**Physics-Based Model-informed Smooth Particle Filter based likelihood approximations for remaining useful life prediction of lithium-ion batteries**

**Authors:** Mo’ath El-Dalahmeh, Maher Al-Greer, Ma’d El-Dalahmeh, and Imran Bashir

School of Computing Engineering and Digital Technologies, Teesside University, Middlesbrough, UK**Centre of Smart Energy and Smart Grid**

### What Is The Research?

- Accurate prediction of the remaining useful life (RUL) in Lithium‐ion batteries (LiBs) is a key aspect of managing its health, in order to promote reliable and secure systems, and to reduce the need for unscheduled maintenance and costs.

- Recent work on RUL prediction has largely focused on refining the accuracy and reliability of the RUL prediction. The author introduces a new online RUL prediction for LiB using smooth particle filter (SPF)‐ based likelihood approximation method incorporating physics-based modeling into a physics based approach. An experimentally validated high-fidelity model is employed to generate big data training data for a comprehensive operating condition matrix. This data is used to train a SPF to predict the RUL of lithium ion batteries
- The proposed algorithm can accurately estimate the unknown degradation model parameters and predict the degradation state by solving the optimisation problem at each iteration, rather than only taking a gradient step, that tends to lead to rapid convergence, avoids instability issues and improves predictive accuracy.

### Methodology

- The aim of the proposed prognostic approach is to improve long-term prediction is to combine the Physics model with a SPF algorithm, so that the model parameters can be dynamically updated.
- As shown in Figure 2, a suitable model is firstly selected based on the available data. Then, the filtering algorithm is constructed and initialized. Finally, the model parameters are updated with filters using historical data, and the updated model is used for RUL prediction.

### Smooth Particle Filter Algorithm

The proposed SPF algorithm can be designed by integrating the SPF-based proposal distribution function selection method with the reweighting strategy-based resampling method, and the flowchart is shown in Figure 3.

The details steps of the SPF algorithm are illustrated as follows.

### What Is The Outcome ?

To demonstration the effectiveness of the proposed solution, the SPF and PF algorithms have been implemented.

- Now, in order to test the accuracy and error of the prediction of the PF and proposed SPF algorithm, different cycle ‘starting points’ were applied, such as 1000, and 2000 cycles are shown.
- Fig. 4 shows the prediction result with PF, and the proposed SPF algorithm for battery at 1 C-rate. It is important to mention that the first 1000 cycles from the data are used as training data to update the prediction process.
- An identical conclusion as that above can be deduced from Fig. 4, which shows the robustness and strong accuracy of the proposed single particle model based SPF (SPM-SPF) algorithm
- The proposed prediction approach outperforms the physics-based classical Particle Filter (PF) approach and the conventional capacity-based approach in prediction accuracy and convergence rate. The best RUL prediction at 2000 is 1398 cycles since the proposed predicting technique has a minimal maximum error. The proposed algorithm’s absolute error was 2 cycles, lower than the physics-based PF’s relative prediction error of 0.0008. (about 6 cycles). RUL prediction is 1407 cycles, relative error 0.003, and absolute error 7.
- From the figures 4-5 prediction results, the physics model-based SPF algorithm considering the battery aging mechanism has better performance. Compared with conventional RUL prediction algorithm (empirical aging model) , the prediction of LIBs RUL is closer to reality after considering the aging mechanism.

### Conclusion

- This work has presented a novel online RUL prediction of LiBs known as SPF algorithm.
- Obtained results clearly indicated that the proposed SPF algorithm can improve the prediction accuracy compared with the classical PF algorithm. The average RUL errors and PDF width of the SPF approach are less than in PF methods. Thus demonstrating that the suggested method is more accurate and steadier.
- RUL prediction was tested with various predicted starting points to assess whether the amount of data influenced the accuracy of the prediction. The findings clearly demonstrated that the amount of data affects the accuracy of the prediction.
- It has also been shown that the earlier the starting point of the prediction, the higher the prediction error rate relative to the higher starting point.
- The proposed approach achieves a more accurate RUL prediction than the traditional capacity-based approach. The results show that the proposed physics-based approach, which extrapolates the degradation parameters, can provide a more accurate and conservative RUL prediction when compared to extrapolating just the capacity.

### References

- El-Dalahmeh M, Al-Greer M, El-Dalahmeh M, Short M. Smooth particle filter-based likelihood approximations for remaining useful life prediction of Lithium-ion batteries. IET Smart Grid. 2021;1–11.
- M. El-Dalahmeh, M. Al-Greer, M. El-Dalahmeh and I. Bashir, “Online Hybrid Prognostic Health Management Prediction Using a Neural Network and Smooth Particle Filter for Lithium-ion Batteries,” 2022 57th International Universities Power Engineering Conference (UPEC), Istanbul, Turkey, 2022, pp. 1-6.

### Awards

- Won the Best Paper Award for our paper entitled (Online Hybrid Prognostic Health Management Prediction Using a Neural Network and Smooth Particle Filter for Lithium-ion Batteries) at the 57th International Universities Power Engineering Conference on Big Data and Smart Grids
- Won the Best Poster Award in 2ndWorld Energy Storage Conference (WESC 2022) Jointly with the 7th UK Energy Storage conference.

**Physics-Based Model-informed Smooth Particle Filter based likelihood approximations for remaining useful life prediction of lithium-ion batteries**

**Authors:** Mo’ath El-Dalahmeh, Maher Al-Greer, Ma’d El-Dalahmeh, and Imran Bashir

School of Computing Engineering and Digital Technologies, Teesside University, Middlesbrough, UK**Centre of Smart Energy and Smart Grid**

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