿真优化方法。利用Legendre多项式的正交性构建Legendre基，将仿真源模型在基函数上分解，提出了稀疏表示多项式响应面；针对复杂产品仿真模型的丰富多样，可能存在着在所选基函数上不够稀疏、采样点数量小于稀疏度的问题，提出了近稀疏响应面模型，能同时适用于稀疏度小于或稍大于采样点数量的情况；针对单一稀疏基难以稀疏表示所有复杂产品仿真模型的情况，提出了稀疏混合表示响应面，利用多组具有不同特征的稀疏基组合后对源模型进行稀疏表示，使稀疏响应面的稀疏性和适用范围大大提高；针对多目标（或多约束）优化问题需要构建多个响应面，而现有响应面方法需要对不同响应面分别采样，提出了稀疏响应面的非自适应采样方法，一组采样点可适用于多个响应面，避免了多次重复采样，突破了现有响应面方法的局限性；针对稀疏响应面的重构算法问题，分别提出了基于1范数、1范数+2范数，以及p（0<p<1）范数的三种响应面逼近方法，从压缩采样中优化恢复更加稀疏的表示系数，及时稳定的获得精确响应面；提出了稀疏响应面基于GPU并行寻优的方法，配合序列二次规划算法，能高校获取全局优化设计点。以此为基础，进行了仿真测试函数和真实工程实例的验证。在测试函数的验证中，稀疏响应面和其他常用响应面模型进行了对比，在更少的采样点情况下，稀疏响应面模型逼近精度和稳定性都有明显的优势，有效的提高了仿真效率。在汽车悬架运动学性能优化的工程实际案例中，仅用60个采样点构建了4个（目标、约束）响应面，较其他响应面方法，其响应面精度更高、优化结果更佳。总之，项目为复杂产品设计提供了理论方法及支撑算法，具有重要理论及工程应用意义。