## 4 Biodiesel Fuels
The engine was operating at 1600-2000 rpm and constant injection pressure of 35 MPa, under a full-load condition. Seven fuel blends with varying ethanol concentrations were prepared, in accordance with ASTM D5501 standard: D100 (pure diesel), D98E2 (98% diesel + 2% ethanol), D96E4, D94E6, D92E8, D90E10, and D88E12. The RMS and spectral kurtosis (SK) are two well-adopted statistical tools in fault diagnosis of rotating machines [63; 86; 87; 88; 89; 90; 91], to assess energy, peakedness (sharpness), and impulsiveness of the vibration signals. While the RMS strongly depends on the acceleration amplitudes and engine speed of a system, the kurtosis is tremendously noise-sensitive and can be markedly affected by the fuel blend type and signal processing techniques (e.g., band pass filter, envelope detection). In their work, the RMS and kurtosis of the vibration (acceleration) signals were calculated to evaluate the efficacy of the engine:  
\[a_{t}=\sqrt{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}. \tag{15}\]5 \[a_{t}=\sqrt{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}. \tag{15}\]6  
where \(N\) is the number of points within a time period, and \(x(t_{k})\) is the acceleration at time of \(t_{k}\). Furthermore, the vibration analysis was conducted by using fast Fourier transform (FFT) and discrete STFT algorithms:  
\[a_{t}=\sqrt{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}. \tag{15}\]7  
where \(x(j)\) is a digital dataset with \(N\) outputs \(X(k)\); and  
\[a_{t}=\sqrt{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}. \tag{15}\]8  
Herein, \(x[n]\) is the discrete-time signal to be transformed, \(x[n]h[n-m]\) is a short-time section of the vibration signal at time \(n\) with the length of \(m\) and window function of \(h[n]\); and \(X(m,\omega)\) is the FFT of each section. Results showed that several factors contribute to the engine vibration, including the fuel uniformity, oxygen solubility, combustion process, fuel injection, fuel powdering, fuel vaporization, and ignition delay. The last four are significantly influenced by the ethanol content in the fuel and can cause engine knocking at high concentrations (e.g., D90E10 and D88E12). Among the studied fuels, D94E6 blend generated more power and torque, while D92E8 enhanced pressure changes through the knocking phenomenon (generating shocks) within the cylinders (see Figure 22). The engine power (\(P\)) was calculated from the available torque (\(T\)) at the engine flywheel and engine speed (\(n\)):  
\[a_{t}=\sqrt{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}. \tag{15}\]9  
As illustrated in Figure 22, a further increase in the engine speed after 1900 rpm (maximum power) resulted in a considerable reduction in the generated torque and power of all fuel blends. Despite their promises, the engine performance was very erratic due to the increase in the unwanted acceleration of the body, and an ignition delay of D94E6, D92E8 fuel blends, respectively (Figure 23). [PERSON] et al. [92] conducted a comparative study on the engine performance and vibration of different fuel blends. Their results demonstrated that, in the diesel engine, vibrations started to rise, whereas in biodiesel and diesel blends (B10 to B30) it declined. This may be due to the reduction in the knocking effect in biodiesel, as well as diesel blends' combustion. As a result of good combustion, the vibration decreases at higher blends of biodiesel. In a recent study, [PERSON] et al. [93] investigated the effect of adding zinc oxide (ZnO) nanoparticles with hydrogen in dual fuel mode to jatropha methyl ester (JME) biodiesel on the engine vibration. The main results of this study are listed as follows: Firstly, increasing nanoparticle size improved the combustion characteristics, which therefore results in significant improvement in vibration behavior.