## 4 Results and Analysis  
### The Process Pressure Signals of Four Cylinders  
The frequency of logging the in-cylinder pressure signals is 0.02 ms meaning that there are around 6000 samples per cycle for this engine operating at 1000 rpm. Following the in-cylinder pressure measurements, the signals have to be processed first. In this engine test, 25 cycles were recorded for one operating point measurement selecting from the total measured cycle (around 200 cycles) and the in-cylinder pressure signals are averaged cycle by cycle to eliminate the fluctuation. Figure 7 shows the pressure signals before and after the cycle's average in the \(p\)-\(\varphi\) and \(p\)-\(V\) diagram respectively, in which it is obvious to see that the in-cylinder pressure signals after 25 cycle's average are smoother than before but the fluctuation still remains, especially in the peak pressure region.  
Figure 8 shows the in-cylinder pressure signals of 4 cylinders. Due to the fire order in the multi-cylinder to keep the engine operating stable, this 4-cylinder diesel engine has 90 \({}^{\circ}\)CA differences between two cylinders and the fire order is 1-3-4-2 as shown in Figure 8a. In Figure 8b, the 4-cylinder pressure signals are moved together along with them being averaged on point by point in the overall cycle (the red curve). Figure 8c shows the zoom-in curves in the peak pressure region. Due to the pressure sensors mounted position, there are regular-looked waves in the peak pressure region. The tendency of the four cylinders is same in regards to the wave crest position and frequency, from which it seems that the four in-cylinder pressure signals average is necessary to eliminate the fluctuation effect in order to get the signals close to the reality.  
Figure 8: In-cylinder pressure of 4 cylinders: (**a**) pressure of 4 cylinders with fire order; (**b**) pressure of 4 cylinders after moving; (**c**) zoom in of peak pressure area.  
Figure 7: In-cylinder pressure before and after cyclic average: (**a**) \(p\)-\(\varphi\) diagram; (**b**) \(p\)-\(V\) diagram.  
Although the in-cylinder pressure signals are smoothed according to cycle by cycle average and the four-cylinder average, the fluctuations still exist in particular in the peak pressure region. Since the waves are caused by the channel effect, the averaged method cannot solve these wave problems resulting in the difficulties for combustion fitting research. Therefore, the smoothing procedure has to continue to eliminate the channel effect's influence as much as possible. Figure 9 compares the final smoothed pressure signals with measurement based on the new smooth method presented in reference [32]. According to Figure 9b, there is only one wave of the peak in-cylinder pressure region and for the other parts the pressure curve is smoothed sufficiently for the following combustion fitting investigation.  
Regarding to the smoothing accuracy, as shown in Table 3, in the aspect of mathematics, there are'sum of squares due to error (SSE)', 'R-square', 'Adjusted R-square', 'Degrees of freedom in the error (DFE)' and 'Root mean squared error (RMSE)' to evaluate the quality of fit. Also, the raw data and the smoothed results of the engine main performance parameters, such as \(P_{max}\), \(T_{max}\), \(P_{EO}\), \(T_{EO}\) and \(P_{i}\), are compared with each other to verify the signals processing accuracy.