Finding equation of a smoothing spline representing experimental data

Hello, I have plotted a graph from the experimental data nd have no idea of the fuction which satifies the graph behavior. So i tried the curve fitting tool and the smoothing spline fits my plot in the tool. How can i find this fuction which satisfies the graph. Any suggestions and better approaches with some step help is appriciated as i am new to matlab.

[Greg Dionne]

The tail end of your signal looks like it can be modeled by an AR process (take a look at arburg or yulear if you have the Signal Processing Toolbox).

Answer 1

[Mukul Rao]

Hello, if you are looking to export this spline fit as either M-code or an object, so it can be evaluated at new points, you can refer this link :

https://www.mathworks.com/help/curvefit/generating-code-and-exporting-fits-to-the-workspace.html#bryraj0

Note that splines are typically piece-wise polynomials, so there's no single function that represents them.

[Srimanish Reddy Enakonda]

Thanks for the link, i already tried it but the problem is, i want to implement that in a multi-body simulation tool which may not accept piece-wise functions for the engine RPM behavior. Is there any better way i can approach this challenge?

[John D'Errico]

You are not going to find a better choice than a spline to represent this curve, and allow you to interpolate it smoothly and accurately. I would point out the odd bump in the middle of the main descent of the curve. So the important question is why do you think the tool does not allow a piecewise function. Perhaps that is more because you don't know how to implement it? My point is perhaps you can use it, but merely need to learn how to do so?

[Srimanish Reddy Enakonda]

The tool doesn't allow a piecewise function because it just handles the interaction behaviour of the engine speed with an expression which is to be mapped to represent the RPM behaviour. But there is an option of MAX function as shown. I have sample formula which is formulated for a different graph. i.e, L=[1:1000]/20; K=max(max(max(abs(sin(L*5))+L/10-1-exp((5-L)*5),0),15-(L-15).^2),10-exp((14-L)*20));

I don't know how to acquire such an equation for any graph we needed or for the one I needed. It would be great to learn such a concept to solve any kind of experimental behaviour graph and can be fused with the simulation. Any suggestions and ideas are welcome.