# Parameter Optimization of the Power and Energy System of Unmanned Electric Drive Chassis Based on Improved Genetic Algorithms of the KOHONEN Network

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## Abstract

**:**

## 1. Introduction

## 2. Establishment of the Simulation Model and Optimization Model

#### 2.1. Establishment of Unmanned Electric Drive Chassis Simulation Model Based on AVL CRUISE

#### 2.2. Modeling of Power System and Energy System

#### 2.2.1. Motor Model

_{d}is the motor armature voltage; E is the armature-induced electromotive force; R

_{a}is the armature circuit resistance; L

_{a}is the armature circuit inductance; i

_{d}is the armature circuit current; K

_{e}is the motor electromotive force constant; ω is the motor speed (r/min); T

_{e}is the electromagnetic torque; T

_{L}is the load torque; J is the moment of inertia (kg/m

^{2}); B is the viscous friction coefficient; and K

_{T}is the motor torque constant.

#### 2.2.2. Battery Model

_{0}is the battery static open circuit voltage; R

_{0}is the ohm polarization resistance, which is mainly affected by the concentration of sulfuric acid in the electrolyte; R

_{r}is the concentration polarization and electrochemical polarization resistance of the storage battery; the RC circuit is formed by R

_{r}; and the capacitor C

_{r}affects the transition process when the working condition of the battery changes.

_{b}is the battery terminal voltage; U

_{0}is the static open circuit voltage of the storage battery; R

_{0}is the polarization internal resistance; R

_{r}is the battery concentration polarization and electrochemical polarization resistance; and C

_{r}is the equivalent capacitance.

_{b}and polarization internal resistance R

_{0}[19]. Therefore, the battery terminal voltage U

_{b}and polarization internal resistance R

_{0}are expressed as functions of SOC, and their mathematical expressions are as follows:

_{r}are quite different during charging and discharging, so the mathematical models [17,20,21] should be established during charging and discharging, respectively, as the following formula:

_{r}·R

_{r}is related to the service life of the battery, which is considered a constant in practical applications.

_{i}of the battery at a certain discharge rate. Generally, the calculation of SOC adopts the ampere time integration method, which is the following formula:

_{0}is the initial state of charge of the battery; i(t) is the instantaneous discharge current; and Q

_{i}is the total capacity of the storage battery.

#### 2.2.3. Supercapacitor Model

_{ep}and then in series with a small resistance R

_{es}. The equivalent circuit structure diagram is shown in Figure 4. The equivalent series resistance R

_{es}represents the charge–discharge loss resistance, representing the energy loss during the charge–discharge process of the supercapacitor, and is related to the charge–discharge voltage loss. The equivalent parallel resistance R

_{ep}represents the leakage loss resistance; i

_{C}is the current flowing through the supercapacitor; C is the ideal equivalent capacitor; i

_{0}is the current flowing through the ideal capacitor C; U

_{C}is the terminal voltage of supercapacitor; and U is the voltage at both ends of ideal capacitor C.

_{ep}is large and the resistance leakage loss is small, the equivalent resistance can be ignored in modeling. The supercapacitor simulation model mainly includes the supercapacitor bank internal resistance module, supercapacitor bank SOC module, and supercapacitor bank voltage module.

#### 2.3. Parameter Optimization of Unmanned Electric Drive Chassis with Power-Energy Coupling

_{1}(x) and selects 100 km power consumption under Chinese urban bus conditions and EUDC conditions as the economic objective function f

_{2}(x). According to the coupling relationship between the composite energy source composed of the CHD-EV1 battery-supercapacitor and the power system, the key parameters of the power system and the energy system are selected as the optimization variables, and the maximum speed, climbing ability, and driving range are used as constraints to optimize the parameters of the unmanned electric drive chassis. The optimization problem is described as follows:

_{j}≥ 0 is the constraint condition, and m is the number of constraints. In this paper, m = 5, x is the optimization parameter, ${x}_{i}^{L}$ and ${x}_{i}^{H}$ are the lower bound value and upper bound value of the i-th parameter, respectively, and n is the number of optimization parameters.

#### 2.4. Optimization Objective

_{1}(x

_{i}) of 0~30 km/h is selected as the dynamic evaluation target. Because the electric medium bus studied in this paper frequently needs to travel in the suburbs, it is faster. Therefore, the power consumption per hundred kilometers f

_{2}(x

_{i}) under Chinese urban bus conditions and EUDC conditions is selected as the economic evaluation target, and the weight coefficient change method is used to transform the multi-objective problem. Finally, the objective function is obtained as follows:

_{1}and w

_{2}are the weight coefficients of the dynamic target and the economic target, respectively. f

_{1tar}and f

_{2tar}are the standard optimization target values of the vehicle acceleration time of 0~30 km/h and the power consumption of 100 km, respectively. By dividing the obtained f

_{1}(x

_{i}) and f

_{2}(x

_{i}) by the defined target values f

_{1tar}and f

_{2tar}, the target function units and quantity levels are standardized. The objective values of the optimization criteria set in this paper are f

_{1tar}= 12 s and f

_{2tar}= 35 kWh/100 km, respectively.

#### 2.5. Optimization Variables

#### 2.6. Constraint Condition

- The difference between the simulated speed at any moment and the speed required by the working condition shall be ≤2 km/h;
- Maximum speed requirement: v
_{max}≥ 90 km/h; - Driving range: ≥100 km;
- Variation range of supercapacitor’s SOC: 20~90%;
- Variation range of battery’s SOC: 30~80%.

## 3. Process Design of Model-in-the-Loop Optimization

## 4. An Improved Isolated Niche Genetic Algorithm Based on the KOHONEN Network (KIGA)

#### 4.1. General Overview of KIGA

- (a)
- The KOHONEN network clustering algorithm is used to divide the initial subpopulation to achieve a more reasonable division of the initial niche;
- (b)
- Two external archives are established to store the individual with the highest fitness and the Pareto solution set found at the initial stage, respectively, to guide the direction of evolution of the algorithm;
- (c)
- The weight of the subobjective function is determined by using the combination method based on the least squares method, and the Pareto solution set is optimized.

_{max}of some subpopulations to ensure the diversity of species in the population and limit the minimum survival size S

_{min}of some subpopulations to avoid these subpopulations being prematurely eliminated. (b) Inactivation of inferior species: In order to speed up the algorithm, the subpopulation with the worst performance in the specified algebra during the evolution process becomes extinct, and the subpopulation is replaced by a new solution in the search space. (c) Homogeneous mutual exclusion: By deleting one of the two similar or identical subpopulations that appear during evolution and replacing it with a new solution in the search space. (d) Weak protection: New subpopulations generally cannot compete with evolved subpopulations in the early stage of evolution, so new populations need to be protected. (e) New and old replacement: When the subpopulation is close to the local optimal solution, the subpopulation is deleted with a certain probability and replaced with a new solution in the search space. In this paper, the probability of new and old replacements is P

_{n}= 0.7. (f) Preferred species retention: In order to ensure that the best performance of the subpopulation can fully evolve, the new and old replacements do not act on the best performance of the subpopulation. The operating parameters of KIGA are shown in Table 3.

_{i}, x

_{j}):

_{1}(x

_{i}, x

_{j}) is the Hamming distance of any two individuals x

_{i}and x

_{j}, A is the fitness distance, and niche radii B and C represent the maximum distance of genotype individuals and phenotype individuals, respectively.

_{ki}(t) is the fitness value of the i-th individual in the k-th subpopulation of the t generation; and n

_{k}(t) is the size of the k

_{th}subpopulation of t generation.

_{k}(t + 1) of the k-th subpopulation of t + 1 generation is

#### 4.2. Establishment of the Initial KIGA Niche Subpopulation Based on KOHONEN Network Clustering

_{c}are excited to varying degrees, and the degree of excitement decreases with the increase in distance, while the neurons outside N

_{c}are inhibited. The structure of the KOHONEN network will change after each execution due to the different neurons excited each time, but no matter which neurons are activated, the final clustering result will not change.

#### 4.2.1. Selection of Sample Feature Vectors

_{1},X

_{2},…,X

_{i},… X

_{m})

^{T}, 1 ≤ i ≤ m. For each individual in the sample, we select the feature vector ${X}_{i}=\left({x}_{i}^{1},{x}_{i}^{2},\cdots ,{x}_{i}^{k}\right)$, where k is the dimension of the feature vector and 1 ≤ k ≤ 7. Subsequently, in order to improve the training efficiency, it is necessary to normalize the data and convert the output function value into a value between 0 and 1.

#### 4.2.2. Design of the Output Layer

#### 4.2.3. Design of the Learning Rate

_{m}is the pre-selected maximum training times.

#### 4.3. Establishment of External Archives

#### 4.4. Pareto Selection Based on Least Squares Combination Weighting

- Using the AHP (analytic hierarchy process) to determine the subjective weight of each index;
- The determination of objective weight by the coefficient of variation method;
- Combining the weight of each index;
- Standardizing the scheme set with n schemes and m evaluation indicators to obtain the decision matrix. Then, the evaluation value of the i-th evaluation object is$${f}_{i}={\displaystyle \sum _{i=1}^{m}{w}_{j}}\cdot {z}_{ij},(i=1,2,\cdots ,n)$$The optimal combination model obtained by the least squares method is as follows:$$\left\{\begin{array}{c}\mathrm{min}{\displaystyle \sum _{i=1}^{n}{\displaystyle \sum _{j=1}^{m}\{{[({w}_{j}-{u}_{j})\cdot {z}_{ij}]}^{2}+{[({w}_{j}-{v}_{j})\cdot {z}_{ij}]}^{2}\}}},\\ s.t.{\displaystyle \sum _{j=1}^{m}{w}_{j}=1},{w}_{j}\ge 0,(j=1,2,\cdots ,m)\end{array}\right.$$
- The objective function in this model is taken as a Lagrangian function, and then the partial derivatives of w
_{j}and λ (λ is a Lagrangian operator) are calculated, respectively, to calculate the comprehensive evaluation value of each scheme. The best scheme is the one with the highest comprehensive evaluation value. The comprehensive evaluation value is

^{T}.

#### 4.5. Algorithm Flow

_{j}:

_{j}represents the set of adjacent neurons at time t;

## 5. Optimization Results and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Clustering graph of neurons in the KOHONEN network. (

**a**) Distance between neighboring neurons. (

**b**) Statistics chart of winning neuron.

**Figure 9.**Optimal target-normalized value in different weights.

**A: Dynamics target. B: Economic objectives. C: Power performance + economic objectives.**

**Figure 12.**Unmanned electric drive chassis energy consumption compared using three algorithms in CBC.

Parameters | Numerical Value | Unit |
---|---|---|

Total mass | 5244 | m/kg |

Air drag coefficient | 0.6 | C_{D} |

Windward area | 6.0168 | A/m^{2} |

Rolling resistance coefficient | 0.019 | f |

Wheel radius | 0.357 | r/m |

Driveline efficiency | 85 | η_{T}/% |

Transmission ratio | [5.568, 2.360, 1.634, 1] | i_{gn} |

Final drive ratio | 6.43 | i_{0} |

Rated power of motor | 40 | P_{e}/kW |

Maximum power of motor | 70 | P_{m}/kW |

Rated torque of motor | 124 | T_{e}/N·m |

Maximum torque of motor | 300 | T_{m}/N·m |

Rated speed of motor | 3000 | n_{e}/(r·min^{−1}) |

Maximum speed of motor | 5000 | n_{m}/(r·min^{−1}) |

Battery capacity | 120 | C/Ah |

Variable Name | Optimization Parameters | Lower Limit | Upper Limit |
---|---|---|---|

x1 | Motor power/kW | 30 | 60 |

x2 | First-gear transmission ratio | 2.8 | 5.7 |

x3 | Second-gear transmission ratio | 1.5 | 2.6 |

x4 | Third-gear transmission ratio | 0.9 | 1.1 |

x5 | Final drive ratio | 3.5 | 7.5 |

x6 | Battery capacity | 100 Ah | 200 Ah |

x7 | Supercapacitor energy storage | 100 Wh | 300 Wh |

Parameter | Numeric Value |
---|---|

Number of variables | 7 |

Population size | 500 |

Iterations to terminate evolution | 600 |

Crossover probability/P_{c} | 0.4 |

Mutation probability/P_{m} | 0.01 |

Maximum allowable size of subpopulation/S_{max} | 80 |

Minimum allowable size of subpopulation/S_{min} | 30 |

**Table 4.**Unmanned electric drive chassis performance comparison before and after parameter optimization.

Optimization Project | Before and after Optimization | |||||||
---|---|---|---|---|---|---|---|---|

Before Optimization | GA | IGA | KIGA | |||||

Optimization Value | Rate of Change | Optimization Value | Rate of Change | Optimization Value | Rate of Change | |||

Optimization variables | First-gear transmission ratio | 5.568 | 5.384 | −3.30% | 5.352 | −3.88% | 5.352 | −3.88% |

Second-gear transmission ratio | 2.605 | 2.714 | 4.18% | 2.652 | 1.80% | 2.643 | 1.46% | |

Third-gear transmission ratio | 1 | 1 | 0.00% | 0.984 | −1.60% | 0.984 | −1.60% | |

Final drive ratio | 6.43 | 6.32 | −1.71% | 6.24 | −2.95% | 6.24 | −2.95% | |

Battery capacity/Ah | 132 | 126 | −4.55% | 120 | −9.09% | 120 | −9.09% | |

Supercapacitor energy storage/Wh | 162 | 178 | 9.88% | 186 | 14.81% | 189 | 16.67% | |

Power | Maximum speed (km/h) | 91 | 92.2 | 1.32% | 92.5 | 1.65% | 92.5 | 1.65% |

Maximum gradient/% | 36.22 | 35.37 | −2.35% | 35.14 | −2.98% | 35.14 | −2.98% | |

0~50 km/h Acceleration time/s | 11.5 | 11.12 | −3.30% | 11.04 | −4.0% | 11.04 | −4.0% | |

Economy | 100 km power consumption (kWh/100 km) | 34.25 | 30.94 | −9.66% | 30.46 | −11.07% | 30.42 | −11.18% |

Driving range/km | 106.3 | 109.7 | 3.20% | 113.9 | 7.15% | 114.7 | 7.90% | |

Comprehensive performance | Acceleration time + 100 km power consumption | 0.970 | 0.902 | −7.07% | 0.891 | −8.18% | 0.890 | −8.26% |

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## Share and Cite

**MDPI and ACS Style**

Wang, W.; Xu, S.; Ouyang, H.; Zeng, X.
Parameter Optimization of the Power and Energy System of Unmanned Electric Drive Chassis Based on Improved Genetic Algorithms of the KOHONEN Network. *World Electr. Veh. J.* **2023**, *14*, 260.
https://doi.org/10.3390/wevj14090260

**AMA Style**

Wang W, Xu S, Ouyang H, Zeng X.
Parameter Optimization of the Power and Energy System of Unmanned Electric Drive Chassis Based on Improved Genetic Algorithms of the KOHONEN Network. *World Electric Vehicle Journal*. 2023; 14(9):260.
https://doi.org/10.3390/wevj14090260

**Chicago/Turabian Style**

Wang, Weina, Shiwei Xu, Hong Ouyang, and Xinyu Zeng.
2023. "Parameter Optimization of the Power and Energy System of Unmanned Electric Drive Chassis Based on Improved Genetic Algorithms of the KOHONEN Network" *World Electric Vehicle Journal* 14, no. 9: 260.
https://doi.org/10.3390/wevj14090260