Cost Function Noise
The numerical calculation of the electromagnetic field introduces various sources of noise to the cost function, particularly because of changes in the finite element mesh. You must provide the optimizer with an estimate of the noise. The noise indicates whether a change during the solution process is significant enough to support achievement of the cost function.
For example, if the cost function, c, is
c = 10000 • |L11|2
where |L11| is the magnitude of the inductance, at the minimum, |L11| is expected to be very small, |L11|≈ 0.
From the solution setup, the error in |L11| is expected to be EL11 ≈ 0.01. The perturbed cost function is therefore
cperturbed = 10000 • (|L11|min + EL11)2
Near the minimum, the error in the cost function Ec is given by
Ec = cperturbed - cmin = 10000 • (0.0 + 0.01)2 - (10000 • 0.0) = 1.0
Therefore, the cost function noise would be 1.0.