# Investigations on Using Intelligent Learning Techniques for Anomaly Detection and Diagnosis in Sensors Signals in Li-Ion Battery—Case Study

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## Abstract

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## 1. Introduction

#### 1.1. Preliminaries—Data Acquisition Equipment and BMS Architectures

#### 1.2. Traditional Model-Based and Deep Learning Data-Driven-Based Models Estimation Techniques—Literature Review

## 2. Materials and Methods

#### 2.1. Li-Ion Model Selection and Simulink Simscape Block Setup

_{2}) for possible integration in a Battery Management System of an HEV/EV [11].

#### 2.1.1. Li-Ion Cobalt Battery Type Model Performance with and without Temperature Effects

#### 2.1.2. Li-Ion Cobalt Type Battery -Analytical Model

#### 2.2. Anomaly Detection and Diagnosis Techniques for Li-Ion Battery—Additive Bias Faults within Voltage and Current Measurement Sensors

#### 2.2.1. Joint State and Parameter EKF Estimation for Fault Detection and Diagnosis of Anomalies in LIB’s Sensors

#### 2.2.2. Data-Driven-Based Deep Learning Shallow Neural Network for Anomaly Prediction into Sensors’ Measurement Dataset

#### 2.2.3. LSTM Li-Ion Battery SOC Estimation and Fault Detection using LSTM Deep Learning Neural Network

- Input gate (i) controls the level of cell state update
- Forget gate (f) controls the level of cell state reset (forget)
- Cell candidate (g) adds information to the cell state.
- Output gate (o) controls the level of cell state added to the hidden state.

_{c}designates the state activation function. The lstmLayer function uses, by default, the sigmoid function, i.e., a hyperbolic tangent function (tanh), to compute the state activation function, as in Equation (9).

- Input gate: ${i}_{t}={\mathsf{\sigma}}_{g}\left({W}_{i}{x}_{t}+{R}_{i}{h}_{t-1}+{b}_{i}\right)$
- Forget gate: ${f}_{t}={\mathsf{\sigma}}_{g}\left({W}_{f}{x}_{t}+{R}_{f}{h}_{t-1}+{b}_{f}\right)$
- Cell candidate: ${g}_{t}={\mathsf{\sigma}}_{c}\left({W}_{g}{x}_{t}+{R}_{g}{h}_{t-1}+{b}_{g}\right)$
- Output gate: ${o}_{t}={\mathsf{\sigma}}_{g}\left({W}_{o}{x}_{t}+{R}_{o}{h}_{t-1}+{b}_{o}\right)$

- Step 1.
- Load dataset input-output measurements (healthy-subscript h, faulty: subscript fv for voltage fault, fc for current fault, and for dataset test to asses the classification accuracy is used the subscript new)Vbat = [Yh Yfv Yh_new Yfc] is battery terminal voltage sequence: healthy-voltage fault-new healthy dataset-current faultSOC = [SOCh SOCfv SOC_new SOCfc] for the battery SOC sequence with the same meaning as for Vbat
- Step 2.
- Create Cell Array for XTrain and YTrain with combinations of Vbat and SOC,Condition Code: 0-Healthy, 1-Fault Voltage,2-Fault Current; 3-False alarm.XTrain = {[Yh,SOCh]’; [Yfv,SOCfv]’; [Yh_new,SOCh_new]’; [Yfc,SOCfc]’; [Yh,SOCfc]’} is training input sequenceYTrain = categorical{[‘0′,’1′,’2′,’3′]} denotes the output training sequence for anomaly classification (diagnosis)
- Step 3.
- Visualize the first time series in a plot. Each line corresponds to a feature.
- Step 4.
- Prepare the dataset for padding: During training, by default, the software splits the training data into mini-batches and pads the sequences so that they have the same length. However, too much padding can have a negative impact on the network performance.

**Remark**

**1.**

- Step 5.
- Choose a mini-batch size of 50 to divide the training data evenly and reduce the amount of padding in the mini-batches.
- Step 6.
- Define the LSTM neural network architecture:
- Step 6.1.
- Specify the input size to be sequences of size 2 (the dimension of the input data: 4 features, each of dimension 2 × 2477)).
- Step 6.2.
- Specify a bidirectional LSTM layer with 250 hidden units, and output to the “last” element of the sequence.
- Step 6.3.
- Specify four classes by including a fully connected layer of size 4 (number of features), followed by a SoftMax layer and the classification layer.
- Step 6.4.
- Specify the options:
- Step 6.4.1.
- Specify solver to be “adam”
- Step 6.4.2.
- Setup the gradient threshold to be 0.5
- Step 6.4.3.
- Setup the maximum number of epochs to be 150.
- Step 6.4.4.
- Specify the sequence length to be “longest” (for the same length)

- Step 7.
- LSTM Training data phasenet = trainNetwork (XTrain, YTrainn, Layers, options)
- Step 8.
- LSTM data Test: test the LSTM with a never seen data input sequence.XTest = {[Yh, SOCh_new]’}YTest = categorical {[‘0′]}
- Step 9.
- LSTM Classification of the test data:YPred = classify (net, XTest), …MinibatchSize = minibatchSize,SequenceLength = “longest”
- Step 10.
- Calculate the classification accuracy of the predictions:acc = sum (YPred==YTest/numel (YTest))

- XTestnew = [Yh_new, SOCh]’;
- YPred = classify (net, XTest1)’,…
- MiniBatchSize =miniBatchSize,…
- SequenceLength = (“longest”);
- acc = sum (YPred –Ytest/numel (Ytest)
- YPred = 0;
- acc = 1;

## 3. Results

#### 3.1. Li-Ion Cobalt Battery Type -Statistics Performance Evaluation

#### Li-Ion Cobalt Battery Generic Model- AEKF SOC Estimator Simulation Results

#### 3.2. MATLAB Simulation Results for Joint Parameter and State Estimation EKF for Fault Detection and Isolation

_{M}denotes a situation that could be met in realistic situations, namely a misclassified fault. The MATLAB simulation results reveal a very accurate estimation and robustness of the traditional EKF SOC estimator and terminal voltage predictor for changes in operating conditions and SOC initial values.

#### 3.3. DLSNN MATLAB Simulation Results

#### 3.4. The LSTM Anomaly Classification-MATLAB Simulation Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The overall system architecture of a smart LIB power system (LCD: liquid-crystal display, SOC: state-of-charge, CAN BUS: controller area network bus, UART: universal asynchronous receiver-transmitter (reproduced from [5]).

**Figure 2.**The BMS architecture with the main functional blocks (reproduced from [14]).

**Figure 3.**The LiCoO2 Battery Simulink Simscape block setup for a preset Li-Ion battery generic 5.4 Ah rated capacity and 7.4 V nominal voltage without Temperature effects [11].

**Figure 4.**Li-ion Battery model parameters and voltage discharging curves for different CC discharging current rates: (

**a**) Nominal current discharge characteristic at 1.1 A; (

**b**) The battery parameters and three current discharge characteristics.

**Figure 5.**Parameters (

**a**), Discharging current rates (

**b**) and Temperature effects (

**c**) for a generic Simscape LiCoO

_{2}battery model.

**Figure 6.**MATLAB Simulink simulations results: (

**a**) OCV-SOC battery curve; (

**b**) the output voltages of both batteries; (

**c**) the charging and discharging batteries constant currents; (

**d**) the batteries SOCs; (

**e**) ambient and cell temperatures in degrees Celsius.

**Figure 7.**Simulink Simscape model of Li-ion model for an FTP-75 driving cycle input current test profile (Notation: eta = η) (see [10]).

**Figure 8.**Deep Learning Shallow Neural Network: (

**a**) DL SNN structure; (

**b**) Training phase; (

**c**) Output Regression; (

**d**) Error Histogram, (

**e**) DLSNN best validation performance.

**Figure 9.**Deep Learning Shallow Neural Network: (

**a**) Training phase; (

**b**) State performance; (

**c**) DLSNN best validation performance; (

**d**) Error Histogram.

**Figure 10.**Deep Learning Shallow Neural Network; (

**a**) The best performance validation; (

**b**) Regression performance; (

**c**) Training phase; (

**d**) Error Histogram.

**Figure 11.**LSTM Neural Network diagrams for classification and regression applications: (

**a**) LSTM for classification; (

**b**) LSTM for Regression; (

**c**) LSTM layer flow detailed for a time series X with C features (channels) of length S; (

**d**) LSTM architecture detailed at layers level. (Reproduced from the reference [41]).

**Figure 12.**MATLAB simulations results: (

**a**) FTP-75 Driving cycle current test profile (

**b**); AEKF SOC battery estimator versus SOC battery model; (

**c**) AEKF battery cell terminal voltage versus true value.

**Figure 13.**MATLAB simulation results: (

**a**)The UDDS driving cycle current test profile; (

**b**) AEKF SOC battery estimator value versus true value; (

**c**) AEKF battery cell terminal voltage versus true value; (

**d**) SOC residual.

**Figure 14.**MATLAB Simulations results: (

**a**) UDDS-EPA driving cycle current test profile; (

**b**) AEKF SOC battery cell estimated value versus SOC true value; (

**c**) AEKF estimate of battery cell value versus true value; (

**d**) SOC residual.

**Figure 15.**AEKF MATLAB simulation results: (

**a**) AEKF Rint estimate versus Rint battery model; (

**b**) AEKF temperature estimate versus LIB model internal temperature; (

**c**) AEKF Faulty LIB SOC model estimate versus LIB SOC model (Voltage fault); (

**d**) AEKF Faulty LIB Terminal voltage (Vbat) estimate versus Faulty LIB model Terminal voltage (Voltage fault); (

**e**) AEKF Voltage Fault estimate; (

**f**) LIB model SOC residual (Voltage fault); (

**g**) LIB model terminal voltage residual (Voltage fault); (

**h**) AEKF Faulty LIB SOC model estimate versus LIB SOC model (Current fault); (

**i**) AEKF Faulty LIB Terminal voltage (Vbat) estimate versus Faulty LIB model Terminal voltage (Current fault); (

**j**) AEKF Current Fault estimate; (

**k**) LIB model SOC residual (Current fault); (

**l**) LIB model terminal voltage residual (Current fault).

**Figure 16.**DLSNN MATLAB simulation results for the healthy scenario: (

**a**) Vbat prediction versus Vbat data set test; (

**b**) Terminal voltage residual.

**Figure 17.**DLSNN Voltage fault scenario MATLAB Simulation results: (

**a**) DLSNN Voltage prediction versus Voltage battery model; (

**b**) DLSNN Voltage Fault prediction error; (

**c**) DLNN Test prediction phase.

**Figure 18.**DLSNN’s third scenario for current fault prediction is (

**a**) Performance validation in the test phase; (

**b**) Current fault prediction error.

**Figure 19.**Deep Learning LSTM classification-Training phase: (

**a**) Training observation1-features; (

**b**) Padding task to keep the same length for sequences (Minibatch size is 50); (

**c**) Training phase Progress for a NN with 250 hidden layer neurons and 1.5 value of the gradient threshold.

**Figure 20.**LSTM neural network deep learning regression: (

**a**)Training phase progress with 250 hidden layer neurons and 1.5 gradient threshold value; (

**b**) Healthy LIB prediction; (

**c**) Voltage fault prediction; (

**d**) Current fault prediction.

Baseline | RMSE | MSE | MAE | Std |
---|---|---|---|---|

Model SOC vs. SOC AEKF | 0.063 | 1.06 × 10^{−6} | 0.001 | 0.044 (AEKF) |

Vbat | SOC | Code | State |
---|---|---|---|

Healthy | Healthy | 0 | H |

Faulty | Faulty | 1 | ${f}_{V}$ |

Faulty | Healthy | 2 | ${f}_{I}$ |

Healthy | Faulty | 3 | ${f}_{M}$ |

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## Share and Cite

**MDPI and ACS Style**

Tudoroiu, N.; Zaheeruddin, M.; Tudoroiu, R.-E.; Radu, M.S.; Chammas, H.
Investigations on Using Intelligent Learning Techniques for Anomaly Detection and Diagnosis in Sensors Signals in Li-Ion Battery—Case Study. *Inventions* **2023**, *8*, 74.
https://doi.org/10.3390/inventions8030074

**AMA Style**

Tudoroiu N, Zaheeruddin M, Tudoroiu R-E, Radu MS, Chammas H.
Investigations on Using Intelligent Learning Techniques for Anomaly Detection and Diagnosis in Sensors Signals in Li-Ion Battery—Case Study. *Inventions*. 2023; 8(3):74.
https://doi.org/10.3390/inventions8030074

**Chicago/Turabian Style**

Tudoroiu, Nicolae, Mohammed Zaheeruddin, Roxana-Elena Tudoroiu, Mihai Sorin Radu, and Hana Chammas.
2023. "Investigations on Using Intelligent Learning Techniques for Anomaly Detection and Diagnosis in Sensors Signals in Li-Ion Battery—Case Study" *Inventions* 8, no. 3: 74.
https://doi.org/10.3390/inventions8030074