# A Review of Lithium-Ion Battery Fault Diagnostic Algorithms: Current Progress and Future Challenges
## 4 Fault Diagnostic Algorithms for the Li-Ion Battery System
### Internal Battery Fault Diagnosis  
#### 4.1.1 Model-Based Methods  
The main principle of model-based fault diagnosis is the use of battery models to generate residuals which are monitored and analyzed to detect faults. There are several types of battery models, including electrochemical, electrical, thermal, and combinations of interdisciplinary models (electro-thermal, etc.) [45]. Each model can be used to assist fault diagnosis, depending on the requirements of the Li-ion battery application. Model-based methods are often used in fault diagnosis for their simplicity and cost-efficiency. Model-based methods include state estimation, parameter estimation, parity equation, and structural analysis. A simplified schematic for state estimation fault diagnostic algorithms is shown in Figure 4.  
Figure 3: The classification of Li-ion battery fault diagnostic algorithms. In some earlier works, [PERSON] et al. [46] proposed a two-step state-estimation based algorithm for Li plating detection, which can lead to degradation and failure of the battery. The algorithm uses an electrochemical model, with the first step being estimating the insertion and extraction rates of Li ions using particle filtering, and the second step being the comparison of the estimated data with the boundary condition to generate alarms at faulty state. This method is effective in detecting Li plating, but the electrochemical model is complicated and not fully understood; hence, it is not reliable and impractical in the BMS. Authors in [47] used impedance spectroscopy to identify the parameters in the equivalent circuit model (ECM) to construct fault models for overcharge and overdischarge conditions. Kalman filters and the multiple-model adaptive estimation (MMAE) technique were proposed to generate residuals from the voltage, and the residuals were evaluated in a probability-based approach to detect overcharge and overdischarge faults. The same authors then proposed the use of extended Kalman filters with MMAE to detect overcharge and overdischarge faults [48]. This method eliminates noises effectively, but the use of multiple models makes it too complex and computationally inefficient. [PERSON] et al. [49] used a bank of Luenberger observers with the ECM to generate residuals from voltage to locate and isolate faults in a series of three Li-ion cells and a bank of learning observers to estimate the isolated fault. This method was able to detect faults caused by changed internal resistance in a cell, but it is not practical for applications with a large number of cells, such as EVs. In more recent works, the internal short circuit fault has been the main focus. [PERSON] et al. [50] proposed an internal short circuit detection method using recursive least squares (RLS) to estimate the parameters of the mean-difference model, which is derived from the ECM. The parameters of all the cells in the pack are statistically analyzed and compared to a set threshold to detect internal short circuit fault. Authors in [51] used an electrochemical-thermal coupled model to confirm that an internal short circuit causes abnormal responses in voltage, temperature, and SOC. The ECM and the energy balance equation (EBE) model were used in the fault diagnostic algorithm instead of the electrochemical-thermal coupled model to lower the computational cost. RLS was utilized to estimate the parameters of these two models, and fault detection was achieved by observing changes in these parameters. The two diagnostic methods above are further developed in [52], where extended Kalman filters and RLS were implemented for state and parameter estimation, specifically SOC, voltage, temperature, and internal resistance. The state estimation and parameter estimation are performed on all the cells, with output data belonging to the mean and worst cells. Different scenarios of deviation from the estimated data indicate different levels of fault, including extra capacity depletion, abnormal heat generation, and internal short circuit.