Dn-最优确切设计的改进单纯形构造法及其在焊接工艺中的应用

Modified Simplex Algorithm of Dn-Optimal Exact Designs and Its Application in Welding Work

详细地研究了Dn 最优确切设计的数值构造法以及对称算法理论,对Evans的单纯形搜索来构造D 最优设计的方法进行了改进·应用改进的Fibonacci技巧来求新增设计点并引入负测度,采取双循环多点迭代的方法来构造多分量对数项混料模型的Dn 最优确切设计,提出了Dn 最优确切设计的改进单纯形构造法;并运用此新方法构造了多分量对数项混料模型的Dn 最优确切设计·将构造出的Dn 最优确切设计,应用在焊接工艺的配料比中,得到较好的预测与回归效果·从而有力地证明了该算法的有效性及Dn 最优确切设计的实际应用价值·

A new algorithm for generating Dnoptimal exact design was put forward by using the modified simplex iteration. On the basis of Evans′s simplex algorithm, the negative measure and Fibonacci sequence were introduced to generate the new design point. With the multicirculation method and symmetric theory, a modified simplex algorithm of Dnoptimal exact design was given. Through this algorithm, the multicomponent mixture regression models with logarithmic term was studied,and its Dnoptimal exact designs was given. An example of the application in a welding work was given, and it gives an evident proof for the Dnoptimal exact design.