The rapid evolution of the transportation sector towards electrification is a critical response to the intertwined challenges of energy scarcity and environmental degradation caused by conventional petroleum-based vehicles. Governments worldwide are championing new energy technologies, with electric vehicles (EVs) at the forefront of this transformation. Central to the EV’s operation is the lithium-ion battery, a component prized for its rapid response, cleanliness, and high energy density. However, the performance and safety of an EV battery pack are not static; they degrade over time due to complex internal physical and chemical processes. This degradation compromises performance and introduces significant safety risks if left unmonitored. Accurate estimation of the State of Health (SOH) is therefore paramount for ensuring the safe, reliable, and economical operation of an EV battery pack. While extensive research exists on lab-based SOH estimation, its direct applicability to the highly dynamic and stochastic conditions of real-world vehicle operation is limited. This work tackles this challenge head-on by utilizing a vast repository of real-world EV operational data. The primary objective is to develop a robust, data-driven methodology for accurately estimating the SOH of an EV battery pack under actual driving conditions. Furthermore, this research extends beyond passive monitoring; it explores a proactive strategy to control vehicle speed trajectories to actively suppress battery aging, thereby extending the operational life of the EV battery pack. The core of this investigation is structured around two main thrusts: developing a comprehensive SOH estimation framework using machine learning, and formulating an optimal control strategy for speed trajectory optimization to minimize capacity fade.
Understanding the Challenges in Battery Health Management
Before delving into the methodological details, it is crucial to define what constitutes SOH and to understand the landscape of existing estimation and mitigation techniques. SOH is a figure of merit that describes the current state of a battery relative to its beginning of life. While it can be defined from the perspective of internal resistance, the most prevalent and physically meaningful definition uses the metric of capacity fade:
$$ SOH = \frac{Q_{current}}{Q_{new}} $$
where \( Q_{current} \) represents the current maximum usable capacity and \( Q_{new} \) is the rated capacity at the beginning of the battery’s life. This definition is intuitive and directly reflects the ability of the EV battery pack to store energy. The existing body of literature, while substantial, reveals several notable deficiencies which are systematically addressed in this work.
Data Acquisition and Foundational Preprocessing
The foundation of this research is a large-scale dataset sourced from a national traffic management information platform in China. This rich dataset comprises operational records for hundreds of vehicles across five distinct models, with data sampled at 10-second intervals. Each record includes essential parameters such as vehicle ID, timestamp, charging status, vehicle speed, cumulative mileage, total pack voltage and current, individual cell voltages, and pack temperatures. However, real-world data of this nature presents numerous challenges, including missing values, sensor noise, communication errors, and unrepresentative data points. The preprocessing stage is therefore a critical first step to ensure the integrity and reliability of subsequent analyses.
The preprocessing pipeline is designed to transform this raw, noisy data into a clean, structured format suitable for feature extraction and model training. The steps included: handling missing or implausible data is achieved through techniques like data imputation, where missing values are estimated via interpolation, and data deletion, where points that represent impossible state transitions or are clear anomalies are removed; the dataset includes a complex alarm system flagging various battery and vehicle-related issues. These flags are analyzed, and data segments corresponding to serious faults are excluded from the analysis to prevent corruption of the dataset; the core of data structuring involves segmenting the continuous time series data into distinct charging and discharging sessions. This is performed based on the vehicle and charging status indicators, ensuring that only complete and valid events are used for further analysis.
Owing to factors like driver behavior and traffic conditions, the discharge data are highly dynamic, characterized by fluctuating currents and voltages. In contrast, charging events, typically constant current multi-stage processes, produce far more stable and reliable data. Sub-figure (a) within the original thesis illustrates this distinction.
To ensure accuracy in the subsequent capacity calculations, strict criteria were implemented for selecting valid charging segments. The preprocessing algorithm sets specific thresholds to refine the data selection, as follows:
| Parameter | Limiting Condition | Rationale |
| :— | :— | :— |
| Rest Time | Rest time \( > t_{rest} \) | Ensures cell voltage is near open-circuit voltage, increasing SOC estimate accuracy |
| Initial SOC | Initial SOC < 30% | Provides a wide SOC window for more reliable capacity calculations |
| Search Time | Total segment time < 24 hours | Avoids accumulative errors over unnecessarily prolonged durations |
| Discharge Capacity | Discharge capacity < 20% of rated capacity | Minimizes errors due to low sampling frequency during intermittent discharge events |
This deliberate selection process minimizes errors and ensures that the data foundation is as precise as possible for extracting meaningful health indicators.
Innovative Capacity Calculation and Feature Engineering for SOH Estimation
The central challenge in estimating the health of an EV battery pack from field data is that its absolute capacity is not a directly measured value. The BMS provides SOC and current, but not the true maximum capacity. To address this, an “inverse ampere-hour integration” method is utilized. This approach calculates the capacity from a chosen charging segment by its change in SOC and the integrated charge:
$$ Q_{label} = \frac{\sum_{start}^{end} \eta I \Delta t}{\Delta SOC} $$
where \(\eta\) represents the coulombic efficiency, \(I\) is the current, and \(\Delta t\) is the sampling interval. The output, \(Q_{label}\), is the capacity for that specific charging event. Recognizing that the actual available capacity degrades slowly, it is assumed to be constant within any given month. Consequently, for each month of data, the maximum calculated capacity value is treated as the ground truth for that period, and all other capacity values for that vehicle in that month are assigned this true value. This creates a set of “labels” for supervised learning.
The raw capacity values calculated from every legitimate charging segment are subject to noise and errors. To refine these labels, a two-stage anomaly detection process is deployed. First, a Local Outlier Factor (LOF) algorithm is implemented, which assesses the local density deviation of a data point with respect to its neighbors. Points with a significantly lower density are flagged as anomalies. Second, the Rmoutliers function, which operates on the principle of the 3-sigma rule, is used. Data points falling outside the range of \( \mu \pm 3\sigma \) are identified as outliers and removed. This rigorous two-step process ensures that the labels provided to the model are representative of the true battery degradation trend rather than transient data glitches.
With reliable SOH labels, the next step is to extract features from the available charging data that correlate strongly with the health state. A universal and statistically robust approach is adopted, focusing on features derived from the constant-current charging process. For a charging segment, the algorithm computes the mean and standard deviation for various signals. To be universally applicable across different charging behaviors and states of charge, and to avoid errors from data at the voltage boundaries, a specific voltage range is extracted from the charge curve. For the lithium iron phosphate (LFP) battery packs used in many vehicles, a range of 3350-3500 mV was chosen for the minimum cell voltage. For the ternary lithium (NMC) battery packs, a similar feature-relevant voltage range is selected. These voltage windows ensure that the features are extracted from a comparable state of charge region across all charging events, thereby covering the majority of charging behaviors. The extracted features are as follows:
- The average values of total pack voltage and current.
- The standard deviation of average cell voltages.
- The mean and standard deviation of individual cell temperatures.
- The accumulated mileage of the vehicle.
In this feature engineering phase, the method selects features not just for their individual relevance, but also for their ability to provide a comprehensive picture of the battery’s state without redundancy. Two analytical techniques are used to screen features: Pearson correlation coefficient and grey relational analysis. The Pearson coefficient measures the strength and direction of a linear relationship between two variables, while grey relational analysis evaluates the degree of similarity between the geometric curves of the feature and the target SOH over time. For final model input, the algorithm retains features with a high correlation to the SOH (\(|r| \ge 0.3\) for Pearson or \(r_i \ge 0.8\) for grey). To minimize collinearity, if two features show an exceptionally high mutual correlation (\(r \ge 0.9\)), the one with the weaker association to SOH is removed, ensuring the optimality of the input feature set.
Comparative Analysis of Machine Learning Models for SOH Estimation
To map the selected features to the SOH of the EV battery pack, three distinct machine learning models are constructed and rigorously evaluated. These models include Gaussian Process Regression (GPR), Support Vector Regression (SVR), and Multiple Linear Regression (MLR). The dataset is divided, with half of the data for training the models and the other half for testing their performance. The estimation accuracy is quantified using four standard metrics: Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE).
The results from the different models are analyzed and compared. For a specific vehicle model, the GPR model provided initial predictions, which were then refined by SVR and MLR models. The subsequent table presents a comparison of their prediction errors. Each regulatory evaluation is presented to provide a comprehensive view of the performance of each model.
| Vehicle Model | GPR | SVR | MLR |
| :— | :— | :— | :— |
| A | 0.090 | 0.080 | 0.060 |
| B | 0.089 | 0.090 | 0.091 |
| C | 0.182 | 0.162 | 0.162 |
| D | 0.405 | 0.042 | 0.044 |
| E | 0.076 | 0.078 | 0.080 |
The results indicate that the SVR model yielded the best performance for vehicle model A, achieving minimal errors. When the SOH estimation is considered against the cumulative mileage of the vehicles, all three models successfully captured the expected degradation trend. To demonstrate the generalizability of the proposed feature extraction and SOH estimation framework, its application is extended to other vehicle models within the dataset, showing robust performance.
Validation across all five vehicle models shows that the proposed framework is broadly applicable. The RMSE for all vehicles remained below 3%, with the best results achieving an RMSE of 2.02%. The MAE remained below 3.6%, further solidifying the model’s accuracy and consistency. The robustness of the proposed method is confirmed by its ability to perform consistently well across different vehicle models, chemistry, and operational histories. The results confirm that the method of selecting features based on statistical information from stable charging data, combined with SVR, offers a highly effective and universal solution for the on-board estimation of EV battery pack SOH.
Modeling and Optimal Control Strategy for Aging Suppression
After accurately estimating the SOH, the research pivots towards a proactive approach for mitigating battery degradation. The objective is to control the vehicle’s speed trajectory to minimize the further aging of the EV battery pack. This is a complex control problem requiring a multi-domain model that integrates vehicle dynamics, motor efficiency, and an electrochemical model of battery aging. A central component of this framework is the battery capacity fade model. This empirical model captures the loss of active material in the battery, which is driven by factors such as temperature, current, and state of charge:
$$ Q_{AM} = \phi(T) \int_{t_1}^{t_N} z|I| dt $$
where \( \phi(T) \) is an Arrhenius-type temperature-dependent function, \(z\) is the State of Charge (SOC), \(I\) is the current, and \(Q_{AM}\) is the total capacity loss due to the loss of active material. For the control model, SOC is discretized into N time steps, and the capacity loss in each step is approximated using a trapezoidal method. The total capacity loss over the horizon is then the sum of these individual losses, where the objective is to reduce the total capacity loss \( J \). In this control problem, the motor torque and friction brake torque are chosen as the control variables, and the states include position, vehicle velocity, and battery SOC. The relationship between these variables is captured by the vehicle longitudinal dynamics:
$$ \dot{v}(t) = \frac{T_{em}i_g + T_{brake} – T_{roll} – T_{grade} – T_{drag}}{mr} $$
where \(v\) is vehicle velocity, \(T_{em}\) is motor torque, \(i_g\) is the gear ratio, \(T_{brake}\) is the friction braking torque, \(T_{roll}\), \(T_{grade}\), and \(T_{drag}\) are the rolling, grade, and aerodynamic resistance torques, respectively, \(m\) is vehicle mass, and \(r\) is the wheel radius. The SOC dynamics are described by the battery equivalent circuit model, considering its open circuit voltage and internal resistance:
$$ \dot{z}(t) = -\frac{U_{oc} – \sqrt{U_{oc}^2 – 4R P_{em}}}{2R Q_{nom}} $$
where \(U_{oc}\) is the open-circuit voltage, \(R\) is the internal resistance, and \(Q_{nom}\) is the nominal capacity. This state-space model creates a direct link between the driver’s actions (motor torque) and the physical stresses on the EV battery pack (SOC and current), enabling the formulation of an optimization problem. The optimization problem is designed to minimize the battery capacity loss over a finite prediction horizon, N, subject to operational constraints. These constraints ensure the solution is practical and safe, including limits on motor torque, permissible speed and acceleration ranges for passenger comfort, and safety constraints on the distance to a preceding vehicle in traffic flow scenarios. The formal optimization problem is shown as follows:
$$ \min_{T_{em}, T_{brake}} J = \sum_{i=1}^{N} \Delta Q_{AM,i} $$
Subject to various dynamic equations and safety constraints. Since this is a non-linear, constrained optimization problem, it is solved at each step using the Sequential Quadratic Programming (SQP) algorithm. SQP is an effective method for such problems, iteratively approximating the problem using a quadratic programming subproblem until convergence is reached.
To implement a real-time control strategy, the Model Predictive Control (MPC) framework is adopted. MPC operates on the principle of a “receding horizon.” At each control step: the current state of the vehicle and its environment (e.g., traffic flow information) is measured; using this state, the optimal control sequence over the next N steps is calculated by solving the optimization model; only the first control action from this optimal sequence is applied to the vehicle; the vehicle moves forward, the horizon shifts by one step, the state is updated, and the process is repeated. This continuous re-optimization makes the strategy robust to model inaccuracies and external disturbances. The parameters used for the simulations, based on a Tesla Model 3 prototype, include a mass of 1761 kg, a battery nominal capacity of 150 Ah, and an open circuit voltage of 400 V.
Simulation Analysis of Speed Trajectory Optimization
The efficacy of the proposed speed trajectory optimization strategy is validated through two primary simulations. The first scenario examines a single vehicle and compares the optimized speed trajectory against a baseline constant-speed strategy over a 100-second drive cycle. The results of this test are summarized below.
| Performance Metric | Baseline Constant Speed | Optimized Trajectory | Improvement (%) |
| :— | :— | :— | :— |
| Energy Consumption | 100% | -9.70% | 9.70% lower |
| Battery Capacity Fade | 100% | -10.33% | 10.33% lower |
The second scenario is more complex, simulating a vehicle following a preceding vehicle over a segment of the Urban Dynamometer Driving Schedule (UDDS) cycle. The objective for the target vehicle is to optimize its own speed to minimize the aging of its EV battery pack while maintaining a safe following distance. The safety distance is constrained between 10 m (minimum) and 50 m (maximum). The simulation evaluates the impact of different MPC look-ahead horizons (N). The results of this test are summarized below.
| Look-ahead Horizon (N) | Computation Time (s) | Battery Capacity Fade Reduction (%) | Energy Consumption Increase (%) |
|---|---|---|---|
| 25 | 0.92 | 20.78 | 20.48 |
| 30 | 0.95 | 33.02 | 18.80 |
| 35 | 1.05 | 34.01 | 18.01 |
| 40 | 1.36 | 34.12 | 17.88 |
In the scenario with traffic flow, the target vehicle adopts a more anticipatory driving style, decelerating earlier and avoiding unnecessary acceleration spikes compared to the preceding vehicle. This smoother driving profile directly translates to fewer charge-discharge cycles and lower peak currents, thereby mitigating the stress on the EV battery pack. From the simulation results shown in the table, a clear trade-off becomes apparent. Increasing the look-ahead horizon N leads to greater battery aging reduction. However, this comes at the cost of higher energy consumption because the strategy becomes less aggressive in using regenerative braking for deceleration (relying more on mechanical friction brakes), leading to kinetic energy being lost as heat rather than recovered. Importantly, the computation time also increases with N. For real-time control, the controller must compute the optimal solution within its sampling time. As observed, when N=35 or N=40, the computation time exceeds the 1-second controller sampling time, which is not feasible for our real-time MPC implementation. Therefore, the optimal balance for this specific application appears to be an N of 30, which provides a substantial 33% reduction in battery aging, has a significant benefit in extending the lifespan of the EV battery pack, but maintains real-time computational feasibility and adequate energy efficiency.
Conclusion and Outlook
This thesis presents a comprehensive and practical framework for the health management of EV battery packs using real-world data. The first part of the research successfully establishes a robust method for estimating the SOH of a battery pack, even when faced with the imperfect conditions of real driving data. By implementing a novel combination of an inverse ampere-hour integration for creating capacity labels and a meticulous feature engineering process, the study constructs accurate SOH predictors. The evaluation of diverse machine learning models confirmed that the selected features, particularly the statistical features derived from stable charging segments, contain sufficient information to predict SOH accurately. The methods employed demonstrate high accuracy and generalizability across various vehicle models, validating their practical applicability. This work successfully overcomes the limitations of laboratory-based models by developing a framework that is specifically tailored for the high-variability and low-sampling-rate characteristics often found in real-world operational data of an EV battery pack.
The second primary contribution of this work is the development of a Model Predictive Control strategy designed to suppress the aging of an EV battery pack. By coupling vehicle dynamics, motor characteristics, and an electrochemical aging model, the controller optimizes the speed trajectory to minimize battery capacity loss. The simulation results conclusively demonstrate that a proactive control mechanism can effectively reduce battery degradation. The strategy’s success in reducing battery aging, however, is a trade-off with energy consumption and is highly dependent on the look-ahead horizon of the MPC. Future research will focus on further refining the models to achieve a better balance between these competing objectives and to consider integrating the SOH estimation model directly into the online control system for a truly closed-loop, adaptive battery management system.