4569846498

436 Multibody Systems Approach to Vehicle Dynamics
n
( ∑
) 2
yi(
xi
x)
i1
Variation due to linear effect S
n
(7.46)
2
( x x)
In addition, the sensitivity of the data set (the ratio of input to output) is
calculated thus:
∑
i1
i
∑
∑
n
1
i(
i i
n
( x
i1
i
y x x)
x)
2
(7.47)
The similarity to the standard least squares method is apparent. The interested
reader is urged to consult Wu and Wu (2000) for further, more
detailed description and background to the method. In that text, the symbols
used differ slightly. The symbols used here have been chosen to avoid
a clash with the familiar vehicle dynamics symbols in use. To use the method,
a typical set of predicted or logged values is taken, consisting of yaw rate
(t), handwheel angle (t) and forward speed V(t). Values for stability factor,
K, and wheelbase, L, are presumed known for the vehicle. Using the
ideal function, ‘expected’ values for are calculated and taken as the input
data series, x. The ‘real’ – either logged or predicted – values of are taken
as the output y and the calculations for and performed as described above.
Once signal-to-noise ratios have been calculated for each ‘state’ in the
orthogonal array, they are processed to produce an effects plot of the type
shown in Figure 7.34. In this case, the array was an L 16 (5-1) two-level array
for processing five design variables and their possible interactions.
Variable A is shown to be dominant, with variables B and E important also.
The signs of the effects are not all the same; variable A is ‘less A gives more
response’ while B and E are ‘less B/E gives less response’. There are no
significant interactions between the variables. Effects plots are produced for
and separately. To calculate effects with the array shown in Figure 7.32,
results from runs 1, 3, 5, 7, 9, 11, 13 and 15 are averaged to give the ‘’
result for variable A. The remaining columns give the ‘’ result for variable
A. For variable B, runs 1, 2, 5, 6, 9, 10, 13 and 14 give the ‘’ result, and so
0.004
0.003
0.002
0.001
0
0.001
0.002
0.003
0.004
A B A × B C A × C B × C D × E D A × D B × D C × E C × D B × E A × E E
Fig. 7.34 A typical effects plot produced by processing the results from an
orthogonal array