# Mechanism of Combustion Noise Influenced by Pilot Injection in PPCI Diesel Engines
## 3 Results and Discussion
### SWT of In-Cylinder Pressure Signals  
Although CPLs can illustrate the impacts of the pilot and main injection on combustion noise, the analysis proceeds only based on the overall combustion noise level and the effects of the pilot and main injection on combustion noise have not been extracted separately. Therefore, a signal decomposition technique is required in this section. DWT has been proven to be an effective tool for decomposing signals. An approximation and a detailed sub-signal are obtained by the decomposition of a single step DWT, which contains the low and high-frequency components of the original signal. However, the procedures of up and down sampling in DWT lead to aliases of the sub-signals [29]. Therefore, the wavelet energy of the sub-signals, which is regarded as an important quantifier for signal intensity [28], cannot be compared precisely. However, in order to address the issues of DWT, a powerful wavelet transform algorithm called SWT is carried out. Instead of the upsampling and downsampling of the signal in DWT, upsampling of the filter coefficients is employed in SWT, and consequently the translation-invariance is accomplished. Thus, each level of SWT contains the same number of samples as the input. Figure 5 shows the tree structures of five-layer SWT. However, SWT can only decompose approximations, namely low and mid-frequency segments. Therefore, SWT is only suitable for the analysis of combustion noise in low and mid frequency ranges. Figure 4: Cylinder pressure levels. (**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. In this research, using Daubechies 10 as the wavelet, in-cylinder pressure was decomposed into five layers by SWT, including an approximation (A5) and five details (D1, D2, D3, D4, D5). Table 3 shows the frequency band of each sub-signal. The sub-signals, D5 and D4, were selected to investigate the combustion noise in the low and mid frequency segments. Nevertheless, the influences of the pilot and main combustion had to be separated. Thus, the sub-signals were divided into two phases: Pilot and main, as presented in Figure 6. The quantifier of combustion noise intensity was the wavelet signal energy, which is defined as:  
\[E_{i,n}=\sum\
olimits_{k=1}^{j}{\left|{x_{n,k}}\right|^{2}}, \tag{2}\]  
where integer \(n\) represents a sub-signal serial number, \(x_{n,k}\) is the SWT coefficient,  
Figure 7a-d present the combustion noise energy of D4 and D5 during the pilot combustion phase for the condition of various pilot injection timing and pilot injection quantity. As can be seen, the values of combustion noise energy in the low-frequency segment (D5) initially drop, and subsequently rise with the increasing pilot injection quantity. It can be interpreted that a larger amount of pilot injection fuel causes more violent pilot combustion, and partial energy in the low-frequency range may transfer to the high-frequency segment, which will be discussed in the next section. However, when the pilot mass is extremely large (8 mm\({}^{3}\)), the combustion noise energy level for all the frequency ranges is largely increased. In addition, advancing the pilot injection timing will also enlarge the combustion noise energy generated by pilot combustion in the low-frequency domain. That is because an extension of the heat release duration of pilot combustion will smooth the process of pilot combustion, which mitigates the mid and high frequency combustion noise energy, as revealed by D4 in Figure 7. Hence, the energy of combustion fluctuation is mainly concentrated on the low-frequency segment. Moreover, for the mid-frequency range, a larger pilot quantity results in higher combustion noise energy.