1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation:
if C=A+B or C=A−B ΔC=ΔA+ΔB
These formulas are derived from the expression for the differential of a function of multiple variables:
if C=f(A,B) dC=∂C∂AdA+∂C∂BdB⇒ΔC=∂C∂AΔA+∂C∂BΔB
and I think that makes sense because the value C is just a function of two variables that happen to be measurements.
2) But this morning, I was told that this is wrong and I should actually use these instead:
if C=A+B or C=A−B (ΔC)2=(ΔA)2+(ΔB)2
which are apparently derived from a general formula:
(ΔC)2=(∂C∂x1Δx1)2+(∂C∂x2Δx2)2+...
or
ΔC=√(∂C∂x1Δx1)2+(∂C∂x2Δx2)2+...
3) So:
- Why is this formula better?
- Where does it come from?
- What does it actually represent? (Do I recognize the shape of a norm in that last formula?)
- What is wrong with the formula of the differential?
I'm asking a lot, but the propagation of uncertainty always confused the ship out of me.
No comments:
Post a Comment