This work was supported by the Chinese Civil Aircraft Project (No. MJ-2017-S49) and the China
Postdoctoral Science Foundation (No. 2021M700331).

1. Establishment of the EHA simulation model
<ol>
	<li>Open the simulation software on a PC.</li>
	<li>Build the simulation model for the EHA (Figure 2), according to the mathematical equations of the EHA model15, and conduct a three-loop PI as the controller. Encapsulate the hydraulic module (Figure 2C), electrical module (Figure 2B), and controller (Figure 2B, D) in three submodels. 
	NOTE: The mathematical equations of the EHA model are as follows in Eq (1): 
	<img alt="Equation 1" src="/files/ftp_upload/63575/63575eq01.jpg" style="margin: auto;" /> (1) 
	In this equation, Ue is the voltage of the armature, Ke is the back electromotive force coefficient of the motor, &#969;m is the rotational speed of the motor, L is the equivalent inductance of the armature, i is the current of the winding, R is the resistance of the winding, Kt is the torque coefficient of the motor, Jm is the rotor moment of inertia, Bm is the friction coefficient of the motor, q is the displacement of the pump, Pf&#160;is the pressure difference between the two chambers in the hydraulic cylinder, A is the effective area of the piston, x is the position of the piston rod, V0 is the effective cavity volume of the hydraulic cylinder, B is the bulk modulus of the hydraulic oil, Kil is the total internal leakage coefficient of the system, M is the mass of the piston and the load, Kf is the viscous damping coefficient of the hydraulic cylinder, and Fex is the external load force.</li>
	<li>Program the adaptive filter based on an NLMS algorithm in an M file, which can be called at runtime. 
	NOTE: The derivation of the adaptive filter based on the NLMS algorithm is shown here. The electromechanical faults can be judged by identifying the winding resistance, and the discretized motor equation is as follows: 
	<img alt="Equation 2" src="/files/ftp_upload/63575/63575eq02.jpg" style="margin: auto;" />&#160; &#160;(2) 
	In this formula, ts is the sampling time, and R(k) and L(k) are the parameters that need to be identified. Eq (2)&#160;can be written as follows: 
	<img alt="Equation 3" src="/files/ftp_upload/63575/63575eq03.jpg" style="margin: auto;" />&#160; &#160;(3) 
	In this formula, <img alt="Equation 4" src="/files/ftp_upload/63575/63575eq04.jpg" style="margin: auto;" /> 
	By adding two items for the parameter vector &#952;(k), the sampling time, ts, can be eliminated to obtain the resistance, R(k). When any one of the three-phase windings fails, R(k) deviates from the normal value. 
	An adaptive filter can be constructed from Eq (3), and the estimation error of the filter is as follows: 
	<img alt="Equation 5" src="/files/ftp_upload/63575/63575eq05.jpg" style="margin: auto;" />&#160; &#160;(4) 
	In this formula, e(k) is a fluctuating random signal. When e(k) is small enough, the estimated value of the filter is &#375;(k). Finally, if it can converge to the real output, y(k), of the system, then the parameter vector &#952;(k) converges to the real system parameters. 
	The least mean square (LMS) algorithm takes the minimum mean square error as the criterion to realize the optimal prediction and filtering. Perform an automatic iterative adjustment to make &#952;(k) converge to the true value of the system. The expression of the cost function is as follows: 
	<img alt="Equation 6" src="/files/ftp_upload/63575/63575eq06.jpg" style="margin: auto;" />&#160; &#160;(5) 
	In this formula, <img alt="Equation 7" src="/files/ftp_upload/63575/63575eq07.jpg" style="margin: auto;" /> 
	Q(k) is the cross-correlation vector of y(k) and x(k). R(k) is the auto-correlation matrix of the input vector. 
	According to the steepest descent method, the recurrence formula for &#952;(k) approaching the optimal solution is as follows: 
	<img alt="Equation 8" src="/files/ftp_upload/63575/63575eq08.jpg" style="margin: auto;" />&#160; &#160;(6) 
	In this formula, &#181; is the adaptive variable step size. In the actual iterative process, the values of the current sampling point are used to estimate Q(k) and R(k), which can be expressed as <img alt="Equation 23" src="/files/ftp_upload/63575/63575eq23.jpg" style="margin: auto;" /> and <img alt="Equation 24" src="/files/ftp_upload/63575/63575eq24.jpg" style="margin: auto;" />. 
	Then, the LMS algorithm can be simplified as follows: 
	<img alt="Equation 9" src="/files/ftp_upload/63575/63575eq09.jpg" style="margin: auto;" />&#160; &#160;(7) 
	The LMS algorithm can make &#952;(k) gradually converge to the real system parameters. 
	In practical applications, the NLMS algorithm is usually used to overcome the slow convergence speed of the LMS algorithm. The constraint of the NLMS algorithm is as follows: 
	<img alt="Equation 10" src="/files/ftp_upload/63575/63575eq10.jpg" style="margin: auto;" />&#160; &#160;(8) 
	With the use of the Lagrange multiplier method to solve the constrained optimization problem, the cost function is as follows: 
	<img alt="Equation 11" src="/files/ftp_upload/63575/63575eq11.jpg" style="margin: auto;" /> 
	<img alt="Equation 12" src="/files/ftp_upload/63575/63575eq12.jpg" style="margin: auto;" />&#160; &#160;(9) 
	In this formula,&#160;&#955; is the Lagrange coefficient. In order to find the minimum value of J(k), find the partial derivative of J(k) to &#952;(k) and set it equal to 0. Calculate the solution as follows: 
	<img alt="Equation 13" src="/files/ftp_upload/63575/63575eq13.jpg" style="margin: auto;" />&#160; &#160;(10) 
	Put Eq (10) into Eq (8), and then get the solution of &#955; as follows: 
	<img alt="Equation 14" src="/files/ftp_upload/63575/63575eq14.jpg" style="margin: auto;" />&#160; &#160;(11) 
	<img alt="Equation 15" src="/files/ftp_upload/63575/63575eq15.jpg" style="margin: auto;" />&#160; &#160;(12) 
	In order to control the incremental change in the parameter vector, a step factor, &#946;, is introduced into this formula, and the expression is as follows: 
	<img alt="Equation 16" src="/files/ftp_upload/63575/63575eq16.jpg" style="margin: auto;" />&#160; &#160;(13) 
	At the same time, in order to avoid the difficulty of numerical calculation due to the small input vector, a relatively small positive constant, &#947;, is introduced. Li et al. proved that when 0 &#60; &#946; &#60; 2 and 0 &#60; &#947; &#60; 1, the NLMS algorithm can achieve better convergence effects16. The final expression is as follows: 
	<img alt="Equation 17" src="/files/ftp_upload/63575/63575eq17.jpg" style="margin: auto;" />&#160; &#160;(14)</li>
	<li>Program the rotational speed estimation algorithm in an M file, which can be called at runtime. 
	NOTE: The derivation of the rotational speed estimation algorithm is shown here. The flow equation of the actuator can be written as follows: 
	<img alt="Equation 18" src="/files/ftp_upload/63575/63575eq18.jpg" style="margin: auto;" />&#160; &#160;(15) 
	When the hydraulic unit is working in a normal condition, the total flow loss, Qf, caused by oil compression and leakage can be approximately expressed as follows: 
	<img alt="Equation 19" src="/files/ftp_upload/63575/63575eq19.jpg" style="margin: auto;" />&#160; &#160;(16) 
	In this formula, &#951; is the volumetric efficiency of the EHA. 
	Thus, the approximate analytical relationship between the speed, &#969;m, and the displacement, x, can be obtained as follows: 
	<img alt="Equation 20" src="/files/ftp_upload/63575/63575eq20.jpg" style="margin: auto;" />&#160; &#160;(17) 
	The discretized rotational speed estimation error equation is as follows: 
	<img alt="Equation 21" src="/files/ftp_upload/63575/63575eq21.jpg" style="margin: auto;" /> 
	In this formula, e&#969;m(k) is the estimated rotational speed error and <img alt="Equation 22" src="/files/ftp_upload/63575/63575eq22.jpg" style="margin: auto;" /> is the estimated rotational speed. Changes in e&#969;m(k) reflect the working condition of the hydraulic unit. When e&#969;m(k) suddenly deviates from the normal value, it means that the condition of the hydraulic unit is abnormal, which can be used to detect hydraulic faults online.</li>
	<li>Build the fault injection module and provide fault injection switches (Figure 2E, F), which can decide whether to inject a fault.</li>
	<li>Set the parameters of the simulation model according to Table 1 by double-clicking the specific component in each submodel.</li>
	<li>Program the drawing software, which can draw simulation curves after completing a group of experiments.</li>
</ol>
2. Simulation of the fault detection methods
<ol>
	<li>Give a position command, which is a sinusoid with an amplitude of 0.01 m and a frequency of 1 Hz.</li>
	<li>Enter the MODELING menu and click the Model Settings button. Set the simulation operation parameters: a Start time of 0 s, a Stop time of 6 s, the Type as Variable-step, and the solver as auto.</li>
	<li>Double-click the fault injection switches to set the model to work in a non-fault condition.</li>
	<li>Click the Run button to run the simulation and receive the non-fault condition results.</li>
	<li>Run the drawing software to draw the curve of the piston rod displacement.</li>
	<li>Double-click the insert electromechanical fault switch to inject an electromechanical fault at 3 s, which sets the resistance to 1,000 &#937; to simulate an open-circuit fault of the motor windings.</li>
	<li>Repeat step 2.4 and step 2.5 to attain the results for the electromechanical fault condition. Run the drawing software to draw the curves of the piston rod displacement and identified resistance.</li>
	<li>Turn the insert hydraulic fault switch to inject a hydraulic fault at 3 s, which increases the leakage value to 2.5 &#215; 10&#8722;9 (m3/s)/Pa to simulate a hydraulic unit fault.</li>
	<li>Repeat step 2.3 and step 2.4 to attain the results for the hydraulic fault condition. Run the drawing software to draw the curves of the piston rod displacement and rotational speed estimation results.</li>
</ol>
3. Establishment of the experimental platform (Figure 3)
<ol>
	<li>Set the PC, EHA, and servo controller in position. The EHA is shown in Figure 4, and the servo controller is shown in Figure 5.</li>
	<li>Wire the electrical parts.
	<ol>
		<li>Connect the EHA sensors to the sensor ports for the servo controller via several aviation plugs.</li>
		<li>Connect the EHA motor drive port to the inverter port for the servo controller via the aviation plug.</li>
		<li>Connect the servo controller to the control power and the drive power via the aviation plug. 
		CAUTION: Turn off the voltage temporarily for safety.</li>
	</ol>
	</li>
	<li>Establish communication between the servo controller and the PC.
	<ol>
		<li>Open the Host Software Interface (Figure 6) on the PC.</li>
		<li>Connect the PC and the servo controller through a 422-to-USB serial cable to set up the communication.</li>
		<li>Provide control power to the servo controller. The control power voltage is 24 V DC.</li>
		<li>Select the appropriate serial port from the VISA Resource Name drop-down window in the software. 
		NOTE: If communication is not successfully established, check the cable or restart the software until RS422 communication is established.</li>
		<li>Click the Run button to start the software.</li>
		<li>Observe the receiving area and the corresponding curves of the software to determine whether the data receiving function is normal. Click the Solenoid Valve 1 button to observe whether the solenoid valve has a pull-in sound, and determine whether the data transmission function is normal.</li>
	</ol>
	</li>
</ol>
4. Experiment for the fault detection method
<ol>
	<li>Provide drive power to the servo controller and set the voltage to 50 V&#160;DC. 
	NOTE: A 50 V DC undervoltage operation ensures safe work since the system is load-free.</li>
	<li>Click the EHA Switch button on the software to set the EHA at a running state. Click the Data Log button to start data logging. The recorded data include the actual position, the target position, the actual speed, the target speed, the bus current, the voltage, etc.</li>
	<li>Conduct a pre-run for the EHA. Give position commands on the software, which include a step of +0.005 m and -0.005 m. Observe whether the EHA is actuating normally. 
	CAUTION: If the EHA does not work normally, check the error immediately before continuing this experiment.</li>
	<li>Give a position command on the software, which is a sinusoid with an amplitude of 0.01 m and a frequency of 1 Hz.</li>
	<li>Observe whether the identified resistance and the estimated rotational speed are consistent with the values under non-fault operating conditions.</li>
	<li>Put the position command back to the original state if the result is correct. Click the EHA Switch button to stop the EHA and cut off the drive power, stop the host computer software, and interrupt the communication between the servo controller and the PC.</li>
	<li>Export the experimental data, analyze the data, and draw curves of the experimental results using drawing software.</li>
	<li>Analyze the experimental results, and compare them with the simulation results to derive conclusions.</li>
</ol>

<ol>
	<li>Fu, Y., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Review+on+design+method+of+electro-hydrostatic+actuator.">Review on design method of electro-hydrostatic actuator.</a> Journal of Beijing University of Aeronautics and Astronautics. 43 (10), 1939-1952 (2017).</li><li>Qi, H., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Modelling+and+simulation+of+a+novel+dual-redundancy+electro-hydrostatic+actuator.">Modelling and simulation of a novel dual-redundancy electro-hydrostatic actuator.</a> 2015 International Conference on Fluid Power and Mechatronics (FPM) IEEE. , 270-275 (2015).</li><li>Chao, Q., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Integrated+slipper+retainer+mechanism+to+eliminate+slipper+wear+in+high-speed+axial+piston+pumps.">Integrated slipper retainer mechanism to eliminate slipper wear in high-speed axial piston pumps.</a> Frontiers of Mechanical Engineering. 17, (2022).</li><li>Yoo, M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+resilience+measure+formulation+that+considers+sensor+faults.">A resilience measure formulation that considers sensor faults.</a> Reliability Engineering&amp; System Safety. 199, 106393 (2019).</li><li>Fang, J., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Online+inverter+fault+diagnosis+of+buck-converter+BLDC+motor+combinations.">Online inverter fault diagnosis of buck-converter BLDC motor combinations.</a> IEEE Transactions on Power Electronics. 30 (5), 2674-2688 (2015).</li><li>Lisnianski, A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Power+system+structure+optimization+subject+to+reliability+constraints.">Power system structure optimization subject to reliability constraints.</a> Electric Power Systems Research. 39 (2), 145-152 (1996).</li><li>Fu, T., Wang, L., Qi, H., Liu, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Fault+diagnosis+and+management+of+electric+hydrostatic+actuator.">Fault diagnosis and management of electric hydrostatic actuator.</a> Machine Tool &amp; Hydraulics. 38 (9), 120-124 (2010).</li><li>Maddahi, A., Kinsner, W., Sepehri, N. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Internal+leakage+detection+in+electrohydrostatic+actuators+using+multiscale+analysis+of+experimental+data.">Internal leakage detection in electrohydrostatic actuators using multiscale analysis of experimental data.</a> IEEE Transactions on Instrumentation and Measurement. 65 (12), 2734-2747 (2016).</li><li>Guo, S., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Hydraulic+piston+pump+in+civil+aircraft:+Current+status,+future+directions+and+critical+technologies.">Hydraulic piston pump in civil aircraft: Current status, future directions and critical technologies.</a> Chinese Journal of Aeronautics. 33 (01), 16-30 (2020).</li><li>Jackson, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Real-time+model-based+fault+detection+and+diagnosis+for+automated+systems.">Real-time model-based fault detection and diagnosis for automated systems.</a> IEEE Industry Applications Society Dynamic Modeling Control Applications for Industry Workshop. , 26-28 (1997).</li><li>Alcorta, G. E., Zolghadri, A., Goupil, P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+novel+non-linear+observer-based+approach+to+oscillatory+failure+detection.">A novel non-linear observer-based approach to oscillatory failure detection.</a> 2009 European Control Conference (ECC). , 1901-1906 (2009).</li><li>Castaldi, P., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Design+of+residual+generators+and+adaptive+filters+for+the+FDI+of+aircraft+model+sensors.">Design of residual generators and adaptive filters for the FDI of aircraft model sensors.</a> Control Engineering Practice. 18 (5), 449-459 (2010).</li><li>Zhu, P., Dong, W., Mao, Y., Shi, H., Ma, X. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Kernel+adaptive+filtering+multiple-model+actuator+fault+diagnostic+for+multi-effectors+aircraft.">Kernel adaptive filtering multiple-model actuator fault diagnostic for multi-effectors aircraft.</a> 2019 12th Asian Control Conference (ASCC). , 1489-1494 (2019).</li><li>Hidayat, R., Ramady, G. D., Lestari, N. S., Mahardika, A. G., Fadriani, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optimization+of+normalized+least+mean+square+algorithm+of+smart+antenna+beamforming+for+interference+mitigation.">Optimization of normalized least mean square algorithm of smart antenna beamforming for interference mitigation.</a> Journal of Physics: Conference Series. 1783, 012085 (2021).</li><li>Fu, J., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Modelling+and+simulation+of+flight+control+electromechanical+actuators+with+special+focus+on+model+architecting,+multidisciplinary+effects+and+power+flows.">Modelling and simulation of flight control electromechanical actuators with special focus on model architecting, multidisciplinary effects and power flows.</a> Chinese Journal of Aeronautics. 30 (1), 47-65 (2017).</li><li>Li, Z., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=New+normalized+LMS+adaptive+filter+with+a+variable+regularization+factor.">New normalized LMS adaptive filter with a variable regularization factor.</a> Journal of Systems Engineering and Electronics. 30 (2), 259-269 (2019).</li></ol>

The authors declare that they have no known competing financial interests or personal relationships that could influence the work reported in this paper.

When conducting these experimental steps, it was important to ensure the real-time capability of the algorithm in order to obtain accurate calculation results. The white noise in the signal acquisition process was adopted to simulate the characteristics of the actual sensor in order to make the simulation closer to reality. In the simulations and experiments, moving average filters were applied to reduce the fluctuation in the identified resistance and estimated rotational speed, which made the fault characteristics more...

The electro-hydrostatic actuator (EHA) is a key component for flight control in more electric aircraft (MEA). The typical structure of an EHA is shown in Figure 1. Its compact structure guarantees high power density, low maintenance, and higher fault tolerance and safety compared with the traditional hydraulic servo actuator (HSA)1. However, the current reliability of the EHA cannot meet the practical requirements of more electric aircraft2. As a result, redundancy technology has been introduced into the design of the EHA. To maximize the effectiveness of the redundancy technology, the operating status of the system should be monitored by a fault detection method3. According to the location where the fault occurs, the fault modes of the EHA can be divided into servo controller faults and power control unit (PCU) faults. PCU faults can be further divided into sensor faults, electromechanical unit faults, and hydraulic unit faults. The fault mechanism of the servo controller has little relationship with the EHA body, and the fault probability of the sensor is much lower than that of the equipment component4. Therefore, we focus on the faults of the electromechanical unit and hydraulic unit in this paper.
Electromechanical unit faults include motor drive module faults and brushless DC motor (BLDCM) faults. Generally, the probability of a power drive electronics (PDE) fault (e.g., a short-circuit fault, an open-circuit fault) is relatively high. When a short-circuit fault occurs, the PDE current rises sharply in a short amount of time, causing severe consequences such as a motor shutdown or damage to the electrical components. Although the motor can maintain its working status after an open-circuit fault occurs, overcurrent and overvoltage for the other electrical components are still inevitable, and secondary faults may consequently happen5. As for the BLDCMs, the motor windings are most prone to faults from a short circuit or an open circuit6. The PDE in the electromechanical unit is connected in series with the corresponding motor windings. The fault detection method designed for the motor windings is also effective when dealing with faults in the PDE. Therefore, electromechanical unit faults, including both in the motor and the PDE, should be detected online.
Hydraulic unit faults include fault occurrences in the fixed-displacement piston pump, integrated valve block, and actuating cylinder7. The EHA&#39;s piston pump is composed of pistons, swash plates, and valve plates; damage to the seal and wear of the valve plate are the main forms of fault8. These two fault modes increase the leakage of the pump. Abnormal changes in the output flow and pressure follow and, eventually, lead to a decrease in the speed of the actuating cylinder and a reduction in the servo performance of the system. The fault modes of the integrated valve block include a pressurized reservoir fault, a check valve fault, a relief valve fault, and a mode selection valve fault. The pressurized reservoir usually adopts a self-boosting design with high reliability. When a fault occurs, however, insufficient charge pressure causes cavitation of the pump, resulting in abnormal output flow. Spring fatigue, component wear, and deformation are common fault modes in the check valves and relief valves. A check valve fault presents as a reverse leakage, which directly leads to abnormal flow. A relief valve fault leads to an invalid protection function, resulting in abnormal pressure. The common faults of the mode selection valve are failure of the return spring and broken wire coils. The former causes in-current switching of the working status, leading to abnormal movement of the actuating cylinder. An actuating cylinder fault results in a decrease in position control precision and dynamic performance. In summary, faults of the hydraulic units cause abnormal flow and pressure9. Since the flow and motor rotational speed are approximately proportional in an EHA system, the rotational speed can be monitored online to detect abnormal flow and pressure due to sudden faults.
Corresponding fault detection methods aimed at the previously mentioned electromechanical unit faults and hydraulic unit faults need to be designed. The methods for fault detection in an electromechanical system mainly include state estimation and parameter identification10. A state observer is built on the basis of a mathematical model of the system that makes a state estimation and determines faults by analyzing the residual sequence generated by the observer. Alcorta et al. proposed a simple and novel nonlinear observer with two correction terms for vibration fault detection in commercial aircraft, which is highly effective11. However, this type of method must solve the robustness problem of the observer. In other words, it must suppress the changes in the residual sequence caused by non-fault information such as model error or external disturbances. Moreover, this method often requires very accurate model information, which is usually difficult to collect in practical engineering applications.
The parameter identification method employs certain algorithms for identifying the important parameters in the system. When a fault occurs, the corresponding parameter value also changes. Therefore, faults can be detected by detecting a change in the parameters. The parameter identification method does not require the calculation of the residual sequence, so it can avoid the effect of disturbances on the detection accuracy. The adaptive filter has been widely used in parameter identification due to its easy implementation and stable performance, meaning it is a favorable and feasible method for electromechanical fault detection12. Zhu et al. proposed a new multi-model adaptive estimation fault detection method based on kernel adaptive filters, which realizes the estimation of the real flight state value and the actuator fault detection online with good performance13.
Referring to the previous research, corresponding fault detection methods have been designed. The resistance of the windings abruptly changes when electrical faults occur, such as open-circuit faults or short-circuit faults. Therefore, an adaptive filter was designed based on an NLMS algorithm to identify the resistance of the windings, which can determine whether an electrical fault has occurred. Combining an adaptive filter with an NLMS algorithm to minimize the change of the parameter vector leads to a better and faster convergence effect14. For hydraulic unit faults, a rotational speed estimation algorithm was proposed based on the clear analytical relationship between the rotational speed of the pump and the position of the actuating cylinder. EHA hydraulic faults were detected online by comparing the estimated rotational speed with the actual speed in real time.
In this paper, a test method combining simulations and experiments was adopted. First, a mathematical model of the EHA was built, and a simulation for the proposed fault detection method was performed. The simulation included the verification of the detection methods in non-fault and fault injection conditions. Then, the fault detection method was realized in the real servo controller. Finally, the results of the simulations and experiments were analyzed and compared to evaluate the efficacy of the fault detection method.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>LabVIEW</td>
			<td>NI</td>
			<td>NI LabVIEW 2018</td>
			<td></td>
		</tr>
		<tr>
			<td>Matlab/SIMULINK</td>
			<td>MathWorks.Inc</td>
			<td>R2020a</td>
			<td></td>
		</tr>
		<tr>
			<td>Personal Computer</td>
			<td>Lenovo</td>
			<td>Y7000 2020H</td>
			<td></td>
		</tr>
		<tr>
			<td>24V Switching Power Supply</td>
			<td>ECNKO</td>
			<td>S-250-24</td>
			<td></td>
		</tr>
		<tr>
			<td>Programmable Current Source</td>
			<td>Greens Pai</td>
			<td>GDP-50-30</td>
			<td></td>
		</tr>
	</tbody>
</table>

design and application of a fault detection method based on adaptive filters and rotational speed estimation for an electro-hydrostatic actuator

The electro-hydrostatic actuator (EHA) is a promising actuating apparatus used in flight control systems for more electric aircraft (MEA) due to its high power density and low maintenance. Since the reliability of the system decreases with increasing complexity, fault detection is becoming increasingly important. In this paper, an adaptive filter was designed based on a normalized least mean square (NLMS) algorithm, which could identify the resistance of the motor windings online to detect electrical faults in the EHA. Additionally, based on the analytical relationship between rotational speed and displacement, a rotational speed estimation method was designed. By comparing the actual rotational speed with the estimated one, hydraulic faults could be detected. To verify the efficacy of the aforementioned method, software was applied for the modeling and simulations, which included fault injection and detection. On this basis, an experimental platform was built and then subjected to a series of validation experiments. The results indicate that the fault detection method has the potential to detect electrical and hydraulic faults in an EHA.

In the simulation, the actual position and target position curve of the EHA piston rod in the non-fault condition is shown in Figure 7. According to the curve, the system was operating normally, with good dynamic characteristics. The actual position and target position curve of the EHA piston rod in the electromechanical fault injection condition is shown in Figure 8. According to the curve, the system could not track the target accurately. The results of the re...

Watch this Scientific Journal Video about Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator at JoVE.com

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

In this paper, an adaptive filter based on a normalized least mean square (NLMS) algorithm and a rotational speed estimation method are introduced to detect the electrical and hydraulic faults of the electro-hydrostatic actuator (EHA). The efficacy and feasibility of the aforementioned methods are verified through simulations and experiments.

The electro-hydrostatic actuator (EHA) is a promising actuating apparatus used in flight control systems for more electric aircraft (MEA) due to its high ...

design-application-fault-detection-method-based-on-adaptive-filters

Research

Education

JoVE Journal

JoVE Core

Electrical Engineering

Mechanical Engineering

Engineering

Unit 1

Symmetrical and Unsymmetrical Faults

Energy Methods

SCIENTISTS IN ACTION

1.5K Views.  Beihang University. Обнаружение неисправностей является ключевой технологией для проверки практичности электрогидростатического привода, также известного как EHA. Этот протокол обладает эффективным методом проектного эксперимента для обнаружения неисправностей EHA. Этот протокол сочета?...

Video: Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Visualization of High Speed Liquid Jet Impaction on a Moving Surface

Two apparatuses for examining liquid jet impingement on a high-speed moving surface are described: an air cannon device (for examining surface speeds between 0 and 25 m/sec) and a spinning disk device (for examining surface speeds between 15 and 100 m/sec). The air cannon linear traverse is a pneumatic energy-powered system that is designed to accelerate a metal rail surface mounted on top of a wooden projectile. A pressurized cylinder fitted with a solenoid valve rapidly releases pressurized air into the barrel, forcing the projectile down the cannon barrel. The projectile travels beneath a spray nozzle, which impinges a liquid jet onto its metal upper surface, and the projectile then hits a stopping mechanism. A camera records the jet impingement, and a pressure transducer records the spray nozzle backpressure. The spinning disk set-up consists of a steel disk that reaches speeds of 500 to 3,000 rpm via a variable frequency drive (VFD) motor. A spray system similar to that of the air cannon generates a liquid jet that impinges onto the spinning disc, and cameras placed at several optical access points record the jet impingement. Video recordings of jet impingement processes are recorded and examined to determine whether the outcome of impingement is splash, splatter, or deposition. The apparatuses are the first that involve the high speed impingement of low-Reynolds-number liquid jets on high speed moving surfaces. In addition to its rail industry applications, the described technique may be used for technical and industrial purposes such as steelmaking and may be relevant to high-speed 3D printing.

Two experimental devices for examining liquid jet impingement on a high-speed moving surface are described: an air cannon device and a spinning disk device. The apparatuses are used to determine optimal approaches to the application of liquid friction modifier (LFM) onto rail tracks for top-of-rail friction control.

Two apparatuses for examining liquid jet impingement on a high-speed moving surface are described: an air cannon device (for examining surface speeds ...

A High Performance Impedance-based Platform for Evaporation Rate Detection

This paper describes the method of a novel impedance-based platform for the detection of the evaporation rate. The model compound hyaluronic acid was employed here for demonstration purposes. Multiple evaporation tests on the model compound as a humectant with various concentrations in solutions were conducted for comparison purposes. A conventional weight loss approach is known as the most straightforward, but time-consuming, measurement technique for evaporation rate detection. Yet, a clear disadvantage is that a large volume of sample is required and multiple sample tests cannot be conducted at the same time. For the first time in literature, an electrical impedance sensing chip is successfully applied to a real-time evaporation investigation in a time sharing, continuous and automatic manner. Moreover, as little as 0.5 ml of test samples is required in this impedance-based apparatus, and a large impedance variation is demonstrated among various dilute solutions. The proposed high-sensitivity and fast-response impedance sensing system is found to outperform a conventional weight loss approach in terms of evaporation rate detection.

This paper presents an impedance-based apparatus for evaporation rate detection of solutions. It offers clear advantages over a conventional weight loss approach: a fast response, high-sensitivity detection, a small sample requirement, multiple sample measurements, and easy disassembly for cleaning and reuse purposes.

This paper describes the method of a novel impedance-based platform for the detection of the evaporation rate. The model compound hyaluronic acid was ...

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Here, we demonstrate the advantages of the laser Doppler vibrometer (LDV) over conventional techniques (the network analyzer), as well as the techniques to create an application-based microelectromechanical systems (MEMS) filter and how to use it efficiently (i.e., tuning the tuning-capability and avoiding both failure and stiction). LDV enables crucial measurements that are impossible with the network analyzer, such as higher mode detection (highly sensitive biosensor application) and resonance measurement for very small devices (fast prototyping). Accordingly, LDV was used to characterize the frequency tuning range and resonance frequency at different modes of the MEMS filters built for this study. This wide range frequency tuning mechanism is based simply on Joule heating from the embedded heaters and relatively high thermal stress with respect to the temperature of a fixed-fixed beam. However, we demonstrate that another limitation of this method is the resulting high thermal stress, which can burn the devices. Further improvement was achieved and shown for the first time in this study, such that the tuning capability was increased by 32% through an increase in the applied DC bias voltage (25 V to 35 V) between the two adjacent beams. This important finding eliminates the need for the extra Joule heating at the wider frequency tuning range. Another possible failure is through stiction and requirement of structure optimization: We propose a simple and easy technique of low frequency square wave signal application that can successfully separate the beams and eliminates the need for the more sophisticated and complicated methods given in the literature. The above findings necessitate a design methodology, and so we also provide an application-based design.

A protocol for a fixed-fixed beam design using a laser Doppler vibrometer (LDV), including the measurement of frequency tuning, modification of tuning capability, and avoidance of device failure and stiction, is presented. The superiority of the LDV method over the network analyzer is demonstrated due to its higher mode capability.

Here, we demonstrate the advantages of the laser Doppler vibrometer (LDV) over conventional techniques (the network analyzer), as well as the techniques ...

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Intelligent robots are part of a new generation of robots that are able to sense the surrounding environment, plan their own actions and eventually reach their targets. In recent years, reliance upon robots in both daily life and industry has increased. The protocol proposed in this paper describes the design and production of a handling robot with an intelligent search algorithm and an autonomous identification function.
First, the various working modules are mechanically assembled to complete the construction of the work platform and the installation of the robotic manipulator. Then, we design a closed-loop control system and a four-quadrant motor control strategy, with the aid of debugging software, as well as set steering gear identity (ID), baud rate and other working parameters to ensure that the robot achieves the desired dynamic performance and low energy consumption. Next, we debug the sensor to achieve multi-sensor fusion to accurately acquire environmental information. Finally, we implement the relevant algorithm, which can recognize the success of the robot&#39;s function for a given application.
The advantage of this approach is its reliability and flexibility, as the users can develop a variety of hardware construction programs and utilize the comprehensive debugger to implement an intelligent control strategy. This allows users to set personalized requirements based on their needs with high efficiency and robustness.

We present a protocol on modular design and production of intelligent robots to help scientific and technical workers design intelligent robots with special production tasks based on personal needs and individualized design.

Intelligent robots are part of a new generation of robots that are able to sense the surrounding environment, plan their own actions and eventually reach ...

A Fabrication and Measurement Method for a Flexible Ferroelectric Element Based on Van Der Waals Heteroepitaxy

Flexible non-volatile memories have received much attention as they are applicable for portable smart electronic device in the future, relying on high-density data storage and low-power consumption capabilities. However, the high-quality oxide based nonvolatile memory on flexible substrates is often constrained by the material characteristics and the inevitable high-temperature fabrication process. In this paper, a protocol is proposed to directly grow an epitaxial yet flexible lead zirconium titanate memory element on muscovite mica. The versatile deposition technique and measurement method enable the fabrication of flexible yet single-crystalline non-volatile memory elements necessary for the next generation of smart devices.

In this paper, we present a protocol to directly grow an epitaxial yet flexible lead zirconium titanate memory element on muscovite mica.

Flexible non-volatile memories have received much attention as they are applicable for portable smart electronic device in the future, relying on ...

A Pipette-Tip Based Method for Seeding Cells to Droplet Microfluidic Platforms

Amongst various microfluidic platform designs frequently used for cellular analysis, droplet-microfluidics provides a robust tool for isolating and analyzing cells at the single-cell level by eliminating the influence of external factors on the cellular microenvironment. Encapsulation of cells in droplets is dictated by the Poisson distribution as a function of the number of cells present in each droplet and the average number of cells per volume of droplet. Primary cells, especially immune cells, or clinical specimens can be scarce and loss-less encapsulation of cells remains challenging. In this paper, we present a new methodology that uses pipette-tips to load cells to droplet-based microfluidic devices without the significant loss of cells. With various cell types , we demonstrate efficient cell encapsulation in droplets that closely corresponds to the encapsulation efficiency predicted by the Poisson distribution. Our method ensures loss-less loading of cells to microfluidic platforms and can be easily adapted for downstream single cell analysis, e.g., to decode cellular interactions between different cell types.

This article presents a protocol for seeding scarce population of cells using pipette-tips to droplet microfluidic devices in order to provide higher encapsulation efficiency of cells in droplets.

Amongst various microfluidic platform designs frequently used for cellular analysis, droplet-microfluidics provides a robust tool for isolating and ...

Application of Design Aspects in Uniaxial Loading Machine Development

In terms of accurate and precise mechanical testing, machines run the continuum. Whereas commercial platforms offer excellent accuracy, they can be cost-prohibitive, often priced in the $100,000 - $200,000 price range. At the other extreme are stand-alone manual devices that often lack repeatability and accuracy (e.g., a manual crank device). However, if a single use is indicated, it is over-engineering to design and machine something overly elaborate. Nonetheless, there are occasions where machines are designed and built in-house to accomplish a motion not attainable with the existing machines in the laboratory. Described in detail here is one such device. It is a loading platform that enables pure uniaxial loading. Standard loading machines typically are biaxial in that linear loading occurs along the axis and rotary loading occurs about the axis. During testing with these machines, a load is applied to one end of the specimen while the other end remains fixed. These systems are not capable of conducting pure axial testing in which tension/compression is applied equally to the specimen ends. The platform developed in this paper enables the equal and opposite loading of specimens. While it can be used for compression, here the focus is on its use in pure tensile loading. The device incorporates commercial load cells and actuators (movers) and, as is the case with machines built in-house, a frame is machined to hold the commercial parts and fixtures for testing.

Here we present a protocol to develop a pure uniaxial loading machine. Critical design aspects are employed to ensure accurate and reproducible testing results.

In terms of accurate and precise mechanical testing, machines run the continuum. Whereas commercial platforms offer excellent accuracy, they can be ...

Design and Fabrication of an Optical Fiber Made of Water

In this report, an optical fiber of which the core is made solely of water, while the cladding is air, is designed and manufactured. In contrast with solid-cladding devices, capillary oscillations are not restricted, allowing the fiber walls to move and vibrate. The fiber is constructed by a high direct current (DC) voltage of several thousand volts (kV) between two water reservoirs that creates a floating water thread, known as a water bridge. Through the choice of micropipettes, it is possible to control the maximal diameter and length of the fiber. Optical fiber couplers, at both sides of the bridge, activate it as an optical waveguide, allowing researchers to monitor the water fiber capillary body waves through transmission modulation and, therefore, deducing changes in surface tension.
Co-confining two important wave types, capillary and electromagnetic, opens a new path of research in the interactions between light and liquid-wall devices. Water-walled microdevices are a million times softer than their solid counterparts, accordingly improving the response to minute forces.

This protocol describes the design and manufacture of a water bridge and its activation as a water fiber. The experiment demonstrates that capillary resonances of the water fiber modulate its optical transmission.

In this report, an optical fiber of which the core is made solely of water, while the cladding is air, is designed and manufactured. In contrast with ...

Implementation of a Nonlinear Microscope Based on Stimulated Raman Scattering

Stimulated Raman scattering (SRS) microscopy uses near-infrared excitation light; therefore, it shares many multi-photon microscopic imaging properties. SRS imaging modality can be obtained using commercial laser-scanning microscopes by equipping with a non-descanned forward detector with proper bandpass filters and lock-in amplifier (LIA) detection scheme. A schematic layout of a typical SRS microscope includes the following: two pulsed laser beams, (i.e., the pump and probe directed in a scanning microscope), which must be overlapped in both space and time at the image plane, then focused by a microscope objective into the sample through two scanning mirrors (SMs), which raster the focal spot across an x-y plane. After interaction with the sample, transmitted output pulses are collected by an upper objective and measured by a forward detection system inserted in an inverted microscope. Pump pulses are removed by a stack of optical filters, whereas the probe pulses that are the result of the SRS process occurring in the focal volume of the specimen are measured by a photodiode (PD). The readout of the PD is demodulated by the LIA to extract the modulation depth. A two-dimensional (2D) image is obtained by synchronizing the forward detection unit with the microscope scanning unit. In this paper, the implementation of an SRS microscope is described and successfully demonstrated, as well as the reporting of label-free images of polystyrene beads with diameters of 3 &#181;m. It is worth noting that SRS microscopes are not commercially available, so in order to take advantage of these characteristics, the homemade construction is the only option. Since SRS microscopy is becoming popular in many fields, it is believed that this careful description of the SRS microscope implementation can be very useful for the scientific community.

In this manuscript, the implementation of a stimulated Raman scattering (SRS) microscope, obtained by the integration of an SRS experimental set-up with a laser scanning microscope, is described. The SRS microscope is based on two femtosecond (fs) laser sources, a Ti-Sapphire (Ti:Sa) and synchronized optical parametric oscillator (OPO).

Stimulated Raman scattering (SRS) microscopy uses near-infrared excitation light; therefore, it shares many multi-photon microscopic imaging properties. ...

Fabrication and Design of Wood-Based High-Performance Composites

Delignified densified wood is a new promising and sustainable material that possesses the potential to replace synthetic materials, such as glass fiber reinforced composites, due to its excellent mechanical properties. Delignified wood, however, is rather fragile in a wet state, which makes handling and shaping challenging. Here we present two fabrication processes, closed-mold densification and vacuum densification, to produce high-performance cellulose composites based on delignified wood, including an assessment of their advantages and limitations. Further, we suggest strategies for how the composites can be re-used or decomposed at the end-of-life cycle. Closed-mold densification has the advantage that no elaborate lab equipment is needed. Simple screw clamps or a press can be used for densification. We recommend this method for small parts with simple geometries and large radii of curvature. Vacuum densification in an open-mold process is suitable for larger objects and complex geometries, including small radii of curvature. Compared to the closed-mold process, the open-mold vacuum approach only needs the manufacture of a single mold cavity.

Delignified densified wood represents a new promising lightweight, high-performance and bio-based material with great potential to partially substitute natural fiber reinforced- or glass fiber reinforced composites in the future. We here present two versatile fabrication routes and demonstrate the possibility to create complex composite parts.

Delignified densified wood is a new promising and sustainable material that possesses the potential to replace synthetic materials, such as glass fiber ...