## 3 Materials and Methods
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Data** \\ \hline Engine type & Spark-ignition, direct-injection \\ Engine displacement volume [cm\({}^{3}\)] & 1984 \\ Engine maximum power [kW] at rotational speed [rpm] & 169/4700–6200 \\ Engine maximum torque [Nm] at rotational speed [rpm] & 350/1500–4400 \\ Vehicle mass [kg] & 1347 \\ Vehicle mileage [km] & 30,000 \\ Transmission type & Automatic \\ Production year & 2022 \\ Emission class & Euro 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the vehicle used for tests in real road traffic conditions. \[\mathrm{P_{r}(n)}=\frac{\mathrm{P(n)}}{\mathrm{P_{ext}(n)}} \tag{2}\]  
where P is the engine power and \(\mathrm{P_{ext}}\) is the effective power corresponding to the maximum engine control setting (based on external characteristics). The above variables can be examined in the following domains [27]:  
* Time;
* Frequency;
* Process values. Statistical characteristics and correlation characteristics could be determined within the time domain. In the frequency domain, primarily, power spectral density was studied [27]. In the studies of variables in the domain of their values, probability density or histograms, linearly related to probability density [27], were determined. The research procedure used in this paper included the following elements:  
1. Registration of the investigated processes in the RDE test. Start-up in the RDE test was performed for an engine that was not heated to a stabilized operating temperature;
2. Low-pass filtration of the recorded process data in order to reduce the share of high-frequency noise in the processes. A fifth-order Savitzky-Golay filter was used for filtration;
3. Determination of statistical characteristics [27] of the investigated processes:  
* Minimum values--Min;
* Maximum values--Max;
* Range--R;
* Mean value--AV;
* Standard deviation--D;
* Coefficient of variation--W;
* Ratio of range to standard deviation--Z;
* Kurtosis--K;
* Skewness--S.
4. Process standardization;
5. Determining the linear correlation coefficients between the investigated standardized processes;
6. Determining the probability density--H--of the investigated standardized processes;
7. Determining the power spectral density--A--of the investigated standardized processes;
8. Formulating the conclusions. A brief explanation of the statistical measures used in this paper is provided below to assist the reader in interpreting the research results:  
* A random variable is a function that assigns numbers to elementary events. Intuitively, it is a projection that transfers the study of probability from an inconvenient probability space to the well-known Euclidean space. Random variables are measurable functions with respect to probability spaces. * A probability space is a structure that allows the description of a random process (i.e., a process the outcome of which is random) by defining the space of elementary events and defining a probability function on its subsets that satisfies the appropriate axioms. * A statistical characteristic is a property of a population (a set of similar items or events) that is the subject of a statistical study. * The range is the difference between the largest and smallest values of a statistical characteristic in a set (or the difference between the largest and smallest observed values of a variable). * The mean value (expected value) is a concept from probability theory, meaning the average, probability-weighted value of a random variable. It is the expected average result of a random experiment repeated many times. * The standard deviation is a classical measure that provides information about the spread from the mean value. * The coefficient of variation is the ratio of the standard deviation and the mean value (expected value).