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In this paper, multiple-model adaptive estimation techniques have been successfully applied to fault detection and identification in lithium-ion batteries. The diagnostic performance of a battery depends greatly on the modeling technique used in representing the system and the associated faults under investigation. Here, both linear and non-linear battery modeling techniques are evaluated and the effects of battery model and noise estimation on the over-charge and over-discharge fault diagnosis performance are studied. Based on the experimental data obtained under the same fault scenarios for a single cell, the non-linear model based detection method is found to perform much better in accurately detecting the faults in real time when compared to those using linear model based method.