This thesis discusses and compares methods which try to approximate the assymptotic variance.

The integration of large-scale battery storage systems can aid the transition to renewable energy and stabilize energy systems for optimization. However, batteries can be cost-prohibitive and unprofitable, highlighting the need for a more comprehensive understanding and modelling of battery degradation. Battery degradation prediction models play a crucial role in battery manufacturing, especially when they can be created using early cycle data. However, a challenge in battery prediction is the lack of diversity for training data, leading to models that are not robust and hard to generalize. Transfer learning can address this issue, as it doesn't require the test and training data to come from similar distributions. This thesis introduces a framework that uses early cycle data to predict battery lifetimes. The framework employs a regularized method, the elastic net, for battery lifetime prediction and Transfer Component Analysis (TCA) for transfer. The major contribution of this thesis is the transfer learning framework that is proposed for battery lifetime prediction, which involves the analysis of various aspects, including when what, and how to transfer. To demonstrate the framework's performance, a dataset based on early cycle data from a real-world case study is used. The results show that the proposed methods outperform existing methods in both the simulation and case study results. Different methods are used for selecting and weighing features before the transfer, resulting in 39 out of 42 improvements in the case study results. In particular, utilizing elastic net coefficients to weigh the features before the transfer yields the optimal approach in 15 out of 21 cases and enhances the RMSE and MAPE compared to not using transfer in 38 out of 42 cases. Additionally, this study, as one of the first studies in this field, provided innovative approaches to quantitatively examine negative transfer. It conducts a comprehensive analysis mainly for univariate distributions, utilizing a robust 2-sample goodness-of-fit test to gain a deeper understanding of the relationship between transfer performance and distributional differences.