# Multiparameter Optimization Framework of Cyberphysical Systems: A Case Study on Energy Saving of the Automotive Engine

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Methodology

#### 3.1. Framework

_{pp}represents the interface information set of the physical space acting on the physical prototype and Φ’

_{pp}represents the interface information set that the physical prototype feeds back to the physical space. Φ

_{cd}and Φ’

_{cd}represent the interactive information sets between digital prototype and cyberspace. The core problem in our work is how to build the bridge between the physical prototype and digital prototype, and how to use the interactive data between them and the cyberphysical space to establish the optimization algorithm and improve the performance of the study object. The problem can be expressed as follows:

_{pp}and Φ’

_{pp}were gathered by the above equipment. The cyberspace and digital prototype engines were investigated preliminarily by engine bench test data measuring and 1-D (1-Dimensional) simulation modeling [24]. Then, the subset data of Φ

_{cd}and Φ’

_{cd}were calculated.

#### 3.2. Optimization Algorithm

_{1}, X

_{2}, X

_{3}, X

_{4}. Together, they constitute the genome of an individual that corresponds to the engine performance of different input parameters. The population is represented as a set of individuals. When initializing a population for CGA starting, 20 individuals are randomly generated, and each of them has different value combinations of chromosomes. Each chromosome is encoded in 8-bit binary. Then, the fitness function f of all the individuals is calculated by the engine model simulation, which is covered in more detail in Section 3.3. The fitness value will be a judgment for the next-generation population evolution. After comparing the effects of the active archive nondominated sorting genetic algorithm adopted by Salata F. [29], we combined the three types of operators named selection operator, crossover operator, and mutation operator with different random sampling rates for new individuals’ evolution. For the execution process of selection operator, the combined method of roulette selection with elite ranking that ensures the selection probability of the excellent individuals and the diversity of population, is used to select the individual for the next generation. In this regard, the individuals are randomly selected as members of the next-generation population and the individuals with bigger fitness function values are more prone to be selected as the member of the next-generation populations. The individuals that do not meet the limits of KI = 0 will be eliminated and do not participate in the formation of the next generation of the population. Secondly, some of the selected individuals will act as the parents and produce new individuals by crossover operator that uses a probability method to select chromosomes for binary bit-swapping. Thirdly, some of the selected individuals will act as the mutants for mutation operator that uses randomizing methods to select chromosomes variation. Then, the new generation population is eventually produced for population evolution. In addition, as the MATLAB and GT-Power cosimulation takes a long time for fitness value calculation, the unique method of MATLAB is used to eliminate the duplicated individuals after mutation, which avoids repetitive calculation and has strong ability to find the global optimization solution. New randomly generated individuals are added to the next-generation populations for the duplicated individuals. The iteration times of population evolution are set in 50 generations. During the iteration, the population base consisting of historical populations is stored, and finally, the global optimization and analysis are carried out by clustering analysis. The k-means clustering algorithm is considered one of the most powerful and popular data mining algorithms [30]. Aiming at the multidimensional data of the population database in this paper, we adopted the k-means clustering algorithm for studying the distribution of population, which aims to learn the influence of different parameters on the optimization goal under different condition grouping at one time.

- (1)
- Traditional genetic algorithm requires a strict fitness function to limit the population range. The precise data label is required to classify the data. CGA has no limitation of strict population range definition.
- (2)
- Traditional genetic algorithm is an optimization method that only focuses on the final results but lacks the analysis and statistics of data changes in the iterative process. CGA facilitates the independent optimization analysis of the population and explores the iterative rule.
- (3)
- The fitness function of traditional genetic algorithm often has a significant impact on the optimization results. For example, in the process of energy-saving optimization of EGR, LIVC, ignition advance angle, and other parameters, a multiparameter design will not only affect the fuel consumption but also affect the torque. If the torque is limited to a wide range in the fitness function, it will result in a comparison of BSFC of different loads, which will affect the judgment of the optimal value. However, if the torque is limited to a narrow range in the fitness function, the optimization of the different torques requires repeated genetic algorithm calculations, which increases the amount of calculation. CGA can realize the energy-saving optimization of different loads and improve optimization efficiency in the process of continuous iterative optimization. The optimization objective of CGA is to automatically obtain the lowest BSFC under different loads by optimizing engine control parameters such as LIVC angle, EGR, ignition advance angle, and air–fuel ratio, and avoid engine knocking. If the traditional genetic algorithm is used, the fitness function should consider the torque changes, and the BSFC for different torques has to be optimized for its own genetic algorithm. The CGA optimization costs less time.

#### 3.3. Optimization Objectives

_{1}, X

_{2}, X

_{3}, X

_{4}) is inversely related to the BSFC of the engine. X

_{1}is the value of LIVC angle that is among 16–66°ABDC (After Bottom Dead Center) according to the VVT (Variable Valve Timing) technology of the original engine. X

_{2}is the value of EGR rate r that is among 0–15% supported by LP-EGR (Low-Pressure Exhaust Gas Recirculation) technology; X

_{3}is the ignition advance angle and its range is −24–4 crank angle ATDC (After Top Dead Centre). X

_{4}is the air–fuel ratio and its optimization range is 12–15.7. The minimum target of the BSFC is the maximum value of the fitness function. The value of the fitness function F can be calculated by the 1-D simulation engine code modeled in GT-Power that will be introduced later. Besides, another variable named KI is the knock index, which is proposed to characterize knock of gasoline engine. According to the Kinetics-fit detonation model in GT-power, when the engine does not knock, the index KI = 0.

#### 3.4. Digital Model and Physical Test Verification

## 4. Results

_{1}is the circulating heat absorption, corresponding to the constant volume heating process 2–3, and q

_{2}is the circulating heat release, corresponding to the constant pressure heat release process 4–1. The calculation formulas for these are as follows:

_{v}is the specific heat capacity at constant volume; C

_{p}is the specific heat capacity at constant pressure; T

_{1}, T

_{2}, T

_{3}, and T

_{4}are the temperatures of corresponding points 1–2–3–4; and the following relationship is satisfied.

_{1}, V

_{2}, V

_{3}, and V

_{4}are the volumes of corresponding points 1–2–3–4, where V

_{2}= V

_{3}.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**The architecture of simulation and optimization model: (

**a**) Clustering genetic algorithm program; (

**b**) Interface between simulink and GT-power software; (

**c**) One-dimensional simulation model of the engine.

**Figure 6.**Comparisons between test data and simulation data: (

**a**) Power comparisons between test data and simulation data; (

**b**) torque comparisons between test data and simulation data; (

**c**) BSFC comparisons between test data and simulation data; (

**d**) exhaust temperature comparisons between test data and simulation data.

**Figure 10.**The contrast of load characteristics between the original engine and EGR dilution coupled with high-expansion-ratio gasoline engine.

Engine Parameters | Value |
---|---|

Displayed volume | 1.8 L |

Stroke | 84.1 mm |

Bore | 82.5 mm |

Connecting Rod | 146 mm |

Compression ratio | 9.6 |

Power Max. (kW/rpm) | 118/5000 |

Torque Max. (N·m/rpm) | 250/2000 |

Number of valves | 4 (2 intake, 2 exhaust) |

Injection | GDI |

Fuel | Gasoline #96 of Chinese Standard |

Speed/rpm | 1000 | 1500 | 2000 | 2500 | 3000 | 3500 | 4000 | 4500 | 5000 | 5500 | 6000 |
---|---|---|---|---|---|---|---|---|---|---|---|

A/F | 15.2 | 14.5 | 14.3 | 14.0 | 13.4 | 13.0 | 12.4 | 11.9 | 11.9 | 11.9 | 12.1 |

Atmospheric pressure/MPa | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |

Temperature/°C | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 |

Ignition angle/°CA | −7.5 | −13.3 | −4 | −1 | 6.2 | 9.2 | 10.8 | 13.0 | 15.5 | 18.6 | 23.7 |

Intake mass/g/s | 19.0 | 41.9 | 65.0 | 65.7 | 79.3 | 91.6 | 103.3 | 120. | 126.7 | 131.8 | 130.9 |

IVO/°CA | −22 | −22 | −15.7 | −12.5 | −12 | −9 | −0.3 | 4.5 | 8.3 | 9.5 | 9.7 |

Throttle percentage/% | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

Operating Point | Statistical Number | The Clustering Center/N·m | EGR Rate |
---|---|---|---|

1 | 91 | 55 | 14.6% |

2 | 253 | 97.1 | 13.6% |

3 | 190 | 120.9 | 15% |

4 | 158 | 150 | 14.5% |

5 | 166 | 177.6 | 15% |

6 | 69 | 206.6 | 5% |

7 | 33 | 247.5 | 7% |

8 | 45 | 305.7 | 2.6% |

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**MDPI and ACS Style**

Sun, Y.; Zhu, Z.; Du, A.; Chen, X.
Multiparameter Optimization Framework of Cyberphysical Systems: A Case Study on Energy Saving of the Automotive Engine. *Actuators* **2021**, *10*, 330.
https://doi.org/10.3390/act10120330

**AMA Style**

Sun Y, Zhu Z, Du A, Chen X.
Multiparameter Optimization Framework of Cyberphysical Systems: A Case Study on Energy Saving of the Automotive Engine. *Actuators*. 2021; 10(12):330.
https://doi.org/10.3390/act10120330

**Chicago/Turabian Style**

Sun, Youding, Zhongpan Zhu, Aimin Du, and Xinwen Chen.
2021. "Multiparameter Optimization Framework of Cyberphysical Systems: A Case Study on Energy Saving of the Automotive Engine" *Actuators* 10, no. 12: 330.
https://doi.org/10.3390/act10120330