HyBaTwin: Web-Based Hybrid Digital Twin Platform for Electric Vehicle Battery Capacity Estimation

Ⅰ . Introduction

Battery management systems (BMS) play a sig- nificant role in monitoring and regulating the health and performance of batteries in electric vehicles (EVs)^[1,2]. One critical functionality of BMS is esti- mating the battery capacity - a key parameter that di- rectly influences the EV’s range, efficiency, and over- all reliability. Accurate and robust capacity estimation is indispensable for informed decision-making during the charge and discharge process^[1]. With the surge in EVs, there is an equal urgency in refining and en- hancing capacity estimation methodologies.

1.1 Background and Motivation

Digital twins (DT) are an emerging subset of the metaverse ecosystem^[3,4], providing virtual replicas of physical entities that enable seamless integration be- tween the digital and physical worlds. The concept of DTs^[1] has been explored for BMS due to their abil- ity to simulate and predict real-world battery behav- iors accurately^[5]. Two main DT types can be devel- oped for BMS: Model and data-driven approaches. Model-based DTs leverage the principles of battery physics to model the intricate processes within the bat- tery^[6]. For instance, in [7], models were constructed to describe the physical processes that occur in Lithium-ion (Li-ion) batteries, such as diffusion. The equations that govern these models were presented in ^[8], ^[9] highlighted the relevance of these models, with the impending limitation. Ultimately, these mod- els face complexities introduced by diverse operating conditions and dynamic environments by EVs. On the other hand, the data-driven DTs are powered by ma- chine learning (ML) algorithms^[10,11].

1.2 Related Works

Numerous studies have explored data-driven ap- proaches for developing battery DTs. The DT pre- sented in [12] explored various ML algorithms for the prediction of battery state, including models such as deep neural networks (DNN), long-short-term memo- ry networks (LSTM), and gated recurrent units (GRU). In [1], similar ML algorithms were explored for predicting battery state based on a DT framework. Other ML models such as Transformers have been utilized by studies in [13] and [14] for predicting bat- tery states. Another advanced ML algorithm, graph neural network was introduced by [15] and [16] were introduced for the state of health estimation in lith- ium-ion batteries. [17] introduced a reference method- ology for developing DTs for Li-ion batteries, high- lighting the role of ML in optimal battery modelling. These models excel at capturing non-linear relation- ships and complex patterns but often need more interpretability.

Hybrid DTs are an approach that combines the strengths of both methods. A hybrid DT aims to har- ness the accuracy of physics-based models and the adaptability of data-driven models, creating a syner- gistic solution that excels in precision and versatility. This integration addresses the limitations of stand- alone models and provides a holistic representation of the battery. In [9], the relevance of exploring the strengths of these two types of DTs and utilizing a hybrid DT was postulated. However, there were no experiments to validate this, and there were no dem- onstrations to show performance. Nevertheless, the pursuit of accuracy is only part of the equation. The need for explainability arises as a critical consid- eration in deploying AI-based solutions, particularly in safety-critical applications like EVs. Understanding why a model makes a specific prediction is paramount for user trust, regulatory compliance, and overall soci- etal acceptance^[18].

Explainable artificial intelligence (XAI) techniques, like Local Interpretable Model-agnostic Explanations (LIME), serve as indispensable tools for shedding light on the decision-making processes of complex models^[19]. These techniques allow users to interpret the factors influencing a model’s predictions, trans- forming a seemingly opaque model into a transparent and trustworthy ally. Moreover, most previous studies need to present a working battery DT that processes battery data in real-time and produces results. The main objective of this study is to develop a web-based, explainable hybrid DT that can resolve the above-list- ed drawbacks.

The key contributions of this paper are as follows:

1. We integrated physics-based modeling and ML algorithms to develop hybrid DT models that create a synergistic effect, enhancing both the accuracy and adaptability of the capacity estima- tion process.

2. We developed and evaluated the performance of four variants of hybrid DT models.

3. We employed the LIME XAI technique to give users a transparent view of the decision-making process and instill confidence in the estimated battery capacity values.

4. We deploy the model to a web-based system to ensure accessibility and ensure that the bene- fits of the Hybrid DT Platform extend beyond specialized laboratories, reaching a broader audience.

5. The experimental results highlight a hybrid GNN DT as the best with the best confidence score and lowest latency.

Ⅱ . Methodology

The methodology employed in this research is a multilayered approach consisting of five modules: Physical module, data module, cognitive module, communication module, and virtual module, as illus- trated in Fig. 1. Each module contributes uniquely to the overall system, ensuring accuracy, interpretability, and user engagement. The following subsections de- tail the processes and tools employed in each module, emphasizing the seamless integration of diverse tech- nologies for a holistic solution.

Fig. 1.

Architecture of Proposed Web-based Hybrid Digital Twin

2.1 Physical Module - Data Collection

The physical module serves as a bedrock for the Hybrid DT, capturing real-world data from the EVs. Sensors measure the relevant data within the battery. In this work, a dataset that replicates real-life data collection was employed. This dataset, from NASA’s Ames Prognostics Center, includes Li-ion battery ex- periments with diverse operational profiles and inten- tional aging effects. Discharge cycles conclude at end-of-life criteria-30% fade in rated capacity (2 Ah to 1.4 Ah)^[8].

2.2 Data Module - Data Pre-processing

A data pre-processing phase occurs after acquiring raw data from the physical module. This involves comprehensive data analysis, outlier detection, ex- ploratory data analysis, handling missing data, and da- ta normalization, as illustrated in Fig. 2. Correlation analysis is also conducted to identify features highly correlated to the battery capacity and can be used in model development.

Fig. 2.

Process flow of the Data module

2.3 Cognitive Module - Model development

The cognitive module is the heart of our method- ology, representing the convergence of the two DT approaches to form the Hybrid DT. This module is instrumental in harnessing the strengths of both ap- proaches to achieve accurate and interpretable pre- dictions of battery capacity.

2.3.1 Model-based Digital Twin

The physics that represents the life degradation of a typical Li-ion battery is complex. The end-of-life of batteries is typically represented as those with 80% availability of their rated maximum capacity. This degradation can be represented using one of the em- pirical models^[20]:

where: [TeX:] $$\begin{equation} L \end{equation}$$ represents the actual battery lifetime at any given time. [TeX:] $$\begin{equation} L^1 \end{equation}$$ signifies the initial available battery lifetime. [TeX:] $$\begin{equation} f_d \end{equation}$$ characterizes the linearized degradation rate per unit time and cycle^[20]. [TeX:] $$\begin{equation} t \end{equation}$$is the discharge time. [TeX:] $$\begin{equation} \delta \end{equation}$$ is the discharge cycle depth, [TeX:] $$\begin{equation} \sigma \end{equation}$$ is the average cycle state of charge, and [TeX:] $$\begin{equation} T_c \end{equation}$$ is the cell temperature. This formulation enables a dynamic representation of the degradation process over time. The exponential term [TeX:] $$\begin{equation} e^{f_d} \end{equation}$$accounts for the cumulative impact of degradation, influencing the overall battery health and availability. The linearized degradation rate can thus be repre- sented as:

Substituting the variable [TeX:] $$\begin{equation} L \end{equation}$$ with battery capacity, [TeX:] $$\begin{equation} C \end{equation}$$ , Eq.1, can be rewritten as:

where, [TeX:] $$\begin{equation} C \end{equation}$$ is the battery capacity, and [TeX:] $$\begin{equation} C_0 \end{equation}$$ is the initial capacity.

The following approximation can represent [TeX:] $$\begin{equation} f_d \end{equation}$$.

Fig. 3.

Model-based Digital Twin

where [TeX:] $$\begin{equation} i \end{equation}$$ denotes the charge-discharge cycle, [TeX:] $$\begin{equation} T_c \end{equation}$$ repre- sents the temperature measured in the cell during the cycle, [TeX:] $$\begin{equation} t_i \end{equation}$$ is the discharging time and [TeX:] $$\begin{equation} k \end{equation}$$ is an empirical constant with a fixed value of 0.13^[20]. The current and future battery capacity can be determined by pass- ing capacity, temperature, and cycle details through this model. Fig. 3 illustrates the model-based DT.

2.3.2 Data-driven Digital Twin

The data-driven employs ML models to simulate the battery behavior. The models learn from data and identify patterns and relationships that physics-based approaches may overlook. Various ML models can be explored for this purpose. This study employed four ML models: a DNN, LSTM, GNN, and a TNN, as illustrated in Fig. 4.

1. Deep Neural Network (DNN): The model em- ployed in this study comprises three dense layers with 64 units in two layers and 1 units in the last dense layer. All layers were activated using the ReLU activation function.

2. Long Short-Term Memory (LSTM): This model comprises an LSTM layer with 64 units, a dense layer of 64 units, and another dense layer with 1.

3. Graph Neural Networks (GNN): This model comprises a 64 unit embedding layer for graph nodes, a global average pooling layer, and an- other dense layer with a 1 unit.

4. Transformers Neural network (TNN): The model employed here is composed of a dense layer of 64 units, which provides shared representation for the input sequence, an attention mechanism consisting of attention weights in a dense layer, a flattened layer, Softmax activation layer, and a concatenation layer. The model terminates with a fully connected dense layer of 64 units and the ReLU activation function.

Fig. 4.

Data-Driven Digital-Twin Approaches

2.3.3 Hybrid Digital Twin

The model-based and data-driven approaches are combined to form a hybrid digital twin, as illustrated in Fig. 5. To achieve this hybrid, the dataset is trans- formed by passing the necessary variables through the model-based formulation; then, the ML models are trained to minimize the difference between the mod- el-based twin and the actual battery data. This differ- ence is termed the residual . Thus, all models are trained to minimize the mean-squared error function represented as:

Fig. 5.

Hybrid Digital Twin

where [TeX:] $$\begin{equation} n \end{equation}$$ is the number of data points. [TeX:] $$\begin{equation} X_{t w i n, i} \end{equation}$$ and [TeX:] $$\begin{equation} X_{i n, i} \end{equation}$$ are the predicted value from the model-based twin and the actual value from the real battery data for the i-th data point, respectively. As illustrated in Fig. 5, both model-based and data-driven approaches receive the experimental data. The output of the model-based ap- proach serves as part of the hybrid model objective.

Integrating the degradation model within the Hybrid DT allows for a comprehensive understanding of battery health and longevity. The empirical nature of the model ensures adaptability to various scenarios, making it a valuable tool in the realm of battery prog- nostics and digital twin development. Furthermore, the ML models can adapt to complex and non-linear sce- narios of actual battery data.

2.3.4 Explainable Hybrid Digital Twin

We incorporated the LIME XAI approach to shed light on the intricate decision-making process of the DT, thus enhancing its interpretability. LIME creates interpretable models locally around specific instances. For the prediction of capacity [TeX:] $$\begin{equation} (C) \end{equation}$$ at a given cycle [TeX:] $$\begin{equation} (i) \end{equation}$$ , the LIME explanation [TeX:] $$\begin{equation} (\phi) \end{equation}$$ can be approximated as a linear model:

[TeX:] $$\begin{equation} \phi_i^L(f)=\arg \min _{\phi \in \Phi} L\left(f, g_\phi, \pi_i\right) \end{equation}$$

Here, [TeX:] $$\begin{equation} g_\phi \end{equation}$$ is a linear model in the local region around cycle [TeX:] $$\begin{equation} i \end{equation}$$ , [TeX:] $$\begin{equation} L \end{equation}$$ is a loss function measuring the difference between the Hybrid DT’s predictions and the linear model’s predictions. [TeX:] $$\begin{equation} \pi_i \end{equation}$$ is a proximity measure be- tween cycle [TeX:] $$\begin{equation} i \end{equation}$$ and the instances sampled for LIME. A confidence score can be derived by aggregating co- efficients from the explanation for a given instance. A high score indicates high confidence in the model predictions, and a low prediction indicates otherwise. This XAI technique provides valuable insights into how specific cycles contribute to the Hybrid DT’s pre- dictions, elucidating the underlying decision mecha- nisms and facilitating a more transparent interpretation.

2.4 Communication Module

This is the bridge between the physical and sub- sequent modules of the hybrid DT platform. Its pri- mary role is to ensure the smooth transmission and reception of data. Wireless communication protocols such as MQTT or HTTP may be employed for seam- less data transmission. Processed and pre-processed data from the data module are forwarded to the cogni- tive module for model training and development. Web socket communication was employed in this study.

2.5 Virtual Module

A 3D battery model is created and hosted on this module, along with the hybrid DT model.

This module provides a bridge between the insights gained from the ML models in the cognitive module and the visualization of these insights for analysis and decision-making. Fig. 6 summarizes the logic behind how users can access the web server and create cus- tom DTs.

Fig. 6.

Process flow of the platform

Web-Based Platform Deployment This aims to make the virtual module accessible to users. An inter- active web application was developed using the Flask framework for the backend and React for the front end.

Development of 3D Battery Models A 3D model was made in the Blender software in the .gltfformat to reproduce the battery in a digital format. By explor- ing Three. js JavaScript library, the 3D model was embedded in the web application.

Integration of Real Data and Simulation Real da- ta is incorporated from the physical module to test the fidelity of the hybrid DT. Diverse scenarios can also be simulated and visualized to examine the im- pact on battery capacity. Users can input different pa- rameters and observe the corresponding results.

Ⅲ. Performance Evaluation and Results

To analyze the feasibility and explainability of the proposed model, we employed all models in- dependently for all battery types. All models were trained using Google Colaboratory with the NVIDIA Tesla K80 GPU. The best model was saved as a file for deployment to the server.

Fig. 7.

Correlation Analysis

Results fr om Data Module Fig. 7 and Table 1 shows the correlation analysis results obtained for Battery B0018. From this result, it is best only to con- duct capacity estimation using the capacity data and corresponding cycle, as these features have the best positive and negative correlations.

Results fr om Cognitive Module After receiving the data from the data module, it was split using a ratio of 80 : 20 for training and validation, respectively. Data from a different battery was then used as a test set. All models were trained to minimize the established loss function, using the adam opti- mizer, for 100 epochs and with a batch size of 20.

The model-based and data-driven DTs were eval- uated based on MSE, while all hybrid DTs were eval- uated on the basis of MSE, latency, and confidence score. Table 2 compares all implemented data-driven DTs with the model-based DT. In analyzing the ex- perimental results, the Model DT demonstrates con- sistently low MSE values across all batteries, estab- lishing itself as a strong baseline. However, when comparing data-driven approaches, specific ob- servations emerge. The DNN DT variant exhibits higher MSE values, suggesting potential limitations in capturing the underlying patterns of the data. In com- parison, the TNN DT incurs the lowest MSE in all batteries.

The data-driven approaches were all independently combined with the model-based DT approach to yield the hybrid variants. The results of this experiment are represented in Table 3. The hybrid LSTM DT variant competes closely with the Model DT in terms of MSE. However, it introduces a slightly higher latency for specific batteries, which warrants careful consid- eration of the trade-offs between predictive accuracy and computational efficiency. The hybrid GNN DT variant, while showcasing MSE comparable to the Model DT, presents higher latency, which is partic- ularly noteworthy for real-time applications. The hy- brid TNN DT variant displays competitive MSE val- ues but is marked by significantly higher latency for select batteries. Regarding explainable AI (XAI) con- fidence, the hybrid GNN DT for B0007 stands out with high confidence in predictions.

Fig. 8.

Comparison of Model and Hybrid Digital Twins for Battery B0005

Fig. 9.

Comparison of Model and Hybrid Digital Twins for Battery B0018

Figs. 8 compares the model and all hybrid DTs. All models in Figs. 8 and 9 were both trained and validated on battery B0005 and tested on B0018 respectively. The results show a competitively close performance across all models.

For results on XAI, we have presented a plot for the explainable model: GNN. Fig. 10 shows an in- stance prediction by the hybrid GNN DT to highlight the XAI results. The results show a very high con- fidence score of about 0. 8. This is also evidenced by the RealversusPredictedValues plot, showing a very accurate prediction for capacity values between cycle 100 and 170. Fig. 11 illustrates a similar result for the Transformer variant. Ultimately, the best approach depends on the specific priorities of the application― balancing predictive accuracy, latency constraints, and the need for explainability.

Fig. 10.

Explainability result for selected instance on GNN Hybrid DT

Fig. 11.

Explainability result for selected instance on Transformer Hybrid DT

Results from Vir tual Module The GNN Hybrid DT was deployed to the web server for instance-based testing. In Fig. 12, a snapshot illustrates the user inter- face of the web-based platform, providing insight into the interactive experience with a monitored battery.

Fig. 12.

Web-Based DT Platform for Battery Capacity Estimation

Ⅳ . Conclusions and Future Works

This study presented early results for a Web-based battery digital twin. The main objective was to address the complexities faced by battery models for develop- ing digital twins. Since battery digital twins can be created from either model-based approaches or da- ta-driven approaches, each with its distinctive merit and constraint, we adopt a hybrid approach. Our hy- brid digital twin approach fuses model-based and da- ta-driven methods for precise battery capacity estimation. Enhanced with XAI, our model demon- strated appreciable accuracy and reliability.

Future studies will focus on improving prediction accuracy and latency and exploring more complex physics-based models and data-driven approaches. Future efforts will also focus on ensuring security in the DT space.