Electric Vehicle NiMH Battery State of Charge Estimation Using Artificial Neural Networks of Backpropagation and Radial Basis
Abstract
:1. Introduction
- High specific energy (greater than 90 Wh/Kg, 30% more than nickel–cadmium technology).
- High specific power (over 200 W/Kg).
- Prominent energy density (over 150 W/L, 40% more than nickel–cadmium technology).
- Cadmium-free technology, resulting in less pollutant emissions.
- The metal alloys used to maintain stable negative electrode performance at high temperatures prove to be more expensive than nickel–cadmium technology.
- Compromised performance at high temperatures due to poor performance of the negative electrode metal alloy characteristics.
- High self-discharge rate between 15 and 25% per month versus approximately 10% for nickel–cadmium batteries.
2. Methodological Development
2.1. Development of the Mathematical Model of the NiMH Battery for the Proposed Model
2.2. Data Collection for the State of Charge of a Nickel Metal Hydride Battery Cell
- Voltage in the discharge process (V): The electrical potential difference between the cell terminals while discharging. The unit used for the respective operations was volts [V]. These data were measured with the help of an AUTEL model MP408 oscilloscope, which manufacturer is AUTEL, the equipment was obtained by an authorized distributor ¨IngeAuto¨ in Ambato, Ecuador.
- Current in the discharge process (I): The number of electrons moving per second. The unit used for the respective operations was amperes [A]. These data were measured with the help of an AUTEL model SA253 clamp meter, which manufacturer is AUTEL, the equipment was obtained by an authorized distributor ¨IngeAuto¨ in Ambato, Ecuador.
- Cell temperature (temp): This is a physical magnitude that indicates the internal energy of a body; the unit used to represent this magnitude was degrees Celsius (°C). This magnitude was measured in the section where the temperature sensors are placed, using an automotive pyrometer model ADD8850, which manufacturer is FLUKE, the equipment was obtained by an authorized distributor ¨dominion¨ in Quito, Ecuador.
2.3. Neural Model Selection
- Multilayer feed-forward backpropagation;
- Radial basis (exact fit).
2.3.1. Multilayer Feed-Forward Backpropagation (FBNN)
2.3.2. Radial Basis Exact Fit (RBNN)
2.4. Selection of the Set of Training Techniques
2.5. Evaluation Criteria for Model Performance
- -
- t = target value;
- -
- o = output value.
- -
- : ith observedred valued;
- -
- : the corresponding predicted value for .
3. Results and Discussion
3.1. Characteristics of the Feed-Forward Backpropagation Multilayer Network
- -
- W: weight;
- -
- b: bias;
- -
- p: input.
3.2. Characteristics of Radial Basis Exact Fit Network (RBNN)
Performance Comparison of FBNN and RBNN
4. Conclusions
5. Recommendations
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Symbol | Description |
Ah | Nominal capacity [Ah] |
I | Current [A] |
Patm | Atmospheric pressure [atm] |
RH | Relative humidity [%] |
T | Temperature [°C or K] |
V | Voltage [V] |
Greek Symbol | |
θ | Each neuron in the input layer |
Subscripts | |
c | The propagation constant |
i,j | Unit vectors |
w/ | With |
w/o | Without |
ωi | Output weight |
Abbreviations | |
ANN | Artificial neural network |
BMS | Battery management system |
BPNN | Backpropagation neural network |
CI | Confidence interval |
CLTC-P | China light-duty vehicle test cycle passenger cars |
ECM | Equivalent circuit models |
EPA | Environmental Protection Agency |
EVs | Electric vehicle |
FBNN | Feed-forward backpropagation neural network |
HEV | Hybrid electric vehicle |
ICE | Internal combustion engine |
MAPE | Absolute percentage error |
Li-ion | Lithium-ion battery |
MLP | Multilayer perceptron |
MSE | Mean square error |
NARXNN | Exogenous input neural network model |
NiMH | Nickel metal hydride |
NiOH | Nickel oxyhydroxide |
NMC | Nickel manganese cobalt |
R^2 | Correlation coefficient |
RBNN | Radial basis exact fit neural network |
RMSE | Root means square error |
SOC | State of charge |
SOH | State of health |
TRAINGDM | Batch gradient descent |
TRAINGDX | Variable-learning-rate backpropagation |
USABC | United States Advanced Battery Consortium |
WLTC | Worldwide Harmonized Light Vehicles Test Procedure |
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Reaction Type | Electrochemical Reaction |
---|---|
Negative electrode | |
Positive electrode | |
Full reaction |
Method | Description | Advantages | Disadvantages |
---|---|---|---|
Coulomb Counting (CC) | Discrete integral of the input current. | Simple, cost-effective, and intuitive method. Combinations with other technologies are possible. High computational efficiency. | It is necessary to know the first SOC value. It is affected by error accumulation. It requires precise current measurement. It cannot handle partial charge/discharge cycles. |
Open- Circuit Voltage (OCV) | Matching of the terminal voltage with the OCV–SOC lookup table. | The physical properties of the cells are considered. Combinations with other technologies are possible. High computational efficiency. | Internal resistance and charge redistribution phenomena decrease the correlation between voltage and state of charge. A flat SOC–OCV curve makes the SOC estimate more sensitive to measurement noise and error. |
Model- Based | SOC estimated from the relationship between measured operation parameters (voltage, current and temperature) and SOC employing a battery-derived model. | It checks the electrical behavior of the battery. It can be used as a model for online monitoring. Parameters change dynamically based on SOC. Combinations with other technologies are possible. | To do this, you need to know the reference initial parameters of the battery. Only new batteries can be precisely parameterized in the laboratory. It requires high computing power. The exactitude of the estimate depends heavily on temperature. |
Machine Learning | SOC estimated with a black-box function approximation tools such as artificial neural networks. | Combinations with other technologies can switch to gray-box functionality. Useful for online and offline monitoring. The accuracy is very high after good training and fine-tuning. | Training the tool requires large amounts of historical data. Collecting training data requires expensive test equipment and lengthy testing. The relationship between voltage, temperature, current and SOC is hidden (black box). Further data processing and filtering may be required. |
State Observer | It uses nonlinear Kalman filters (KFs) for estimating SOC as a state variable of the system. | Self-correction method. It can provide information about estimates accuracy. High accuracy and robustness. | It can be computationally intensive and complex. It requires an accurate model of electrochemical cells. Instability if the gain is undesirable. |
Description | |
---|---|
Applications | Any type of accumulators. Dynamic and static accumulator applications. |
Working principle | Black-box type. |
Advantages | No in-depth knowledge of the system is required for its development. |
Disadvantages | The architecture of the neural network is obtained empirically. A large amount of data is necessary to determine the weights of the network. |
Nominal voltage | 10.8 V |
Nominal capacity | 3.8 Ah |
Anode material (+) | NiOH |
Cathode material (−) | Metal hydride |
Electrolyte | 30% potassium hydroxide |
Measuring range | −20 °C a 537 °C |
Spectral resolution | 6–14 µm |
Precision | ±1 °C |
Field of view | 12:1 |
Remark | Laser marker < 1 mW |
FBNN | Value |
---|---|
Neurons input layer | 2–3 |
Neurons hidden layer | 5/20/50/100–7/20/50/100 |
Neurons output layer | 1 |
Transfer function | Tansig |
Learning function | LearnGDM |
Training function | GDM/GDX |
Training data | 240–320 |
Test data | 36–48 |
Iterations | 500 |
Training algorithms | GDM/GDX |
Epoch Training | 500 |
Number of layers | 2–3 |
Performance function | MSE |
Method | Structure | Training (Two Layers) | Validation (Two Layers) | Test (Two Layers) | Output (Two Layers) | RMSE | MAPE [%] | R2 | MSE | Simulation Time [s] |
GDM | 3-7-1-1 | 0.9967 | 0.99869 | 0.98214 | 0.9944 | 0.0225 | 2.5404 | 0.9895 | 0.0005 | 0.46 |
GDM | 3-20-1-1 | 0.99231 | 0.9954 | 0.99913 | 0.99408 | 0.0218 | 3.0122 | 0.9891 | 0.0004 | 0.47 |
GDM | 3-50-1-1 | 0.9860 | 0.8238 | 0.9936 | 0.9883 | 0.0317 | 1.802 | 0.9775 | 0.0010 | 0.49 |
GDM | 3-100-1-1 | 0.9547 | 0.9698 | 0.9453 | 0.9577 | 0.0449 | 3.1871 | 0.9189 | 0.0065 | 0.54 |
GDX | 3-7-1-1 | 0.9998 | 0.99979 | 0.9156 | 0.99732 | 0.0154 | 1.0841 | 0.9945 | 0.0002 | 0.45 |
GDX | 3-20-1-1 | 0.99549 | 0.99871 | 0.99958 | 0.9968 | 0.0166 | 1.0906 | 0.9937 | 0.0002 | 0.46 |
GDX | 3-50-1-1 | 0.9720 | 0.9953 | 0.9934 | 0.9754 | 0.0527 | 1.128 | 0.9547 | 0.0027 | 0.48 |
GDX | 3-100-1-1 | 0.97 | 0.9878 | 0.9860 | 0.96951 | 0.0546 | 2.2416 | 0.9423 | 0.0029 | 0.52 |
Method | Structure | Training (Three Layers) | Validation (Three Layers) | Test (Three Layers) | Output (Three Layers) | RMSE | MAPE [%] | R2 | MSE | Simulation Time [s] |
GDM | 3-7-1-1-1 | 0.98232 | 0.9899 | 0.99784 | 0.98645 | 0.9881 | 5.2704 | 0.9826 | 0.0008 | 0.48 |
GDM | 3-20-1-1-1 | 0.98521 | 0.99713 | 0.99673 | 0.9896 | 0.0290 | 3.5956 | 0.9806 | 0.0008 | 0.49 |
GDM | 3-50-1-1-1 | 0.9754 | 0.9218 | 0.9914 | 0.9743 | 0.0494 | 9.4703 | 0.9509 | 0.0024 | 0.52 |
GDM | 3-100-1-1-1 | 0.966 | 0.9848 | 0.9688 | 0.96755 | 0.1257 | 13.61 | 0.94014 | 0.01580 | 0.54 |
GDX | 3-7-1-1-1 | 0.99892 | 0.87623 | 0.99921 | 0.99576 | 0.0188 | 0.0688 | 0.9918 | 0.0003 | 0.46 |
GDX | 3-20-1-1-1 | 0.99613 | 0.99979 | 0.99952 | 0.99729 | 0.0290 | 0.2332 | 0.9947 | 0.0002 | 0.49 |
GDX | 3-50-1-1-1 | 0.9858 | 0.8680 | 0.9924 | 0.9838 | 0.0370 | 0.7934 | 0.9686 | 0.0013 | 0.53 |
GDX | 3-100-1-1-1 | 0.9841 | 0.9907 | 0.9824 | 0.9846 | 0.0359 | 1.2021 | 0.9703 | 0.0012 | 0.55 |
Type | Method | Structure | RMSE | MAPE [%] | R2 | MSE |
---|---|---|---|---|---|---|
FBNN | GDX | 3-7-1-1 | 0.01543 | 1.084147 | 0.994577 | 0.0002381 |
RBNN | c = 1 | 1-80-1-1 | 0.0111 | 1.100115 | 0.997195 | 0.000124 |
Method | Structure | Training (Two Layers) | Validation (Two Layers) | Test (Two Layers) | Output (Two Layers) | RMSE | MAPE [%] | R2 | MSE | Simulation Time [s] |
GDM | 2-5-1-1 | 0.99507 | 0.87284 | 0.99681 | 0.99309 | 0.0228 | 1.0987 | 0.9882 | 0.0005 | 0.44 |
GDM | 2-20-1-1 | 0.98348 | 0.99386 | 0.99669 | 0.9835 | 0.0375 | 0.93 | 0.9678 | 0.0014 | 0.46 |
GDM | 2-50-1-1 | 0.85041 | 0.9562 | 0.9633 | 0.8597 | 0.0348 | 0.8807 | 0.9731 | 0.0012 | 0.51 |
GDM | 2-100-1-1 | 0.91944 | 0.86181 | 0.76445 | 0.89773 | 0.1205 | 10.5666 | 0.8065 | 0.0145 | 0.53 |
GDX | 2-5-1-1 | 0.99964 | 0.99932 | 0.94449 | 0.99706 | 0.0161 | 0.9188 | 0.9939 | 0.0002 | 0.43 |
GDX | 2-20-1-1 | 0.99604 | 0.998 | 0.99922 | 0.99605 | 0.0143 | 0.6995 | 0.9952 | 0.0002 | 0.46 |
GDX | 2-50-1-1 | 0.9972 | 0.98502 | 0.99115 | 0.99432 | 0.0223 | 0.9455 | 0.9888 | 0.0004 | 0.51 |
GDX | 2-100-1-1 | 0.9818 | 0.9587 | 0.9810 | 0.9743 | 0.0449 | 9.9170 | 0.9545 | 0.0020 | 0.54 |
Method | Structure | Training (Three Layers) | Validation (Three Layers) | Test (Three Layers) | Output (Three Layers) | RMSE | MAPE [%] | R2 | MSE | Simulation Time [s] |
GDM | 2-5-1-1-1 | 0.97995 | 0.98521 | 0.92245 | 0.97263 | 0.0478 | 9.2449 | 0.9486 | 0.0022 | 0.43 |
GDM | 2-20-1-1-1 | 0.98267 | 0.99399 | 0.97755 | 0.98399 | 0.0376 | 0.6453 | 0.9692 | 0.0014 | 0.45 |
GDM | 2-50-1-1-1 | 0.9639 | 0.99092 | 0.9847 | 0.97281 | 0.0615 | 3.1376 | 0.9491 | 0.0037 | 0.50 |
GDM | 2-100-1-1-1 | 0.95593 | 0.98829 | 0.8557 | 0.9649 | 0.0546 | 2.6622 | 0.9326 | 0.0029 | 0.55 |
GDX | 2-5-1-1-1 | 0.99575 | 0.99965 | 0.99958 | 0.99704 | 0.0161 | 0.9955 | 0.9940 | 0.0002 | 0.45 |
GDX | 2-20-1-1-1 | 0.99591 | 0.99936 | 0.99911 | 0.99728 | 0.0145 | 0.7528 | 0.9952 | 0.0002 | 0.47 |
GDX | 2-50-1-1-1 | 0.9721 | 0.9765 | 0.9239 | 0.9669 | 0.0585 | 0.1928 | 0.9358 | 0.0034 | 0.51 |
GDX | 2-100-1-1-1 | 0.9732 | 0.9053 | 0.9872 | 0.9542 | 0.0640 | 2.4428 | 0.9136 | 0.0041 | 0.56 |
Type | Method | Structure | RMSE | MAPE [%] | R2 | MSE |
---|---|---|---|---|---|---|
FBNN | GDX | 2-5-1-1 | 0.016188 | 0.91880714 | 0.99398 | 0.0002620 |
RBNN | c = 1 | 1-80-1-1 | 0.011196 | 1.09924788 | 0.997163 | 0.0001253 |
Experiment | FBNN w/o Temp | FBNN w/ Temp | RBNN w/o Temp | RBNN w/ Temp |
---|---|---|---|---|
test 1 | 0.99399 | 0.99255 | 0.98320 | 0.98990 |
test 2 | 0.98242 | 0.98761 | 0.99340 | 0.99015 |
test 3 | 0.97425 | 0.98409 | 0.98450 | 0.99490 |
test 4 | 0.99305 | 0.98761 | 0.97564 | 0.98906 |
test 5 | 0.99465 | 0.99139 | 0.98912 | 0.98960 |
test 6 | 0.99331 | 0.98655 | 0.99036 | 0.99394 |
test 7 | 0.98867 | 0.99402 | 0.98536 | 0.98976 |
test 8 | 0.98857 | 0.99036 | 0.99020 | 0.99369 |
test 9 | 0.98572 | 0.99321 | 0.98334 | 0.99206 |
test 10 | 0.97873 | 0.99414 | 0.97342 | 0.99523 |
Factor | N | Mean | Stand. Dev. | CI de 95% |
---|---|---|---|---|
FBNN w/o temp | 10 | 0.98734 | 0.00700 | (0.98400; 0.99067) |
FBNN w/ temp | 10 | 0.99015 | 0.00350 | (0.98682; 0.99349) |
RBNN w/o temp | 10 | 0.98485 | 0.00642 | (0.98152; 0.98819) |
RBNN w/ temp | 10 | 0.991829 | 0.002413 | (0.988491; 0.995167) |
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Hernández, J.A.; Fernández, E.; Torres, H. Electric Vehicle NiMH Battery State of Charge Estimation Using Artificial Neural Networks of Backpropagation and Radial Basis. World Electr. Veh. J. 2023, 14, 312. https://doi.org/10.3390/wevj14110312
Hernández JA, Fernández E, Torres H. Electric Vehicle NiMH Battery State of Charge Estimation Using Artificial Neural Networks of Backpropagation and Radial Basis. World Electric Vehicle Journal. 2023; 14(11):312. https://doi.org/10.3390/wevj14110312
Chicago/Turabian StyleHernández, Jordy Alexander, Efrén Fernández, and Hugo Torres. 2023. "Electric Vehicle NiMH Battery State of Charge Estimation Using Artificial Neural Networks of Backpropagation and Radial Basis" World Electric Vehicle Journal 14, no. 11: 312. https://doi.org/10.3390/wevj14110312