**1. Introduction**

UAVs are very suitable for performing tasks in spacious indoor and outdoor environments, such as personnel search and rescue, material transportation, military patrol and surveillance, pesticide spraying, crop seeding, etc. Due to the increasing complexity of the tasks performed by drones, the sensors and actuators on the drone are becoming more and more complex, and the reliability requirements of the drone are getting higher and higher during the mission. Once the drone has a serious fault in flight, it will cause more serious property losses, and in more serious cases, it may cause casualties [1]. During the flight of the drone, any minor fault can easily cause the drone itself to malfunction, thereby affecting the sensors, actuators, and other related equipment on the drone. Therefore, the safety and reliability of UAVs is now an issue worthy of study and discussion. At the same time, we also need to specifically consider the different types of faults of different types of UAV [2].

**Citation:** Yang, P.; Wen, C.; Geng, H.; Liu, P. Intelligent Fault Diagnosis Method for Blade Damage of Quad-Rotor UAV Based on Stacked Pruning Sparse Denoising Autoencoder and Convolutional Neural Network. *Machines* **2021**, *9*, 360. https://doi.org/10.3390/ machines9120360

Academic Editors: Hongtian Chen, Kai Zhong, Guangtao Ran and Chao Cheng

Received: 4 November 2021 Accepted: 14 December 2021 Published: 16 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

For various faults on the drone, the drone control system can respond to the faults on the drone only when the system identifies and diagnoses each fault, respectively, so as to minimize the loss of personnel and property in the case of UAV faults. One of the main issues is the identification of faults in drones. The identification of faults is mainly divided into knowledge-based fault methods, model-based fault diagnosis methods, and data-based fault diagnosis methods.

The main knowledge-based fault diagnosis methods are symbolic expert systems [3], symbolic directed graph (SDG) methods, and fault tree methods. In [4], the symbolic directed graph is introduced, the symbolic directed graph is mainly a graphical model based on causality. In [5], the fault diagnosis method based on the fault tree is mainly introduced, the fault tree uses a graphical method for fault diagnosis. A fault tree is formed by connecting the fault in the system and the cause of the system fault. When the system fails, the cause of the system fault is deduced from the current fault state of the system from the bottom to the top. As a knowledge-based fault diagnosis method, the diagnosis model is simple, and the diagnosis results are easier to apply in practical engineering. However, because knowledge-based fault diagnosis requires learning the types of faults to be diagnosed, when a fault that is not in the knowledge base occurs in the system, the system will not be able to provide the correct diagnosis result.

The model-based fault diagnosis method [6] is based on the accurate mathematical model of the system. In the analytical model of the system, the residual signal between the input and output of the system is obtained by observation and measurement. By analyzing the residual signal in the system, the difference between the actual output and the expected output of the system can be obtained. Therefore, the system can be diagnosed based on these.

The data-driven fault diagnosis method is to classify and identify all the non-faulty and faulty data of the system, so the system's fault diagnosis can be realized without obtaining the precise mathematical model of the system. Data-based fault diagnosis methods mainly include machine learning methods [7], signal processing methods [8], information fusion methods [9], rough set methods [10], multivariate statistical analysis methods [11], etc. Because the data-based fault diagnosis method does not rely on the accurate model of the system for diagnosis, it is better to use the data-based method for fault diagnosis for complex high-level systems that are difficult to accurately model. However, because the data-based fault diagnosis method does not depend on the internal structure of the system, the interpretability of the results of system fault diagnosis is not very good [12].

At present, many intelligent fault diagnosis methods have been proposed in various research fields. In literature [13,14], the bearing is taken as the research object to study the relationship between the data collected by the bearing in different types of damage; in article [15,16], the fault diagnosis of drill is realized by analyzing the thermal image and vibration data of drill; in [17,18], the researchers took the battery pack as the research object and applied the intelligent fault diagnosis algorithm proposed by themselves to the actual battery system to diagnose the battery pack; in the research field of gearbox and high-speed train, a large number of fault diagnosis methods have also been proposed; in [19,20], it was studied how to judge the fault type through the collected signal when the gearbox fails; several new intelligent fault diagnosis methods are mainly proposed in [21–23], and good results have been achieved in the fault diagnosis of high-speed trains. Although many fault diagnosis methods have been proposed, there are still few intelligent fault diagnosis methods for UAVs. Therefore, we choose the quad-rotor UAVs as the research object in this paper.

During the operation of the quad-rotor UAV, the actuator or structure of the drone malfunctioned due to the operation problem of the pilot or due to some non-human reasons. In the literature [24], the researchers collected the vibration signal of the aircraft frame through the analysis of these data to diagnose whether the motor is malfunctioning. In [25], the researchers artificially damaged the rotor of the drone, and then collected the noise of the drone during the flight, and used the deep learning method to analyze and process the noise to realize the fault diagnosis of the system. The collection of sound

signals has strict requirements on the environment, so this method cannot be applied in practice. In the literature [26], the author introduced the convolutional neural network with a wide convolution kernel into the fault diagnosis method, and diagnosed the bearing data through the convolutional neural network. A wide convolution kernel can improve the anti-interference ability of convolutional neural network to some extent. In reference to the problem of inaccurate diagnosis results for data with large noise signals, the literature [27] proposed to denoise the data based on the stack denoising autoencoder, and achieved good results, but due to the introduction of a new network structure, the convergence speed of the training network has been adversely affected to a large extent. Most of the existing fault diagnosis algorithms need to preprocess the data to eliminate the noise interference in the data, thereby improving the accuracy of classification, but there are few methods to directly classify the original noisy data and obtain a good classification accuracy.

In response to the above-mentioned problems, we adopted a method called Stacked Pruning Sparse Denoising Autoencoder and Convolutional Neural Network (sPSDAE-CNN) to identify and classify the actuator damage fault of the UAV. The main contribution of this paper is as follows:


**Figure 1.** Three kinds of intelligent fault diagnosis framework. ( **A**) The feature extraction of unsupervised learning [28]. (**B**) The traditional method. ( **C**) The method used in this article.

At present, there is much research on sensor fault and actuator fault of four-rotor UAVs. In article [29,30], it is mainly studied to diagnose the actuator fault of four-rotor UAV by using the traditional model class method, including hybrid observer and adaptive neural network observer. In [31], Kalman filter is mainly used to process the sensor data of UAV and then to diagnose the possible sensor faults. In [32], researchers proposed a disturbance observer to observe the faults in the system and then realized diagnosis and fault-tolerant control through sliding mode control method.

However, there is little research on the fault of UAV blade damage. In the process of a UAV mission, when the UAV blade is damaged to a certain extent, when the damage does not exceed the threshold, the UAV may still be able to perform the mission in the environment of small interference. However, at this time, the stability of the UAV has been greatly damaged, and there may be some risks during the mission. Therefore, we need to evaluate the blade damage of UAV through the proposed method, and timely evaluate the health state of UAV, so as to prevent UAV crashes. At the same time, we also introduce a sparse pruning stack noise reduction autoencoder to improve the adaptability of the model to high noise data. In addition, pruning operation is added to improve the algorithm complexity of the model. At present, most fault diagnosis methods for four-rotor UAVs are verified by numerical simulation. This paper collects experimental data on the actual aircraft and verifies the algorithm, which has good practicability.

There is not a simple linear relationship between the damage of the drone blades and the sensor data of the drone. Therefore, the sensor data of the drone blades under different damage conditions are analyzed by using the deep learning method, and a deep learning model about the relationship between the sensor data of the drone and the damage degree of the blades is obtained, and the model is optimized.

The remaining organizational structure of this article is as follows: Section 2 briefly introduces the convolutional neural network and the stack denoising autoencoder. Section 3 introduces the intelligent fault diagnosis method based on sPSDAE-CNN. In Section 4, we use experiments to verify the sPSDAE-CNN method, and compare and analyze it with some commonly used methods. At the end of Section 5, we draw conclusions and propose future work by summarizing the work.

### **2. Introduction to the Convolutional Neural Network and Stack Denoising Autoencoder**

### *2.1. A Brief Introduction to Convolutional Neural Networks*

In this part, we will briefly introduce the convolutional neural network and the stack denoising autoencoder. For more details about the neural network, please refer to the literature [33]. Convolution neural network is a multilevel deep neural network [34]. Its basic structure consists of the input layer, convolution layer, activation layer, pooling layer, full connection layer, and output layer. Generally, there are several convolution layers and pooling layers, and the general structure is a convolution layer connected with a pooling layer. Each neuron in the input is locally connected to the input, and the weighted summation with the local input through the corresponding connection weight and the bias is added to obtain the input of the neuron. This process is equivalent to the convolution process, so it is called a convolutional neural network.
