The Lithium-ion battery (Li-ion) has become the dominant energy storage solution in many applications, such as hybrid electric and electric vehicles, due to its higher energy density and longer life cycle. For these applications, the battery should perform reliably and pose no safety threats. However, the performance of Li-ion batteries can be affected by abnormal thermal behaviors, defined as faults. It is essential to develop a reliable thermal management system to accurately predict and monitor thermal behavior of a Li-ion battery. Using the first-principle models of batteries, this work presents a stochastic fault detection and diagnosis (FDD) algorithm to identify two particular faults in Li-ion battery cells, using easily measured quantities such as temperatures. In addition, models used for FDD are typically derived from the underlying physical phenomena. To make a model tractable and useful, it is common to make simplifications during the development of the model, which may consequently introduce a mismatch between models and battery cells. Further, FDD algorithms can be affected by uncertainty, which may originate from either intrinsic time varying phenomena or model calibration with noisy data. A two-step FDD algorithm is developed in this work to correct a model of Li-ion battery cells and to identify faulty operations in a normal operating condition. An iterative optimization problem is proposed to correct the model by incorporating the errors between the measured quantities and model predictions, which is followed by an optimization-based FDD to provide a probabilistic description of the occurrence of possible faults, while taking the uncertainty into account. The two-step stochastic FDD algorithm is shown to be efficient in terms of the fault detection rate for both individual and simultaneous faults in Li-ion batteries, as compared to Monte Carlo (MC) simulations.

Photoplethysmography (PPG) signals have been widely used for heart rate (HR) monitoring. Compared to the electrocardiogram (ECG), PPG signals can be easily collected with wearable devices such as smart watches at a lower cost. However, PPG signals are often contaminated by the motion artifact (MA) and noises, which greatly deteriorate the signal quality and pose significant challenges on HR monitoring. In this paper, a new algorithm, using the spectral subtraction and the Neural Network (NN), is developed for accurate HR tracking in the presence of MA and noises. Specifically, the spectral component of MA is estimated from the acceleration (ACC) signals and then removed from the spectra of PPG. In addition, a NN model is developed based on new features extracted from ACC signals to identify the relationship between the ACC and HR variations in consecutive time windows. Such information is further used as a reference to select the spectral peak corresponding to the actual HR. A post-processing algorithm is used to correct mis-identified HR and to improve the accuracy. The NN-based algorithm is validated using the 2015 IEEE Signal Processing Cup Dataset. Our algorithm achieves an average absolute error of 1.03 beats per minutes (BPM) (standard deviation: 1.82 BPM), which outperforms previously reported works in the literature.