**3. Methodology**

### *3.1. In-Cylidner Measured Pressure Signals Processing*

The measured in-cylinder pressure signals fluctuate especially in the peak pressure region, which will easily bring calculation errors during the combustion fitting process. Therefore, the measured pressure signals have to be processed firstly based on mathematics methods. On the other hand, some useful and effective methods can be used to improve the accuracy such as a pressure signals smooth approach based on the heat release calculation proposed by the author to ensure the accuracy of the signals' application to some extent [32].

### *3.2. Seiliger Process and Seliger Process Parameters Obtain*

The Seiliger process is an efficient way to characterize the diesel engine combustion process, which divides the combustion process into finite stages to describe main phenomena of combustion characteristics. The definition and interpretation of Seiliger process and Seiliger parameters were described in author's previous articles. Based on the stages number definition, there are 5-point Seiliger and 6-point Seiliger cycles [42]. Figure 4 shows the six-point Seiliger process model with both the basic and the advanced Seiliger process. The stages can be described as follows:


**Figure 4.** Six-point Seiliger process definition: (**a**) *p*-*V* diagram; (**b**) *T*-*ϕ* diagram.

The Seiliger process can be described by a finite number of parameters that fully specify the process together with the initial (trapped) condition and the working medium properties. The definition of the Seiliger stages and the Seiliger parameters are given in Table 2. Among these Seiliger parameters *a*, *b* and *c* are the combustion parameters indicating the isochoric combustion stage, isobaric combustion stage and isothermal combustion stage respectively. The polytropic compression exponent *ncomp* and effective compression ratio *rc* model the polytropic compression process while the polytropic expansion exponent *nexp* and expansion ratio *re* model the polytropic expansion process. In the case that all the Seiliger parameters are known, the pressures, temperatures, work and heat in the various stages of the Seiliger cycle can be calculated.


**Table 2.** Seiliger process definition and parameters.

Figure 5 shows how to obtain the Seiliger parameters based on measures in-cylinder pressure signals. The first line is the fit procedure to smooth the in-cylinder pressure signals, after which the Seiliger parameters are determined according to the combination of equivalence criteria between Seiliger process and in-cylinder process of the real engine. The Seiliger parameters are obtained from the 'Seiliger fit model' (model (4)), in which the fitting algorithms have to be investigated to improve the accuracy and speed the simulation time. Finally, the in-cylinder performance based on the Seiliger process characterizes the cylinder process and in particular the 'combustion shape' in order to compare the fitting results to the real engine (smoothed signals).

**Figure 5.** Flow chart of the overall simulation procedure to calculate Seiliger parameters.
