# A Review of Lithium-Ion Battery Fault Diagnostic Algorithms: Current Progress and Future Challenges
## 4 Fault Diagnostic Algorithms for the Li-Ion Battery System
### External Battery Fault Diagnosis  
#### 4.2.1 Model-Based Methods  
For external battery fault diagnosis, model-based methods are often implemented to detect sensor faults and cooling system faults. In some earlier works, [PERSON] et al. [70] proposed the use of nonlinear parity equations to generate residuals for voltage, current, and fan setting from the ECM, thermal, and SOC models. The thresholds for the residuals were selected using the probability density function. Current and voltage sensor faults, as well as cooling fan fault, were then detected and isolated. However, this method can only detect faults of large magnitude due to errors from the observer. In [71], sensor fault detection was achieved using the Kirchhoff circuits' equations to generate current and voltage residuals and the temperature diffusion model to generate temperature residuals. This method has a low computational cost but is sensitive to measurement noises. In more recent works, [PERSON] et al. [72] used the proportional-integral-observer-based method to accurately detect and estimate current sensor fault, as a means to improve the state of energy estimation. In [73], a model-based diagnostic scheme using sliding mode observers designed based on the electrical and thermal dynamics of the battery was developed. A set of fault detection filter expressions was derived on the sliding surfaces of each observer. The outputs of these filters were used as residual signals to detect, isolate, and estimate voltage, current and temperature sensor faults, under the assumption that the faults and their time derivatives are bounded and finite. [PERSON] et al. [35] proposed a parameter estimation method using RLS to detect and isolate voltage and current sensor faults. The ECM was used, and the estimated parameters were put through a weighted moving average filter and a statistical cumulative sum (CUSUM) test to evaluate the generated residuals for any abnormalities. This method was also able to detect sensor faults when the battery underwent degradation accurately. The authors in [36] presented a fault diagnostic method for current and voltage sensor faults using state estimation, specifically SOC estimation. The residual was generated from the true SOC, calculated by the coulomb counting method, and the estimated SOC, obtained by the recursive least squares and unscented Kalman filter joint estimation method. Due to sensor noises in real applications, there are some uncertainties associated with the threshold selection for the residuals in this method, which require further research. A group of authors produced a series of studies on sensor fault diagnosis using structural analysis [2; 34; 74] and an extended Kalman filter [75; 76; 77]. In [34] and [74], structural analysis was applied to obtain the structurally overdetermined part of the system model by analyzing the structural model represented by an incidence matrix. Sequential residual generation was then used as a diagnostic test to detect different faults, including voltage and current sensor faults and cooling system faults, by calculating the unknown variables in a sequence. The specific fault was isolated with many different minimal structurally overdetermined sets. This method was improved in [2] by applying an extended Kalman filter to address the issue of inaccurate initial SOC. In addition, a statistical CUSUM test was implemented to evaluate the generated residuals from the diagnostic tests to determine the presence of a fault. This addition, however, made the proposed method significantly more computationally complex. Another model-based fault diagnostic method was developed by the same authors using an extended Kalman filter in [75]. The extended Kalman filter was used to estimate the output voltage from the ECM to generate residuals between measured and estimated values. The residuals were then evaluated by a statistical CUSUM test to detect current and voltage sensor faults.