## 4 Discussion and Final Remarks
### Limitations and Future Work  
As demonstrated in a previous study [21], aging trajectories should fall within a suitable operational envelope, leading to the main [16] aging mechanisms, for which an extensive number of aging trajectories is required. Therefore, our diagnosis approach depends on reliable and extensive accelerated test data. These trajectories can be generated using electrochemically based models to predict aging and performance. Another consideration when applying our approach is the treatment of noise and outliers in the aging trajectory [20], which may mislead the trajectories. Finally, uneven exposure to aging stress factors might lead to cell spreading, which, specifically in the second life, must be accounted for to ensure scalability from the cell to the pack level. Although this is a proof-of-concept, we plan to obtain additional battery aging data to expand the aging trajectories in future work. We recommend conducting post-mortem analyses to confirm the knee points based on measurable side reaction contributions to aging and cell spreading trends.  
The strength of our approach proposed in this work lies in leveraging both interpretable and performance-oriented machine learning tools through aging trajectory contributions to decompose a real cycle. Nevertheless, we plan for future work considering (i) simulating aging trajectories, including combinations of temperature, SOC ranges, DOD, and calendar aging effects, (ii) validating our approach with publicly available data, and (iii) evaluating the effect of spreading (aggregating trajectories) at the module level to simulate pack behaviour [5]. Thus, we will focus on extending the validation of our approach using extensive datasets obtained from real-world applications. This validation is crucial to assess the approach's effectiveness under different combinations of stress factors,  
\begin{table}
\begin{tabular}{c c c} \hline
**Model 1** & **Model 2** & **RMSE** \\ \hline TAM & RF-DTW & 0.6 \\ DTW & TAM & 0.9 \\ DTW & RF-DTW & 1.7 \\ DTW & PRFTN & 2.4 \\ DTW & RF & 2.5 \\ RF-DTW & PRFTN & 2.8 \\ RF & RF-DTW & 3.1 \\ TAM & PRFTN & 5.0 \\ TAM & RF & 5.3 \\ RF & PRFTN & 6.1 \\ \hline \end{tabular}
\end{table}
Table 2: RMSE of pairwise model combinations for similarity prediction.  
including SOC windows, DODs, and calendar effects. As we consider the feasibility of generalizing our approach, we plan to apply it to different chemistries. Moreover, the similarity-based architecture is inherently adaptable to other energy storage technologies, such as supercapacitors; for this, a tailored library of degradation trajectories must be obtained for specific failure modes and aging signatures.  
Potential misclassification due to high diversity is a special consideration when obtaining aging trajectories. For instance, two completely different combinations of stress factors may result in nearly identical aging trajectories, a phenomenon known as trajectory degeneracy. Since our approach aims to classify based on stress factors using only aging curves, the capacity versus cycle is no longer uniquely informative, affecting RF accuracy and proximity-based methods that rely on decision boundaries in a feature space or class separability. To minimize the impact of trajectory degeneracy, we recommend including information about the data as a feature in the aging trajectory datasets to distinguish similar trajectories.  
Our diagnosis approach and considerations for future work provide a basis for its scalability, as each aging trajectory represents an independent aging stress path. It is easily modularizable with new data and effective for online implementation. Once trained, trajectory-based diagnosis can be easily matched to incoming cycles online, enabling real-time inference and reliable aging diagnosis while maintaining a low computational cost.