Electric vehicles (EVs) rely on power batteries as their primary energy source. The performance of the battery pack is a critical factor that directly influences the overall vehicle characteristics, including driving range, acceleration capability, and maximum climbing grade. Therefore, accurate estimation of the remaining capacity of an electric vehicle battery is of great theoretical significance and practical value for the battery industry. In this dissertation, I focus on the prediction of the remaining capacity of an electric vehicle battery, aiming to provide a reliable method for battery management systems.
This work begins with a review of the development history and current status of power batteries. Several conventional forecasting methods for remaining capacity are analyzed, including the capacity experiment method, open-circuit voltage method, internal resistance method, electrolyte density method, ampere-hour integration method, and recovery effect method. Each of these methods has limitations when applied to the complex operating conditions of an electric vehicle battery. The electric vehicle battery is characterized by multiple constraints, and its input–output relationship is difficult to define through a deterministic system. In contrast, neural networks possess the ability to approximate arbitrary nonlinear and uncertain systems. Consequently, I adopt neural network methods for remaining capacity prediction and demonstrate their effectiveness.
In this research, I select lithium iron phosphate (LiFePO4) batteries as the study object. Based on the working principle of LiFePO4 batteries, I collect actual operating voltage and current data at different temperatures. After analyzing the voltage, current, and temperature characteristics of the electric vehicle battery, I propose a prediction method based on the back-propagation (BP) neural network and establish a prediction model. To overcome the tendency of the BP algorithm to become trapped in local minima and its slow convergence rate, I further propose an intelligent prediction method that combines BP neural network and genetic algorithm (GA), namely the GA-BP algorithm. From the perspective of network structure parameters and network training parameters, I improve the established prediction model. The research results show that the improved prediction model not only ensures prediction accuracy but also enhances efficiency.
Finally, I build an experimental system based on the previously completed work. This system is used to predict data that were not actually measured. Through comparison and analysis between the verification data and the predicted results, the errors are found to be within the allowable range for engineering applications, thereby verifying the reliability and accuracy of the system.
1. Introduction and Problem Statement
The growing concern over petroleum prices and environmental pollution has accelerated the global development of electric vehicles. Electric vehicles include pure electric vehicles, hybrid electric vehicles, and fuel cell vehicles, all of which rely on electric energy stored in batteries. The performance of the electric vehicle battery is the key bottleneck restricting the commercialization and widespread adoption of electric vehicles. Traditional lead-acid batteries, nickel-cadmium batteries, nickel-metal hydride batteries, sodium-sulfur batteries, and lithium-ion batteries each have their own advantages and disadvantages. Among them, LiFePO4 batteries stand out due to their high safety, long cycle life, environmental friendliness, and stable discharge platform. Therefore, the research on the remaining capacity prediction of LiFePO4 batteries is extremely meaningful for electric vehicle battery management.
The main problems in current capacity measurement techniques are the long testing time, complex wiring, and the destructive effect on battery life. For example, the traditional capacity test method requires a long constant-current discharge to accumulate ampere-hours, which is accurate but time-consuming. The cycle life test is often destructive and requires several weeks. Moreover, the actual operating conditions of an electric vehicle battery are highly dynamic, with large current fluctuations and temperature variations, making precise estimation even more challenging.
I summarize the conventional remaining capacity estimation techniques for electric vehicle batteries in the following subsections.
1.1 Capacity Experiment Method
In this method, a fully charged battery is discharged at a constant current (typically the 10-hour rate) until the terminal voltage reaches the cut-off voltage. The capacity is calculated as:
$$C = I \cdot t$$
where $C$ is the actual capacity in Ah, $I$ is the discharge current in A, and $t$ is the discharge time in h. Although this method is the most accurate, it is inefficient and cannot be used for online monitoring.
1.2 Open-Circuit Voltage Method
The open-circuit voltage (OCV) has an approximately linear relationship with the state of charge (SOC) for some battery chemistries. Table 1 shows a typical relationship between SOC and OCV for a nickel-metal hydride battery.
| State of Charge (%) | 100 | 87 | 75 | 62 | 50 | 37 | 25 | 12 | 0 |
|---|---|---|---|---|---|---|---|---|---|
| Open-circuit voltage (V) | 2.11 | 2.09 | 2.07 | 2.05 | 2.03 | 2.01 | 1.99 | 1.97 | 1.95 |
The OCV method is not suitable for online monitoring because the battery must be at rest to obtain a stable open-circuit voltage. Moreover, the relationship is only approximate and varies with temperature and aging.
1.3 Internal Resistance Method
Internal resistance can reflect battery health, but it does not have a strict mathematical relationship with remaining capacity. The internal resistance of a battery is very small, and measurement errors caused by instruments and manual operation can seriously interfere with the results. Thus, this method lacks practical accuracy for online SOC estimation of an electric vehicle battery.
1.4 Electrolyte Density Method
For lead-acid batteries, the density of the electrolyte correlates with SOC. Since OCV equals the density plus a constant (approximately 0.85 V for lead-acid), and OCV is roughly linear with capacity, density also approximates capacity. Table 2 gives an example.
| State of Charge (%) | 100 | 87 | 75 | 62 | 50 | 37 | 25 | 12 | 0 |
|---|---|---|---|---|---|---|---|---|---|
| Sulfuric acid density (g/cm³) | 1.26 | 1.24 | 1.22 | 1.20 | 1.18 | 1.16 | 1.14 | 1.12 | 1.11 |
However, real-time measurement of electrolyte density is difficult and not practical for an electric vehicle battery in service.
1.5 Ampere-Hour Integration Method
The ampere-hour (Ah) integration method measures the discharge current and integrates it over time to obtain the delivered capacity. It is simple and suitable for varying current conditions. The remaining capacity is computed as:
$$ C_I = \int_0^t \varpi_i \cdot i \, d\tau $$
where $C_I$ is the capacity at current $I$, $i$ is the instantaneous current, and $\varpi_i$ is a weighting coefficient. This coefficient can be derived from the Peukert equation:
$$ K T I^n = 1 \quad \text{or} \quad C = K I^{1-n} $$
leading to
$$ \varpi_i = \frac{C}{C_i} = \left( \frac{I}{i} \right)^{n-1} $$
The Ah integration method does not consider the internal chemical state, temperature effects, self-discharge, or aging of the electric vehicle battery. Therefore, its error tends to accumulate over time unless periodic recalibration is performed.
1.6 Other Methods
The recovery effect method estimates the final stabilized voltage after a long rest period, but it requires waiting for voltage recovery and is unsuitable for real-time applications. Physicochemical models, such as fourth-order dynamic models, are comprehensive but require many empirical parameters and are computationally heavy.
2. Battery Characteristics and Discharge Experiments
2.1 Working Principle of LiFePO4 Batteries
The lithium-ion battery reaction can be expressed as:
$$ \text{LiMO}_2 + \text{C} \underset{\text{discharge}}{\overset{\text{charge}}{\rightleftharpoons}} \text{Li}_{1-x}\text{MO}_2 + \text{Li}_x\text{C} $$
For LiFePO4 batteries, the positive electrode material is LiFePO4. During charging, lithium ions deintercalate from the positive electrode and intercalate into the negative carbon electrode. The process is reversed during discharge. The cell voltage range is typically 2.0 V to 4.2 V, and the theoretical specific capacity is about 170 mAh/g, with practical capacities above 130 mAh/g.
2.2 Performance Indicators
Several electrical parameters define the performance of an electric vehicle battery:
- Voltage: Electromotive force (EMF), open-circuit voltage, rated voltage, working voltage, and cut-off voltage.
- Capacity: Theoretical capacity, actual capacity, and rated capacity (Ah).
- Energy and specific energy: Measured in Wh and Wh/kg.
- Power and specific power: Determines the acceleration capability of the EV.
- Self-discharge rate and cycle life: Important for long-term reliability.
The discharge rate is defined as:
$$\text{Discharge rate} = \frac{\text{Discharge current (A)}}{\text{Rated capacity (Ah)}} $$
For example, a battery with a rated capacity of 100 Ah discharging at 50 A is a 0.5C rate, requiring 2 hours to fully discharge.
2.3 Discharge Experiment Setup
I conducted experiments on type 26650P LiFePO4 cells with a nominal voltage of 3.2 V and a rated capacity of 3 Ah. The equipment included a ZEEMOO850 battery testing system and a ZEEMOO3000E internal resistance tester. The experimental procedure was as follows:
- Charge the cell to 3.65 V and rest for 5 hours.
- Perform constant-current discharge at various current levels using the ZEEMOO850.
- Measure the internal resistance at open-circuit voltages using the ZEEMOO3000E.
- Record voltage, current, and discharged capacity data via an Excel interface.
The voltage measurement used either a two-wire or four-wire configuration depending on the current magnitude. For large currents, the four-wire method eliminates contact resistance effects:
$$ U = E + I R_0 $$
where $U$ is the terminal voltage, $E$ the electromotive force, $I$ the current, and $R_0$ the internal resistance. Current measurement employed a shunt resistor to convert the current into a voltage signal for computer-based acquisition.
2.4 Experimental Results
I collected discharge curves under different constant currents and temperatures. Figure 1 (not shown here, but available in the original dissertation) illustrates that higher discharge currents lead to faster voltage drops and lower delivered capacities. Figure 2 (omitted) shows the relationship between discharge voltage and time for currents of 1 A, 3 A, 6 A, and 9 A. Figure 3 (omitted) displays the remaining capacity versus time. Figure 4 (omitted) compares discharge curves at different ambient temperatures, indicating that temperature significantly affects the discharge capacity, especially at low temperatures.
Some sample data from the discharge experiments are listed in Table 3.
| Discharge current (A) | Discharge voltage (V) | Discharged capacity (Ah) |
|---|---|---|
| 3 | 3.2267 | 0.04991 |
| 3 | 3.2142 | 0.29978 |
| 3 | 3.2132 | 0.34967 |
| 3 | 3.2015 | 0.69943 |
| 4 | 3.0848 | 1.2242 |
| 4 | 3.0817 | 1.1797 |
| 5 | 3.0833 | 1.9852 |
| 5 | 3.0817 | 1.9435 |
| 6 | 3.1104 | 2.6189 |
| 6 | 3.1078 | 2.5190 |
| 7 | 3.0169 | 2.5266 |
| 8 | 2.7566 | 0.47167 |
| 9 | 2.9892 | 2.7233 |
I also measured the internal resistance at different open-circuit voltages. The results shown in Table 4 indicate that the internal resistance remains nearly constant over the discharge range for this cell type. Therefore, I do not include internal resistance as a major input in the prediction model.
| Open-circuit voltage (V) | Internal resistance (mΩ) |
|---|---|
| 3.65 | 22.32 |
| 3.37 | 22.46 |
| 3.082 | 22.36 |
| 2.854 | 22.37 |
| 2.564 | 22.45 |
| 2.372 | 22.43 |
| 2.005 | 22.48 |
3. Prediction Model Based on BP Neural Network
3.1 Modeling Mechanism of Neural Networks
Nonlinear system identification using neural networks aims to choose an appropriate network structure and training algorithm to approximate the input–output relationship of the real system. The NARMAX model is often used:
$$ y_m(k) = f_m(y_m(k-1), \ldots, y_m(k-n_y), u(k-1), \ldots, u(k-n_u)) $$
where $u$ is the input and $y$ is the output. Neural networks are trained using supervised learning, where error functions such as the mean squared error (MSE) are minimized.
Several learning algorithms exist: Hebbian learning, gradient descent, delta rule, and back-propagation (BP). The BP algorithm is the most widely used for multilayer feedforward networks. Its weight update rule is:
$$ \omega_{ji}(k+1) = \omega_{ji}(k) + \eta \delta_j y_i(k) $$
where $\eta$ is the learning rate, $\delta_j$ is the local gradient, and $y_i$ is the input from neuron $i$.
For sigmoid activation functions, the derivative is:
$$ f'(v_j) = f(v_j) (1 – f(v_j)) $$
The BP algorithm can be summarized as:
- Initialize all weights and biases to small random values.
- For each training sample, perform forward propagation to compute outputs.
- Compute the output errors.
- Back-propagate the errors and update weights using:
$$ \omega_{ji}(n+1) = \omega_{ji}(n) + \eta \delta_j y_i(n) $$
Repeat until the total error reaches the desired target.
3.2 Model Inputs and Outputs
I derived the functional relationship from the discharge experiments. At a given time, the remaining capacity $C(t)$ is related to the discharged capacity $C_1(t)$ and the rated capacity $C_0$:
$$ C(t) = C_0 – C_1(t) $$
Since the internal resistance varies only slightly, I simplified the relationship to:
$$ f(U(t), I(t), t, C(t)) = 0 $$
In practice, the discharge time may be unknown, so I eliminate it and express the remaining capacity as:
$$ C(t) = g(U(t), I(t)) $$
Discretizing with sampling period $T$:
$$ C(k) = f(U(k), I(k), T) $$
Thus, the neural network takes two inputs — discharge voltage and discharge current — and outputs the remaining capacity. Figure 1 in the original dissertation shows the BP network architecture with two input nodes, one hidden layer with 11 nodes, and one output node.
3.3 BP Network Training and Prediction
I used the matlab neural network toolbox to train the model with the experimental data. The performance function is the mean squared error:
$$ \text{MSE} = \frac{1}{mp} \sum_{j=1}^{p} \sum_{R=1}^{m} (\hat{y}_{Rj} – y_{Rj})^2 $$
where $m$ is the number of output nodes, $p$ is the number of training samples, $\hat{y}_{Rj}$ is the expected output, and $y_{Rj}$ is the actual output.
Using a training set of 30 samples and one hidden layer with 11 nodes, I first validated the model with 6 A discharge data (not used in training). The testing curves showed that the BP model could follow the general trend, but the prediction errors were non-negligible. The training time was 22.1324 seconds. Table 5 gives a comparison of predicted remaining capacity for a few test points.
| Voltage (V) | Current (A) | Actual remaining capacity (Ah) | Predicted remaining capacity (Ah) | Relative error (%) |
|---|---|---|---|---|
| 3.434 | 8.9973 | 2.985 | 2.8380 | 4.91 |
| 3.284 | 8.9966 | 2.084 | 1.9550 | 4.32 |
| 3.255 | 8.9966 | 1.938 | 1.8300 | 3.61 |
| 3.202 | 8.9966 | 0.563 | 0.6530 | 3.09 |
The results indicated that the pure BP model could satisfy requirements with moderate accuracy, but for higher precision and faster real-time estimation of an electric vehicle battery, the BP network requires improvement.
4. Improved Prediction Using GA-BP Algorithm
4.1 Genetic Algorithm Fundamentals
Genetic algorithms are stochastic global search methods inspired by natural selection and genetics. They operate on a population of candidate solutions encoded as chromosomes. The main operations are selection, crossover, and mutation. Key features include:
- Search from a population, not a single point, reducing the risk of local optima.
- No derivative information is needed, only fitness values.
- Strong robustness and implicit parallelism.
The fitness function is often defined as the reciprocal of the sum of squared errors:
$$ f(i) = \frac{1}{E(i)} $$
$$ E(i) = \sum_{p} \sum_{k} (T_k – V_k)^2 $$
Selection probability is proportional to fitness:
$$ P_s = f_i / \sum_{j=1}^{N} f_j $$
4.2 GA-BP for Network Structure Parameters
The hybrid GA-BP algorithm first uses GA to search for optimal initial weights and biases. These values are then used as the starting point for BP training. The procedure is:
- Initialize a population of random weight vectors (real encoding, population size 30).
- Evaluate fitness of each individual.
- Apply selection, crossover (probability $P_c = 0.6$), and mutation (probability $P_m = 0.2$) to generate new individuals.
- Insert new individuals into the population and evaluate again.
- If the error meets the GA target $\varepsilon_{GA}$, stop GA and use the best chromosome as initial weights.
- Train the BP network with these initial weights until the desired precision $\varepsilon_{BP}$ is achieved.
Using the same inputs (voltage and current) and output (remaining capacity), the GA-BP algorithm produced optimized initial weights $W_1$, $W_2$, and biases $B_1$, $B_2$. The prediction curve showed excellent agreement with the real measured values. The training time reduced dramatically to 2.7340 seconds, versus 22.1324 seconds for standard BP, while the prediction accuracy improved.
4.3 GA Optimization of Network Training Parameters
The BP training parameters — maximum epochs, learning rate, and target error — strongly influence convergence speed. I used a three-level nested GA optimization:
- Inner loop: optimize goal (target MSE) with fixed lr and epochs.
- Middle loop: optimize lr with fixed epochs.
- Outer loop: optimize epochs.
The GA settings for goal optimization are listed in Table 6.
| Parameter | Value |
|---|---|
| Population size | 4 |
| Search range | 0.01 – 0.08 |
| Termination generations | 10 |
| Binary encoding length | 3 |
| Crossover probability | 0.6 |
| Mutation probability | 0.01 |
After the inner loop, the optimal goal was found to be 0.02, yielding a training time of 22.9530 s (with the original BP structure; note that the comparison is consistent). Next, with the outer loop optimizing lr and goal, the optimal lr was 0.013 and goal 0.07, reducing training time to 9.9043 s. Finally, when all three parameters were optimized, the best combination was epochs=1550, lr=0.012, and goal=0.08, giving a training time of only 2.7500 s. Table 7 summarizes these steps.
| Optimized parameters | Epochs | Learning rate | Goal | Training time (s) |
|---|---|---|---|---|
| None (BP only) | 2000 | 0.015 | 0.001 | 22.1324 |
| Goal | 2000 | 0.015 | 0.02 | 22.9530 |
| Goal + lr | 2000 | 0.013 | 0.07 | 9.9043 |
| Goal + lr + epochs | 1550 | 0.012 | 0.08 | 2.7500 |
4.4 Comprehensive Optimization
To balance accuracy and training speed, I combined the optimized initial weights and the optimized training parameters. The final model used initial weights from the GA search, a goal of 0.08, epochs of 1750, and a learning rate of 0.015. The training time was 6.3750 seconds. The prediction curve shown in the dissertation demonstrates that the model fits the actual data closely for most sample points, with an average error around 0.3 Ah. This comprehensive optimization achieves both high prediction accuracy and improved training efficiency for the electric vehicle battery remaining capacity.
4.5 Prediction Accuracy Comparison
I compared the prediction results from the standard BP model and the GA-BP model using several test points. Table 8 presents the outcomes.
| Current (A) | Voltage (V) | Actual remaining capacity (Ah) | BP predicted (Ah) | GA-BP predicted (Ah) | Method | Relative error (%) |
|---|---|---|---|---|---|---|
| 3 | 3.2267 | 2.955 | 2.8110 | 2.8800 | BP | 4.81 |
| 3 | 3.2267 | 2.955 | — | 2.8800 | GA-BP | 2.53 |
| 3 | 3.2132 | 2.6552 | 2.5202 | 2.7242 | BP | 4.52 |
| 3 | 3.2132 | 2.6552 | — | 2.7242 | GA-BP | 2.34 |
| 3 | 3.2015 | 2.3055 | 2.3355 | 2.2175 | BP | 1.32 |
| 3 | 3.2015 | 2.3055 | — | 2.2175 | GA-BP | 2.93 |
| 3 | 3.1917 | 2.0556 | 2.1636 | 1.9906 | BP | 3.61 |
| 3 | 3.1917 | 2.0556 | — | 1.9906 | GA-BP | 2.16 |
| 3 | 3.1876 | 1.9556 | 1.8146 | 2.0006 | BP | 4.69 |
| 3 | 3.1876 | 1.9556 | — | 2.0006 | GA-BP | 1.51 |
| 3 | 3.1757 | 1.6558 | 1.5958 | 1.5958 | BP | 2.01 |
| 3 | 3.1757 | 1.6558 | — | 1.5958 | GA-BP | 2.03 |
| 3 | 3.1696 | 1.5059 | 1.6259 | 1.5899 | BP | 4.05 |
| 3 | 3.1696 | 1.5059 | — | 1.5899 | GA-BP | 2.83 |
From Table 8, the GA-BP algorithm achieves an average relative error of about 2–3%, which is significantly lower than that of the standard BP algorithm. The improvement is consistent across all test points.
5. Experimental System and Generalization Verification
5.1 Establishment of the Prediction System
I built a complete experimental system for electric vehicle battery remaining capacity prediction. The system consists of a trained GA-BP neural network model with the following configuration:
- Network structure: 2 inputs, 11 hidden neurons, 1 output.
- Initial weights and biases: obtained from GA optimization (as given in the original thesis).
- Training parameters: goal = 0.08, learning rate = 0.012, epochs = 1550.
The optimized initial weight matrices $W_1$ and $W_2$, and bias vectors $B_1$ and $B_2$ are listed below:
$$ W_1 = \begin{bmatrix} -0.0090 & 0.5820 \\ 0.3877 & 0.1891 \\ -0.2328 & 0.1273 \\ -0.2127 & 0.1972 \\ -0.3801 & 0.6126 \\ -0.2952 & 0.8903 \\ -0.3591 & 0.0859 \\ -0.2105 & 0.3088 \\ -0.6778 & 0.3019 \\ -0.5918 & 0.3165 \\ -0.2864 & 0.3599 \\ \end{bmatrix} $$
$$ W_2 = \begin{bmatrix} -0.2084 & -0.2235 & 0.1563 & 0.6178 & 0.0618 & -0.6310 & -0.2696 & -0.2862 & -0.3209 & -0.7957 & 0.4142 \\ \end{bmatrix} $$
$$ B_1 = \begin{bmatrix} -0.1061 \\ 0.4113 \\ 0.2258 \\ 0.4827 \\ -0.3245 \\ -0.5378 \\ -0.6311 \\ -0.2888 \\ -0.5434 \\ -0.2097 \\ -0.4065 \\ \end{bmatrix} , \quad B_2 = \begin{bmatrix} 0.4126 \\ \end{bmatrix} $$
5.2 Prediction of Unmeasured Data
To verify the generalization capability of the model, I used a discharge current of 3 A and selected voltage points from 3.3 V to 3.1 V with a step of 0.02 V. These points were not part of the original training samples because the data acquisition system sampled every 60 seconds, leaving gaps in the measured dataset. The predicted remaining capacities are shown in Table 9.
| Discharge current (A) | Discharge voltage (V) | Predicted remaining capacity (Ah) |
|---|---|---|
| 3 | 3.3 | 2.9735 |
| 3 | 3.28 | 2.9682 |
| 3 | 3.26 | 2.8653 |
| 3 | 3.24 | 2.7192 |
| 3 | 3.22 | 2.5634 |
| 3 | 3.2 | 2.3436 |
| 3 | 3.18 | 1.9438 |
| 3 | 3.16 | 1.7466 |
| 3 | 3.14 | 1.5968 |
| 3 | 3.12 | 1.3569 |
| 3 | 3.1 | 1.2442 |
Next, I predicted data for a current of 2.5 A, which was not included in the training set at all. Table 10 lists the predicted values.
| Discharge current (A) | Discharge voltage (V) | Predicted remaining capacity (Ah) |
|---|---|---|
| 2.5 | 3.4 | 2.9846 |
| 2.5 | 3.38 | 2.9666 |
| 2.5 | 3.36 | 2.8935 |
| 2.5 | 3.34 | 2.7752 |
| 2.5 | 3.32 | 2.6024 |
| 2.5 | 3.3 | 2.4368 |
| 2.5 | 3.28 | 2.0456 |
| 2.5 | 3.26 | 1.8985 |
| 2.5 | 3.24 | 1.7123 |
| 2.5 | 3.22 | 1.4650 |
| 2.5 | 3.2 | 1.3368 |
5.3 Validation with Measured Data
To confirm the predictions, I performed actual discharge tests with a sampling interval of 10 seconds for both 3 A and 2.5 A currents. The measured remaining capacities were compared with the predictions, as shown in Tables 11 and 12.
| Current (A) | Voltage (V) | Predicted capacity (Ah) | Measured capacity (Ah) | Relative error (%) |
|---|---|---|---|---|
| 3 | 3.4 | 2.9735 | 2.9315 | 1.39 |
| 3 | 3.38 | 2.9682 | 2.9552 | 0.43 |
| 3 | 3.36 | 2.8653 | 2.8893 | 0.80 |
| 3 | 3.34 | 2.7192 | 2.6862 | 1.09 |
| 3 | 3.32 | 2.5634 | 2.5114 | 1.73 |
| 3 | 3.3 | 2.3436 | 2.3836 | 1.33 |
| 3 | 3.28 | 1.9438 | 1.9098 | 1.13 |
| 3 | 3.26 | 1.7466 | 1.7676 | 0.69 |
| 3 | 3.24 | 1.5968 | 1.5648 | 1.07 |
| 3 | 3.22 | 1.3569 | 1.3309 | 0.87 |
| 3 | 3.2 | 1.2442 | 1.2142 | 1.00 |
| Current (A) | Voltage (V) | Predicted capacity (Ah) | Measured capacity (Ah) | Relative error (%) |
|---|---|---|---|---|
| 2.5 | 3.4 | 2.9846 | 2.8966 | 2.93 |
| 2.5 | 3.38 | 2.9666 | 2.8906 | 2.53 |
| 2.5 | 3.36 | 2.8935 | 2.9545 | 2.03 |
| 2.5 | 3.34 | 2.7752 | 2.7062 | 2.29 |
| 2.5 | 3.32 | 2.6024 | 2.6544 | 1.73 |
| 2.5 | 3.3 | 2.4368 | 2.3708 | 2.21 |
| 2.5 | 3.28 | 2.0456 | 1.9686 | 2.56 |
| 2.5 | 3.26 | 1.8985 | 1.9765 | 2.62 |
| 2.5 | 3.24 | 1.7123 | 1.6453 | 2.23 |
| 2.5 | 3.22 | 1.4650 | 1.4130 | 1.73 |
| 2.5 | 3.2 | 1.3368 | 1.2888 | 1.60 |
The results confirm that the GA-BP-based prediction system estimates the remaining capacity of an electric vehicle battery with a maximum relative error of about 3%, which is well within the acceptable tolerance for engineering applications. The system successfully predicts values for both non-sampled voltage points and current levels not included in the training set, demonstrating excellent generalization capability.
Conclusion
In this dissertation, I have addressed the challenging problem of remaining capacity prediction for an electric vehicle battery. The key contributions and conclusions are as follows:
- I conducted comprehensive discharge experiments on LiFePO4 batteries and analyzed their voltage, current, and temperature characteristics. The data confirmed that the electric vehicle battery is a highly nonlinear system whose remaining capacity cannot be easily modeled by traditional deterministic equations.
- I established a BP neural network model with two inputs (discharge voltage and discharge current) and one output (remaining capacity). The model demonstrates acceptable accuracy for moderate requirements but suffers from slow convergence and local minima problems.
- To overcome these drawbacks, I developed a GA-BP hybrid algorithm. The genetic algorithm optimizes the initial weights and biases of the BP network, effectively preventing the training process from getting trapped in local optima. This improved the prediction accuracy and reduced the training time dramatically.
- I further optimized the BP training parameters (goal, learning rate, and epochs) using a nested GA approach. The optimized parameters reduced training time from over 22 seconds to less than 3 seconds while maintaining high accuracy.
- Finally, I built a complete experimental system and validated its performance by predicting unmeasured data at non-sampled voltage points and at a current level not used in training. The relative errors between predicted and measured remaining capacities were within 3%, verifying the reliability and accuracy of the proposed system.
This work demonstrates that the combination of neural networks and genetic algorithms provides a powerful tool for electric vehicle battery remaining capacity prediction. The proposed model can be embedded into a battery management system for real-time monitoring and state-of-health estimation. Future research could extend this approach to account for temperature effects, battery aging, and self-discharge, which would further improve the universality and accuracy of the prediction system.