# 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
#### 4.2.2 Non-Model-Based Methods  
For cell connection fault diagnosis, entropy theory and statistical analysis methods have been proposed. [PERSON] et al. [78] used demonstration data from 96 cells in series collected over three months to obtain cell resistances from the ECM. By calculating the Shannon entropy of the cell resistances, the contact resistance fault was successfully isolated. In [39], the authors proposed a method of fault detection for the connection of Li-ion cells based on entropy. Cell voltage data was obtained and filtered using the discrete cosine filter method. Ensemble Shannon entropy, local Shannon entropy, and sample entropy were applied to predict the time and location of the connection failure occurrence based on voltage fluctuations. Sample entropy produced the most accurate results but required a large amount of data, while ensemble Shannon entropy was able to predict the connection fault between cells effectively. [PERSON] et al. [79] used the wavelet decomposition with three layers developed by [PERSON] to smooth the voltage signal and eliminate noise interference. After the wavelet transformation, the Shannon entropy of charge and discharge cycles was calculated, and the change in entropy was monitored to detect real-time cell connection fault. However, this method can be easily affected by the set value of the interval parameters. [PERSON] et al. [80] proposed the use of a modified Z-score test to analyze the abnormal voltage coefficients to detect cell connection fault. The temperature rise rate was utilized as a secondary parameter to determine the severity of the fault. However, using this method, a fault occurring at a location where there is no cross-voltage test cannot be reliably detected.  
Since battery packs are often made up of many cells in series, topology-based fault diagnostic methods have been proposed by a few studies. [PERSON] et al. [81] proposed a fault-tolerant voltage measurement method, where the voltage sum of multiple cells was measured instead of the voltage of individual cells. A matrix interpretation of the sensor topology was developed to isolate sensor and cell faults by locating abnormal signals. Since this method is sensitive to measurement noises, the authors further developed an improved measurement topology in [82], where the noise limit and trend of the interleaved voltage measurement method were derived to improve the noise sensitivity. In [83], a multi-fault diagnostic strategy based on an interleaved voltage measurement topology and an improved correlation coefficient method was presented, which can diagnose several types of faults, such as internal and external short circuits, sensor faults and connection faults. The voltage measurement method correlated each battery and contact resistance with two different sensors to accurately identify the location and type of faults. The improved correlation coefficient method was used to monitor fault signatures to eliminate the effect of battery inconsistencies and measurement errors. These topology-based methods can isolate various faults accurately, but they are only suitable for battery packs that have multiple cells in series with interleaved voltage measurements.