## 1 Introduction
This lack of transparency hinders the understanding of how predictive results are derived and sometimes makes it challenging to provide interpretable outcomes. Additionally, in certain cases, a single model may have poor generalization capability, leading to potential errors in predictive results [14]. Fusion methods generally combine two or more prediction methods. [PERSON] et al. [15] proposed an approach that integrates Broad Learning (BL) into extreme learning machines to generate feature nodes by mapping input data. Subsequently, the mapped features undergo an enhancement operation to generate augmented nodes, from which additional feature information is obtained. This approach not only improves accuracy but also saves time. Additionally, [PERSON] et al. utilized Long Short-Term Memory Networks and Recurrent Neural Networks (LSTM-RNN) to learn the long-term correlations of lithium-ion battery capacity degradation [16]. However, they do not consider the transient capacity recovery phenomenon that occurs in lithium-ion batteries during the discharge cycle process, which might potentially impact the prediction accuracy of the State of Health. To address this issue, various signal decomposition methods have been proposed. [PERSON] et al. introduced the Empirical Mode Decomposition (EEMD) method [17]. EEMD has the advantages of not requiring predefined basis functions and being efficient. However, in practical applications, the issue of mode mixing in Intrinsic Mode Functions (IMFs) often arises. To overcome this problem, the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) can offer a better solution [18]. Additionally, some have employed the Fixed Bandwidth Wavelet Decomposition (WDT) [19], which is based on the fast wavelet transform algorithm. It captures signal characteristics across different frequency ranges, offering high computational efficiency. Using wavelet functions as high-pass filters, the signal is decomposed into locally regenerative trends, while scale functions, serving as low-pass filters, decompose the signal into globally degenerative trends. In practical applications, Discrete Wavelet Transform (DWT) decomposes the original signal into signals of different scales, and by utilizing inverse wavelet transform, it reconstructs the signal, thereby eliminating noise interference during the charging and discharging cycles of lithium batteries [20]. The DELM network is a deep neural network renowned for its exceptional accuracy in time series forecasting. It achieves this by employing the Extreme Learning Machine-Autoencoder (ELM-AE) for weight initialization through a hierarchical unsupervised training approach, eliminating the necessity of backpropagation. Consequently, DELM surpasses ELM in terms of prediction accuracy. However, it is essential to recognize that DELM's initialization is susceptible to the random input weights and hidden layer thresholds [21]. In order to address this sensitivity, researchers have investigated the utilization of the Genetic Algorithm (GA) for global optimization. While GA has the capability of achieving optimal solutions, it may suffer from slow convergence. An alternative approach is the Whale Optimization Algorithm (WOA), which has exhibited better performance in terms of solution speed and convergence accuracy compared to the Particle Swarm Optimization (PSO). However, similar to GA, WOA may still face challenges in avoiding local optima during the optimization process. Therefore, this study employs wavelet decomposition to eliminate the interference caused by the transient capacity rebound phenomenon in lithium battery capacity on the prediction. The improved whale optimization algorithm with nonlinear convergence factor and adaptive weighting is utilized to optimize the deep extreme learning machine for modeling and analyzing the decomposed global trends and local degenerative trends. Ultimately, the predictive results of each trend are effectively integrated to obtain the estimation of lithium battery health status.