## 5 Experimental Results and Discussion  
### CWT Analysis  
Continuous wavelet transform (CWT) is used to extract dynamic responses from the non-stationary raw vibration data and localize them in joint frequency and time domains. To obtain reliable results, an average of 80 engine cycles was used to further suppress random noise and short duration interferences. Figure 19 shows a typical CWT result of the liner vibration under the operating condition of 1800 rpm and 40 Nm. The time-frequency characteristics in Figure 19a are very informative and can be viewed with key patterns as follows:  
Impact Co and Impact Cs mark the significant responses, which occur near combustion TDC at 360\({}^{\circ}\) in the frequency ranges of 6000 to 8000, and 8000 to 12,000 Hz. These events well correspond to the in-cylinder peak pressure, which conforms to numerical predictions in Section 3.2 and Figure 11.  
Impact A to Impact F mark other distinctive responses, which correspond with piston slap-induced dynamic events and are consistent with Section 3.3 and Figure 13. The frequency band of these dynamic responses, from 900 to 4000 Hz, is highly correlated with the liner's first four modal frequencies. Three other events, Impact G, H and I, around 2000 Hz, predicted in the dynamic simulation are also observable in Figure 19a. It follows that repeated impacts can be caused by a sustained high-amplitude side-thrust force, agreeing with the prediction of the established FE model. Since the peak pressure and PRR of biodiesel are not as high as those of diesel, the combustion shock-induced responses Impact Co and Impact Cs of biodiesel are located in the frequency range from 5000 to 7000 and 10,000 to 12,000 Hz, slightly lower than the diesel, as shown in Figure 20. However, in the entire work cycle, biodiesel showed more abundant and intensive response events than the diesel, which is agreeable with the numerical prediction in Section 3.3 and Figure 14. This may be due to the prolonged combustion duration as a result of a larger amount of biodiesel injection (biodiesel possesses a lower calorific value). The extended mixed-controlled combustion phase can cause a relative increase in the kinetic energy of piston side slaps, thereby resulting in the increase in response intensity and the number of observable events. Figure 19: Continuous wavelet transform (CWT) of vibration signal fueled with diesel under 40 Nm and 1800 rpm: (**a**) CWT result of measured acceleration response; (**b**) Measured in-cylinder pressure and calculated piston side-thrust force. The time-frequency responses of the liner to combustion shocks under a lower load are similar to those under higher load conditions, which are marked as Impact Cs in Figure 21. However, the combustion is smoother when they are in a frequency band from 4000 to 7000 Hz, which is 2000 Hz lower than that of the higher load. Smoother combustion leads to a piston movement that excites a greater number of low-frequency components, so that almost all slap-induced events over 2000 Hz are markedly reduced. Figure 21: Continuous wavelet transform (CWT) of vibration signal fueled with diesel under 10 Nm and 1800 rpm; (**a**) CWT result of measured acceleration response; (**b**) Measured in-cylinder pressure and calculated piston side-thrust force. Figure 20: Continuous wavelet transform (CWT) of vibration signal fueled with biodiesel under 40 Nm and 1800 rpm; (**a**) CWT result of measured acceleration response; (**b**) Measured in-cylinder pressure and calculated piston side-thrust force. As shown in Figure 22, after the combustion TDC, the slap-induced events fueled with biodiesel are weaker than those with fossil diesel, which may be attributed to the enhanced compound effect between the combustion force and the inertia force of the piston, as mentioned in Section 3.4. There are significant differences in the response characteristics between the different fuels.