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6.6 RLC-Circuit Example 89

Its amplitude is governed by the impedance Z of the circuit and there is a
phase shift . Both depend on the frequency f and the components in the
circuit:

v

u
u

f

Z Z R L C t R
f L (6.4)

f C

f L
f

R L C atan fC (6.5)
R
Following Friedman (1991), we varied the variables in the range:
R
L [H]
C F

f
[ Hz]

which results in a impedance range Z and the phase lag

between .
The PSOM training sets are generated by active sampling (here com-
puting) the impedance Z and for combination of one out of n resistors
values R, one (of n) capacitor values C, one (of n) inductor values L,at
n different frequencies f. As the embedding space we used the d
dimensional space X spanned by the variables x R L C f Z .

Type n Z-RMS -RMS Z-NRMS -NRMS
C-PSOM 3 243 31 0.51 0.43
C-PSOM 4 130 25 0.24 0.34
L-PSOM 3 of 5 61 25 0.11 0.34
L-PSOM 3 of 7 25 19 0.046 0.25

Table 6.1: Results of various PSOM architectures for the m dimensional
prediction task for the RLC circuit impedance.

Table Tab. 6.1 shows the root mean square (RMS and NRMS) results
of several PSOM experiments when using Chebyshev spaced sampling
and nodes placement. Within the same parameter regime Friedman (1991)
reported results achieved with the MARS algorithm. He performs a hyper-
rectangular partitioning of the task variable space and the fit of uni- and