【摘要】 为解决现有基于统计和随机过程理论等方法无法给出粗糙度参数直观计算的问题,基于函数逼近理论提出一种通过优化函数模板来构造粗糙度参数计算公式的方法.首先利用遗传算法优化初始函数模板各参数,得到一组全局近似最优解集;再以此解集作为初值,用Levenberg–Marquardt(LM)算法求解更好的局部最优解集,并交替使用遗传算法和LM算法,直到收敛或达到算法最大切换次数;最后根据收敛精度、逼近性能对函数模板进行增长或剪枝,并继续交替使用2种优化算法直到满足循环退出条件.数值实验表明,该算法具有较好的寻优能力和较强的鲁棒性,能用于构造粗糙度参数计算公式,操作简单且具有一定的工程实用价值.更多还原

【Abstract】 Based on the function approximation theory, the formulas for calculating surface roughness parameters are obtained by optimizing the coefficients of the function template. At first, a global approximate solution set is obtained by optimizing the initial function template using genetic algorithm. Then, the set is taken as the initial value of Levenberg–Marquardt(LM) algorithm to obtain the better local optimal solution set, and the two algorithms are used in turn until the solutions are convergent or the largest switching times are reached. At last, according to the convergence precision of the solutions and the value of each monomial, the growth or trim operation is conducted on the function template, and the two optimization algorithms are executed again; until the termination conditions are satisfied. The numerical simulation examples show the algorithm has the better ability to find the optimal solution and the good robustness. Moreover, the method is easy to carry out, and can be used in engineering practice.更多还原