中文摘要：

针对性能指标与影响因素间响应模型未知的试验设计与分析的优化问题进行理论研究和算例分析。利用装备系统的先验信息扩展回归基函数，构造二次回归模型来刻画系统的内在关系。基于模型驱动的最优设计，提出了相应的点交换迭代法以及梯度上升法选取最优试验点。为解决试验点数小于回归函数的维数时信息矩阵退化的问题，提出了基于成本和距离的“再筛选”方法，从已有的最优确切设计基础上“再筛选”试验点。将稀疏理论引入到回归试验设计中，把具有稀疏性的回归试验设计模型参数估计问题转换为稀疏重构问题。利用MP算法对回归模型进行参数估计，保证较高的参数估计精度。结合算例，对提出的试验设计优化方法和参数估计方法进行验证，表明最优确切设计比经典最大熵设计的精度更高。

英文摘要：

Aiming at a specific case that the response model between the performance index and influenc- ing factors is unknown, this paper discusses the optimization problems of its corresponding experimental design and analysis theoretically and confirms methods by an example analysis. Prior information of the equipment system is used to extend regression basis functions, then the quadratic regression model is constructed to depict the internal relation of the system. Based on model-oriented optimum design, this paper proposes two optimization algorithms named point-exchange method and gradient ascent method to obtain optimal experimental points. Knowing that if the number of supporting points is less than the dimension of regression parameter vector, the determinant of information matrix is identically equal to zero, so that the paper suggests two ＇re-sift＇ principles of ＇cost＇ and ＇distance＇ to obtain reduced op- timal experiment points based on the pre-existing optimal exact design. Sparse theory is introduced to experimental analysis, transforming the parameter estimation problem of the regression model into a sparsity-reconstruction problem. Adopting MP algorithm to estimate parameters of the model can guarantee high accuracy. According to the empirical analysis, it can be concluded that optimal exact design is more accurate than classical maximum entropy design using MP algorithm.