topic Re: linéarisation of a quasi-linear function with logarithmic scale and logarithmic axis. in Mathcad

linéarisation of a quasi-linear function with logarithmic scale and logarithmic axis.

ESAB — Mon, 24 Nov 2025 15:10:20 GMT

Hello,

I’m trying to linearize this type of curve using the simplest possible function:

I tried many kinds of fits, but none of them worked.

Do you have any idea how to do that?

thank you, Emilien

Re: linéarisation of a quasi-linear function with logarithmic scale and logarithmic axis.

Werner_E — Mon, 24 Nov 2025 17:34:09 GMT

Are you looking for something like this:

BTW, not sure if it makes any sense, but a sinusoidal seems to make a nice fit (in the range given)

Prime 11 file attached

Re: linéarisation of a quasi-linear function with logarithmic scale and logarithmic axis.

ESAB — Tue, 25 Nov 2025 15:22:50 GMT

Hi Werner,

That's exactly what I wanted — a perfect fit! I've never found this kind of solution before.

Thank you very much.

Re: linéarisation of a quasi-linear function with logarithmic scale and logarithmic axis.

Werner_E — Wed, 26 Nov 2025 07:28:56 GMT

If the graph in the log-log-plot should be a straight line we know that the function must be y=a*x^b.
But its better to fit the logarithmic data to a linear function rather than fitting the original data to a power function. Fitting the original data would mean that the deviation from the first values (order of magnitude 10^6, 10^5) has a much greater impact on the calculation of the total error than the deviation from the last values (10, 1). Therefore, the solution (see the file I posted) is almost exclusively just the connection of the first two data points and the rest is virtually ignored.

EDIT:

Here is a way to get a pretty good fit using the original data and a power function. The method is to minimize the relative error instead of the absolute error(s) which genfit, line and the other fit methods do.

The outcome is (function f5) is a bit different from the result of the linear regression of the log data (Function f2) and on optical inspection I would say that f2 still is the better fit. But you have to decide which fit better your specific needs.