**1. Introduction**

Lithium-ion (Li-ion) batteries are the most popular form of energy storage in the world, amounting to 85.6% of energy storage systems utilized in 2015. Although it has the highest price, it shows the lowest cost per cycle [1]. The substantial demand for Li-ion batteries is due to portable devices and electric vehicles (EVs). Li-ion batteries are used in EVs due to their high power and energy density, long life span, and low environmental impact. EVs require a battery system that consists of hundreds or thousands of single cells. In order to manage this large number of cells, the battery pack needs a battery managemen<sup>t</sup> system (BMS). It is important that the performance of the BMS is accurate and reliable, to ensure the performance and safety in EVs application. The functions of the BMS include state of charge (SOC) and state of health (SOH) estimation, and over-current and over-voltage protection [2]. These functions rely heavily on voltage and current sensor measurements [3]. It is possible for the sensors to experience malfunctions during the operation of the battery, due to manufacturing defects or environmental factors. The estimation of the SOC (similar to a fuel meter in conventional vehicles) and the SOH (similar to an odometer), would be a ffected if there were any faults with the sensors, leading to over-charge and/or over-discharge phenomenon which would degrade the battery faster. The current and voltage protection would also fail to work properly due to faulty sensors. This can lead to more catastrophic failures since the current and voltage can exceed their operational limits

undetected, due to incorrect sensor readings [4]. Even though a sensor fault with a small magnitude does not immediately a ffect the battery performance, it can have a significant e ffect over time. This can be prevented by detecting and resolving the sensor fault promptly after it develops. Although the authors are not aware of any published data on the failure rates of BMS sensors in EVs, it is reasonable to anticipate some failures due to the nature of the application. The sensors are subject to vibration and physical damage from collisions, which can ultimately lead to disconnection or resistance build-up of the wires and cause deviations in the readings. Therefore, it is critical to develop an algorithm that can reliably and accurately diagnose any faulty operation of the voltage and current sensors in real time.

The reviews on fault mechanism and diagnosis approaches for Li-ion batteries can be found in [2,5]. Desirable characteristics of a fault detection and isolation (FDI) scheme include quick detection and diagnosis, isolability, robustness, adaptability, low modelling requirements, and a reasonable balance between storage and computational requirements [6]. Several existing FDI methods were able to accomplish some of the desired characteristics stated above. An extended Kalman filter was used in [4] to diagnose sensor faults, but fault isolation was not achieved. This study confirms that the battery can be over-charged or over-discharged due to sensor faults, caused by the inaccuracy of SOC estimation. In [7], the nonlinear parity equation approach, coupled with sliding mode observers, were used to develop an FDI scheme to detect sensor faults for a single battery cell. A set of Luenberger and learning observers were used in [8] for simultaneous single-fault isolation and estimation of a faulty cell in a battery string. In [9], an FDI strategy using structural analysis theory and statistical inference residual evaluation was presented, but the computational e ffort was rather high. An FDI scheme using sliding mode observers with equivalent output error injection was introduced in [10], with findings that show false detection rate is a ffected by the variation in model parameters. All of the methods mentioned above work under the assumption that the battery model parameters remain constant throughout the battery pack's life span. However, the parameters can be a ffected by degradation, a significant property of battery operation. There has not been any mention of cell degradation in any FDI works or literature.

There are a few models used to illustrate battery behavior, but the equivalent circuit model (ECM) is the most widely used in FDI works [5]. The parameters of the ECM were derived using conservation of species, conservation of charge, and reaction kinetics in [11]. The results show that the parameters have physical meanings and can be a ffected by the chemistry of the battery, as well as the environment of operation. Therefore, degradation of the battery would have some e ffects on the parameters. The existing FDI schemes can be improved by integrating degradation into the ECM. However, this has been proven to be a di fficult task. Currently, battery degradation models can be obtained by fitting experimental data under constant conditions. However, this is not an appropriate model for battery degradation in EVs applications, due to its complex operating state [12]. Experimental models are also less accurate, time-consuming, and costly. Adaptive models are more accurate, but require training to estimate the parameters that correlate with degradation. Moreover, the models can have high computational e ffort which is not suitable for real-time BMS applications [13]. Another approach is needed to e ffectively diagnose faults while considering the e ffect of degradation on ECM parameters, which this paper will present.

The key contribution of this paper is the proposal of a model-based sensor FDI scheme for Li-ion battery in EVs while considering battery degradation. The ECM parameters are expected to change during battery operation due to the e ffect of degradation. The paper studies and confirms this e ffect through a series of experiments. The proposed FDI scheme uses the recursive least squares (RLS) method to estimate the ECM parameters in real time, then applies a weighted moving average (WMA) filter coupled with a cumulative sum control chart (CUSUM) to detect any voltage and current sensor faults. The use of RLS is suggested because of its low computational demand and easy implementation [14]. The implementation of the WMA filter eliminates the concern of battery degradation, in addition to the e ffect of SOC and temperature on ECM parameters. Furthermore, the sensor faults are isolated based on the responsiveness of the parameters when a specific fault occurs. Finally, the Urban Dynamometer Driving Schedule (UDDS) cycle with sensor fault simulation is applied to validate and evaluate the performance of the proposed FDI scheme for a lithium iron phosphate (LFP) cell.

The rest of this paper is organized as follows: Section 2 describes the battery model used for this work, while Section 3 outlines the details of the proposed FDI scheme. Section 4 provides the experimental design and analysis of the effect of degradation and various faults on the parameters. The evaluation of the proposed fault diagnosis scheme is presented in Section 5, and the resulting conclusions are given in Section 6.
