How can multiple curves (multiple families of curves) be fitted into one equation?
Thread Content
This post was last edited by yyuucc on 2019-8-18 21:25. As the title suggests, in the process of process design, it is common to need to refer to graphs composed of multiple curves, as shown in the figure below. If a unified equation of the form m1= f(vs/ut , uf/vt ) can be established, then calculations can be carried out in Excel without the need to consult such graphs. The question is: how can these multiple curves be fitted into one equation? Everyone is welcome to discuss.
This post was last edited by yyuucc on 2019-8-18 21:31. Let me offer some initial ideas: I first tried to represent it as a surface, as shown in the image above. But when trying to turn this surface into a surface equation, no suitable model could be found.......
Personally, I find it quite difficult; this involves curve fitting for two independent variables, and the results obtained are only approximate values, with some data points possibly showing significant deviations.
The ability to represent something as a cluster of curves rather than using a single equation is often due to the fact that the relationship in question is of a stable form and extremely complex; expressing it through an equation is not intuitive, and it is difficult to solve analytically.