# Mechanism of Combustion Noise Influenced by Pilot Injection in PPCI Diesel Engines
## 3 Results and Discussion
### SWPT of In-Cylinder Pressure Signals  
From the previous section, the influences of the pilot and main combustion on low and mid-frequency combustion noise were analyzed separately. However, combustion noise in the high-frequency domain plays a key role in radiated noise as well, which should be investigated in detail. According to Figure 5, SWT could only decompose approximations, from which it is hard to obtain the  
Figure 8: Main combustion noise energy of D4 and D5. (**a**) Pilot injection timing = \(-9^{\circ}\) ATDC; (**b**) pilot injection timing = \(-14^{\circ}\) ATDC; (**c**) pilot injection timing = \(-19^{\circ}\) ATDC; (**d**) pilot injection timing = \(-24^{\circ}\) ATDC. information for high-frequency components. Nevertheless, SWPT can simultaneously separate the approximations and details of the signal, which would be expected to refine the combustion noise energy in the high-frequency segment. Therefore, with Daubechies 10 as the wavelet, SWPT was performed and the in-cylinder pressure signal was decomposed into three layers. Figure 9 shows the tree structure of the three-layer SWPT. Here, T\({}_{3,n}\) symbolizes sub-signal n in the third layer. The frequency range of each sub-signal is listed in Table 4. The sub-signal, T\({}_{3,0}\), was not used to investigate high-frequency combustion noise, due to the fact that it only contains information about the low and mid frequency segment. In this section, the sub-signals are also divided into two phases just like the previous section, and the pilot and main combustion noise energy in the high-frequency domain were both calculated using the same computational method (Equation (2)). The results are shown in Figures 10 and 11. Obviously, pilot injection influences the combustion noise energy of the sub-signals, T\({}_{3,1}\) and T\({}_{3,3}\), whose frequency bands are 1125-2250 Hz and 3375-4500 Hz, respectively. Furthermore, a larger pilot injection quantity results in higher combustion noise energy in general. Additionally, the combustion noise energy level drops with the pilot injection timing advancing, which corresponds to the inference in Section 3.3. Additionally, Figure 11 depicts the main combustion noise energy in the high-frequency domain. It is worthy to note that the main injection only affects the sub-signal, T\({}_{3,1}\), corresponding to the frequency segment of 1125-2250 Hz. When the pilot injection mass increases, the combustion noise energy of the main injection is progressively reduced. Besides, earlier pilot injection timing causes a larger main combustion noise energy only in the case with a pilot injection quantity of 2 mm\({}^{3}\), and significant changes are not observed for conditions of other pilot masses, which reveals that the influence of the pilot injection timing on combustion noise energy during main combustion is quite small. \begin{table}
\begin{tabular}{c c} \hline \hline
**Sub-Signals** & **Frequency Band (Hz)** \\ \hline T\({}_{3,0}\) & 0–1125 \\ T\({}_{3,1}\) & 1125–2250 \\ T\({}_{3,2}\) & 2250–3375 \\ T\({}_{3,3}\) & 3375–4500 \\ T\({}_{3,4}\) & 4500–5625 \\ T\({}_{3,5}\) & 5625–6750 \\ T\({}_{3,6}\) & 6750–7875 \\ T\({}_{3,7}\) & 7875–9000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Frequency band of each sub-signal in the SWPT. Figure 9: Tree structure of the three-layer stationary wavelet packet transforms. Furthermore, for the purpose of determining the significant factor that influences high-frequency combustion noise, comparisons between pilot and main combustion noise energy, namely Figures 10 and 11, were carried out. In the condition of retarded pilot injection timing, just like -9\({}^{\circ}\) ATDC, although the pilot mass (2 mm\({}^{3}\)) is relatively smaller than the amount of main injection fuel (30 mm\({}^{3}\)), the combustion noise energy of pilot injection is nearly equal to that of main injection. In addition, the pilot combustion noise energy is significantly larger than the main combustion noise energy when the pilot quantity increases over 2 mm\({}^{3}\).