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微分参数 [wēi fēn cān shù]
differential parameter
- 摘要为了验证最佳摄动量法在偏微分方程参数反演中的有效性，基于最佳摄动量法研究了一维波动方程参数反问题，得出了此类问题的数值解法。
In this paper, for proving the efficiency of the best perturbation method in getting the parameter of partial differential equations, the parameter inverse problem of one dimensional wave equation is studied based on the best perturbation method, so as to obain the numerical method to the problems of the kinds. - 文摘:为了解决直接求解展成法加工中存在的复杂双参数包络问题时的困难，提出通过数学变换，将此包络问题转化为假想平面产形轮与工件之间的展成问题来进行研究.推导了假想产形面的方程和各阶偏导矢，于是可获得产形面的微分几何参数.通过分析假想平面产形轮与工件之间的展成运动，即可得到被展成齿面上任意指定点的全部一至三阶微分几何参数.
Abstract: In order to solve the double parameters enveloped in the geartooth flank generating,the complicated double parameter envelope is simplified to the generating process between work-piece and imaginary crown generating gear by means of mathematical transformation.The equation of the imaginary crown generating surface and the partial derivatives are deduced,so the differential geometric parameters of the generating surface can be obtained.By analyzing the generating motion between the imaginary crown generating gear and the work-piece,all the first to third order geometric parameters of the generated tooth flank at any given point can be calculated. - 本文应用系统理论，建立了水质多参数输入输出之间的响应关系；根据河流水文水质变化特点和参数反问题的需求，建立了水质常微分方程多参数反问题模型.根据常微分方程参数反问题的数学理论，作者给出了两参数和多参数水质常微分方程反问题的解的存在性、唯一性的理论证明过程和结论；还针对水质现有监测资料的测验误差和插值近似计算误差造成参数反问题的不稳定性，将三次样条插值函数、超定方程最小二乘法和正则化算法有机地结合使用，成功地给出了水质参数反问题的稳定化算法.最后给出了应用计算结果.
The water quality respond relation of input-output measurements are established by systematic theory in this paper.According to the peculiarity of hydrology and the necessity of water quality inverse problem the multi-parameter inverse problem model based on ordinary differential equation is developed.The existence and uniqueness of the solution of the ordinary differential equation about two parameters or multi-parameter are to be proved.The unstability depending on errors between monitoring data and interpolation approximate data are analyzed and demonstrated.Cubic spline interpolation function,the least two multiply and positive rule method are conjoined for obtained solution of multi-parameter.The results from this algorithm indicats its efficient to the multi-parameter identification in water quality modeling.
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