Here’s a conundrum for you (or me actually, but any pointers would help).
I’m measuring the tension in a wire versus the movement of something on the end of that wire – the something is normally supported and the idea is to measure how much pull it takes to get it moving. In theory you’d see a small linear movement due to elastic stretch in the wire as the tension increases (measuring is done on the wire, not the weight), then a different linear movement as the tension overcomes the weight and the whole thing starts moving. Unfortunately noise, recording accuracy and general real life complications mean the two linear bits are a bit fuzzy and the transition between the two theoretically linear sections is a bit indeterminate.
So I need to fit a line to the first (elastic) part of the movement, a line to the second part of the movement and then the intersection between those two is a pretty good indication of the number I’m looking for. Trouble is it’s hard to spot the difference between the two sections of data to do the line fitting – I’m thinking along the lines of finding 2 lines (4 unknowns) and a transition point (1 unknown) that minimises the mean squared error of the data from the lines, but not sure that gives me enough to solve the problem.
I’ve got a degree in hard sums so can deal with mathsy stuff, can do all the Excel hacking but just wondered if anyone had any cunning pointers to likely looking algorithms/methods.