## 3 Results
### Examples of Time-to-Failure Distributions with Complex-Valued Coloured Noise Excitations  
As stated above in Section 3.2, the choice of the specific coloured noises and the energy injection location brings different _von Mises Equivalent Stress PSD maps_. But the latter are fed to the cumulative damage and fatigue estimation spectral methods in Section 2.4 and Appendix D to obtain the _Equivalent Range of Stress Cycles_\(S_{eq}(x,y)\) of Equation (D.2). Therefore, a specific evaluation of the _Time-to-Failure_ maps in Equation (14) corresponds to each of the choices. Table 1 gathers the basic statistics of these different choices. Note that also the results from _white-rap noise_ are included, although the Auto Power spectrum of that excitation was not depicted, being the amplitude modulation even among the frequency lines, except for the the randomness in the _complex amplitude_ and _phase_. The starting of the crack, or of the failure, is supposed to happen in the dof with the minimal value of each _Time-to-Failure_ distribution, whereas the less injured location is the one with the maximum _Time-to-Failure_. As highlighted by the basic statistical descriptors  
\begin{table}
\begin{tabular}{r r r r r r r r r r} \hline
**Noise Colour** & **Dof** & \multicolumn{1}{c}{_min_} & **Dof** & \multicolumn{1}{c}{_max_} & \multicolumn{1}{c}{_Mean_} & \multicolumn{1}{c}{_Std.Dev._} & \multicolumn{1}{c}{_Variance_} & \multicolumn{1}{c}{_Skeuness_} & \multicolumn{1}{c}{_Kurtosis_} \\
**+ Shaker** & \multicolumn{1}{c}{_min_} & & **[h]** & _max_ & **[h]** & **[h]** & **[h]** & **[h\({}^{2}\)]** & & **[l]** & **[l]** \\ \hline violet rap S1 & 1 & 2.462e+00 & 1107 & 3.240e+04 & 9.713e+02 & 2.719e+03 & 7.394e+06 & 6.936e+00 & 5.943e+01 \\ violet rap S2 & 1 & 2.510e-01 & 934 & 5.300e+03 & 3.790e+02 & 5.502e+02 & 3.027e+05 & 3.372e+00 & 1.568e+01 \\ blue rap S1 & 343 & 1.661e-01 & 1687 & 3.567e+02 & 3.609e+01 & 5.053e+01 & 2.554e+03 & 2.654e+00 & 8.724e+00 \\ blue rap S2 & 1 & 5.277e-02 & 2325 & 1.139e+02 & 1.554e+01 & 1.605e+01 & 2.576e+02 & 2.173e+00 & 5.555e+00 \\ white rap S1 & 1 & 5.549e-04 & 699 & 1.803e-01 & 3.121e-02 & 2.384e-02 & 5.684e-04 & 2.019e+00 & 6.452e+00 \\ white rap S2 & 1 & 2.773e-04 & 1452 & 3.239e-01 & 3.368e-02 & 3.753e-02 & 1.409e-03 & 3.170e+00 & 1.364e+01 \\ pink rap S1 & 1 & 3.942e+00 & 756 & 1.166e+03 & 1.815e+02 & 2.068e+02 & 4.279e+04 & 2.155e+00 & 4.525e+00 \\ pink rap S2 & 1 & 3.405e-01 & 1277 & 2.423e+03 & 1.062e+02 & 1.755e+02 & 3.081e+04 & 4.862e+00 & 3.297e+01 \\ red rap S1 & 2907 & 1.063e+03 & 2835 & 4.354e+05 & 4.951e+04 & 5.640e+04 & 3.180e+09 & 2.175e+00 &(_min_, _max_, _Mean_, _Standard_ _Deviation_, _Variance_, _Skewness_, _Kurtosis_), each _Time-to-Failure_ distribution is totally deterministic, as the whole approach implies, and has no relation to a Gaussian distribution. Therefore, a strong variability in each _Time-to-Failure_ map is underlined by Table 1, linked to the excitation type and application point. For the specific specimen tested, most of the crack would start in dof 1, at a corner of the sensed region (but slightly inside the plate borders), where the plate undergoes stronger motions in comparison with other positions. Also, looking at the _Mean_ value of the _Time-to-Failure_ maps, it appears that shaker 2 gives generally a shorter expected life than shaker 1, with relatively minor values of _Standard_ _Deviation_ and _Variance_, except for the _white-rap noise_ excitation. This can be explained by stronger participations of the bending vibrations when excited from shaker 2, again underlining the relevance of the energy injection location in each specific _recetpaces_-based formulation. At the same time, it is important to recall the _scanning_-related problems in SLDV-datasets, especially from shaker 2, which surely have a distorting influence on the weight certain frequencies have in the calculations of \(S_{\text{eq}}(x,y)\). Again, the quality of the _full-field receptances_ is crucial for a successful SHIM.