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Estimating State of Charge for xEV batteries using 1D Convolutional Neural Networks and Transfer Learning

Arnab Bhattacharjee, Ashu Verma, Sukumar Mishra, Tapan K Saha

arXiv:2011.00841v2eess.SPcs.LG

TL;DR

Electric-vehicle batteries lack a fuel-gauge-like system for showing the energy remaining to drive. The paper proposes a wide 1D CNN SoC estimator with transfer learning; its estimation errors are lower than or at par with state-of-the-art machine-learning estimators tested under similar conditions, and transfer learning performs at par with similar models using less training data.

  • Problem

    Battery-powered electric vehicles lack a fuel-gauge-like system to show how much energy remains for driving.

    Source: §I · p. 1

  • Method

    The paper proposes a model-free, deep, wide 1D CNN SoC estimator and a transfer-learning framework for generalizability and data efficiency.

    Source: §I · p. 2

  • Results

    The estimator’s errors were lower than or at par with state-of-the-art machine-learning SoC estimators tested on the same dataset under similar training conditions and validation metrics.

    Source: §VI · p. 12

  • Takeaways & Limitations

    With transfer learning, the model performs almost at par with similar models using substantially less training data.

    Source: C. Transfer learning on different… · p. 12

Abstract

from arXiv · show

In this paper we propose a one-dimensional convolutional neural network (CNN)-based state of charge estimation algorithm for electric vehicles. The CNN is trained using two publicly available battery datasets. The influence of different types of noises on the estimation capabilities of the CNN model has been studied. Moreover, a transfer learning mechanism is proposed in order to make the developed algorithm generalize better and estimate with an acceptable accuracy when a battery with different chemical characteristics than the one used for training the model, is used. It has been observed that using transfer learning, the model can learn sufficiently well with significantly less amount of battery data. The proposed method fares well in terms of estimation accuracy, learning speed and generalization capability.

I. INTRODUCTION

Battery state of charge (SoC) cannot be measured directly, yet indicates remaining charge and energy in electric vehicles. The paper proposes a model-free, wide 1D CNN estimator and transfer-learning framework against a background of existing estimation methods and task-specificity.

I. INTRODUCTION

  • SoC, the remaining charge relative to nominal battery capacity, cannot be directly measured and supports applications including EV range estimation and charging operations.Battery-powered vehicles lack a fuel-gauge-like system for showing the energy remaining to drive.Source: §I · p. 1
  • Lookup tables give approximate, nonscalable estimates and may require battery rest; ampere-hour integration depends on known initial SoC and precise current, while model-based accuracy depends on battery-model quality.Model-based models also rely on simplifying assumptions, and noisy parameter estimation can bias model parameters and lead to faulty state estimation.Source: §I · pp. 1–2
  • Model-free methods learn nonlinear mappings from observable battery variables when the full battery model is unknown; prior SoC neural estimators include fuzzy and feed-forward networks.Recurrent alternatives include dynamically driven RNNs, LSTMs, VARMA-LSTM, and GRUs,.Source: §I · p. 2
  • A CNN-LSTM SoC estimator had combined convolutional spatial features with recurrent temporal features, while standalone CNN use for SoC estimation had not previously been observed, to the authors’ knowledge.CNNs are also used for image and time-series processing.Source: §I · p. 2
  • Deep-learning estimators can be task-specific; prior transfer learning for an LSTM-based SoC estimator used shallow networks and had high estimation errors.Source: §I · p. 2
  • The paper proposes a model-free deep, wide 1D CNN whose width identifies long- and short-term battery-data trends, with transfer learning for generalizability and data efficiency.The authors report estimation error better than or at least at par with state-of-the-art estimators, shorter offline training, and accurate target-dataset learning from substantially less data with transfer learning.Source: §I · p. 2

II. PROPOSED METHOD

The method models SoC as a time-series mapping from observed battery variables to current charge, using a fixed historical window and a CNN learned through an error-minimization objective.

A. Problem Statement

  • The estimator maps voltage, current, and temperature over a fixed historical window to the SoC at the window’s final timestep.The window spans timesteps k − tw + 1 through k.Source: A. Problem Statement · p. 2
  • The method optimizes a 1D CNN’s weights and biases to map time-varying battery features to SoC.The CNN parameters belong to the CNN parameter space ΘC.Source: A. Problem Statement · p. 3
  • MSE is the training objective; the paper motivates it partly through its Gaussian-noise interpretation and continuous gradients.The authors state that MSE corresponds to a KL-divergence loss under Gaussian probability-density assumptions.Source: A. Problem Statement · p. 3
  • MAE and MAX measure average and maximum absolute estimation error, respectively, and are used to validate performance on unseen data.The authors say low values indicate close tracking of true SoC at almost all sample points.Source: A. Problem Statement · p. 3
  • The CNN weights are updated by backpropagation with the Adam optimizer.Source: A. Problem Statement · p. 3

B. CNN for SoC Estimation

The proposed 1D CNN uses temporal convolution and pooling to extract battery features, with differently sized filters intended to capture short- and long-term dependencies. Two architectures differ in how their final feature maps feed into dense layers.

B. CNN for SoC Estimation

  • 1D convolutional kernels stride along the temporal dimension, and convolutional and pooling layers extract temporally relevant features.The model takes voltage, current, and temperature values from timesteps k − tw + 1 to k to predict SoC at timestep k.Source: B. CNN for SoC Estimation · p. 3
  • The first convolution uses three filter shapes to capture both long- and short-term temporal dependencies in the battery inputs.The filter shapes are (tw/10) × 3, (tw/5) × 3, and (tw/2) × 3.Source: B. CNN for SoC Estimation · p. 3
  • The merge-first architecture concatenates flattened final feature maps before a dense layer, while the dense-first architecture sends them to three separate dense layers.Both architectures use a final neuron to produce the SoC estimate.Source: B. CNN for SoC Estimation · p. 4, Figure 1 · p. 4, Figure 2 · p. 4

C. Regularization in CNN model

Regularization constrains CNN weights to reduce prediction variance and improve generalizability and noise robustness. The model uses both architectural and external regularization.

C. Regularization in CNN model

  • Regularization constrains learnable weights to reduce prediction variance, improve generalizability, and increase robustness to noise.CNNs also have architectural regularization through local receptive fields, shared filter weights, and pooling.Source: C. Regularization in CNN model · p. 4
  • The model applies L2 regularization to the final-layer weights with coefficient 1e −4.The L2 norm of the final-layer weight vector is added to the training loss.Source: C. Regularization in CNN model · p. 4
  • Convolutional-layer dropout drops weights with probability 20%.Source: C. Regularization in CNN model · p. 4

D. Knowledge Transfer across datasets

Deep-learning models can perform poorly when their task or domain changes. The paper frames cross-battery SoC estimation as transductive transfer learning and initializes a target CNN from a source CNN trained on Dataset A.

D. Knowledge Transfer across datasets

  • A deep-learning algorithm trained on one task and domain may perform poorly when either changes at test time.Source: D. Knowledge Transfer across datasets · pp. 4–5
  • Cross-battery SoC estimation is treated as transductive transfer between related domains with the same feature spaces and tasks but different feature distributions.The paper uses two public datasets, Panasonic 18650 PF and LG 18650, to study transfer learning empirically.Source: D. Knowledge Transfer across datasets · p. 5
  • The target CNN is initialized with the source CNN's final weights; its dense-layer weights are frozen while its convolutional layers are updated on target data.The paper says this initialization allows faster convergence with less target data than random initialization; it motivates updating convolutional layers because target-domain feature selection may differ.Source: D. Knowledge Transfer across datasets · p. 5

III. DATASET DESCRIPTION

The experiments use two public lithium-ion battery datasets, each available at 10 Hz and downsampled versions at 1 Hz and 0.1 Hz. Dataset A is a Panasonic NCA cell tested across multiple temperatures and drive cycles.

III. DATASET DESCRIPTION

  • For both battery types, the original 10 Hz drive-cycle data was also downsampled to 1 Hz and 0.1 Hz for analysis.Source: §III · p. 5

A. Dataset A – Panasonic 18650 PF battery dataset

B. Dataset B – LG 18650 HG2 battery dataset

Dataset B is an LG 18650 HG2 NMC cell dataset tested across six temperatures and multiple drive cycles. The experiments also consider independent post-normalization feature noise, including a Gaussian noise condition and a nonlinear noise construction.

B. Dataset B – LG 18650 HG2 battery dataset

C. Additive Noise in Data

  • Two noise types are added to normalized features, independently across data dimensions; Noise A is Gaussian with ϵ ∼ N(0, 0.01).Source: C. Additive Noise in Data · p. 6
  • Noise B is constructed using uniform draws for z0 and η, a Gaussian draw for x, and a nonlinear transformation to produce ϵ.The passage defines N as Gaussian and U as uniform distributions.Source: C. Additive Noise in Data · p. 6

IV. EXPERIMENTAL SETUP

  • The experimental setup is organized into three subsequent sections.Source: §IV · p. 6

A. Architecture Selection

The authors select a 1D CNN architecture by comparing four designs, then evaluate the selected model across history-window sizes, sampling frequencies, and noise conditions.

A. Architecture Selection

  • Four CNN designs vary convolutional-layer count and dense-layer arrangement; the best-performing design is selected for later experiments.Selection uses Panasonic data sampled at 10 Hz, with tw = 500, and evaluates US06 and HWFET at three ambient temperatures.Source: A. Architecture Selection · p. 6, Table I · p. 6

B. Model training and evaluation

C. Transfer learning on different dataset

The transfer-learning experiments initialize an LG-target model with weights learned on Panasonic data, then assess performance under different noise, sampling, and target-data conditions.

C. Transfer learning on different dataset

  • A Panasonic-trained CNN initializes an identical model for LG data, with source and target conditions matched for sampling frequency, noise, and history size.The target LG data are sampled at 10 Hz or 1 Hz.Source: C. Transfer learning on different… · pp. 7–8

V. RESULTS AND DISCUSSIONS

  • The described LG comparisons report MAE and MAX across noise types and history sizes, with figures covering 1 Hz and 0.1 Hz data.The results section introduces findings from the experiments but this passage does not state specific outcomes.Source: Figure 11 · p. 8, Figure 12 · p. 8, §V · p. 8

C. Transfer learning on different dataset

  • The full-data condition uses all 45 LG training cycles and tests tw values of 1000, 500, and 100; the 40%-data condition fixes tw at 500.In the latter condition, each training cycle is retained with probability 0.4; noise effects are also studied.Source: C. Transfer learning on different… · p. 8

A. Architecture Selection

The selected dense-first, two-convolution-layer architecture achieves the reported minimum errors; evaluation finds comparable-or-lower errors than cited estimators, with trade-offs across history size and noise.

A. Architecture Selection

  • At 25 °C, the dense-first architecture with two convolutional layers reaches a minimum MAE of 0.58% and MAX of 2.78%.This design is selected for further experiments as the 2C−DF architecture.Source: A. Architecture Selection · p. 8, Table II · p. 9

B. Model Evaluation

  • Increasing tw sharply reduces MAE and MAX at first, with improvement saturating after 500; tw = 1000 is usually only marginally better than 500.The authors identify tw = 500 as the most optimal tested balance of accuracy and computational expense.Source: B. Model Evaluation · pp. 9–11
  • At 0.1 Hz, downsampling leaves too few test samples for tw = 1000 and for reliable separate-cycle results at tw = 500.The tw = 500 results therefore combine US06 and HWFET; tw = 1000 results are omitted.Source: B. Model Evaluation · p. 10
  • The proposed estimator gives lower or comparable errors to cited estimators on the same dataset, while requiring fewer training epochs than the cited LSTM and GRU models.The comparison names,,, and; the LSTM and GRU training times are described as thousands of epochs.Source: B. Model Evaluation · p. 11
  • Noise A often yields lower errors than no added noise, while the model remains robust under the higher, non-Gaussian Noise B condition.The authors attribute the Noise A pattern to white Gaussian noise acting as an L2 regularizer during training.Source: B. Model Evaluation · pp. 10–11

C. Transfer learning on different dataset

Transfer learning performs at least comparably to training without transfer learning and retains near-comparable performance with less LG data; the reported approach also converges faster.

C. Transfer learning on different dataset

  • With transfer learning, the CNN performs at par or better than an identical model trained without transfer learning on similarly conditioned data.Full-LG-data transfer results are shown across noise conditions and tw values; the comparison includes 10 Hz and 1 Hz results.Source: C. Transfer learning on different… · pp. 11–12
  • Using only 40% of LG training data, transfer learning achieves performance almost at par with similar models.The reduced-data comparison fixes tw at 500 and is shown in the transfer-learning results.Source: C. Transfer learning on different… · pp. 11–12
  • At 1 Hz, transfer learning performs worse in most cases with tw = 1000 than with tw = 500; this pattern is not reported at 10 Hz.The authors suggest that extra history may require filtering more information to identify relevant features.Source: C. Transfer learning on different… · p. 12
  • Transfer learning converges faster because only a small segment of the transferred weights, corresponding to convolutional layers, is retrained.The training-loss figure compares no transfer learning, full-data transfer learning, and transfer learning with 40% data.Source: C. Transfer learning on different… · p. 12, Figure 21 · p. 12

VI. CONCLUSION

The proposed 1D CNN estimates SoC from observable historical data, with errors lower than or at par with comparable state-of-the-art machine-learning methods. The paper also reports robustness across experiments and data-efficient transfer across battery chemistries.

VI. CONCLUSION

  • Its estimation errors were lower than or at par with state-of-the-art machine-learning SoC estimators tested on the same dataset under similar training conditions and validation metrics.Source: §VI · p. 12
  • Experiments varied sampling frequency, history size, noise content, and CNN initialization, and the estimator performed robustly across them.Source: §VI · p. 12
  • As a model-free method, it estimates SoC from observable historical data without requiring special battery-chemistry knowledge, while transfer learning supports data efficiency and generalization across chemistries.Source: §VI · p. 12
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