lithium-ion (li-ion) batteries are commonly used in various industrial and domestic applications, such as portable communication devices, medical equipment, and electric vehicles. however, the li-ion battery performance degrades over time due to the aging phenomenon, which may lead to system performance degradation or even safety issues, especially in vehicle and industrial applications. reliable battery health monitoring and prognostics systems are extremely useful for improving battery performance, to diagnose the battery’s state-of-health (soh), and to predict its remaining-useful-life (rul). in general, it is challenging to accurately track the battery's nonlinear degradation features as battery degradation parameters are almost inaccessible to measure using general sensors. in addition, a battery is an electro-chemical system whose properties vary with variations in environmental and operating conditions. although there are some techniques proposed in the literature for battery soh estimation and rul analysis, these techniques have clear limitations in applications, due to reasons such as lack of proper representation of the posterior probability density functions to capture and model the nonlinear dynamic system of li-ion batteries. in addition, these techniques cannot effectively deal with the time-varying system properties, especially for long-term predictions. to tackle these problems, a novel hybrid prognostic framework has been developed in this phd work for battery soh monitoring and rul prediction. it integrates two new models: the model-based filtering method and the evolving fuzzy rule-based prediction technique. the strategy is to propose and use more efficient techniques in each module to improve processing, accuracy and reliability. firstly, a newly enhanced mutated particle filter technique is proposed to enhance the performance of particle filter technique and improve the modeling accuracy of the battery system’s degradation process. it consists of three novel aspects: an enhanced mutation approach, a selection scheme, and an outlier detection method. secondly, an adaptive evolving fuzzy technique is suggested for long-term time series forecasting. it has a novel error-assessment method to control the fuzzy cluster/rule generation process—also, a new optimization technique to enhance incremental learning and improve modeling efficiency. finally, a new hybrid prognostic framework integrates the merits of both proposed techniques to capture the underlying physics of the battery systems for its soh estimation, and improve the prognosis of dynamic system for long-term prediction of li-ion battery rul. the effectiveness of the proposed techniques is verified through simulation tests using some commonly used-benchmark models and battery databases in this field, such as the one from the national aeronautics and space administration (nasa) ames prognostic center of excellence. test results have shown that the proposed hybrid prognostics framework can effectively capture the battery soh degradation process, and can accurately predict its rul.