# State-of-Health Identification of Lithium-Ion Batteries Based on Nonlinear Frequency Response Analysis: First Steps with Machine Learning

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Nonlinear Frequency Response Analysis (NFRA)

#### 2.2. SoH Degradation Model Based on Machine Learning

#### Correlation Analysis

#### 2.3. Feature Extraction and Sensitivity Analysis

#### 2.4. Support Vector Regression

## 3. Case Study

#### 3.1. Measurements and Cells

#### 3.2. Results and Discussion

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Vetter, J.; Novak, P.; Wagner, M.; Veit, C. Ageing Mechanisms in Lithium-Ion Batteries. J. Power Sources
**2005**, 147, 269–281. [Google Scholar] [CrossRef] - Barré, A.; Deguilhem, B.; Grolleau, S.; Gérard, M.; Suard, F.; Riu, D. A review on Lithium-Ion Battery Ageing Mechanisms and Estimations for Automotive Applications. J. Power Sources
**2013**, 241, 680–689. [Google Scholar] [CrossRef] - Agubra, V.; Fergus, J. Lithium ion battery anode aging mechanisms. Materials
**2013**, 6, 1310–1325. [Google Scholar] [CrossRef] [PubMed] - Verma, P.; Maire, P.; Novák, P. A Review of the Features and Analyses of the Solid Electrolyte Interphase in Li-Ion Batteries. Electrochim. Acta
**2010**, 55, 6332–6341. [Google Scholar] [CrossRef] - Petzl, M.; Kasper, M.; Danzer, M.A. Lithium Plating in a Commercial Lithium-Ion Battery—A Low- Temperature Aging Study. J. Power Sources
**2014**, 275, 799–807. [Google Scholar] [CrossRef] - Waldmann, T.; Hogg, B.I.; Wohlfahrt-Mehrens, M. Li plating as unwanted side reaction in commercial Li-ion cells—A review. J. Power Sources
**2018**, 384, 107–124. [Google Scholar] [CrossRef] - Fleischhammer, M.; Waldmann, T.; Bisle, G.; Hogg, B.I.; Wohlfahrt-Mehrens, M. Interaction of Cyclic Ageing at High-Rate and Low Temperatures and Safety in Lithium-Ion Batteries. J. Power Sources
**2015**, 274, 432–439. [Google Scholar] [CrossRef] - Wu, C.; Zhu, C.; Ge, Y.; Zhao, Y. A Review on Fault Mechanism and Diagnosis Approach for Li-Ion Batteries. J. Nanomater.
**2015**, 2015, 8. [Google Scholar] [CrossRef] - Lewerenz, M.; Marongiu, A.; Warnecke, A.; Sauer, D.U. Differential voltage analysis as a tool for analyzing inhomogeneous aging: A case study for LiFePO
_{4}|Graphite cylindrical cells. J. Power Sources**2017**, 368, 57–67. [Google Scholar] [CrossRef] - Rezvanizaniani, S.M.; Liu, Z.; Chen, Y.; Lee, J. Review and recent advances in battery health monitoring and prognostics technologies for electric vehicle (EV) safety and mobility. J. Power Sources
**2014**, 256, 110–124. [Google Scholar] [CrossRef] - Broussely, M.; Biensan, P.; Bonhomme, F.; Blanchard, P.; Herreyre, S.; Nechev, K.; Staniewicz, R. Main Aging Mechanisms in Li Ion Batteries. J. Power Sources
**2005**, 146, 90–96. [Google Scholar] [CrossRef] - Zhou, Y.; Huang, M.; Chen, Y.; Tao, Y. A novel health indicator for on-line lithium-ion batteries remaining useful life prediction. J. Power Sources
**2016**, 321, 1–10. [Google Scholar] [CrossRef] - Liu, Q.; Du, C.; Shen, B.; Zuo, P.; Cheng, X.; Ma, Y.; Yin, G.; Gao, Y. Understanding undesirable anode lithium plating issues in lithium-ion batteries. RSC Adv.
**2016**, 6, 88683–88700. [Google Scholar] [CrossRef] - Schindler, S.; Bauer, M.; Petzl, M.; Danzer, M.A. Voltage relaxation and impedance spectroscopy as in-operando methods for the detection of lithium plating on graphitic anodes in commercial lithium-ion cells. J. Power Sources
**2016**, 304, 170–180. [Google Scholar] [CrossRef] - Remmlinger, J.; Buchholz, M. State-of-Health Monitoring of Lithium-Ion Batteries in Electric Vehicles by on-board Internal Resistance Estimation. J. Power Sources
**2011**, 196, 5357–5363. [Google Scholar] [CrossRef] - Sepasi, S.; Ghorbani, R.; Liaw, B.Y. Inline state of health estimation of lithium-ion batteries using state of charge calculation. J. Power Sources
**2015**, 299, 246–254. [Google Scholar] [CrossRef] - Wang, Y.; Pan, R.; Yang, D.; Tang, X.; Chen, Z. Remaining Useful Life Prediction of Lithium-ion Battery Based on Discrete Wavelet Transform. Energy Procedia
**2017**, 105, 2053–2058. [Google Scholar] [CrossRef] - Dubarry, M.; Svoboda, V.; Hwu, R.; Yann Liaw, B. Incremental Capacity Analysis and Close-to-Equilibrium OCV Measurements to Quantify Capacity Fade in Commercial Rechargeable Lithium Batteries. Electrochem. Solid-State Lett.
**2006**, 9, A454–A457. [Google Scholar] [CrossRef] - Waldmann, T.; Iturrondobeitia, A.; Kasper, M.; Ghanbari, N.; Aguesse, F.; Bekaert, E.; Daniel, L.; Genies, S.; Gordon, I.J.; Löble, M.W.; et al. Review—Post-Mortem Analysis of Aged Lithium-Ion Batteries: Disassembly Methodology and Physico-Chemical Analysis Techniques. J. Electrochem. Soc.
**2016**, 163, A2149–A2164. [Google Scholar] [CrossRef] - Pastor-Fernández, C.; Uddin, K.; Chouchelamane, G.H.; Widanage, W.D.; Marco, J. A Comparison between Electrochemical Impedance Spectroscopy and Incremental Capacity-Differential Voltage as Li-ion Diagnostic Techniques to Identify and Quantify the Effects of Degradation Modes within Battery Management Systems. J. Power Sources
**2017**, 360, 301–318. [Google Scholar] [CrossRef] - Hung, M.H.; Lin, C.H.; Lee, L.C.; Wang, C.M. State-of-Charge and State-of-Health Estimation for Lithium-Ion Batteries based on Dynamic Impedance Technique. J. Power Sources
**2014**, 268, 861–873. [Google Scholar] [CrossRef] - Osaka, T.; Mukoyama, D.; Nara, H. Review—Development of Diagnostic Process for Commercially Available Batteries, Especially Lithium Ion Battery, by Electrochemical Impedance Spectroscopy. J. Electrochem. Soc.
**2015**, 162, A2529–A2537. [Google Scholar] [CrossRef] - Lu, L.; Han, X.; Li, J.; Hua, J.; Ouyang, M. A Review on the Key Issues for Lithium-Ion Battery Management in Electric Vehicles. J. Power Sources
**2013**, 226, 272–288. [Google Scholar] [CrossRef] - Harting, N.; Wolff, N.; Röder, F.; Krewer, U. Nonlinear Frequency Response Analysis (NFRA) of Lithium-Ion Batteries. Electrochim. Acta
**2017**. [Google Scholar] [CrossRef] - Murbach, M.D.; Schwartz, D.T. Extending Newman’s Pseudo-Two-Dimensional Lithium-Ion Battery Impedance Simulation Approach to Include the Nonlinear Harmonic Response. J. Electrochem. Soc.
**2017**, 164, E3311–E3320. [Google Scholar] [CrossRef] - Wolff, N.; Harting, N.; Heinrich, M.; Röder, F.; Krewer, U. Nonlinear Frequency Response Analysis on Lithium-Ion Batteries: Pseudo-Two-Dimensional Porous Electrode Model Based Investigation. Electrochim. Acta
**2017**, 260, 614–622. [Google Scholar] [CrossRef] - Okazaki, S. Second-Order Harmonic in the Current Response to Sinusoidal Perturbation Voltage for Lead-Acid Battery. J. Electrochem. Soc.
**1985**, 132, 1516–1520. [Google Scholar] [CrossRef] - Ramschak, E.; Peinecke, V.; Prenninger, P.; Schaffer, T.; Baumgartner, W.; Hacker, V. Online Stack Monitoring Tool for Dynamically and Stationary Operated Fuel Cell Systems. Fuel Cells Bull.
**2006**, 2006, 12–15. [Google Scholar] [CrossRef] - Ramschak, E.; Peinecke, V.; Prenninger, P.; Schaffer, T.; Hacker, V. Detection of Fuel Cell Critical Status by Stack Voltage Analysis. J. Power Sources
**2006**, 157, 837–840. [Google Scholar] [CrossRef] - Mao, Q.; Krewer, U. Sensing Methanol Concentration in Direct Methanol Fuel Cell with Total Harmonic Distortion: Theory and Application. Electrochim. Acta
**2012**, 68, 60–68. [Google Scholar] [CrossRef] - Mao, Q.; Krewer, U. Total Harmonic Distortion Analysis of Oxygen Reduction Reaction in Proton Exchange membrane fuel Cells. Electrochim. Acta
**2013**, 103, 188–198. [Google Scholar] [CrossRef] - Vidakovic, T.R.; Panic, V.V. Nonlinear Frequency Response Analysis of the Ferrocyanide Oxidation Kinetics. Part I. A Theoretical Analysis. J. Phys. Chem. C
**2011**, 115, 17341–17351. [Google Scholar] - Sbarufatti, C.; Corbetta, M.; Giglio, M.; Cadini, F. Adaptive prognosis of lithium-ion batteries based on the combination of particle filters and radial basis function neural networks. J. Power Sources
**2017**, 344, 128–140. [Google Scholar] [CrossRef] - Yang, D.; Wang, Y.; Pan, R.; Chen, R.; Chen, Z. A neural network based state-of-health estimation of lithium-ion battery in electric vehicles. Energy Procedia
**2016**, 105, 2059–2064. [Google Scholar] [CrossRef] - Dong, H.; Jin, X.; Lou, Y.; Wang, C. Lithium-ion battery state of health monitoring and remaining useful life prediction based on support vector regression-particle filter. J. Power Sources
**2014**, 271, 114–123. [Google Scholar] [CrossRef] - Panchal, S.; Mcgrory, J.; Kong, J.; Fraser, R.; Fowler, M.; Dincer, I.; Agelin-Chaab, M. Cycling degradation testing and analysis of a LiFePO4 battery at actual conditions. Int. J. Energy Res.
**2017**, 41, 2565–2575. [Google Scholar] [CrossRef] - Ye, M.; Guo, H.; Xiong, R.; Yang, R. Model-based State-of-charge Estimation Approach of the Lithium-ion Battery Using an Improved Adaptive Particle Filter. Energy Procedia
**2016**, 103, 394–399. [Google Scholar] [CrossRef] - Wang, Y.; Yang, D.; Zhang, X.; Chen, Z. Probability based remaining capacity estimation using data-driven and neural network model. J. Power Sources
**2016**, 315, 199–208. [Google Scholar] [CrossRef] - Gibbons, J.D.; Chakraborti, S. Nonparametric statistical inference. In International Encyclopedia of Statistical Science; Springer: Berlin/Heidelberg, Germany, 2003; Volume 15, p. 645. [Google Scholar] [CrossRef]
- Jovic, A.; Brkic, K.; Bogunovic, N. A review of feature selection methods with applications. In Proceedings of the 2015 38th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), Opatija, Croatia, 25–29 May 2015; pp. 1200–1205. [Google Scholar] [CrossRef]
- Dy, J.G.; Brodley, C.E. Feature Selection for Unsupervised Learning. J. Mach. Learn. Res.
**2004**, 5, 845–889. [Google Scholar] - Fu, T.C. A review on time series data mining. Eng. Appl. Artif. Intell.
**2011**, 24, 164–181. [Google Scholar] [CrossRef] - Severson, K.; Chaiwatanodom, P.; Braatz, R.D. Perspectives on process monitoring of industrial systems. In Proceedings of the 9th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes (SAFEPROCESS), Paris, France, 2–4 September 2015; pp. 931–939. [Google Scholar]
- Smola, A.J.; Sc Olkopf, B. A tutorial on support vector regression. Stat. Comput.
**2004**, 14, 199–222. [Google Scholar] [CrossRef] - Zhou, J.; Liu, D.; Peng, Y.; Peng, X. Dynamic battery remaining useful life estimation: An on-line data-driven approach. In Proceedings of the 2012 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Graz, Austria, 13–16 May 2012; pp. 2196–2199. [Google Scholar] [CrossRef]
- Schölkopf, B.; Smola, A.J. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond; MIT Press: Cambridge, MA, USA, 2002. [Google Scholar]
- Cortes, C.; Vapnik, V. Support-vector networks. Mach. Learn.
**1995**, 20, 273–297. [Google Scholar] [CrossRef] - Liao, L.; Köttig, F. Review of Hybrid Prognostics Approaches for Remaining Useful Life Prediction of Engineered Systems , and an Application to Battery Life Prediction. IEEE Trans. Reliab.
**2014**, 63, 191–207. [Google Scholar] [CrossRef]

**Figure 1.**Ishikawa diagram of the various ageing factors leading to Lithium-ion battery degradation.

**Figure 2.**Strengths-Weakness-Opportunities-Threats (SWOT) analysis of the NFRA for LIB characterisation.

**Figure 5.**Electrode manufacturing and cell assembling at the Battery LabFactory Braunschweig (BLB). (

**a**) BLB-Electrode production; (

**b**) BLB-Pouch cell. (Picture credits: Hanno Keppel/Battery LabFactory, TU Braunschweig).

**Figure 6.**NFR spectra during cycle ageing at each 50th cycle, measured with ${I}_{AC}$ = 1.6 C; the impedance spectrum initial to cycle ageing in the inset, is measured with C/15 C.

**Figure 7.**Correlation coefficient ${\rho}_{S}$ for estimating the correlation degree of the variables NFR and cycle number.

**Figure 8.**Ageing-sensitive features in the NFR spectra extracted from high correlating training data sets.

**Figure 10.**Degradation model for SoH estimation calculated by support vector regression (SVR) based on a highly ageing-sensitive data feature and in the inlet, the degradation feature values extracted from the data (blue) as well as the calculated values by the SVR model (red).

Parameters | Symbol | Cell 1 | Cell 2 |
---|---|---|---|

Initial capacity | ${C}_{0}$/mAh | 32.8 | 33.6 |

Initial resistance | ${R}_{0}$/$\mathsf{\Omega}$ | 0.21 | 0.29 |

Anode thickness | ${\delta}_{a}$$\mathsf{\mu}$m | 44 | 45 |

Cathode thickness | ${\delta}_{c}$$\mathsf{\mu}$m | 52 | 58 |

Calendering degree anode | ${\Pi}_{a}$/% | 10 | 10 |

Calendering degree cathode | ${\Pi}_{c}$/% | 10 | 0 |

Mass fraction anode | ${\zeta}_{a}$/wt% | 0.90 | 0.93 |

Mass fraction cathode | ${\zeta}_{c}$/wt% | 0.90 | 0.90 |

Mass fraction inactive compounds anode | ${\zeta}_{add,a}$/wt% | 0.10 | 0.07 |

Mass fraction inactive compounds cathode | ${\zeta}_{add,c}$/wt% | 0.10 | 0.10 |

Porosity anode | ${\epsilon}_{a}$/- | 0.60 | 0.59 |

Porosity cathode | ${\epsilon}_{c}$/- | 0.57 | 0.64 |

Geometric surface area anode | ${A}_{geo,a}$/cm${}^{2}$ | 30.25 | 30.25 |

Geometric surface area cathode | ${A}_{geo,c}$/cm${}^{2}$ | 30.25 | 30.25 |

**Table 2.**Typical time constants and frequency ranges of processes identified for analysed LIB in the NFR spectra.

$\mathit{\tau}$/s | $\mathit{\omega}$-Range/Hz | Process |
---|---|---|

50 to 1 | 0.02 to 1 | Solid diffusion |

1 to 0.003 | 1 to 300 | Electrochemical reactions |

0.003 to 0.0001 | 300 to 10,000 | Ionic transport processes at interfaces |

**Table 3.**Correlation ranges ${\mathit{\omega}}_{Corr}$, correlation coefficients and underlying LIB processes.

${\mathit{\omega}}_{\mathit{C}\mathit{o}\mathit{r}\mathit{r}}$/Hz | Correlation Coefficient | Process |
---|---|---|

A: <0.2 Hz | >0.95 | Solid diffusion |

B: 0.2 to 150 | 1 | Electrochemical reactions |

C: >150 | Random | Ionic transport |

**Table 4.**Validation of the degradation model using identical and non-identical cells at different SoHs.

Cell | Type | SoH${}_{\mathit{i}}$ | SoH${}_{\mathit{S}\mathit{V}\mathit{M}}$ | Accuracy/% |
---|---|---|---|---|

B | identical | 28 | 29 | 3 |

C | identical | 63 | 66 | 4 |

D | non-identical | 100 | 96 | 4 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Harting, N.; Schenkendorf, R.; Wolff, N.; Krewer, U.
State-of-Health Identification of Lithium-Ion Batteries Based on Nonlinear Frequency Response Analysis: First Steps with Machine Learning. *Appl. Sci.* **2018**, *8*, 821.
https://doi.org/10.3390/app8050821

**AMA Style**

Harting N, Schenkendorf R, Wolff N, Krewer U.
State-of-Health Identification of Lithium-Ion Batteries Based on Nonlinear Frequency Response Analysis: First Steps with Machine Learning. *Applied Sciences*. 2018; 8(5):821.
https://doi.org/10.3390/app8050821

**Chicago/Turabian Style**

Harting, Nina, René Schenkendorf, Nicolas Wolff, and Ulrike Krewer.
2018. "State-of-Health Identification of Lithium-Ion Batteries Based on Nonlinear Frequency Response Analysis: First Steps with Machine Learning" *Applied Sciences* 8, no. 5: 821.
https://doi.org/10.3390/app8050821