Antecedentes históricos del principio de legalidad

The correlation analysis is done for three groups: All experiments (ALL EXP) and its two sub-groups of all experiments with centered steering axis (CTR ALL = STA + BPC), and finally all experiments with BSTAM in active mode (BSTAM).

Within these three groups, all characteristic values are correlated with one another173, obtaining correlation coefficients R and probability values p for the probability of get- ting a correlation R as large as the observed value by random chance, when the true correlation is zero. In case p is small (p < 0.05) the correlation R is assumed to be sig- nificant. In a next step, scatter plots are generated and linear regression lines are intro- duced174, as exemplarily illustrated in Figure 5.4.

172 _{Note that a much higher number of tests was conducted especially for the standard reference}

(STA LOW). However, the captured data files were physically corrupted and could not be evaluated. Moreover, many more tests were done during the development phase of the prototype motorcycle with different tires and only partially functional measurement setup. While these are consequently also not taken into account for numerical evaluation, the gained subjective impressions of the test rider are however a valuable help for the interpretation of the remaining small number of complete data sets.

173 _{Using the “corrcoef”-command in MATLAB ® Software.} 174 _{Using the “polyfit”-command in MATLAB ® Software.}

Setup R p g1 in Nm/(m/s²) g2 in Nm

ALL EXP 0.691 1.52 10-41 _{7.73 -17.2}

CTR ALL (STA + BPC) 0.512 2.53 10-12 _{5.62 -1.55}

ALL BSTAM 0.197 0.0319 2.27 3.99

Figure 5.4: Example of a scatter plot between two characteristic values

Along with the correlation coefficients R and probabilities p, also the slope and axis intercept parameters g1 and g2 of the regression lines have been computed for all possi-

ble correlations. If x is the first characteristic value and y the second that is correlated to the first (in the example x is the mean deceleration and y the steering torque deviation), the regression line is defined by the following equation:

(5.24)

The unit of the slope parameter is [g1] = [y]/[x] and that of the axis intercept [g2] = [y],

which can be read for the example from the table in Figure 5.4. As a side note, the full correlation results are listed in tables (for R, p, g1, and g2 parameters) in appendix A.5.

Regarding the example scatter plot with the correlation of steering torque deviation and mean deceleration in Figure 5.4, it is apparent, that BSTAM experiments have typically been conducted at partial decelerations, while 2/3 of experiments with centered steering

axis have been done at high decelerations (ABS). A high correlation of R = 0.691 has been found for all experiments, while the decomposition into the two subgroups reveals

5.3 Global Analysis of All Test Results

setups with centered steering than for BSTAM (R = 0.197, g1 = 2.27 Nm/(m/s²)), which

hints at a certain decoupling of the correlation through BSTAM.

Results of Correlation Analysis

Finally, all combinations of characteristic values, where a correlation of R ≥ 0.35 is obtained at least within one of the three experiment groups (ALL EXP, CTR ALL, ALL BSTAM) are analyzed in detail and entered into global correlation charts (cf. Figure 5.5) that follow the arrangement scheme presented in Table 5.3.

Only correlations with a correlation coefficient of R ≥ 0.3 are entered into the scheme, following the illustration patterns as shown in the legend of Figure 5.5. For reasons of a better overview, dominating correlations (towards deceleration, pressure increase rate, stationary steering torque demand and dynamic steering unsteadiness) have not been illustrated using arrows, but rather letters (a, p, T, W) in either of the four corners of each characteristic value field correlated to it.

The correlation charts in Figure 5.5 (a through c) are to be regarded differentially. First, the chart (a) for ALL experiments confirms both the expected horizontal and vertical coupling among the characteristic disturbance values along the chain of effects. Moreo- ver, a strong coupling of the majority of variables is given towards the mean pressure increase rate, the mean deceleration and the stationary steering torque. Before the back- ground, that the experiments with active BSTAM exhibit a distinctively higher station- ary steering torque and were moreover conducted as partial braking experiments, while the experiments with centered steering axis comprise 2/3 of maximal braking maneuvers,

it lies at hand, that the picture will change, if the correlations are regarded separately for the two subgroups of experiments.

Regarding correlation chart (b) for the experiments with centered steering in Figure 5.5, the strong horizontal coupling of disturbance values remains approximately at the same level, while the vertical coupling along the chain of effects appears partially weaker, especially between the steering and roll disturbances. It is however still present with correlation factors R > 0.4. While the coupling of many variables towards the pressure increase rate and mean deceleration remains, the coupling towards the initial steering torque is lessening, however still present. This can be explained by the fact of variations in riding style (lean in, lean with, and lean out), which will be addressed in more detail for the analysis of individual experiment groups in chapter 5.4.

Regarding the correlation chart (c) for the BSTAM experiments in Figure 5.5, the hori- zontal coupling remains at a lower level and the vertical coupling along the chain of effects is greatly weakened, especially between the disturbances in steering torque and steering angle values. Most of all, the coupling of all result variables towards the brake pressure increase rate and the mean deceleration level are completely nullified, under-

lining the effectiveness of BSTAM in this respect. A relatively strong coupling of some variables remains however towards the stationary steering torque. The reason is, that the higher the compensation ratio is chosen, the higher is the stationary steering torque demand, while at the same time reducing the disturbance values to a greater extend. Hence, the resulting negative correlations (marked “-T”) are arising.

As a side note on negative couplings that are valid for all three experiment groups, the higher the initial speed, the lower the initial steering angle in accordance with chapter 2.1.5. And, the more the rider starts off with a lean in riding style, the less will he be moved further inward for a stand up of the vehicle.

In conclusion of the correlation analysis it can be stated, that both the horizontal and vertical coupling are there, as expected, so that the variables in each group may be discussed together, as well as along the chain of effects. This finding is also in line with the subjective impression of the test rider.