Fault diagnosis of drone motors driven by current signal data with few samples

Multi rotor unmanned aerial vehicles (UAVs) are extensively utilized across various domains, and the motor constitutes a pivotal element in the UAV power system. The majority of UAV failures and crashes stem from motor malfunctions, underscoring the imperative need for comprehensive research on fault diagnosis in UAV motors to ensure the stable and reliable execution of flight tasks. This study focuses on quadrotor UAVs as the research subject and devises targeted fault simulation experiments based on the structural features and operational characteristics of the DC brushless motor used in quadrotor UAVs, specifically examining the stator, rotor, and bearings. To address challenges related to the UAV’s own loads, limited space for redundant parts, and the high cost and difficulty associated with installing sensors for traditional fault diagnostic signals such as vibration and temperature, this study opts to use current signals as a substitute. This approach resolves the issue of challenging data collection for UAVs and investigates a current signal based fault diagnosis method for UAV motors. Lastly, in response to the limited training samples available for fault data due to the UAV’s highly sensitive characteristics regarding the health status of its components and flight stability, traditional machine learning and deep learning methods encounter difficulties in identifying representative features with a small number of training samples, leading to the risk of overfitting and reduced model accuracy in fault diagnosis. To overcome this challenge, we propose a hybrid neural network fault diagnosis model that incorporates a width learning system and a convolutional neural network (CNN). The width learning system eliminates temporal characteristics from the original current signal, capturing more comprehensive and representative sample features in the width feature space. Subsequently, the CNN is employed for feature extraction and classification tasks. In empirical small sample fault diagnosis experiments using current signal data for UAV motors, our proposed model outperforms other models used for comparison.

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Introduction
In recent years, unmanned aerial vehicle (UAV) technology has undergone rapid development, expanding its application scenarios and use cases.Owing to its user friendly operation, robust scalability, and cost effectiveness, UAVs have found widespread utilization in diverse fields such as agriculture, plant protection [1,2], and disaster rescue [3].However, extended operations, challenging working environments, and deliberate damage can impact the overall health status of UAVs, leading to system failures, loss of control, substantial economic losses, and even casualties.While hardware redundancy has conventionally been favored to enhance UAV flight reliability, this approach introduces increased operational burdens and manufacturing costs, it does not apply to unmanned aircraft systems [4].To address these challenges and reduce costs, it is imperative to research straightforward, efficient, and precise UAV fault diagnosis methods.The shift from hardware redundancy to fault diagnosis involves extracting fault information from UAV system and sensor data, analyzing the causes of faults, and ensuring the stable and reliable execution of UAV flight tasks [5,6].
The mainstream fault diagnosis methods encompass three approaches: signal analysis [7,8], model based [9][10][11], and data driven [12].Signal based processing methods mainly achieve fault diagnosis through some kind of information processing and extraction of signal features, usually using signal models such as spectral analysis and wavelet transform of correlation function to analyze their correlation signals and determine whether a fault occurs or not, the method reduces the dependence on mathematical models, but the lack of accurate mathematical models makes it insufficient to diagnose early potential faults.Model based methods necessitate accurate physical mathematical models or prior expert knowledge.As nonlinearity becomes more pronounced in UAV dynamics, the enhancement of physical mathematical models is imperative; otherwise, they struggle to capture and reflect nonlinear characteristics.Data driven UAV fault diagnosis methods rely on the utilization of system and sensor monitoring data during operation for fault diagnosis.This approach effectively circumvents the challenges associated with system modeling complexities and the limited a priori knowledge of experts.Commonly employed techniques encompass multivariate statistical analysis [13], traditional machine learning [14][15][16] (such as support vector machine (SVM)), and deep learning [17,18].Notably, deep learning based fault diagnosis methods harness the robust feature extraction capabilities of neural networks to directly extract fault information from raw signal data.This results in high fault diagnosis accuracy and strong generalization.Guo et al [19] proposed an uncertainty aware long short term memory (LSTM) based fault diagnosis method for UAV actuator assembly.This method excels in comparison to other models concerning fault degree detection and fault type classification.It takes into consideration the uncertainty in fault diagnostic modeling within the LSTM method and the variations under different flight conditions.Sadhu et al [20] introduced a novel UAV fault diagnosis framework relying on deep convolutional and LSTM neural networks, enabling fault diagnosis based on actual sensor data.Al-Haddad and Jaber [21] presented a fault diagnosis scheme using a discrete wavelet with a hybrid transform and deep neural network with multiple hidden layers for UAV fault diagnosis and prediction.They employed various feature selection methods to enhance the model's fault diagnosis capabilities.The aim was to achieve a faster and more efficient UAV fault diagnosis method, making the fault diagnosis timeliness align more closely with real world scenarios.Certain existing literature combines elements of both model based and data-driven approaches: Thanaraj et al [22] introduced a hybrid fault diagnosis model by integrating the extreme learning neuro fuzzy algorithm with extended Kalman filtering to address the challenge of identifying undetected actuator faults in UAVs.Experimental evidence confirmed the model's high diagnostic efficiency and sensitivity.Song et al [23] sought to address the challenge of identifying and localizing rotor faults in quadcopter UAVs, which can be complex.They fused the extended state observer and deep forest methodologies to enable fault diagnosis in quadcopters of unknown fault size.Zhang et al [24] introduced a fault detection framework based on a hybrid deep domain adaptive BiLSTM network and Hampel filtering.The primary goal of this framework is to leverage the collected data to detect faults in fixed wing UAVs, even when operating under unknown conditions.
When investigating the data driven method for diagnosing faults in multirotor UAV motors, the foremost consideration is the practicality of the data and the feasibility of data acquisition.Existing sources of UAV fault diagnosis data predominantly include the UAV flight control system, vibration signal data, acoustic signal data, and temperature signal data, as detailed in table 1 through specific literature research.The primary function of the flight control system is to facilitate positioning, with a low sampling frequency in its data acquisition.Multirotor UAVs derive power from motor driven propellers to execute flight tasks, and a majority of historical accidents have been precipitated by failures in the UAV power system.The motor serves as the fundamental power source for the UAV's propulsion system, constituting the essential component for UAV flight.However, it is also a primary locus for faults.When the UAV engages in in-flight tasks, the motor's operational speed can reach as high as 5000 r min −1 or even exceed this threshold.The flight control system is unable to discern variations in rotational speed, rendering the data acquired by the flight control system inadequate for addressing the diagnostic requirements of multirotor UAV motor faults [25].The cost associated with sensors required for the acquisition of vibration, sound, and temperature signal data is prohibitively high.Additionally, the limited installation space and payload capacity of the UAV pose constraints, making the excessive installation of supplementary sensor modules detrimental to the UAV's stability during flight.During motor operation, the current signal undergoes changes corresponding to variations in motor working conditions.Leveraging the current signal enables real time monitoring

Data sources
References Characteristics Flight control system [13,[28][29][30] Low sampling frequency Vibration signals [31][32][33][34][35][36] Sensitive to mechanical faults, high cost Acoustic signals [37][38][39] Sensitive, inconvenient to install Temperature signals [27] Sensitive, high cost, inconvenient to install of the motor's operational status, and the convenience and low cost of the current signal collection are noteworthy.Moreover, the sensors demonstrate high integration levels, with many mid to high end electronic speed control systems incorporating built in current and voltage detection modules.Consequently, the investigation into UAV motor fault diagnosis methods based on the current signal proves to be more practical.Nevertheless, the inherent weakness of mechanical fault characteristics in the current signal restricts its diagnostic efficacy, necessitating a thorough consideration in the study of fault diagnosis methods based on current signals [26,27].Most existing fault diagnosis studies based on current signals focus on industrial motors or related components [40][41][42].However, UAV motors present unique challenges due to their compact size, faster rotational speed, and frequency transitions compared to industrial counterparts.Moreover, conventional UAV fault diagnosis models often rely on ample training data [43,44].Yet, UAV fault diagnosis poses a typical small sample problem.This arises from the stability characteristics of UAV flights, which primarily operate under normal conditions.Conducting faulty flight tests is costly and perilous, while data obtained from simulation software often fails to reflect real world scenarios [45].Consequently, acquiring UAV fault data remains challenging.Traditional small sample fault diagnosis methods such as transfer learning [46], meta learning [47], and generative adversarial networks [30] necessitate complex processing techniques and significant computational resources.Moreover, authenticity concerns regarding virtual samples further complicate the situation.These approaches are ill-suited for addressing the need for fast and accurate UAV motor fault diagnosis in the face of high rotational speeds and frequent frequency transformations.Therefore, there is a pressing need to develop a small sample fault diagnosis method for UAVs that is characterized by simplicity, practicality, and swift response based on real data.
This paper focuses on the motor of a quadrotor UAV and investigates a data driven fault diagnosis method based on current signals.Considering the requirements for UAV flight stability and the limited training data due to the UAV's sensitivity to component health status, traditional machine learning and deep learning methods struggle to identify representative features and suffer from low fault classification accuracy when dealing with a small number of training samples [45,48].Treating the fault diagnosis of UAV motors as a small sample classification problem, a hybrid neural network with small sample learning capabilities is proposed, leveraging the broad learning system (BLS) [49] and convolutional neural network (CNN) [50] for the analysis of current signal data to address the challenges of small sample fault diagnosis in UAV motors.BLS is different from the traditional neural network model in the 'depth' of the superposition of the 'lateral expansion' approach, simple structure, fast response, strong generalization, can obtain more representative features from the original data, and then use the CNN powerful local feature extraction capabilities, to achieve a limited sample of UAV motor fast and accurate fault diagnosis.In the experimental section, we compared the proposed model with traditional SVMs [51], SVM combined with handcrafted feature extraction methods (including db4 and sym4 wavelet packet transforms, Fourier transforms), LSTM [52], CNN, and BLS models.This validation demonstrated the ability of the proposed model in data driven fault diagnosis of small sample drone motor faults using current signal data.The main contributions of this study are as follows: 1 The remainder of the paper is structured as follows: section 2 introduces the BLSCNN fault diagnosis model based on the width learning system and CNN.Section 3 delves into the design of fault experiments and data collection for UAV motors.Section 4 assesses the efficacy of the proposed method using the acquired data.Lastly, in section 5, conclusions are drawn, and future directions are outlined.

Broad convolutional hybrid neural network model
Deep learning models are renowned for their potent feature extraction capabilities and have found extensive application across various domains.However, these models thrive under the assumption of having substantial training data.In the case of UAV operations, the aircraft's flight stability is profoundly sensitive to the condition of its actuators.Given the incapability of operating for extended durations in a faulty state, collecting a large volume of fault sample data proves to be immensely challenging.This presents a formidable obstacle for UAV fault diagnosis.In this paper, the challenge of UAV fault diagnosis with limited samples is addressed by framing it as a small sample classification problem.A hybrid neural network model is proposed, combining the BLS and CNN to tackle this issue.

BLS feature mapping
The BLS is a novel random weight neural network model, introduced by Chen and Liu [49], and built upon the foundation of the random vector functional link neural network [53].In contrast to traditional neural networks, the width learning system adopts a 'lateral expansion' approach to eliminate depth based superposition, thereby reducing the complexity of the neural network model.Its straightforward structure and swift responsiveness have led to its widespread use across various domains [54].The BLS primarily comprises an input layer, a feature mapping layer, an augmentation node layer, and an output layer.In this model, the network node weights of the feature mapping layer and the enhancement node layer are randomly generated.This results in a more diverse representation of the original sample features following network mapping.The specific network structure is illustrated in figure 1.
The algorithmic flow of the BLS is as follows.
Assuming the sample dataset is denoted as X, it consists of N samples, with each sample having M dimensions represented as a matrix X ∈ R N×M .The corresponding labeling matrix is Y ∈ R N×C .Within the feature mapping layer of the BLS, there are n feature mapping windows, each with K nodes.In each of these feature mapping windows, normalized data undergoes linear mapping using a feature mapping function φ i (i = 1, …, n).As a result, the data can be represented as follows after feature mapping in the ith window: ( Style: The matrix W ei ∈ R M×K represents a randomly generated optimal feature mapping weight matrix, which is determined through a sparse self-encoder.Matrix β ei ∈ R N×1 corresponds to the randomly generated bias matrix.In practical applications, we employ matrix φ i and use linear mapping functions. The results of feature mapping obtained from all n windows are combined to form N×nk , which serves as the output of the feature mapping layer.Z in is then forwarded to the augmentation node layer.The structure of the augmentation node layer mirrors that of the feature mapping layer.Assuming there are m windows and q nodes, each window conducts nonlinear mapping using the activation function ζ j (j = 1, …, m) pairs.The result of feature mapping for the jth window in the augmentation node layer is given by: ( Style: The matrix W hj ∈ R nk×q represents the randomly generated node weight matrix for the augmentation layer, while β hj ∈ R N×1 is the corresponding bias matrix.The activation function ζ j can be chosen from various nonlinear activation functions to effectively extract the nonlinear features within the data.
Likewise, the results of feature mapping from the m windows in the augmentation node layer are consolidated to derive The final feature matrix A is obtained by merging the outcomes of the feature mapping layer Z in with the results of the augmentation node layer H jm , The network structure of the BLS is characterized by its simplicity.Through a sequence of linear and nonlinear feature mapping processes executed by the feature mapping layer and the augmentation node layer, the initial data is projected into the width feature space.This minimizes the reliance on temporal characteristics of the original samples, while simultaneously affording the samples more extensive and logically sound feature variations.

CNN feature extraction
The original UAV motor current signal data exhibit clear temporal characteristics.Traditional deep learning models such as CNN and LSTM tend to depend on and extract these timing features from the original signal for feature extraction.However, with a limited number of training samples, they struggle to obtain representative features, leading to a diminished accuracy in fault diagnosis.In this paper, we employ the BLS to transform the features of the original current signal data.This mapping effectively renders the sample features independent of the time series, incorporating more varied characteristics.The resultant features are then input into a one dimensional CNN for tasks related to feature extraction and classification.For a deeper understanding of the CNN's theoretical foundations, readers can refer to the literature [50].Assuming the number of input data features for the network is denoted as T, the network's structural parameters were determined through exploratory experiments, as detailed in table 2. The CNN possesses a robust capability for local feature extraction.The CNN used in this paper comprises four convolutional layers.To ensure the seamless transition of data from one convolutional layer to the next, a batch normalization layer is introduced after each convolutional layer.This layer standardizes the convolutional output data, ensuring network training stability and generalization capacity.Subsequently, a ReLu activation layer is added to guarantee the network's ability for nonlinear fitting.The ReLu activation layer further reinforces the network's nonlinear fitting capability.Model training is conducted using the cross entropy loss function as the target function, thereby accomplishing the classification task.

Fault diagnosis algorithm flow
Deep learning models are celebrated for their feature extraction capabilities, but their insatiable appetite for vast training datasets presents a substantial hurdle when dealing with the constraints of limited data in UAV motor fault diagnosis.In this paper, we approach UAV motor fault diagnosis as a small sample classification problem.Our approach begins by utilizing the BLS to map the original data's features.This step helps eliminate the temporal characteristics present in the original data and projects it into a width feature space.We then leverage the powerful local feature extraction capabilities of the CNN to extract features from this projected data.Our method involves identifying the sample features within the context of the width feature space.Training for the small sample classification task is carried out using the cross entropy loss function as the target loss function.This allows us to achieve UAV motor fault diagnosis within a small sample background.The flowchart of the algorithm and the overall pseudo-code of the BLSCNN model are shown in figure 2 and table 3, respectively.
Randomly generated feature mapping weights 15. Non linear activation function activation

Construction of the data acquisition system
The core components of a quadrotor UAV motor comprise the motor casing, rotor, stator, bearings, end caps, and terminals.Among these, the stator, rotor, and bearings are the primary elements responsible for electronic operation.When the motor is in operation, the coil windings on the stator generate a magnetic field, and this magnetic field interacts with the permanent magnets on the rotor, supplying the power necessary for the rotor's rotation.The bearings are positioned at the ends of the motor's rotating shaft.Their role is to reduce heat and wear resulting from friction, in addition to providing vibration dampening and noise reduction.This ensures that the rotor rotates smoothly, accurately, and efficiently, ultimately guaranteeing the stability and flight performance of the UAV [55].The three main modules of the stator, rotor, and bearing are susceptible to failures, and any failure within these modules can result in reduced operational performance of the UAV motor.Such failures may lead to increased motor temperature and elevated vibration, and, in severe cases, affect the UAV's flight, potentially leading to a crash [56].To comprehensively investigate UAV motor failure characteristics and validate the practical applicability of the theoretical methods proposed in this paper, we selected the QM2812 980 kv DC brushless motor of the F450 quadcopter UAV as our research subject.We designed failure simulation experiments targeting the stator, rotor, and bearings, taking into account the motor's operational characteristics.Data was collected at three different motor speeds: 5000 r min −1 , 5500 r min −1 , and 6000 r min −1 , to verify the effectiveness of the theoretical methods across these varying operating conditions.

Experimental design for UAV motor failure
The stator, rotor, and bearing are critical components of UAV motor operation, and they are also the primary modules where faults may occur.Any failure within these modules can result in a decline in the UAV motor's operational performance, increased motor temperature, heightened vibration, and, in severe instances, it may even affect the UAV's flight, potentially leading to a crash.To comprehensively investigate the characteristics of UAV motor failures and enable accurate fault diagnosis, this paper focuses on designing faults within these three modules.The motor fault locations of the corresponding modules are shown in figures 4-6.

Bearing fault.
Bearings installed on the drone are positioned at both ends of the motor rotor shaft, serving the crucial role of supporting the rotating components of the motor.They effectively reduce heat and wear generated by friction, while also providing damping for vibration and noise reduction.This ensures that the motor rotor rotates smoothly, with precision and efficiency, ultimately contributing to the stability and flight performance of the drone.Should a bearing experience a failure, it can lead to uneven motor rotation, noise generation, and in more severe cases, motor damage.Given the operational characteristics of bearings, this study simulates wear and failures in the outer ring, cage, rolling body, and rolling elements of the bearing at the drive end of the motor using micro milling cutters.

Rotor fault.
The rotor, comprising permanent magnets and the rotor shaft, is pivotal to motor functionality.During operation, magnetic fields interact, inducing rotational force in the rotor.However, motor overload caused by high temperatures can diminish or eradicate magnetism in the permanent magnets.Additionally, severe external impacts can cause rotor shaft bending, leading to axis misalignment and disrupting motor operation.Rotor failure design encompasses external impacts resulting in rotor shaft bending, axis misalignment, and partial demagnetization of permanent magnets due to high temperatures.

Stator fault.
The stator, serving as the stationary component of the motor, comprises a coil of copper wire wound within the motor casing.When current flows through the stator, it generates a magnetic field, which interacts with the rotor's magnetic field to produce motor rotation.Motor overload, resulting in elevated temperatures, is the primary cause of stator failure due to insulation layer breakdown in the stator winding.This paper investigates two types of stator failures: turn to turn short circuits within the copper coil and partial wear of the outer connecting wire leading to interline short circuits.Fault injection involves using a micro milling cutter to remove the insulation layer of the wire.The specific fault location is illustrated in the figure below.
This paper encompasses a fault simulation design for the three key components of the UAV motor: the stator, rotor, and bearing.To evaluate the efficacy of the proposed UAV fault diagnosis method, vibration and three phase current signals from the motor were concurrently collected at speeds of 5 k rpm, 5.5 k rpm, and 6 k rpm under both normal and various fault conditions.
To mitigate the impact of noise during the synchronous operation of multiple motors, we collect the current signal from a single motor.Simultaneously, to safeguard the motor and ensure the experiment's safety, the UAV motor operates under a no load condition concerning the industrial control blade equipment.Adhering to the sampling theorem, which posits that for analog to digital signal conversion, a sampling frequency exceeding twice the highest frequency in the signal guarantees complete information retention in the digital signal.In our study, we employ a sampling frequency of 100 kHz, equivalent to 100 000 samples per second.With motor operating speeds at 5000, 5500, and 6000 rpm, corresponding to operating frequencies of 83.33 kHz, 91.67 kHz, and 100 kHz, respectively, our experimental sampling frequency significantly surpasses the motor operating frequency.This ensures precise sampling and reconstruction of the signal, capturing 10 000 data points for each state and speed.
The dataset encompasses the UAV motor data in eight faulty and normal states, across three rotational speeds.Timing diagrams for each dataset are depicted in figures 7-9.
This study utilizes the WCS1800 Hall current sensor to capture the current signal within the UAV motor circuit.The sensor transforms the current signal ranging from −35 A to 35 A into a voltage signal spanning 0.3 V to 4.7 V, which is then relayed to the signal acquisition card.Notably, when the current signal in the circuit reaches 0 A, the Hall current sensor outputs a consistent 2.5 V to the signal acquisition card.The output voltage timing diagrams, representing the motor current signal converted by the WCS180 Hall current sensor at three distinct rotational speeds (5000 rpm, 5500 rpm, and 6000 rpm), are depicted in figures 7-9, respectively.Each figure is organized from top to bottom, showcasing the timing diagrams of the current signal under nine different states: healthy operation, bearing support frame failure, outer ring failure, rolling body failure, inner ring failure, motor shaft bending, rotor permanent magnet demagnetization, stator phase to phase short circuit, and turn to turn short circuit.Upon examining the figures above, it is evident   The BLSCNN model is derived through the fusion of BLS and CNN, with its primary characteristic being the utilization of BLS to map features from the original current signal.Subsequently, these mapped features are conveyed to the CNN for feature extraction and classification tasks.It is noteworthy that the structural composition of each component within the model mirrors that of the original model, as detailed in section 2. The learning rate, a pivotal hyperparameter in deep learning, exerts control over the model's learning progress, influencing the network's potential success and the duration required to effectively locate the global minimum for completing prediction or classification tasks.The training efficacy of the BLSCNN model is notably influenced by the learning rate of the CNN.Within the scope of this paper, we initiate our discussion by conducting experiments about the selection of CNN's learning rate.Our investigation delves into the impact of distinct learning rates denoted as α on the model, all while maintaining an identical number of samples and iteration steps.Specifically, when α assumes values of 0.05, 0.01, 0.005, 0.0001, and 0.0005, the nuanced variations in accuracy and loss throughout the model training process are graphically illustrated in figures 10 and 11.
Upon examination of figures 10 and 11, it is evident that within identical experimental settings, an excessively large  learning rate (e.g.0.05) causes the model to fail to converge.Instead, it hovers around a particular value, neglecting the optimal value.Conversely, a learning rate set too small (e.g.0.0001) leads to slow model convergence, resulting in instances where it falls into a local optimum and fails to achieve optimal training results.A learning rate of 0.001 allows the CNN to converge swiftly and accurately when confronted with UAV motor current data, reaching and stabilizing at a 100% accuracy rate at the fastest rate.This paper opts for a learning rate of 0.001 for both CNN and BLSCNN.
In addition to the CNN's learning rate, it is imperative to discuss and ascertain the values of several key parameters for the BLS model: the number of feature mapping windows N1, the number of feature mapping nodes N11 per feature mapping window, the fixed number of enhancement windows N2 (set to 1 in this paper), and the number of enhancement nodes N22.These parameters collectively define the complexity and computational accuracy of the BLS model.An overly simplistic model is vulnerable to interference and noise, which does not align with practical requirements.Drawing upon insights from BLS and exploratory experiments, this paper initially sets N1, N11, and N22 to 10, 20, and 500, respectively.Subsequently, the model's performance is evaluated as each parameter increases, with the experimental results presented below.
Combined with the algorithmic process and theoretical formulas of the BLS model, it is evident that the number of feature mapping windows and the number of feature mapping nodes per feature mapping window correspond to the degree of linear mapping of the original signal data and the dimensionality of the features after mapping, respectively.Additionally, the number of enhancement nodes represents the dimensionality of the nonlinear mapping and the dimensionality after activation.In the experimental results presented in table 6, we augmented the number of windows or nodes in both the linear and activation parts of the BLS model's nonlinear mapping.Consequently, the model became more complex, resulting in longer test completion times, and exhibited significant enhancements across all fault diagnosis indicators.This confirms that the parameters utilized in this paper are suitable for fault diagnosis experiments on UAV motor current signals.
Table 7 presents the other model parameters and algorithms used for comparing them, where the parameters of the BLSCNN align with those of the BLS and CNN models.Similarly, the parameters of the SVM model, when combined with db4, sym4 wavelet packet transform, and Fourier transform for classification tasks, remain consistent with those of the standalone SVM model.

Analysis of experimental results
To assess the model's fault diagnosis capability in the context of limited samples, this study examines the impact of varying numbers of training samples on the model's performance at three operational speeds: 5k rmp, 5.5k rmp, and 6k rmp,    represents the tabulated information.Figure 15 presents a line graph depicting the classification accuracy of each model as a function of the number of samples across three rotational speeds.
A noticeable disparity in classification accuracy among models becomes apparent when dealing with a limited number of training samples.Remarkably, the WPT + SVM model, incorporating Db4 and Sym4 wavelets, and the proposed BLSCNN model exhibit considerably higher classification accuracy compared to other models, surpassing 50% even with only 10 training samples.However, the WPT + SVM model is found to be less sensitive to an increase in training samples compared to the BLSCNN model.Specifically, the BLSCNN model achieves a rapid 90% classification accuracy when the training samples reach 300.The gap in classification accuracy among models diminishes as the number of training samples increases to 300.Progressing from 10 to 80 training samples, the BLSCNN model attains 90% accuracy more swiftly, and the gap among models further narrows as the number of training samples reaches 300.
Moreover, the rate of accuracy improvement stabilizes with a continued increase in training samples, indicating the gradual release of the model's feature extraction capability.Notably, when the number of training samples reaches 1000 or even 2000, the gap in classification accuracy among models becomes less than 5%.The WPT + SVM model demonstrates less sensitivity to an increase in sufficient training samples compared to the BLSCNN model.The SVM model, in general, performs less favorably than other models under ample training samples.This combination of manual feature extraction and machine learning typically requires intricate and rigorous feature extraction engineering to reach a higher upper limit.Throughout these experiments, the BLSCNN model consistently exhibits the highest classification accuracy across all three speeds.
Additionally, a notable finding in the experiment is the subpar performance of the FFT + SVM model compared to the original SVM model across various numbers of training samples.This discrepancy arises from the fact that, during normal operation of the UAV motor, the circuit current maintains a fixed operating frequency.The fault experiments in this study involve introducing fault frequencies of each component onto the fixed operating frequency of the current.As the fault frequency weakens, analyzing faults from the frequency domain results in inherent challenges, as the circuit's current operating frequency domain dominates the fault frequency domain features, making feature extraction challenging.Consequently, FFT + SVM, when approaching fault diagnosis from a frequency perspective, yields inferior results.
Of the other algorithmic models used to compare, LSTM is a typical deep learning method for extracting temporal signal features from data.It places a strong emphasis on capturing the overall temporal characteristics of the data.When dealing with UAV motor current signals, LSTM requires a larger amount of training data to accurately distinguish feature differences between different classes.In comparison, CNN also falls within the realm of deep learning, but it specializes in local feature extraction.CNN assigns greater significance to localized features and relies less on the overall temporal characteristics of the samples when compared to LSTM.Therefore, with the same number of training samples, CNN excels in capturing and identifying a wider range of diverse features, consistently achieving higher classification accuracy compared to LSTM.
However, in all experiments, CNN consistently performed worse than the BLSCNN model.For instance, when using 10 samples for training, the classification accuracy of CNN stood at 51.89%, 45.24%, and 35.84% at 5 K, 5.5 K, and 6 K RPMs, respectively.This accuracy was notably lower than that of BLSCNN by margins of 3.8%, 12.87%, and 17.27%.As the number of training samples increased, the performance gap between CNN and BLSCNN persisted.It was only after the number of training samples exceeded 500 that the gap gradually diminished to less than 5%.This trend continued until the number of training samples reached 2000, at which point BLSCNN still exhibited slightly superior performance compared to CNN.
Interestingly, BLS consistently underperforms in comparison to the other models as the number of training samples increases.It ranks at the bottom of the list among the several methods used.This can be attributed to the simpler structure of BLS, which was originally designed to address the challenge of training deep learning models with vast amounts of data.However, it cannot effectively select and extract features when confronted with a limited number of training samples.
In this paper, we present an alternative perspective on BLS as a method for rapidly processing temporal data.Leveraging BLS, the original current signal timing data is transformed into a broader feature space, and CNN is employed to perform feature extraction and classification tasks.As a result, we propose a UAV motor fault diagnosis model based on BLSCNN.The feature mapping layer of BLS comprises multiple windows, each containing multiple neural network nodes.This multilevel parallel network structure allows BLS to analyze the complex structure and characteristics of the data from various perspectives.Unlike traditional methods such as FFT or wavelet packet transforms, which rely on linear transformation for feature extraction, BLS utilizes activation functions in the augmentation node layer to perform nonlinear mapping of linear mapping results.This parallel multi angle mapping nonlinear feature enhancement approach empowers BLS with the capability for both linear and nonlinear feature extraction.The experimental findings indicate that the process of initially subjecting the original current timing signal data to BLS feature mapping, followed by input into CNN, serves to substantially reduce CNN excessive reliance on timing characteristics for identification.In the expanded feature space, the samples exhibit a more reasonable and diverse set of features.Consequently, even with a limited number of samples, it becomes possible to capture the majority of characteristics shared by the same type of samples.When combined with CNN feature extraction and classification capabilities, this approach enables BLSCNN to outperform CNN with a small number of training samples, even surpassing the performance of other methods used for comparison.
For a more detailed exploration of each model's ability to accomplish fault diagnosis tasks based on UAV motor current signals, this paper presents the confusion matrix for the test results of each model using 80 training samples for visual analysis (notably, BLSCNN achieves an accuracy close to or reaching 90% with 80 training samples).Figure 16 displays the confusion matrices for test results at three different speeds.From left to right the working speeds are 5K, 5.5K, 6K.
In the series of confusion matrix sets displayed in figure 16, blue squares represent correct classifications, while orange squares represent incorrect classifications, with the numbers within the squares indicating the count of classified samples.The darkness of the square corresponds to the magnitude of the count, with darker colors indicating a higher number of samples.Upon inspecting the confusion matrix group in the figure, it becomes evident that SVM, LSTM, and BLS rarely achieve a perfect classification for C1-C9 (where a square on the diagonal shows a 100% correct classification in blue, while the horizontal and vertical squares represent 0% correct classification).This is attributed to the limited feature extraction   Moreover, during UAV flight operations, its sensitivity to the health status of each power system component is crucial.If it fails to promptly detect and identify faults, thereby signaling the operator to return for maintenance, it may lead to catastrophic crashes, resulting in significant economic losses and endangering lives.In this study, each trained model was evaluated with 80 training samples, and the recognition time for new test data was compared.There are 100 test data samples for each motor's operating state, totaling 900 test data points.The specific experimental results obtained are presented in table 8 and figure 17.The better experimental results are bolded in table 8.
The LSTM and BLS models exhibit significantly shorter processing times, mainly because LSTM features are In summary, this paper presents a study on UAV motor fault diagnosis driven by current signals.The challenges arise from the limited availability of research data due to the UAV's flight stability characteristics and its sensitivity to the health of its internal components.This limitation results in a constrained number of samples available for training.Traditional SVM struggles to find decision boundaries with significant margins, potentially leading to suboptimal classification performance on new data.LSTM and CNN both exhibit varying degrees of dependence on the timing characteristics of the original signal for feature extraction.In this scenario, when dealing with a limited number of training samples, the representativeness of the samples is compromised.Consequently, it becomes challenging to capture the underlying structural characteristics of the data, resulting in lower classification accuracy.In this paper, BLS is used as a fast response feature mapping method to map the original timing signal into the width feature space to obtain richer and more representative features, which effectively avoids the dependence of CNN on the timing features of the original signal, and the BLSCNN model obtained by combining BLS and CNN outperforms the models used for the comparison with the same number of training samples; meanwhile, the response time of this model to face the new test data meets the requirements of practical use.

Conclusions and future work
When researching data driven multi rotor UAV motor fault diagnosis methods, current signals are undoubtedly based on feasibility and practicality when compared to commonly used data such as flight control system, sound, and temperature.This paper initially designs fault simulation experiments to mimic the structure and operational characteristics of UAV motors.It collects relevant current signal data, laying the foundation for research on UAV motor fault diagnosis methods, particularly in the context of limited sample availability.To tackle the challenges related to fault data acquisition difficulties, limited data availability, and low diagnosis accuracy, this paper introduces a hybrid neural network model that combines BLS and CNN.Initially, BLS is employed to perform feature mapping on the original current signal data, extracting more representative sample features within a broader feature space.Subsequently, CNN is utilized for feature extraction and fault diagnosis tasks.The proposed model features a simple structure and quick response times.Experimental results have demonstrated that, by utilizing BLS for feature mapping on the original current signal data, over reliance on and extraction of time domain features by CNN is reduced.Consequently, CNN can extract more representative and distinguishable features even from a limited number of samples, enhancing its fault diagnosis capabilities compared to SVM, manual feature extraction combined with SVM, LSTM, and standalone CNN or BLS models.Additionally, the response and recognition time for new test data is considerably lower than that of traditional CNN, presenting a practical and straightforward theoretical approach for researching motor fault diagnosis in multi rotor UAVs.
The research presented in this paper focuses on unloaded paddle scenarios, which deviate somewhat from actual UAV motor operating conditions.Our future research endeavors will explore methods for UAV motor fault diagnosis under load, hover, and flight conditions while ensuring safety.Additionally, it is important to note that faults in multi rotor UAVs are not confined solely to motors, and occurrences of faults are not always isolated.Therefore, synchronously considering faults across various UAV system components is essential.Addressing this challenge involves developing methodologies for identifying and detecting multi fault scenarios when multiple faults occur simultaneously, requiring in depth research and analysis.

Figure 1 .
Figure 1.Network structure of the BLS.

Figure 3
illustrates the developed system for acquiring fault data from the quadrotor UAV motor and the associated fault diagnosis platform.The data acquisition system primarily comprises the UAV system, Hall current sensor, constant current source adapter, data acquisition card, and computer host.One of the fixed three phase motor lines passes through the Hall current sensor, which converts the motor's current change data into voltage signals.These voltage signals are then transmitted to the data acquisition card.The data acquisition card is responsible for analog to digital conversion of the current signal and subsequently transmits the collected data to the computer for analysis.The parameters of each component are detailed as follows.The parameters of each component are shown in table4.

Figure 10 .
Figure 10.Variation of accuracy during CNN training at different learning rates.

Figure 11 .
Figure 11.Variation of loss during CNN training at different learning rates.

Figure 12 .
Figure 12.Classification accuracy of the model with numbers of training samples at 5 K rpm.

Figure 13 .
Figure 13.Classification accuracy of the model with different numbers of training samples at 5.5 K rpm.

Figure 14 .
Figure 14.Classification accuracy of the model with different numbers of training samples at 6 K rpm.

Figure 15 .
Figure 15.Line graph of model classification accuracy with sample size at each speed.

Figure 16 .
Figure 16.Confusion matrix of test results for each model at each rotational speed for 80 training samples.
Consequently, SVM struggles to grasp the intricate structure of the data, resulting in difficulty when identifying accurate decision boundaries over sufficiently large intervals.The traditional manual feature extraction combined with SVM has a low upper model limit.As a result, their classification effectiveness diminishes when confronted with new data.LSTM encounters a similar issue, wherein its heavy reliance on and extraction of temporal features hinder its ability to discern representative and distinctive features when only a limited number of samples are accessible.The confusion matrices for CNN and BLSCNN indicate their capability to precisely classify the types of faults related to the current in the motor signals (C8-C9).When diag-nosing mechanical component faults based on the current signals, which exhibit weak variability, the model must possess a robust feature extraction and recognition capability of CNN and BLSCNN, it is evident that the most significant difference in the experimental results lies in their ability to identify mechanical faults (C2-C7).BLSCNN conducts feature extraction, classification, and identification from the BLS feature space, thereby avoiding excessive dependence on the temporal characteristics of the original signals.It can effectively identify mechanical faults with weaker transformations in the current signals.The classification performance for C3 and C4 is slightly poorer than for other categories, but this limitation is also overcome by the increase in the number of training samples.

Figure 17 .
Figure 17.Histogram of time spent on test data for each model.

Table 1 .
UAV fault diagnostic data research.

Table 2 .
Structural parameters of convolutional neural network.

Table 5 .
Corresponding codes for motor operating states.
5.5k rmp, and 6k rmp were also collected at a sampling frequency of 100 kHz, resulting in a total of 27 groups of data, with each group containing 10 000 K sample points.Samples for model training and testing are prepared by segmenting the data into non overlapping slices of 10 000 K sample points per dataset.Each slice has a size of 2048 sample points and moves one sample point per slice.The samples obtained from these slices are then normalized to create the training and testing sample sets.

Table 6 .
BLS parameter selection experiment results.

Table 7 .
Main parameters of BLSCNN model components.14 illustrate the outcomes of the exploratory experiments regarding the influence of various sample sizes on the model's fault diagnosis capabilities at three rotational speeds: 5 K, 5.5 K, and 6 K, respectively.The table presents the classification accuracy of each model with varying numbers of training samples, while the bar chart visually

Table 8 .
Comparison of time on test sets for each model (unit: seconds).capabilities of BLS when working with a small number of training samples.Regarding SVM, the training samples are not adequately representative of the entire dataset.