How should I determine the best alpha after L-curves as shown in following figure? The curve is not smooth enough, do I need a curve for fitting? Then how to determine the best alpha？

Hi @Anne_st
the choice of alpha is a bit arbitrary unfortunately. The L curve analysis helps, but it is not always a clear cut. In your case I would choose 2e-9 but look at the friction coefficient to make sure it is not too noisy
Cheers
Mathieu

6 days later

Thanks for your reply！
Furthermore，in L-curve analysis, can the value of alpha not select corner value? What other indicators can be combined to determine the value of alpha? Such as the error between simulated and observed speeds? I saw in an article that the alpha he chose was not the corner value in L-curve. Is this method advisable?

Hi @Anne_st
as I mentioned in my previous message, there is no "right" or "wrong" way to select the amount of regularization you want to apply. It is very subjective. The L-curve analysis is simple because you get to find the highest level of regularization that does not affect the overall fit to the data. But sometimes, if you plot your control (B or friction coefficient) you may still see that it is very irregular and you may want to apply a bit more smoothing. That's what I generally do and it looks like it is the strategy that was adopted in the paper you mention. The corner is also never very clear, so there is a lot of leeway. In most publications, people don't even do an L-curve analysis and choose parameters based on "experience". Don't overthink it really...
Mathieu