A Fault Diagnosis Approach for Electromechanical Actuators with Simulating Model under Small Experimental Data Sample Condition

: Electromechanical actuators (EMAs) have shown a high efﬁciency in ﬂight surface control with the development of more electric aircraft. In order to identify the abnormalities and potential failures of EMA, a methodology for fault diagnosis is developed. A simulating model of EMA is ﬁrst built to perform different working states. Based on the modeling of EMA, the corresponding faults are then simulated to re-generate the fault data. Afterwards, a gated recurrent unit (GRU) and co-attention-based fault diagnosis approach is proposed to classify the working states of EMA. Experiments are conducted and a satisfying classiﬁcation accuracy on simulated data is obtained. Furthermore, fault diagnosis on an actual working system is performed. The experimental results demonstrate that the proposed method has a high efﬁciency.


Introduction
Recently, more electric aircraft (MEA) initiatives have focused on increasing the penetration of the electrical systems into the aircrafts, in order to decrease the weight and increase the overall efficiency [1,2].Once restricted to airborne hydraulic distribution systems, the move towards MEA has considerably progressed with advances in electrically powered actuators.Electromechanical actuators (EMAs) present a solution which exploits a mechanical drivetrain to reach the control surface [3].Compared with the alternatives (e.g., classical hydraulic systems and electro-hydrostatic actuators), the EMAs simply control the motor and leverage on a planetary roller screw pair to translate the rotary motion into linear motion, which has brought paradigm shifts to power the MEA transmission.As one of the commercial aircrafts, the Boeing 787 applies EMAs to landing gear braking, a spoiler, as well as a trimmable horizontal stabilizer [4,5].
In spite of the reduced complexity and easy maintenance, EMAs are currently used in fewer safety-critical control surfaces or tasks with redundant alternatives [6].This is due to the fact that the failure risks and accumulated reliability experience are absent [7].That is, the latent failures of EMAs relegate them to still be implemented on secondary flight controls.Consequently, the fault diagnosis of EMA is mostly studied, which paves the way for deeply understanding the fault occurrence and its principle [8,9].
Theoretically, fault diagnosis aims at detecting and identifying any type of potential abnormalities and faults [10,11].Numerous artificial intelligence techniques and statistical learning methods have been widely used in fault diagnosis, such as k-nearest neighbor (k-NN) algorithms [12], Bayesian classifier [13], support vector machine (SVM) [14], and deep learning approaches [15].In recent years, deep-learning algorithms have underpinned the state-of-the-art implementations for fault diagnosis tasks [16,17].More precisely, the deep-learning-based methods use a large number of samples for model training, based on which they predict the underlying failures [18,19].Consequently, a set of complete data that represent both normal and faulty cases is required [20].However, fault data collection in EMA remains challenging, especially in expensive and precise components, which cannot be threatened to recreate fault occurrences.Furthermore, failure tests on EMAs in actual working conditions are highly-priced and time-consuming, which also poses a major limitation of data-based fault describing and distinguishing [21].For these reasons, the system virtual simulating is highlighted [22].As mentioned in [23], 'virtual simulation is defined as the creation of interactive environments that replicate a real-world scenario'.Using the virtual simulator, the dynamic model of EMA can be devised and the faults can be injected [24,25].Therefore, the signals that characterize the EMA working states are measured by virtual sensing elements in simulated tests, which provides opportunities to collect samples for fault diagnosis model training.
This paper develops a virtual simulator in line with the functionalities of EMA in practical working conditions, while focusing on the components' failure principle to generate and inject faults into the simulated model.For fault diagnosis, a deep-learning-based network is proposed, while the fault data are collected for model training.Fault signals from both simulation tests and in-service EMA are measured and sent to the proposed model, to verify the efficiency of the proposed fault diagnosis method.
The remainder of this paper is organized as follows.The background knowledge of EMA is presented in Section 2. Section 3 details the virtual simulator of EMA.The deep-learning based fault diagnosis model is presented in Section 4. The experimental results are provided in Section 5. Finally, the conclusions are drawn in Section 6.

Prerequisite 2.1. Architecture of EMA
The schematic diagram of EMA is presented in Figure 1.In general, an EMA is made up of a mechanical actuating assembly and an electronic controller.More precisely, the mechanical actuating assembly consists of a servo motor and mechanical transmission components (i.e., a planetary roller screw pair), to convert the electric drive into mechanical power [26].The controller is used to determine the current by voltage pulse width modulation (PWM) to the motor, according to the position demand.The motor rotates forward and in reverse in line with the output control commands from the controller [27].The planetary roller screw pair then converts the rotational motion into linear movement of the EMA rod end [28].In response, signals of position, velocity, and current are detected and sent to the controller as feedback.
In general, four categories of faults exist in EMA: motor, mechanical system, sensor and electronics.To the best of our knowledge, motor malfunction is the most important among all these faults.With respect to the motor components, the failure probability of bearings is 41% following with the stator accounting for 37%.More precisely, almost 80% stator failures result from winding insulation faults.A small inter-phase short circuit or short to ground can also lead to the collapse of the flight control system, which is more severe than the damage of bearings.Therefore, a sensor that detects the motor current is also used to monitor the working state.Several current studies deal with the electrical failures of the motor in EMA.

Fault Diagnosis of EMA
Fault diagnosis of EMAs has received a certain amount of interest in recent years.Despite the lack of reliable fault statistics, state-of-the-art methods work on detecting the faults of components before the system evolves into catastrophic consequences.Specifically, Yu et al. proposed the concept of extended analytical redundancy relations, based on which a fault diagnosis approach is developed for nonparametric fault identification of electromechanical systems [20].Moreover, Daniele et al. applied the fuzzy inference system to detect failures on the electric motor of EMAs [16].Aiming to predict multiple failure modes, Zhang et al. estimated the EMA working data on both the simulation model and experiment platform of EMA [32].Notably, studies on deep-learning-based EMA fault recognition models are ongoing.Siahpour et al. devised a CNN-based model across distinguishing sensing data [18].Likewise, Zhang et al. proposed a method by integrating a gated recurrent unit, attention mechanism, and similarity measure.In addition, a model based on a sparse feature and long short-term memory network has been developed [19].With the faults injected, experimental results validated the working performance of the deep learning method.

Simulation Model Development
For the purpose of fault diagnosis, an EMA simulator is first developed to inject fault data into it.The virtual model of EMA is constructed in line with the actual EMA to simulate its working states, as illustrated in Figure 2. As previously mentioned, the mechanical assembly of the proposed EMA model contains a reduction gear, a bearing, and a planetary roller screw, while the electrical components are a triple-loop controller, a In general, four categories of faults exist in EMA: motor, mechanical system, sensor and electronics.To the best of our knowledge, motor malfunction is the most important among all these faults.With respect to the motor components, the failure probability of bearings is 41% following with the stator accounting for 37%.More precisely, almost 80% stator failures result from winding insulation faults.A small inter-phase short circuit or short to ground can also lead to the collapse of the flight control system, which is more severe than the damage of bearings.Therefore, a sensor that detects the motor current is also used to monitor the working state.Several current studies deal with the electrical failures of the motor in EMA.

Fault Diagnosis of EMA
Fault diagnosis of EMAs has received a certain amount of interest in recent years.Despite the lack of reliable fault statistics, state-of-the-art methods work on detecting the faults of components before the system evolves into catastrophic consequences.Specifically, Yu et al. proposed the concept of extended analytical redundancy relations, based on which a fault diagnosis approach is developed for nonparametric fault identification of electromechanical systems [20].Moreover, Daniele et al. applied the fuzzy inference system to detect failures on the electric motor of EMAs [16].Aiming to predict multiple failure modes, Zhang et al. estimated the EMA working data on both the simulation model and experiment platform of EMA [32].Notably, studies on deep-learning-based EMA fault recognition models are ongoing.Siahpour et al. devised a CNN-based model across distinguishing sensing data [18].Likewise, Zhang et al. proposed a method by integrating a gated recurrent unit, attention mechanism, and similarity measure.In addition, a model based on a sparse feature and long short-term memory network has been developed [19].With the faults injected, experimental results validated the working performance of the deep learning method.

Simulation Model Development
For the purpose of fault diagnosis, an EMA simulator is first developed to inject fault data into it.The virtual model of EMA is constructed in line with the actual EMA to simulate its working states, as illustrated in Figure 2. As previously mentioned, the mechanical assembly of the proposed EMA model contains a reduction gear, a bearing, and a planetary roller screw, while the electrical components are a triple-loop controller, a permanent magnet synchronous motor (PMSM), together with the motor drive.The control command is transformed into the motor torque and rotating speed, and therefore drives the movement of the screw through the mechanical assembly.The moving relationship of the mechanical drivetrain is performed using mathematical equations.
permanent magnet synchronous motor (PMSM), together with the motor drive.The control command is transformed into the motor torque and rotating speed, and therefore drives the movement of the screw through the mechanical assembly.The moving relationship of the mechanical drivetrain is performed using mathematical equations.The mechanical assembly: considering the working principle of EMA, the planetary roller screw is the key component which aims to match the torque and speed between the motor and the external load by transitional mechanism [26].Mathematically, the motion o where   and   , respectively, represent the axial speed and output force of the screw,   and   , respectively, denote the torque and rotating speed of the motor, and  is the lead of planetary roller screw.The energy loss within the transmitting pairs should also be considered, including the inertia effect, friction loss.The inertia of the planetary roller screw is negligible in the system and is equivalently converted to that of the motor rotor.The friction loss can be simplified proportionally to the rotating speed, known as viscous friction.Consequently, the motion of the mechanical drivetrain is given by: where  and   , respectively, represent the inertia moment and viscous friction coefficient equivalent to the motor rotor.The model of mechanical assembly, containing a planetary roller screw, sensing elements, and the external load, is developed in AMESim; see Figure 3.All the components are obtained from the AMESim standard library, while the load is given by directly inputting dynamic force.The mechanical assembly: considering the working principle of EMA, the planetary roller screw is the key component which aims to match the torque and speed between the motor and the external load by transitional mechanism [26].Mathematically, the motion o where v s and F s , respectively, represent the axial speed and output force of the screw, ω m and T m , respectively, denote the torque and rotating speed of the motor, and p is the lead of planetary roller screw.The energy loss within the transmitting pairs should also be considered, including the inertia effect, friction loss.The inertia of the planetary roller screw is negligible in the system and is equivalently converted to that of the motor rotor.The friction loss can be simplified proportionally to the rotating speed, known as viscous friction.Consequently, the motion of the mechanical drivetrain is given by: where J and B m , respectively, represent the inertia moment and viscous friction coefficient equivalent to the motor rotor.The model of mechanical assembly, containing a planetary roller screw, sensing elements, and the external load, is developed in AMESim; see Figure 3.All the components are obtained from the AMESim standard library, while the load is given by directly inputting dynamic force.
permanent magnet synchronous motor (PMSM), together with the motor drive.The control command is transformed into the motor torque and rotating speed, and therefore drives the movement of the screw through the mechanical assembly.The moving relationship of the mechanical drivetrain is performed using mathematical equations.The mechanical assembly: considering the working principle of EMA, the planetary roller screw is the key component which aims to match the torque and speed between the motor and the external load by transitional mechanism [26].Mathematically, the motion o where   and   , respectively, represent the axial speed and output force of the screw,   and   , respectively, denote the torque and rotating speed of the motor, and  is the lead of planetary roller screw.The energy loss within the transmitting pairs should also be considered, including the inertia effect, friction loss.The inertia of the planetary roller screw is negligible in the system and is equivalently converted to that of the motor rotor.The friction loss can be simplified proportionally to the rotating speed, known as viscous friction.Consequently, the motion of the mechanical drivetrain is given by: where  and   , respectively, represent the inertia moment and viscous friction coefficient equivalent to the motor rotor.The model of mechanical assembly, containing a planetary roller screw, sensing elements, and the external load, is developed in AMESim; see Figure 3.All the components are obtained from the AMESim standard library, while the load is given by directly inputting dynamic force.The electrical module: the electrical module is mainly used to transform the control command into the mechanical assembly inputs for actuating.The triple-loop controller contains three control units: a position controller, a velocity controller, and a current controller (see Figure 2 for details).The current controller exploits the spatial vector control to meet the requirement of high-frequency switching of the motor driver.Circular rotating magnetic field generated by a space vector are dedicatedly designed to improve the tracking accuracy of the current loop.The speed and position loops use the Proportional Integral (PI) control, which ensures the settling time and the steady-state accuracy.
Furthermore, a three-phase inverter and six Insulated Gate Bipolar Transistor (IGBTs) are used as the motor driver.The three-phase inverter receives the PWM signals from the spatial vector controller, regulates the on-off switching of all the IGBTs, and thus delivers a three-phase sinusoidal voltage to the motor stator.
In line with the three-phase voltage on the stator, the rotating speed and the electromagnetic torque of rotor are generated.The transformation between the two-phase rotating reference frame (dq) and the three-phase stationary coordinate system (abc) is performed using the constant-power Clarke and Park transformation and inverse transformation: where u, L, and i, respectively, represent the voltage, inductance, and current of dq coordinate, R s denotes the equivalent resistance of each stator winding, ϕ f is the permanent magnet flux linkage, and n is the number of the motor pole-pairs.The overall EMA model, containing the mechanical assembly and the electrical module, is built on the platform of AMESim (see Figure 4 for details).The motor and its driver are devised using standard components, while the hysteresis controller and PI controllers are developed based on mathematical expressions.More precisely, all the key parameters of EMA, such as the equivalent moment of inertia to the rotor and screw viscous damping coefficient, as well as the control parameters of the PI controller, are identified using a differential evolution algorithm [33].
The electrical module: the electrical module is mainly used to transform the control command into the mechanical assembly inputs for actuating.The triple-loop controller contains three control units: a position controller, a velocity controller, and a current controller (see Figure 2 for details).The current controller exploits the spatial vector control to meet the requirement of high-frequency switching of the motor driver.Circular rotating magnetic field generated by a space vector are dedicatedly designed to improve the tracking accuracy of the current loop.The speed and position loops use the Proportional Integral (PI) control, which ensures the settling time and the steady-state accuracy.
Furthermore, a three-phase inverter and six Insulated Gate Bipolar Transistor (IG-BTs) are used as the motor driver.The three-phase inverter receives the PWM signals from the spatial vector controller, regulates the on-off switching of all the IGBTs, and thus delivers a three-phase sinusoidal voltage to the motor stator.
In line with the three-phase voltage on the stator, the rotating speed and the electromagnetic torque of rotor are generated.The transformation between the two-phase rotating reference frame (dq) and the three-phase stationary coordinate system (abc) is performed using the constant-power Clarke and Park transformation and inverse transformation: where , , and , respectively, represent the voltage, inductance, and current of dq coordinate,   denotes the equivalent resistance of each stator winding,   is the permanent magnet flux linkage, and  is the number of the motor pole-pairs.The overall EMA model, containing the mechanical assembly and the electrical module, is built on the platform of AMESim (see Figure 4 for details).The motor and its driver are devised using standard components, while the hysteresis controller and PI controllers are developed based on mathematical expressions.More precisely, all the key parameters of EMA, such as the equivalent moment of inertia to the rotor and screw viscous damping coefficient, as well as the control parameters of the PI controller, are identified using a differential evolution algorithm [33].

Simulation Model Verification
The efficiency of the proposed EMA model in failure simulation is assessed.The simulation parameters are obtained based on the differential evolution algorithm [33,34].Each parameter presented in Table 1 obtains an optimal value after the differential evolution.In terms of step signals, system overshoot, steady-state error, and settling t typically employed to characterize the tracking accuracy.During the input sign from 0 to −10 mm, the steady-state error is less than 0.2% with the settling time o When the input jumps to 10 mm, the steady-state error varies within 0.3%, and tling time is 0.21 s.No overshoot is generated during tracking.For the 2 Hz sin signal, amplitude attenuation and phase lag of the proposed model are com which are 0.18 mm and 28.1° within the stabilization.The simulation results strate that the proposed model has a satisfying performance in both tracking a and settling time.Consequently, the proposed EMA simulator can be applied to t injecting process for fault data generation.In terms of step signals, system overshoot, steady-state error, and settling time are typically employed to characterize the tracking accuracy.During the input signal drop from 0 to −10 mm, the steady-state error is less than 0.2% with the settling time of 0.20 s.When the input jumps to 10 mm, the steady-state error varies within 0.3%, and the settling time is 0.21 s.No overshoot is generated during tracking.For the 2 Hz sine input signal, amplitude attenuation and phase lag of the proposed model are computed, which are 0.18 mm and 28.1 • within the stabilization.The simulation results demonstrate that the proposed model has a satisfying performance in both tracking accuracy and settling time.Consequently, the proposed EMA simulator can be applied to the fault injecting process for fault data generation.

EMA Fault Diagnosis Method
At this stage, a sine signal is considered as the control command of EMA, whose amplitude is 2 mm and the frequency ranges from 0.3 Hz to 6 Hz with an interval of 0.3 Hz.The external load is of 0 N and 500 N.
Forty sets of different working conditions are performed.The three-phase current of the motor is measured to characterize the working state of EMA.Notably, all these 40 sets of data refer to general working conditions while singular condition is currently not considered.

Fault Injection
As previously mentioned, the open circuiting of the motor stator is a serious fault to the control system and motor, which accounts for a high proportion of all the EMA faults.Therefore, the motor open circuit malfunction is simulated, containing an open circuit of stator windings and IGBT in motor driver.In general, the unstable power supply, ground faults, and mechanical vibrating shock can result in the disconnection.An open circuit in phase A indicates the current of this phase approaches 0, as shown in Figure 6.Consequently, the current summation of the other two phases is also equal to 0. Using this property, the open circuit fault is injected into the EMA simulator.Specifically, an electric switch is inserted to A phase to control the output current, as presented in Figure 7.With the fault injected, the current of phase A is 0 while those of the other phases tremendously increases.Figure 8 exhibits the three-phases current of A-phase open circuit while the normal state data is also given for comparison.
At this stage, a sine signal is considered as the control command of EMA, whose amplitude is 2 mm and the frequency ranges from 0.3 Hz to 6 Hz with an interval of 0.3 Hz.The external load is of 0 N and 500 N.
Forty sets of different working conditions are performed.The three-phase current of the motor is measured to characterize the working state of EMA.Notably, all these 40 sets of data refer to general working conditions while singular condition is currently not considered.

Fault Injection
As previously mentioned, the open circuiting of the motor stator is a serious fault to the control system and motor, which accounts for a high proportion of all the EMA faults.Therefore, the motor open circuit malfunction is simulated, containing an open circuit of stator windings and IGBT in motor driver.In general, the unstable power supply, ground faults, and mechanical vibrating shock can result in the disconnection.An open circuit in phase A indicates the current of this phase approaches 0, as shown in Figure 6.Consequently, the current summation of the other two phases is also equal to 0. Using this property, the open circuit fault is injected into the EMA simulator.Specifically, an electric switch is inserted to A phase to control the output current, as presented in Figure 7.With the fault injected, the current of phase A is 0 while those of the other phases tremendously increases.Figure 8 exhibits the three-phases current of A-phase open circuit while the normal state data is also given for comparison.Forty sets of different working conditions are performed.The three-phase curren of the motor is measured to characterize the working state of EMA.Notably, all these 40 sets of data refer to general working conditions while singular condition is currently no considered.

Fault Injection
As previously mentioned, the open circuiting of the motor stator is a serious fault to the control system and motor, which accounts for a high proportion of all the EMA faults.Therefore, the motor open circuit malfunction is simulated, containing an open circuit of stator windings and IGBT in motor driver.In general, the unstable power sup ply, ground faults, and mechanical vibrating shock can result in the disconnection.An open circuit in phase A indicates the current of this phase approaches 0, as shown in Figure 6.Consequently, the current summation of the other two phases is also equal to 0 Using this property, the open circuit fault is injected into the EMA simulator.Specifical ly, an electric switch is inserted to A phase to control the output current, as presented in Figure 7.With the fault injected, the current of phase A is 0 while those of the othe phases tremendously increases.Figure 8 exhibits the three-phases current of A-phase open circuit while the normal state data is also given for comparison.A-phase open circuit represents i A ≈ 0 and i B + i C = 0. On the other hand, the IGBTs of the inverter work in a high-voltage condition, which generate a large amount of heat during the high-frequency switching.Therefore, the IGBTs always suffer from the alternation of cold and heat, and are therefore subjected to continuous shear stress.Due to the fact that two IGBTs exist for each phase, each IGBT has the risk of disconnection during the work process.Hence, the faults are defined as the open circuit of upper-bridge IGBT (Figure 9a), lower-bridge IGBT (Figure 9b), and both IGBTs (Figure 9c) of each phase.The open circuit of IGBT will result in increasing the phase voltage and phase current, and further lead to the motor instability.On the other hand, the IGBTs of the inverter work in a high-voltage condition, which generate a large amount of heat during the high-frequency switching.Therefore, the IGBTs always suffer from the alternation of cold and heat, and are therefore subjected to continuous shear stress.Due to the fact that two IGBTs exist for each phase, each IGBT has the risk of disconnection during the work process.Hence, the faults are defined as the open circuit of upper-bridge IGBT (Figure 9a), lower-bridge IGBT (Figure 9b), and both IGBTs (Figure 9c   Moreover, the sensor malfunction is also injected to validate the efficiency of the fault diagnosis method.On the contrary, the sensor malfunction is the most controllable to conduct on actual failure tests, due to the fact that it does not destroy the crucial component within the EMA structure.The sensor failures can lead to abnormal feedback of the closedloop control and an unreliable system deviation.As illustrated in Figure 2, the EMA system involves a displacement sensor to detect the output rod displacement, a speed sensor to detect the motor speed, and a current sensor to detect the stator current.Theoretically, a sensor fault in the outer loop will result in a more uncontrollable system state.Therefore, the sensors' failures containing an open circuit of displacement sensor and a velocity sensor, are also injected into the EMA simulator to generate fault data.The three-phase current of the normal and failure conditions is generated (Figures 13 and 14).In addition, the reproduction of these sensor faults is implemented on the actual working EMA, which aims at demonstrating the validity of the fault diagnosis approach in practical use.

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Actuators 2022, 11, x FOR PEER REVIEW Moreover, the sensor malfunction is also injected to validate the efficiency fault diagnosis method.On the contrary, the sensor malfunction is the most cont to conduct on actual failure tests, due to the fact that it does not destroy the cruc ponent within the EMA structure.The sensor failures can lead to abnormal feed the closed-loop control and an unreliable system deviation.As illustrated in Figu EMA system involves a displacement sensor to detect the output rod displace speed sensor to detect the motor speed, and a current sensor to detect the stator Theoretically, a sensor fault in the outer loop will result in a more uncontrollable state.Therefore, the sensors' failures containing an open circuit of displacemen and a velocity sensor, are also injected into the EMA simulator to generate fau The three-phase current of the normal and failure conditions is generated (Fig and 14).In addition, the reproduction of these sensor faults is implemented on th working EMA, which aims at demonstrating the validity of the fault diagnosis ap in practical use.Actuators 2022, 11, x FOR PEER REVIEW Moreover, the sensor malfunction is also injected to validate the efficiency fault diagnosis method.On the contrary, the sensor malfunction is the most contro to conduct on actual failure tests, due to the fact that it does not destroy the crucia ponent within the EMA structure.The sensor failures can lead to abnormal feedb the closed-loop control and an unreliable system deviation.As illustrated in Figure EMA system involves a displacement sensor to detect the output rod displacem speed sensor to detect the motor speed, and a current sensor to detect the stator cu Theoretically, a sensor fault in the outer loop will result in a more uncontrollable s state.Therefore, the sensors' failures containing an open circuit of displacement and a velocity sensor, are also injected into the EMA simulator to generate faul The three-phase current of the normal and failure conditions is generated (Figu and 14).In addition, the reproduction of these sensor faults is implemented on the working EMA, which aims at demonstrating the validity of the fault diagnosis app in practical use.

Fault Diagnosis Method Based on Gated Recurrent Unit (GRU) and Co-Attention Network
In this section, a network is proposed to identify the working state of the EMA under different conditions.The model is designed using the GRU and the co-attention mechanism, as shown in Figure 15.
In this section, a network is proposed to identify the working state of the EMA under different conditions.The model is designed using the GRU and the co-attention mechanism, as shown in Figure 15.GRU is a variation of recurrent neural networks (RNNs) proposed by Cho et al. [35], which is generally used to learn sequential features from an input data stream using historical ones.A GRU is established on two gates and activation functions to integrate the previous memory into the current input, and thus update the output.The GRU is able to weaken the gradient vanish and get easily converged with a simple structure.On the other hand, the co-attention network deals with the interaction of different parts, and extracts the discriminative features from the input.In a deep-learning model, the integration of a co-attention mechanism aims at reducing the unrelated information and obtaining the essential information within the sequence.With respect to different types of sensing signals of the EMA simulator, the proposed model is based on the coattention network, which aims at highlighting the significances of the time-varying and co-dependent data.The attentive information of each part is taken into account towards the final fault identification.
A given sequence of signals  = [ 1 ,  2 , ⋯   , ⋯   ] ∈   is exactly detected from the coaxial-rotor unit.  is considered as the ith input vector of the proposed model.The input signals are fed into the three consecutive fully-connected layers to obtain sparse vectors while preserving features.For each layer, the leaky-Rectified Linear Unit (leaky-ReLU) function is used to activate the feature of   .The leaky-ReLU is expressed as: where  represents the function slope for a negative input, which is generally a constant between 0 and 1, set to 0.2 in the proposed model.Therefore: GRU is a variation of recurrent neural networks (RNNs) proposed by Cho et al. [35], which is generally used to learn sequential features from an input data stream using historical ones.A GRU is established on two gates and activation functions to integrate the previous memory into the current input, and thus update the output.The GRU is able to weaken the gradient vanish and get easily converged with a simple structure.On the other hand, the co-attention network deals with the interaction of different parts, and extracts the discriminative features from the input.In a deep-learning model, the integration of a co-attention mechanism aims at reducing the unrelated information and obtaining the essential information within the sequence.With respect to different types of sensing signals of the EMA simulator, the proposed model is based on the co-attention network, which aims at highlighting the significances of the time-varying and co-dependent data.The attentive information of each part is taken into account towards the final fault identification.
A given sequence of signals is exactly detected from the coaxial-rotor unit.x i is considered as the ith input vector of the proposed model.The input signals are fed into the three consecutive fully-connected layers to obtain sparse vectors while preserving features.For each layer, the leaky-Rectified Linear Unit (leaky-ReLU) function is used to activate the feature of x i .The leaky-ReLU is expressed as: where leak represents the function slope for a negative input, which is generally a constant between 0 and 1, set to 0.2 in the proposed model.Therefore: and: where w is the weight matrix and b is the bias vector.Both parameters are determined by model training.
Similarly, y i is considered as the input of the following two-layer activation and thus an h i is obtained: Hence, features of the inputs can be thoroughly gleaned.
As previously mentioned, the sensing signals are encoded by GRU to capture the internal characteristics of the working state in time-sequence.For the vector u i sent to a GRU cell, the previous information from the last hidden unit is integrated.Consequently, the output h i is generated: h i is kept as the hidden representation for the next-step processing within its GRU cell.At this stage, considering the input sequence of With an increasing amount of detected sensing data, a more accurate description of the working system can be accessed.Nevertheless, the more input signals are collected, the more complicated the processing procedures will be.In this paper, since all the data are sensed to characterize the working state, the three-phase current signals are fused to facilitate the processing rather than neglecting any important information.The co-attention mechanism is then performed to eliminate the irrelevant properties and obtain the essential features.Considering the interaction among different working parts in the system, the sensing signals on each part apparently affect the other sensor outcomes, and vice versa.For the vectors h i and h j , the attentive weight matrix can be calculated based on the interactive learning of the co-attention network: where M ∈ R n×n represents the parameter matrix and h T i denotes the transpose of h i .Furthermore, for the current sequence the attention mecha- nism is given by: where B is the bias matrix that is finetuned during the training process.At this stage, the outcome vector R with the basic feature of the system, is sent to a softmax classifier to identify the working conditions: and: where C represents the number of different working conditions.Thus, the fault classification result is given by:

Model Training
The training process of the proposed model is performed using the cross entropy and L 2 regularization as the loss function: where g i is the real distribution of sentiment, y i is the predicted one, and λ r is the weight of L 2 regularization.
The gradients as well as the other parameters are updated by back propagation with the learning rate λ l :

Experimental Setting
Experiments are conducted to verify the efficiency of the proposed fault diagnosis method.As previously mentioned, the model inputs are three-phase current signals that describe the EMA working states.Two general categories of failures (i.e., open circuit of motor and sensor malfunction) are simulated.The former contains 9 distinguishing faults while the latter contains 2 faults.Since 40 different working conditions exist, 440 sets of fault data and 40 sets of normal data are generated.Data of every single working state are simulated for 3 s, with a frequency of 1 kHz.For each data set, 1024 points of data are randomly picked in time sequence.In addition, for each data point, the following 512 points are considered as a data sample for further processing.Consequently, 491,520 (1024 × 480) sets of data are generated.All the samples are subdivided into the sets of training, validating, and testing with a ratio of 8:1:1.
The proposed model is finetuned with an ADAM optimizer with β 1 = 0.9, β 2 = 0.999 and ε = 1 × 10 −8 .The initialization parameters are used for 1000 iterations to optimize the related parameters.All the parameter matrices are randomly generated in the distribution of U (−0.1, 0.1), while the bias is initialized to 0. The hidden states dimension of the GRU cell is set to 300, with a learning rate of 0.001.Both the batchsize and the training epoch are set to 10.Moreover, the L 2 regularization weight is set to 0.0001, and the dropout rate is set to 0.5 to prevent overfitting.

Results
In this experiment, the accuracy is considered as the evaluation metric used to characterize the working performance.Table 2 presents the testing accuracy of each fault diagnosis task, for each working condition.2 demonstrate the universality of the proposed model, due to the accuracy consistency in different working conditions.

Experimental Verification
In this experiment, the sensor failure is used for representation to perform the actual experimental setup, which aims at identifying the outperformance of the proposed model.The test rig is illustrated in Figure 16.To confirm the consistency of the proposed and the actual EMA, time-domain and frequency-domain analysis are conducted.Figure 17 presents the tracking responses to a 1 Hz sinusoidal signal of both simulated and actual EMAs, with a tracking error within 0.1 mm.According to the bode diagram of Figure 18, the similarity between the two EMAs reaches 95%, which demonstrates the efficiency of the EMA simulator in fault data generation.
Among all the evaluation settings, the motor driver open circuit diagnosis has the best and most consistent performance compared to that of the other methods.The accuracy of the motor driver open circuit classification ranges between 98.0% and 98.6%.The best-performing outcome in this group is the diagnosis of the A-phase upper-bridge IGBT open circuit.The results obtained on motor stator open circuit range from 97.5% to 98.0%, and therefore they are slightly lower than those obtained on motor driver open circuit.In addition, the diagnosis accuracy of sensor malfunction and normal state are 95.9% and 97.8%, respectively.Consequently, the experimental results in Table 2 demonstrate the universality of the proposed model, due to the accuracy consistency in different working conditions.

Experimental Verification
In this experiment, the sensor failure is used for representation to perform the actual experimental setup, which aims at identifying the outperformance of the proposed model.The test rig is illustrated in Figure 16.To confirm the consistency of the proposed simulator and the actual EMA, time-domain and frequency-domain analysis are conducted.Figure 17 presents the tracking responses to a 1 Hz sinusoidal signal of both simulated and actual EMAs, with a tracking error within 0.1 mm.According to the bode diagram of Figure 18, the similarity between the two EMAs reaches 95%, which demonstrates the efficiency of the EMA simulator in fault data generation.According to the simulation-based outcomes, no-load working state has a sinus dal signal as the control command with a 2 mm amplitude and 0.6 Hz to 1.8 Hz freque cies and an interval of 0.3 Hz.Under this condition, a spring is further taken to apply 500 N external load to the EMA.The failures can be regenerated by disconnecting t sensing cables of the displacement sensor.The normal state and the sensor malfuncti are performed with a total number of 20 working conditions.For each working cond tion, the data sequence contains 1024 sets of three-phase currents of the motor, that a collected as test samples and sent to the fault diagnosis method.
The testing results are presented in Figure 19.The average classification accuracy the proposed model is 89.4%,where 90.7% are for normal state and 88.1% for sens malfunction.When a failure occurs in the actual system, the current signals variation of the same property with that of the simulation data.In addition, only if multiple da sequences representing a fault are simultaneously detected, the working state can be d termined as a fault.Consequently, a satisfying fault diagnosis accuracy is still accessib The proposed model fails to retain the performance of the simulating experimental ou comes.This is due to the fact that the three-phase current of the motor in the actual sy tem contains noise, which can introduce measurement errors into the signals.Notab the variation of input signals merely results in a marginal drop of the classification acc racy, which indicates the stability of the proposed model.Since the proposed model able to classify faults on actual working systems by simulated data training, it is reaso  According to the simulation-based outcomes, no-load working state has a sinuso dal signal as the control command with a 2 mm amplitude and 0.6 Hz to 1.8 Hz freque cies and an interval of 0.3 Hz.Under this condition, a spring is further taken to apply 500 N external load to the EMA.The failures can be regenerated by disconnecting t sensing cables of the displacement sensor.The normal state and the sensor malfunctio are performed with a total number of 20 working conditions.For each working cond tion, the data sequence contains 1024 sets of three-phase currents of the motor, that a collected as test samples and sent to the fault diagnosis method.
The testing results are presented in Figure 19.The average classification accuracy the proposed model is 89.4%,where 90.7% are for normal state and 88.1% for sens malfunction.When a failure occurs in the actual system, the current signals variation of the same property with that of the simulation data.In addition, only if multiple da sequences representing a fault are simultaneously detected, the working state can be d termined as a fault.Consequently, a satisfying fault diagnosis accuracy is still accessib The proposed model fails to retain the performance of the simulating experimental ou comes.This is due to the fact that the three-phase current of the motor in the actual sy tem contains noise, which can introduce measurement errors into the signals.Notab the variation of input signals merely results in a marginal drop of the classification acc racy, which indicates the stability of the proposed model.Since the proposed model able to classify faults on actual working systems by simulated data training, it is reaso able to expect better performance in practical use.The testing results are presented in Figure 19.The average classification accuracy of the proposed model is 89.4%,where 90.7% are for normal state and 88.1% for sensor malfunction.When a failure occurs in the actual system, the current signals variation is of the same property with that of the simulation data.In addition, only if multiple data sequences representing a fault are simultaneously detected, the working state can be determined as a fault.Consequently, a satisfying fault diagnosis accuracy is still accessible.The proposed model fails to retain the performance of the simulating experimental outcomes.This is due to the fact that the three-phase current of the motor in the actual system contains noise, which can introduce measurement errors into the signals.Notably, the variation of input signals merely results in a marginal drop of the classification accuracy, which indicates the stability of the proposed model.Since the proposed model is able to classify faults on actual working systems by simulated data training, it is reasonable to expect better performance in practical use.

Discussion
The data detected from an actual EMA system is also sent to more fault diagnosis methods for working performance comparison.To be specific, the recurrent neural network (RNN) and the long short-term memory (LSTM) are taken to substitute the GRU in the proposed model.The fault classification results are given in Table 3. Apparently, our model outperforms RNN on the average classification accuracy.By contrast, the application of LSTM has a slightly better performance than our model.Both LSTM and GRU are the variants of basic RNN.Thus, it is acceptable that the outcomes of LSTM-and GRU-based models are comparable.With more training data detected, the model can be developed in a more effective way, as it is the case.

Conclusions
This paper proposed a methodology on the task of EMA fault diagnosis.A virtual model of EMA which is in line with the actual EMA, is first developed to simulate its working states.The fault data corresponding to the actual failures in EMA are then injected into the EMA simulator to generate fault signals for processing.Moreover, a deeplearning-based approach is developed for the diagnosis of faults based on working states classification.In this fault diagnosis model, the GRU cells are used to capture the characteristics of different states while a co-attention network is used to remove the unrelated features and integrate the discriminative information.The performance of the proposed model is validated on three categories of working states.The experimental re-

Discussion
The data detected from an actual EMA system is also sent to more fault diagnosis methods for working performance comparison.To be specific, the recurrent neural network (RNN) and the long short-term memory (LSTM) are taken to substitute the GRU in the proposed model.The fault classification results are given in Table 3. Apparently, our model outperforms RNN on the average classification accuracy.By contrast, the application of LSTM has a slightly better performance than our model.Both LSTM and GRU are the variants of basic RNN.Thus, it is acceptable that the outcomes of LSTM-and GRU-based models are comparable.With more training data detected, the model can be developed in a more effective way, as it is the case.

Conclusions
This paper proposed a methodology on the task of EMA fault diagnosis.A virtual model of EMA which is in line with the actual EMA, is first developed to simulate its working states.The fault data corresponding to the actual failures in EMA are then injected into the EMA simulator to generate fault signals for processing.Moreover, a deep-learning-based approach is developed for the diagnosis of faults based on working states classification.In this fault diagnosis model, the GRU cells are used to capture the characteristics of different states while a co-attention network is used to remove the unrelated features and integrate the discriminative information.The performance of the proposed model is validated on three categories of working states.The experimental results demonstrate that the proposed model achieves a higher accuracy (by 95.0%) for all the evaluation settings.Furthermore, the verification of the fault diagnosis model on actual EMA is also performed, which further confirms the efficiency in practical use.
Since the collection of all the failures of EMA is too complicated, it is impossible to detect faults of all the categories.The diagnosis of an increasing number of faults requires further studies.Although the proposed model can classify the working state of EMA due to the current simulation model and laboratory condition, the possibility of further accurate identification of more faults is still an open question.

Figure 4 .
Figure 4.The simulation model of EMA.

Figure 5 .
Figure 5. Simulation response to different inputs.(a) Response to step input; (b) Response to sinusoidal input.

Figure 8 .
Figure 8. Fault data of A-phase open circuit.(a) A-phase current; (b) B-phase current.(c) C-phase current.

Figure 12 .
Figure 12.Fault data of A-phase both IGBT open circuits.(a) A-phase current; (b) B-phase current.(c) C-phase current.

Figure 13 .
Figure 13.Fault data of displacement sensor open circuit.(a) A-phase current; (b) B-phase current.(c) C-phase current.

Figure 14 .
Figure 14.Fault data of velocity sensor open circuit.(a) A-phase current; (b) B-phase current.(c) C-phase current.

Figure 17 .Figure 17 .Figure 18 .
Figure 17.Time domain analysis of simulated and actual EMA.(a) Response to a 1 Hz sinusoidal signal; (b) response error.

Figure 18 .
Figure 18.Frequency domain analysis of simulated and actual EMA.(a) Amplitude margin; (b) phase margin.

Figure 19 .
Figure 19.Experimental results obtained on the actual EMA.

Figure 19 .
Figure 19.Experimental results obtained on the actual EMA.

Table 1 .
Specifications for EMA model simulation.

Table 2 .
Fault diagnosis accuracy.Among all the evaluation settings, the motor driver open circuit diagnosis has the best and most consistent performance compared to that of the other methods.The accuracy of the motor driver open circuit classification ranges between 98.0% and 98.6%.The bestperforming outcome in this group is the diagnosis of the A-phase upper-bridge IGBT open circuit.The results obtained on motor stator open circuit range from 97.5% to 98.0%, and therefore they are slightly lower than those obtained on motor driver open circuit.In addition, the diagnosis accuracy of sensor malfunction and normal state are 95.9% and 97.8%, respectively.Consequently, the experimental results in Table

Table 3 .
Fault classification accuracy of different algorithm.

Table 3 .
Fault classification accuracy of different algorithm.