## 3 Results of Diagnostic Tests
### Selection of Signals and Diagnostic Parameters  
The experiment planning methods were also applied in the selection of useful diagnostic symptoms. The signal vector was reduced in the preliminary tests which use statistical measures [1; 3; 4; 19]. The basis for this was a correlation matrix for the selection of parameters independent of one other. Figure 6: The influence of rotational speed of camshaft \(n_{\alpha}\) on values of amplitude estimates of acceleration vibration signal on the injector valve for fuel setting 58% along with an approximation line for the polynomial model (**a**); (**b**) the effect of engine load on the amplitude measures of vibration acceleration signals received in the injection subsystem along with an example error field: _aver_—average value, peak—crest value, \(p\)-\(p\)—peak to peak value, _rms_—root-mean-square value, _rmsb_—_lower borderline_, _rmst_—upper borderline, _RL_—relative load. Figure 7: An example of original acceleration vibration signal (**a**) and continuous wavelet transform (**b**). The coefficient of correlation was determined between values of diagnostic parameters obtained in subsequent measurements and independent variables by the formula:  
\[k=\frac{\sum\limits_{i=1}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{\sqrt{ \sum\limits_{i=1}^{n}{(x_{i}-\overline{x})}^{2}\sum\limits_{i=1}^{n}{(y_{i}- \overline{y})}^{2}}} \tag{18}\]  
where: \(i\)--the sequence number of the input or output quantities, \(x_{i}\)--successive value of the given entrance size, \(\overline{x}\)--average value of the input quantity in the set of observations, \(y_{i}\)--successive value of the given diagnostic parameter, \(\overline{y}\)--average value of the diagnostic parameter in the set of observation. A hypothesis of a lack of correlation between variables was also tested. The similarity of bivariate distributions of the input quantities and diagnostic parameters in the general population was examined. Based on the test results, the hypothesis was verified that the measured input values \(X\) and the diagnostic parameters \(Y\) are not correlated, i.e., \(H_{o}\): \(k=0\), against the alternative hypothesis \(H_{1}\): \(k\) 0. The value of the correlation coefficient \(k\) from the sample and the Student's t-value were calculated:  
\[t=\frac{k}{\sqrt{1-k^{2}}}\sqrt{n-2} \tag{19}\]  
If inequality is obtained from the comparison of the calculated value of t with the critical value, the \(H_{o}\) hypothesis about the lack of correlation between diagnostic parameters and the input quantities should be rejected. When, on the other hand, it has no basis to reject the null hypothesis \(H_{o}\), the variables mentioned are not correlated (the number \"0\"). Values of the correlation coefficient [3; 4; 19] for assessment of the usefulness of exemplary diagnostic parameters in time, amplitudes, frequency and wavelet domain was presented in work [18]. For the assessment of diagnostic parameters, the values of statistical measures were also determined for the spectral parameters in the preliminary tests and are presented in Table 1. A second degree spectral moment is calculated from the formula:  
\[m_{2}=\int\limits_{-\infty}^{\infty}{f^{2}S(f)df} \tag{20}\]  
The values of the correlation coefficient within the scope of very strict dependencies (more than 0.9) were considered useful (Figure 8). The statistical analysis presented enabled the preliminary reduction of the observation vector in the principal research. Spectral polyharmonic symptoms in the low frequency band have proved to be the most useful in the studies conducted hitherto [3; 19].