# Review of Artificial Intelligence-Based Failure Detection and Diagnosis Methods for Solar Photovoltaic Systems

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## Abstract

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## 1. Introduction

_{2}emission into the atmosphere due to the combustion of fossil fuels [3,4], which leads to global warming, GHG emissions, climate change, and other environmental issues [5]. Owing to the global commitment to overcome these issues by reducing fossil fuel energy generation to the bare minimum, the renewable industry has experienced an exponential growth and development in recent years. Renewable energy sources, especially solar [6,7], have been increasingly adopted for residential, commercial, and industrial applications [8,9,10]. The 2020 first quarter (Q1 2020) report of the National Renewable Energy Laboratory (NREL) stated that at the end of 2019, the installed solar PV capacity totaled 627 GW

_{DC}, an increase of 115 GW

_{DC}from the previous year [11].

## 2. Types of PV System Faults

#### 2.1. Shading Faults

#### 2.2. Arc Faults

#### 2.3. Line-Line Faults

#### 2.4. Ground Faults

#### 2.5. Other Faults

## 3. Artificial Intelligence and Machine Learning

#### 3.1. Machine Learning Types

#### 3.1.1. Supervised Learning

#### 3.1.2. Unsupervised Learning

#### 3.1.3. Semi-Supervised Learning

#### 3.1.4. Reinforcement Learning

#### 3.1.5. Multitask Learning

#### 3.1.6. Ensemble Learning

#### 3.1.7. Neural Network Learning

#### 3.1.8. Instance-Based Learning

#### 3.1.9. Evolutionary Computation

## 4. Artificial Intelligence-Based Failure Detection and Diagnosis Methods

#### 4.1. Neural Network-Based Methods

- The shadow ratio is defined by the solar height and solar azimuth angles, which may be simply calculated from the time of day for a specific geographic location. Therefore, the neural network’s inputs are the sun’s irradiation levels, angle, and ambient temperature. The neural network’s output has the highest solar PV array output power.
- Experimental data are acquired by taking measurements numerous times a day, for several days, while the solar PV array is partially shaded by a nearby object. One set of measured data is used to train the neural network, while the other is used to test it. The neural network’s accuracy in estimating the PV array’s maximum output power is tested using the test data.
- With low computational effort, the neural network can forecast the output power of solar PV arrays at any solar irradiation level, at any time of day, and at varied ambient temperatures over a long period of time.

Authors | Reference | Year | Contribution |
---|---|---|---|

A.M. Pavan, A. Mellit, D. De Pieri, S.A. Kalogitou | [80] | 2013 | Evaluation of the effect of soiling in large PV plants using BNN and regression polynomial |

F. Aziz, A. Ul Haq, S. Ahmad, Y. Mahmoud, M. Jalal, U. Ali | [82] | 2020 | Classification of line-line fault, open-circuit fault, partial shading, and arc fault using the convolutional neural net |

G. Liu, W. Yu | [84] | 2018 | Diagnosis of open-circuit fault, overall shading effect, and partial shading effect using the Elman neural net |

W. Chine, A. Mellit, V. Lughi, A. Malek, G. Sulligoi, A.M Pavan | [66] | 2016 | Identification of eight different faults using ANN |

K.H. Chao, C.L Chiu, C.J. Li, Y.C. Chang | [85] | 2011 | Islanding phenomenon detection in PV systems using ANN |

E. Garoudja, A. Chouder, K. Kara, S. Silvestre | [86] | 2017 | Detection and diagnosis of faults in the DC side of PV systems using the probabilistic neural network |

M.N. Akram, S. Lotfifard | [56] | 2015 | Modeling and health monitoring of the DC side of PV systems using the probabilistic neural network |

H. Mekki, A. Mellit, H. Salhi | [87] | 2016 | ANN based modeling and fault detection of partially shaded PV modules |

A. Coleman, J. Zalewski | [88] | 2011 | Intelligent fault detection and diagnosis in the PV system using the Bayesian belief network |

M. Chang, C. Hsu | [64] | 2019 | PV O&M optimization using ANN |

A. H. Mohamed, A.M. Nassar | [72] | 2015 | PV system fault diagnosis using the genetic algorithm-optimized ANN |

D.D. Nguyen, B. Lehman, S. Kamarthi | [89] | 2009 | Performance evaluation and shadow effects in PV arrays using ANN |

D. Riley, J. Johnson | [90] | 2012 | Prognostics and health management of PV systems using ANN |

#### 4.2. Regression-Based Methods

Authors | Reference | Year | Contribution |
---|---|---|---|

F.H. Jufri, S. Oh, J. Jung | [91] | 2019 | Detection of abnormal conditions in PV systems using the combined regression and support vector machine |

S. Spataru, D. Sera, T. Kerekes, R. Teodorescu | [92] | 2013 | Condition monitoring of PV array based on the online regression model |

S. Shapsough, R. Dhaouadi, I. Zualkernan | [94] | 2018 | Predicting the performance of soiled PV modules using the linear regression and BP neural network |

W. Rezgui, N.K. Mouss, M.D. Mouss, M. Benbouzhid | [95] | 2014 | Reversed polarity fault prognosis in PV generators using the regression algorithm |

#### 4.3. Decision Tree-Based Methods

^{2}. In the statistical failure detection approach, the local outlier factor (LOF) algorithm was used to find the density-based local outliers. With LOF, each point’s local density is compared to its k-nearest neighbors (k-NN), and if the point’s density is significantly lower than its neighbors, then the point is in a sparser region than its neighbors, indicating that it is an outlier. Moreover, outlier testing was done using the Bonferroni outlier test algorithm. Based on the linear regression model of the observed and simulated dc power of the array, this program returns the Bonferroni p-value for the most extreme observation. In addition, the seasonal hybrid extreme studentized deviates (S-H-ESD) algorithm was used to find anomalies in a time series dataset that follows an approximately normal distribution. The S-H-ESD technique is an extension of the generalized extreme studentized deviates (ESD) algorithm that uses the time series decomposition and robust statistical measures in conjunction with ESD to detect both global and local anomalies [98]. For the detected failure classification, logic and decision trees were developed. In addition, the decision trees were trained using continuous samples divided in a 70:30% train to test the set ratio utilizing the acquired datasets that included the feature patterns seen during normal and faulty operations. Moreover, they were produced using supervised learning procedures. The accuracy of the proposed FDRs for fault detection and classification was demonstrated in the obtained results for three fault types (inverter failure, bypass diode faults, and partial shading fault), which showed that accuracy rates of 98.7, 95.3, and 96.6% were recorded for inverter failure, bypass fault, and partial shading, respectively. The authors in [96] presented a decision tree-based fault detection and classification for the PV array with an easy and straightforward model training process. Under the creation of a decision tree model for an experimental PV system in both normal and faulty working situations, the authors employed the PV array voltage, current, operating temperature, and irradiance as attributes for the training and test sets. The collected data and pre-processed training set are chosen at random from the experimental data and utilized to create the decision tree model using the WEKA software [99], after which the model is evaluated and validated on unseen real data. Fast training and classification phases, explicit interpretation, and straightforward implementation as an algorithm are all advantages of the proposed decision tree paradigm. Another benefit of the model is that it can detect problems in real time, with detection accuracy ranging from 93.56 to 99.98% and classification accuracy ranging from 85.43 to 99.8%, depending on the model’s size. The authors of [97] proposed a defect detection and diagnostic technique for grid connected PV systems (GCPVS) based on the C4.5 decision tree algorithm (which is one of the most popular machine learning algorithms for classification problems [97]), in which a non-parametric model is utilized to forecast the state of the GCPVS through a learning task. Three numerical attributes (ambient temperature, irradiation, and power ratio) which are calculated from the measured and estimated power, as well as two targets (the first of which is either a healthy or a faulty state for detection, and the second of which contains four classes of labels named free fault, string fault, short-circuit fault or line-line fault for diagnosis) are chosen to form the final used data. The dataset was divided into two halves, with 66% utilized for learning and 34% for testing. Then, over the course of 5 days, additional data were collected to measure the robustness, effectiveness, and efficiency of both models. The dataset is required for the learning process in order to construct the decision tree. As a result, an acquisition system is developed to be able to record and store data, such as climatic variation, as well as electrical variables, such as current, voltage, and power at the MPP. Three attributes are chosen, including temperature ambient, irradiation, and the power ratio, which is calculated from the estimated power by the Sandia model and the measured power of GCPVS production. The Sandia model is an empirical relationship that is used to estimate the generated power from a system in a healthy state at MPP using STC data. Since this model has unknown parameters, the flower pollination algorithm (FPA) is used to find the optimal parameter values that correspond to the smallest root mean square error between the estimated Sandia output and the measured power. As a result of the high correlation between the power ratio and the system state, a nominal property called target is constructed as a class label in each instance data in order to accurately forecast these errors. Two major approaches lead to the construction phase. To begin, a splitting criteria is used to select the best split attribute. Thereafter, the tree grows in length as this technique is repeated iteratively in order to categorize all of the instances or to verify one of the stopping criteria. Then, once the tree model has been obtained, a pruning process is carried out to remove the unneeded sub-trees in order to minimize the overfitting phenomena, which can result in a reduction in model complexity due to the reduced tree size. According to the test findings, the models have a great prediction performance in the detection with high accuracy, while the diagnostic model has an accuracy of 99.8%.

Authors | Reference | Year | Contribution |
---|---|---|---|

A. Livera, G. Makrides, J. Sutterlueti, G.E. Georghiou | [67] | 2017 | Advanced failure detection algorithm and PV performance outlier decision classification |

Y. Zhao, L. Yang, B. Lehman, J.F. De Palma, J. Mosesian, R. Lyons | [96] | 2012 | Detection and classification of PV array faults based on the decision tree algorithm |

R. Benkercha, S. Moulahoum | [97] | 2018 | C4.5 decision tree algorithm-based fault detection and diagnosis for grid-connected PV systems |

#### 4.4. Support Vector Machine-Based Methods

Authors | Reference | Year | Contribution |
---|---|---|---|

W. Rezgui, H. Mouss, K. Mouss, M.D. Mouss, M. Benbouzid | [100] | 2014 | Short-circuit fault diagnosis in PV generators using a smart SVM algorithm |

W. Rezgui, N.K. Mouss L.H. Mouss, M.D. Mouss, Y. Amirat, M. Benbouzid | [101] | 2014 | Short-circuit and impedance faults smart diagnosis in PV generators using the k-NN optimized SVM classifier |

T. Hu, M. Zheng, J. Tan, L. Zhu, W. Miao | [102] | 2015 | PV system intelligent monitoring based on solar irradiance big data and wireless sensor networks |

#### 4.5. Neuro-Fuzzy-Based Methods

^{2}. As shown in Figure 8, an optional shadow detection algorithm acting before the increased series losses detection system, which could improve the detection accuracy of the system, is also implemented in the diagnostic system. This strategy is especially significant, since the increased series losses and partial shadow circumstances are difficult to discern, as they diminish a PV system’s peak output and fill factor. Rather than the controlled laboratory circumstances, the study focuses on estimating the increased series resistance in the field. The method has been tested using experimental measurements. In addition, it has shown good detection rates across a wide range of irradiance levels, as well as in the presence of diverse sizes and patterns of partial shadows. Moreover, the authors showed that a dedicated partial shadow detection algorithm, implemented in the diagnostic system and functioning prior to the higher series losses detection method, improves the overall system’s detection accuracy.

Authors | Reference | Year | Contribution |
---|---|---|---|

P. Ducange, M. Fazzolari, B. Lazzerini, F. Marcelloni | [103] | 2011 | Intelligent system for the detection of PV system faults based on TSK-FRBS |

K. Karakose, K. Firildak | [105] | 2014 | Shadow detection system based on fuzzy logic using the obtained PV array images |

B. Grichting, J. Goette, and M. Jacomet | [106] | 2015 | Arc fault detection algorithm in PV systems based on the cascaded fuzzy logic |

S. Spataru, D. Sera, T. Kerekes, R. Teodorescu | [107] | 2012 | Increased series losses detection in the PV array based on fuzzy inference systems |

Z. Yi, A.H. Etemadi | [108] | 2017 | Detection of PV system faults based on the multi-resolution signal decomposition and fuzzy inference system |

M. Dhimish, V. Holmes, B. Mehrdadi, M. Dales | [109] | 2017 | PV system diagnostic technique based on the six layer detection algorithm |

M. Dhimish, V. Holmes, B. Mehrdadi, M. Dales, P. Mather | [110] | 2017 | Fault detection in PV systems based on the theoretical curves modeling and fuzzy classification system |

S. Samara, E. Natsheh | [65] | 2020 | Using the NARX network and linguistic fuzzy rule-based system to diagnose PV panel faults |

#### 4.6. Wavelet-Based Methods

_{sw}= 25 ms is less than 1 μs, which is negligible. As a result, the detection time is mostly determined by the length of the time window. The results of the studies reveal that the detection algorithm is capable of delivering an alarm in a timely manner following the initiation of an arc fault. Typical operations, such as load changes, can also generate nuisance tripping, which can be reduced with this detection system. In [112], a modified wavelet-based technique termed the wavelet packet transform (WPT) was developed for the detection of diverse disturbances caused by faults in grid-connected solar PV systems. The study continued to evaluate the proposed WPT approach to methods based on the ordinary wavelet transform (WT) under various operating settings. In addition, qualitative and quantitative evaluations suggest that the WPT outperforms WT in terms of detection performance. The WPT uses a set of low-pass and high-pass filters to breakdown the signal retrieved at PCC. It gives both approximate and precise coefficients. Moreover, it extensively decomposes both components in order to determine the signal’s frequency agreements. The breakdown procedure carried out in both components is what gives them their value. Wavelet transforms, on the other hand, do only a one-sided decomposition, segmenting only the low-pass frequency components and not the high-pass frequency components. When WT is subjected to noisy or transitory environments, this feature can compromise its performance. In [113], wavelet transformations were used to offer an online fault detection method for power conditioning systems (PCS). Switch open faults and over harmonics are detected using a multi-level decomposition wavelet transform approach. Using the normalized standard deviation of the wavelet coefficient, a quick and accurate diagnostic function is also achievable, allowing the suggested method to detect islanding conditions. Simple calculations (a time correlation generated by sequential multiplication and addition) and exact diagnostic capabilities of fault identification with good simulation outputs to check and evaluate its claims characterize the method’s algorithm. The multi-level decomposition wavelet transform provides the method’s straightforward calculation characteristic. At each wavelet tree level, the algorithm extracts wavelet coefficients from the measured signal, and errors are discovered and categorized using the wavelet coefficient changes. Using a three-level MLD tree, the fault detection technique was created for PCS fault scenarios. Switch open and over harmonic are the two scenarios considered. The PCS uses a semiconductor switch, such as a field effect transistor (FET) or an IGBT, to convert DC solar voltage to AC grid current. The switch open can be attributed to a switching device failure, whereas the over harmonic can be attributed to a controller or sensor failure. The cases of switch short faults are not taken into account here. The system is protected by the over-current limiting function or melting fuse when the switches are in short fault, and the PCS ceases running. The PCS current has a distorted waveform when the switches are open faulted, and it continues to provide high order harmonics to the grid. An UP and DOWN switch failure in the inverter bridge might be categorized as an open switch problem. The authors of [114] used the discrete wavelet transform (DWT) to analyze the traced I-V curve of a residential PV system and define these coordinated points in the related diagnosis effort. The DWT was utilized to implement the fault diagnosis of residential PV systems as a preprocessing tool. It enables feature extraction through signal decomposition and noise reduction. The reduced short-circuiting current of partially shaded cells is represented by the vertical height or current in a PV string identified by the DWT method, whilst the horizontal or voltage distance from the VOC to the inflex is connected to the number of bypassed modules. The approach is divided into two sections, namely passive and active. In the passive diagnosis section, a residue signal is generated by comparing the measured PV power signal and simulated model in real time to monitor the alarm signal and abnormal condition in the system, using the model base fault diagnosis technique. After the manifest and certainty error signals have been determined, the flash test is used as the active and second portion of the test procedure. During this phase, the step load is separated from the PV and power generation, and the MPPT mode of the inverter is interrupted. The I-V curve of the PV array is tracked and logged by modifying the inverter switching pattern for a deeper inspection and interpretation. The model provided in [115] for the defect diagnosis of PV arrays was improved using improved wavelet neural networks, wavelet neural networks, and back propagation neural networks. The training technique now includes a Gaussian function, which is utilized as an activation function, an additional momentum mechanism, and an adaptive learning rate method. The conclusion is taken from simulation findings that the proposed technique in this study is capable of efficiently diagnosing the PV array problem with good performance accuracy, convergence time, and stability under the identical conditions of the network input and desired output. The proposed fault diagnosis algorithm is summarized in Figure 9. Four PV system fault types are diagnosed using the model, namely short-circuit, open-circuit, abnormal degradation, and partial shading. There are five network output layer variables since the system requires the precise diagnosis of four types of problems and no fault condition. The selection of the number of hidden layer nodes in a neural network is a difficult topic with no theoretical foundation to follow. The number of hidden layer nodes is critical to the network’s success. If the number is too little, we may not acquire a network from training, implying that the network’s robustness is poor and its anti-noise ability is weak, making it unable to recognize models that have never been seen before. If the hidden layer’s node number is too big, the learning time will be too long, and the error will not be minimal. Furthermore, there could be an issue with overfitting. As a result, based on an empirical equation, the trial and error method is commonly employed to identify the appropriate number of concealed nodes.

Authors | Reference | Year | Contribution |
---|---|---|---|

X. Yao, L. Herrera, S. Ji, K, Zou, J. Wang | [111] | 2014 | Detection of DC arc fault based on the characteristic study and time-domain discrete wavelet transform |

P.K. Ray, A. Mohanty, B.K. Panigrahi, P.K. Rout | [112] | 2018 | Fault analysis in solar PV system based on the modified wavelet transform |

I.S. Kim | [113] | 2016 | Online fault detection algorithm in PV system based on the wavelet transform |

M. Davarifar, A. Rabhi, A. Hajjaji, E. Kamal, Z. Daneshifar | [114] | 2014 | Partial shading fault diagnosis based on the discrete wavelet transform |

X. Li, P. Yang, J. Ni, J. Zhao | [115] | 2014 | Improved wavelet neural network algorithm-based method of fault diagnosis in PV array |

M. Mansouri, A. Al-khazraji, M. Hajji, M.F. Harkat, H. Nounou, M. Nounou | [116] | 2017 | Wavelet optimized EWMA-based fault detection method for the PV system application |

#### 4.7. Other Methods

^{2}and temperatures of 25–40 °C, the suggested detection model has an average accuracy of 88.23% in identifying the fault under low/high solar radiation and various temperatures. The authors of [127] presented another interesting fault detection and diagnosis method based on a laterally primed adaptive resonance theory (LAPART) neural network. It is a low-cost way of automatically detecting and diagnosing PV system issues. The LAPART algorithm was taught how to detect fault states using real-world data that were classified as normal system behavior. The algorithm was then given new data and three-fault data points for an initial test. The system was given synthetic data to examine its performance over a statistically significant month-long dataset, and it was able to correctly identify flaws within the dataset. The LAPART algorithm’s accuracy is determined by its ability to deliver a high likelihood of detection, while reducing false alarms. The number of true positive values generated by the FDD process is compared to the total number of actual positive values to determine the likelihood of detection. The LAPART architecture combines two fuzzy adaptive resonance theory (ART) algorithms to build a system for predicting outcomes based on the learnt associations. The single fuzzy ART algorithm’s fundamental equations include category selection, match criterion, and learning. The goal is to create the optimal template matrix for the provided dataset. The approach employs category selection to discover the existing template matrix that best matches the provided input. In addition, for fast learning applications, the free parameter is frequently set to 10-7. The match criterion then checks to verify if the template matrix and input that is compared fulfill the user-defined vigilance parameter criterion. Depending on the level of intricacy requested, the vigilance free parameter can range from 0 to 1. A high vigilance value of 0.9, for example, yields high complexity but limited generality, whereas a low parameter of 0.5 yields the opposite. Finally, if it passes, the template is changed to reflect what has been learned. The LAPART algorithm is created by linking the two fuzzy ARTs (FARTs), which is seen graphically in Figure 11. The L matrix, which connects the A and B templates, connects the A and B FARTs. Each FART has its own set of vigilance settings, and inputs are delivered to both the A and B sides at the same time during the learning process. The A and B sides work together to generate and update the templates, while also forming links. Testing inputs are only applied to the A side after the training is complete, allowing them to resonate with the already acquired templates. The L matrix’s relationships are then used to link with the B side and generate the prediction results.

Authors | Reference | Year | Contribution |
---|---|---|---|

Y. Zhao, R. Ball, J. Mosesian, J. De Palma, B. Lehman | [13] | 2015 | Graph-based semi-supervised learning algorithm for PV fault detection and classification |

H. Momeni, N. Sadoogi, M. Farrokhifar, H.F. Gharibeh | [117] | 2020 | Graph-based semi-supervised learning method of PV array fault diagnosis and correction |

Y. Wu, Z. Chen, L. Wu, P. Lin, S. Cheng, P. Lu | [118] | 2017 | SA-RBF kernel extreme learning machine-based intelligent fault diagnosis for PV array |

Y. Yagi et al. | [119] | 2003 | Diagnostic technology and expert system for PV system using the learning method |

E. Garoudja, K. Kara, A. Chouder, S. Silvestre, S. Kichou | [121] | 2016 | Short- and open-circuit fault detection in PV system based on the offline and online evaluation of measured coefficient |

Y. Zhao, Q. Liu, D. Li, D. Kang, Q. Lu, L. Shang | [71] | 2019 | Hierarchical context-aware anomaly detection using the unsupervised learning and multimodal anomaly classification method |

Z. Chen, L. Wu, S. Cheng, P. Lin, Y. Wu, W. Lin | [122] | 2017 | Optimized kernel extreme learning machine and I-V characteristics based intelligent fault diagnosis in PV array |

Y. Zhao, B. Lehman, R. Ball, J. Mosesian, J.F. De Palma | [123] | 2013 | Outlier detection based rules for solar PV array fault detection |

F. Shariff, N.A. Rahim, W.P. Hew | [124] | 2015 | Online monitoring of grid-connected PV system based on the Zigbee data acquisition system |

H. Lin, Z. Chen, L. Wu, P. Lin, S. Cheng | [125] | 2015 | Online monitoring and fault diagnosis of PV array based on the genetic algorithm optimized BP neural network |

C.L. Kuo, J.L. Chen, S.J. Chen, C.C. Kao, H.T. Yau, C.H. Lin | [126] | 2017 | PV energy conversion system fault detection using the fractional order color relation classifier |

C.B. Jones, J.S. Stein, S. Gonzalez, B.H. King | [127] | 2015 | Photovoltaic system fault detection and diagnostics using the laterally primed adaptive resonance theory neural network |

A. Khoshnami, I. Sadeghkhani | [128] | 2018 | PV array fault detection based on sample entropy |

## 5. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Distribution of AI-based fault detection and diagnosis methods for PV systems found in the available literature.

**Figure 2.**Schematic block diagram of Bayesian regularization [80].

**Figure 3.**Flowchart showing the proposed method of PV array fault diagnosis and existing methods [82].

**Figure 4.**Block diagram of the proposed fault detection technique based on the threshold approach and ANN [66].

**Figure 5.**Proposed fault detection flowchart diagram [87].

**Figure 6.**Condition monitoring systems’ learning phase [92].

**Figure 7.**Proposed intelligent system’s schematics [103].

**Figure 8.**Proposed diagnostic system of partial shadow detection, increased series losses detection, and advanced system analysis and monitoring for the PV module [107].

**Figure 9.**Proposed fault diagnosis method based on the wavelet neural network [115].

**Figure 10.**Flowchart on the establishment of the proposed fault diagnosis model [122].

**Figure 11.**Creation of LAPART algorithm through linking two fuzzy ARTs [127].

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Abubakar, A.; Almeida, C.F.M.; Gemignani, M.
Review of Artificial Intelligence-Based Failure Detection and Diagnosis Methods for Solar Photovoltaic Systems. *Machines* **2021**, *9*, 328.
https://doi.org/10.3390/machines9120328

**AMA Style**

Abubakar A, Almeida CFM, Gemignani M.
Review of Artificial Intelligence-Based Failure Detection and Diagnosis Methods for Solar Photovoltaic Systems. *Machines*. 2021; 9(12):328.
https://doi.org/10.3390/machines9120328

**Chicago/Turabian Style**

Abubakar, Ahmad, Carlos Frederico Meschini Almeida, and Matheus Gemignani.
2021. "Review of Artificial Intelligence-Based Failure Detection and Diagnosis Methods for Solar Photovoltaic Systems" *Machines* 9, no. 12: 328.
https://doi.org/10.3390/machines9120328