# Innovative Calibration Method for System Level Simulation Models of Internal Combustion Engines

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## Abstract

**:**

## 1. Introduction

^{®}[22] for the model-based calibration (MBC Toolbox) by trying Multistart points gradient-based, Patternsearch and Genetic algorithms. Additionally, the required time for ICESM calibration using the optimization methods increases approximately exponentially with the number of tuning parameters, which imposes an additional limitation when applying a large number of tuning parameters characteristic of models of modern engines.

## 2. Engine Simulation Model

## 3. Governing Equations

#### 3.1. Internal Combustion Engine Simulation Model Governing Equations

#### 3.1.1. Convective Heat Transfer

#### 3.1.2. Heat Conduction

#### 3.1.3. Lumped (0-Dimensinal) Solid Wall

#### 3.1.4. Heat Transfer Element

#### 3.1.5. Cylinder Balance Equations

**W**, represents the burned fuel (FB), combustion products (CP) and fuel vapor (FV). The species concentration of air is derived by:

_{FB}, w

_{CP}, w

_{FV}, w

_{air}) are considered. Therefore, the gas property database is prepared for an arbitrary fuel or fuel blend in [4], taking into account chemical equilibrium considerations used in every time step during the solution of the balance equations in the cylinder and in the air path.

#### 3.1.6. Storage Element with Constant Volume

#### 3.1.7. System Boundary

#### 3.1.8. Gas Flow Transfer Element

#### 3.1.9. Gas Flow Transfer Element with Finite Length (TEL)

_{L}= A

_{R}= A) are given by Equations (25)–(27) in [29] (p. 2900), where $L$ (left) and $R$ (right) represent the up- and down-stream side of the pipe-like element, respectively. This approach also enables modeling of the pressure recovery from the orifice to the left-hand side of the pipe. From Equation (27) [29] (p. 2900) the temperature in the orifice can be calculated:

#### 3.1.10. Turbocharger

#### 3.2. Response Surface Methodology

#### 3.3. Definition of the Optimization Problem

## 4. Calibration Method

#### 4.1. Division of the ICESM into Sub-Systems

#### 4.2. Selection of the Calibration Parameters

#### 4.3. Classification of Calibration Parameters

- CBPs determined by the physics-based approaches (Figure 4).
- CBPs determined by the optimization methods (Figure 4), which can be further divided into:
- 2a.
- CBPs characterized by the dominant influences of a single CBP on only one observed simulation quantity excluding those of item 1.
- 2b.
- CBPs related to the engine domain excluding those of item 1 and 2a.
- 2c.
- CBPs related to a non-engine domain excluding those of item 1, 2a and 2b.

#### 4.4. Physics-Based Calibration of the Sub-Systems

#### 4.4.1. Air Cleaner, Intercooler, Catalyst and Exhaust Gas Recirculation Cooler (SS 1–4)

#### 4.4.2. Combustion Model (SS 6)

#### 4.5. Evaluation of the Calibration Parameters with Optimization Methods

- Direct search of CBPs in a closed loop with the simulation model and searching algorithm based on simple control logic (e.g., bisection method or application of the PID controller elements [26]).
- RSM-based optimization methods presented in Section 3.2 and Section 3.3.

#### 4.5.1. Calibration of the Turbocharger (SS 5)

#### 4.5.2. Calibration of the Entire ICESM

- Number of the remaining CBPs.
- Type of the remaining CBPs.
- Strength of influence of the CBPs of different calibration loops or calibration STEPs on the merit function.

#### 4.5.3. Response Surface Methodology-Based Calibration Approach

#### 4.5.4. Calibration Loops of the Employed ICESM

#### 4.6. Calibration Method Summary

## 5. Results and Discussion

#### 5.1. Comparison of Different Approaches to Determine the Calibration Parameters

#### 5.2. Results Obtained with Hybrid Calibration Method

#### 5.2.1. Results of Physics-Based Calibration of Sub-Systems SS 1–4

#### 5.2.2. Results of the Optimization-Based Calibration of the Turbocharger Sub-System (SS 5)

#### 5.2.3. Results of the Entire ICESM Calibration

- CBP 16 and CBP 17 indicate different values by the SS 5 calibration (Table 6) compared to the entire ICESM (Table 7 and Table 8) which was discussed in Section 4.5.1.
- CBP 16 indicates that the CBP changes the values in each calibration loop as shown in Table 7, Table 8 and Table 9. Calibration in multi-loops improves the final agreement between the results of the simulation and measurements as shown in Figure B1c (Appendix B).

- Overall, the agreement between the results of the simulations and measurements at all operating points is very good and meets expectations imposed by the high fidelity ICESM.
- Figure 12 and Figure 13 show good agreement of the measured and simulated cylinder pressure traces, which confirms the good agreement of the measured and simulated BMEP presented in Figure 9a and Figure B1i for the ICESM calibrated with the HCM. Furthermore, good agreement of the measured and simulated pressure traces also confirms the plausibility and high accuracy of the models of the cylinder (Section 3.1.5) and of all the models adjacent to the cylinder. Good agreement of measured and simulated pressure traces thus implies the plausibility of the gas path model and the valve flow functionality, of the heat transfer modeling framework and of the models of the in-cylinder phenomena including the ROHR input, which was calculated [17] by the BURN utility available in [1].
- Good fidelity of the ICESM is obtained already after calibration loop 1; however, such a model is in general applicable only for steady state as interaction with the cooling domain is calibrated in calibration loop 2. Calibration loop 2 thus does not significantly improve the fidelity of the steady-state results, whereas it makes the ICESM applicable for transient simulations. Figure 14 and Figure B1 indicate that calibration loop 3 improves the fidelity of the ICESM compared to calibration loop 2.
- The lower value of the merit function at 1000 rpm in calibration loop 1 originates from the smaller deviations of the ${T}_{31}$ and ${T}_{41}$. The latter is related to the higher temperature of the engine block (TCBP 2–5 in Table 7) and the lower wall heat losses in the turbine reasoned by the lower turbine HTMp (CBP 17 listed in Table 6 vs. Table 8).
- To validate the HCM method, it is very important to compare the simulation and measurement results at the points that were not subjected to the calibration procedure. This was done at 1600 rpm and 2600 rpm. Figure 13a, Figure B1 and Figure 14 indicate very good agreement at these two points, which confirms the high level of generality of the proposed HCM.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

0D | zero-dimensional |

1D | one-dimensional |

2D | two-dimensional |

3D | three-dimensional |

BMEP | brake mean effective pressure |

CA | crank angle |

CBP | calibration parameter |

CL | calibration loop |

CP | combustion products |

CPU | central processing unit |

DOC | diesel oxidation catalyst |

DoE | Design of experiment |

DPS | default parameters |

EGR | exhaust gas recirculation |

FB | fuel burned |

FMEP | friction mean effective pressure |

FV | fuel vapor |

HCM | Hybrid Calibration Method |

ICE | internal combustion engine |

ICESM | internal combustion engine simulation model |

NEDC | New European Driving Cycle |

OM | one step optimization method |

OP | operating point |

PID | proportional-integral-derivative |

RBF | Radial Basis Function |

RSM | response surface methodology |

SS | sub-system |

TEL | gas flow transfer element with finite length |

## Appendix A

**Figure A1.**Flowchart for steps s1–s7 of CBP evaluation applying RSM-based optimizations in one calibration loop.

**Figure A2.**Flowchart for steps s8–s16 of CBP evaluation applying RSM-based optimizations in one calibration loop.

## Appendix B

**Figure B1.**Comparisons of simulation and measurement results at steady-state operation with the included deviation interval ±3.5% at full-load operating points (1000, 1600, 2000, 2600, 3000 and 3800 rpm) and part-load operating points (775, 1000, 1600, 1800, 2200 and 2400 rpm) after calibration of the applied ICESM using HCM is completed. The subscript $sim$ in the label of the quantities of the y-axes denotes the simulation result whereas CLs 1–3 in the titles of the legend represent the ICESM calibration loops: (

**a**) Compressor inlet pressure; (

**b**) Intake manifold pressure; (

**c**) Exhaust manifold pressure; (

**d**) Turbine outlet pressure; (

**e**) Compressor outlet temperature; (

**f**) Intake manifold temperature; (

**g**) Exhaust manifold temperature; (

**h**) Turbine outlet temperature; (

**i**) Engine BMEP; (

**j**) Peak firing pressure; (

**k**) Air mass-flow; (

**m**) EGR rate.

## Appendix C

**Figure C1.**Comparisons of simulation (sim) and measurement (exp) results during engine hot transient NEDC operation at given engine speed and injected fuel: (

**a**) Engine torque; (

**b**) Engine speed; (

**c**) Air mass-flow; (

**d**) Turbocharger speed; (

**e**) Boost pressure ${p}_{21}$; (

**f**) Instantaneous and cumulated fuel consumption.

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**Figure 1.**Elements, components (group of elements) of the ICESM and typical set of measurement data in standard measurement investigations of turbocharged engines in labeled positions 1, 2, …, 10 with dark blue circles used for the ICESM calibration.

**Figure 2.**Division of the applied ICESM into feasible sub-systems and employed CBPs labeled with green and golden-yellow circles: (

**a**) Air cleaner (SS 1), intercooler (SS 2), catalyst (SS 3), EGR cooler (SS 4), turbocharger (SS 5), engine block (SS 6) and all CBPs; (

**b**) Division of engine block structure into two heat transfer domains, i.e., with constant and variable wall temperature approach and corresponding CBPs; (

**c**) CBPs within cylinder and turbocharger housing.

**Figure 3.**Scheme of the gas flow transfer element with the finite length consisting of the orifice followed by the element with length $L$ [29].

**Figure 5.**Slices of the $\widehat{\u2206BMEP}$ surface response model (Equation (34)) at 3800 rpm, full-load operating point depending on CBPs (x1–x17) listed in Table 1 at given lower and upper bounds. Ascending numbers in colored circles represent the grade of influence of the certain CBP (smaller number, bigger influence): (

**a**) Air cleaner FrMp; (

**b**) Intercooler FrMp; (

**c**) Intercooler HTMp; (

**d**) Gas-intake port wall HTMp; (

**e**) Gas-exhaust port wall HTMp; (

**f**) Gas-piston/head wall HTMp; (

**g**) Gas-cylinder liner wall HTMp; (

**h**) Start of combustion offset; (

**i**) Intake port wall-coolant HTMp; (

**j**) Exhaust port wall-coolant HTMp; (

**k**) Piston wall-coolant HTMp; (

**l**) Head wall-coolant HTMp; (

**m**) Cylinder liner wall-coolant HTMp; (

**n**) Liner block wall-coolant HTMp; (

**o**) Turbine efficiency correction factor; (

**p**) Exhaust gas-turbine wall-ambient HTMp; (

**q**) Catalyst flow coefficient (${C}_{d}$).

**Figure 6.**Flowchart of CBPs’ evaluation of the SS 1, SS 2 and SS 4 shown in Figure 2a; ${\dot{m}}_{in}$ denotes sub-system inlet mass-flow, ${p}_{in}$ inlet pressure, ${T}_{in}$ inlet temperature, $AF{R}_{in}$ inlet air–to-fuel ratio, ${p}_{out}$ outlet pressure, ${T}_{w}$ cooling media temperature (e.g., air or water) and ${T}_{out}$ outlet temperature;

^{1}Input/output data needed/evaluated only in the case of considered heat transfer in the corresponding sub-system.

**Figure 8.**Comparison of the absolute differences between the results of simulation and measurement for pressure and temperature (Table 2) at the 3800 rpm full-load steady-state operating point applying three different approaches for CBPs determination in the applied ICESM. DPS represents simulation results achieved with the default CBPs available during the ICESM model set-up, and OM results achieved by using a one-step optimization method and CL one to three simulation results obtained by the HCM employed in three CLs: (

**a**) Absolute differences of the pressures ${p}_{11}$, ${p}_{IM}$, ${p}_{31}$ and ${p}_{41}$; (

**b**) Absolute differences of the temperatures ${T}_{21}$, ${T}_{IM}$, ${T}_{31}$ and ${T}_{41}$.

**Figure 9.**Comparison of absolute differences between the results of simulation and measurement for engine performance data (Table 2) and the merit function at 3800 rpm full-load steady-state operating point applying three different approaches for CBP determination in the applied ICESM. DPS represents simulation results achieved with the default CBPs available during the ICESM model set-up, OM results achieved by using one-step optimization method and CLs one to three simulation results obtained by the HCM employed in three CLs: (

**a**) Absolute differences of the air mass-flow, $BMEP$ and peak cylinder pressure ${p}_{C,MAX}$; (

**b**) Magnitude of the merit function.

**Figure 10.**Comparison of the computational time for the applied ICESM calibration at four full-load operating points and 20 CBPs with two different approaches, one-step optimization method (OM) and HCM.

**Figure 11.**Evaluated FrMp of the air cleaner and the measured pressure drop depending on the measured air mass-flow at full load operating points.

**Figure 12.**Simulated (sim) and measured (exp) cylinder pressure traces at part-load steady-state operating points: (

**a**) 775 rpm and 0.24 bar BMEP; (

**b**) 1600 rpm and 3.22 bar BMEP.

**Figure 13.**Simulated (sim) and measured (exp) cylinder pressure traces at full-load steady-state operating points: (

**a**) 2600 rpm and 19.8 bar BMEP; (

**b**) 3800 rpm and 15.0 bar BMEP.

**Figure 14.**Magnitude of the merit function at six engine full-load steady-state operating points for CLs 1–3.

**Table 1.**Calibration parameters that are the subject of the ICESM calibration and the CBPs assigned variables x1, …, x17 used for the sensitivity analysis.

No. | Calibration Parameter | Assigned Variable | Description | Lower, Upper Bound |
---|---|---|---|---|

1 | CBP 1 ^{1,6} | x1 | Air cleaner friction multiplier ($FrMp$) | 1, 4 (-) |

2 | CBP 2 ^{1,6} | x2 | Intercooler $FrMp$ | 0.1, 3 (-) |

3 | CBP 3 ^{1,6} | x3 | Intercooler heat transfer multiplier ($HTMp$) | 0.1, 3 (-) |

4 | CBP 4 ^{3,5,6,8} | x4 | Gas-intake port wall $HTMp$ | 0.5, 1.8 (-) |

5 | CBP 5 ^{3,5,6,8} | x5 | Gas-exhaust port wall $HTMp$ | 0.5, 1.8 (-) |

6 | CBP 6 ^{3,5,6,8} | x6 | Gas-piston/head wall $HTMp$ | 0.5, 1.8 (-) |

7 | CBP 7 ^{3,6,8} | x7 | Gas-cylinder liner wall $HTMp$ | 0.5, 1.8 (-) |

8 | CBP 8 ^{2,6,8,10} | x8 | Start of combustion offset | −3, 3 (°CA) |

9 | CBP 9 ^{1,7} | - | Rate of heat release curve (ROHR) | (J/°CA) |

10 | CBP 10 ^{4,5,6,9} | x9 | Intake port wall-coolant $HTMp$ | 0.1, 1.5 (-) |

11 | CBP 11 ^{4,5,6,9} | x10 | Exhaust port wall-coolant $HTMp$ | 0.5, 1.8 (-) |

12 | CBP 12 ^{4,5,6,9} | x11 | Piston wall-coolant $HTMp$ | 0.5, 2.0 (-) |

13 | CBP 13 ^{4,5,6,9} | x12 | Head wall-coolant $HTMp$ | 0.5, 2.0 (-) |

14 | CBP 14 ^{4,5,6,9} | x13 | Liner wall-coolant $HTMp$ | 0.5, 2.0 (-) |

15 | CBP 15 ^{4,5,6,9} | x14 | Liner block wall-coolant $HTMp$ | 1, 8 (-) |

16 | CBP 16 ^{2,6,8,9,10} | x15 | Turbine efficiency correction factor ($T{u}_{eff,Mp})$ | 0.65, 1.2 (-) |

17 | CBP 17 ^{2,6,9,10} | x16 | Exhaust gas-turbine wall-ambient ($TuHTMp)$ | 1, 30 (-) |

18 | CBP 18 ^{1,6} | x17 | Restriction flow coefficient (${C}_{d}$) | 0.1, 0.35 (-) |

19 | CBP 19 ^{1} | - | EGR cooler $FrMp$ | 1, 2 (-) |

20 | CBP 20 ^{1} | - | EGR cooler $HTMp$ | 1, 15 (-) |

21 | TCBP 1 ^{3,8} | - | Intake port wall temperature (${T}_{w,IP}$) | $({T}_{cl}-15)$, ${T}_{cl}$ (°C) |

22 | TCBP 2 ^{3,8} | - | Exhaust port wall temperature (${T}_{w,EP}$) | 120, 270 (°C) |

23 | TCBP 3 ^{3,8} | - | Piston wall temperature (${T}_{w,P}$) | 140, 290 (°C) |

24 | TCBP 4 ^{3,8} | - | Head wall temperature (${T}_{w,H}$) | 120, $({T}_{w,P}-15)$ (°C) |

25 | TCBP 5 ^{3,8} | - | Liner wall temperature (${T}_{w,L}$) | 110, 240 (°C) |

^{1}CBPs determined by the physic-based approaches;

^{2}CBPs characterized by the dominant influences of a single CBP on only one observed simulation quantity;

^{3}CBPs related to the engine domain;

^{4}CBPs related to the cooling domain;

^{5}Global CBPs;

^{6}CBPs involved in the sensitivity analysis;

^{7}ROHR is in comparison with other CBPs curve depending on °CA;

^{8,9,10}CBPs subjected to the calibration loops 1, 2 and 3 of the entire ICESM calibration.

**Table 2.**Measurement data used for the merit function evaluation by calibration of the ICESM in Figure 1.

No. j | Measurement location | Quantity | Description |
---|---|---|---|

1 | 3 | ${p}_{11}$ | compressor inlet pressure |

2 | 4 | ${T}_{21}$ | intercooler inlet temperature |

3 | 5 | ${p}_{IM}$ | intake manifold pressure |

4 | 5 | ${T}_{IM}$ | intake manifold temperature |

5 | 7 | ${p}_{31}$ | exhaust manifold pressure |

6 | 7 | ${T}_{31}$ | exhaust manifold temperature |

7 | 8 | ${p}_{41}$ | turbine outlet pressure |

8 | 8 | ${T}_{41}$ | turbine outlet temperature |

9 | 2 | ${\dot{m}}_{air}$ | air mass-flow rate |

10 | 10 | $BMEP$ | break mean effective pressure |

11 | 6 | ${p}_{c,max}$ | peak firing pressure |

No. | Constraint | Value-s |
---|---|---|

1 | $\left|\u2206{\widehat{T}}_{21}\right|\le $ ^{1, 2} | ${b}_{1}$ (%) |

2 | $\left|\u2206{\widehat{T}}_{IM}\right|\le $ ^{1, 2} | ${b}_{2}$ (%) |

3 | $\left|\u2206{\widehat{p}}_{31}\right|\le $ ^{1, 2} | ${b}_{3}$ (%) |

4 | $\left|\u2206{\widehat{T}}_{31}\right|\le $ ^{1, 2} | ${b}_{4}$ (%) |

5 | $\left|\u2206{\widehat{p}}_{41}\right|\le $ ^{1, 2} | ${b}_{5}$ (%) |

6 | $\left|\u2206{\widehat{T}}_{41}\right|\le $ ^{1, 2} | ${b}_{6}$ (%) |

7 | $\left|\u2206{\widehat{\dot{m}}}_{air}\right|\le $ ^{1, 2} | ${b}_{7}$ (%) |

8 | $\left|\u2206\widehat{BMEP}\right|\le $ ^{1, 2} | ${b}_{8}$ (%) |

9 | $\left|\u2206{\widehat{p}}_{C,MAX}\right|\le $ ^{1, 2} | ${b}_{9}$ (%) |

10 | ${\widehat{T}}_{w,P}\le $ ^{1, 2, 3} | 200 °C @ 1000 rpm 290 °C @ $N$ > 1000 rpm |

11 | ${\widehat{T}}_{w,L}\le $ ^{1, 2} | ${\widehat{T}}_{w,EP}$ °C |

12 | ${\widehat{T}}_{w,P,1000}<{\widehat{T}}_{w,P,2000}\cdots $ ^{1, 2} | ${\widehat{T}}_{w,P,3800}$ °C |

13, 14 | ${l}_{b}\le \left(\widehat{{T}_{w,P}-{T}_{w,L}}\right)\le $ ${u}_{b}$ ^{1, 3} | ${l}_{b}$ = 20 °C, ${u}_{b}$ = 50 °C, |

15, 16 | ${l}_{b}$ $\le \left(\widehat{{T}_{w,P}-{T}_{w,EP}}\right)\le $ ${u}_{b}$ ^{1, 3} | ${l}_{b}$ = 20 °C, ${u}_{b}$ = 40 °C |

17 | $\left(\widehat{{T}_{31,s}-{T}_{41,s}}\right)=$ ^{2} | $\left({T}_{31,e}-{T}_{41,e}\right)$ °C |

18 | $\left(\widehat{{T}_{w,P}-{T}_{w,H}}\right)\ge $ ^{2, 3} | 15 °C |

19 | ${\widehat{T}}_{w,EP}\le $ ^{2} | ${\widehat{T}}_{w,H}$ °C |

20 | ${\widehat{T}}_{w,\mathrm{I}P}\ge $ ^{2, 3} | 98 °C |

^{1}Constraints used in the calibration loop (CL) 1;

^{2}Constraints used in CL 2 and CL 3;

^{3}Constraints specific for the applied ICESM.

**Table 4.**Evaluated CBPs (Table 1) of the sub-systems SS 1–3 at full-load operating points.

No. | CBPs | 1000 rpm | 2000 rpm | 3000 rpm | 3800 rpm |
---|---|---|---|---|---|

1 | CBP 1 ^{1} (-) | 1.70 | 2.21 | 2.92 | 3.28 |

2 | CBP 2 ^{1} (-) | 2.23 | 1.2 | 1.42 | 1.59 |

3 | CBP 3 ^{1} (-) | 0.60 | 1.71 | 1.79 | 1.83 |

4 | CBP 18 ^{1} (-) | 0.19 | 0.28 | 0.319 | 0.321 |

^{1}CBPs determined with physics-based approaches.

**Table 5.**Evaluated CBPs (Table 1) of the sub-system SS 4 at part-load operating points.

No. | CBPs | 775 rpm | 1000 rpm | 1600 rpm | 1800 rpm | 2200 rpm | 2400 rpm |
---|---|---|---|---|---|---|---|

1 | CBP 18 ^{1} (-) | 0.1 | 0.08 | 0.08 | 0.1 | 0.16 | 0.17 |

2 | CBP 19 ^{1,11} (-) | 1.53 | 1.53 | 1.53 | 1.53 | 1.53 | 1.53 |

3 | CBP 20 ^{1} (-) | 2.5 | 8.6 | 5.3 | 7.9 | 12 | 13.9 |

^{1}CBPs determined with physics-based approaches;

^{11}CBP determined only based on one reference measured operating point.

**Table 6.**Evaluated CBPs (Table 1) of the sub-system SS 5 at full-load operating points.

No. | CBPs | 1000 rpm | 2000 rpm | 3000 rpm | 3800 rpm |
---|---|---|---|---|---|

1 | CBP 16 ^{2} (-) | 0.91 | 1 | 0.97 | 0.99 |

2 | CBP 17 ^{2} (-) | 6.4 | 15.3 | 18.2 | 20.9 |

^{2}CBPs characterized by the dominant influences of a single CBP on only one observed simulation quantity.

**Table 7.**Evaluated CBPs (Table 1) in calibration loop 1 at full-load operating points.

No. | CBPs | 1000 rpm | 2000 rpm | 3000 rpm | 3800 rpm |
---|---|---|---|---|---|

1 | CBP 4 ^{3,5} (-) | 1.58 | 1.58 | 1.58 | 1.58 |

2 | CBP 5 ^{3,5} (-) | 0.73 | 0.73 | 0.73 | 0.73 |

3 | CBP 6 ^{3,12} (-) | 1 | 1 | 1 | 1 |

4 | CBP 7 ^{3} (-) | 1.18 | 0.98 | 0.85 | 0.78 |

5 | CBP 8 ^{2} (°CA) | −0.04 | 0.45 | 0.68 | 1.03 |

6 | CBP 16 ^{2} (-) | 0.83 | 0.99 | 0.94 | 0.92 |

7 | TCBP 1 ^{3,5,12} (°C) | 100 | 100 | 100 | 100 |

8 | TCBP 2 ^{3} (°C) | 162 | 192 | 215 | 221 |

9 | TCBP 3 ^{3} (°C) | 201 | 222 | 245 | 261 |

10 | TCBP 4 ^{3,12} (°C) | 186 | 207 | 230 | 246 |

11 | TCBP 5 ^{3} (°C) | 162 | 192 | 215 | 221 |

^{2}CBPs characterized by the dominant influences of a single CBP on only one observed simulation quantity;

^{3}CBPs related to engine domain;

^{5}Global CBPs;

^{12}CBP was not subjected to RSM-based optimizations because of the applied assumptions presented in Section 4.5.4.

**Table 8.**Evaluated CBPs (Table 1) in calibration loop 2 at full-load operating points.

No. | CBPs | 1000 rpm | 2000 rpm | 3000 rpm | 3800 rpm |
---|---|---|---|---|---|

1 | CBP 10 ^{4,5} (-) | 0.67 | 0.67 | 0.67 | 0.67 |

2 | CBP 11 ^{4,5} (-) | 1.19 | 1.19 | 1.19 | 1.19 |

3 | CBP 12 ^{4,5} (-) | 1.03 | 1.03 | 1.03 | 1.03 |

4 | CBP 13 ^{4,5} (-) | 1.07 | 1.07 | 1.07 | 1.07 |

5 | CBP 14 ^{4,5} (-) | 1.15 | 1.15 | 1.15 | 1.15 |

6 | CBP 15 ^{4,5} (-) | 3.74 | 3.74 | 3.74 | 3.74 |

7 | CBP 16 ^{2} (-) | 0.79 | 1.00 | 0.96 | 0.92 |

8 | CBP 17 ^{2} (-) | 8.9 | 15.6 | 19.9 | 21.5 |

^{2}CBPs characterized by the dominant influences of a single CBP on only one observed simulation quantity;

^{4}CBPs related to cooling domain;

^{5}Global CBPs.

**Table 9.**Evaluated CBPs (Table 1) in calibration loop 3 at full-load operating points.

No. | CBPs | 1000 rpm | 2000 rpm | 3000 rpm | 3800 rpm |
---|---|---|---|---|---|

1 | CBP 8 ^{2} (°CA) | 0.85 | 0.25 | 0.68 | 0.88 |

2 | CBP 16 ^{2} (-) | 0.83 | 0.98 | 0.95 | 0.98 |

^{2}CBPs characterized by the dominant influences of a single CBP on only one observed simulation quantity.

**Table 10.**Evaluated CBPs (Table 1) in calibration loop 3 at part-load operating points.

No. | CBPs | 775 rpm | 1000 rpm | 1600 rpm | 1800 rpm | 2200 rpm | 2400 rpm |
---|---|---|---|---|---|---|---|

1 | CBP 8 ^{2} (°CA) | −0.64 | −0.22 | −0.31 | −0.91 | -2.55 | -1.05 |

2 | CBP 16 ^{2} (-) | 0.65 | 0.86 | 1.1 | 0.98 | 1.01 | 1 |

3 | CBP 17 ^{2} (-) | 4.5 | 2.25 | 3 | 2.4 | 11.9 | 12.7 |

^{2}CBPs characterized by the dominant influences of a single CBP on only one observed simulation quantity.

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Prah, I.; Trenc, F.; Katrašnik, T. Innovative Calibration Method for System Level Simulation Models of Internal Combustion Engines. *Energies* **2016**, *9*, 708.
https://doi.org/10.3390/en9090708

**AMA Style**

Prah I, Trenc F, Katrašnik T. Innovative Calibration Method for System Level Simulation Models of Internal Combustion Engines. *Energies*. 2016; 9(9):708.
https://doi.org/10.3390/en9090708

**Chicago/Turabian Style**

Prah, Ivo, Ferdinand Trenc, and Tomaž Katrašnik. 2016. "Innovative Calibration Method for System Level Simulation Models of Internal Combustion Engines" *Energies* 9, no. 9: 708.
https://doi.org/10.3390/en9090708