Intelligent Fault-Tolerant Control System Design and Semi-Physical Simulation Validation of Aero-Engine

In order to improve the reliability and real-time of the control system of aero-engine, an intelligent fault-tolerant control system based on the online sequential extreme learning machine (OS-ELM) is proposed against the sensor faults. This system can realize the online fault diagnosis and signal reconstruction without a system model. And while considering the traditional PID control robustness and poor anti-interference ability and other shortcomings, an improved global fast non-singular terminal sliding mode control method is used to obtain better control effects, effectively solve the uncertainty problem in aero-engine, and give full play to aero-engine performance. To verify the feasibility and effectiveness of this system based on the above method, a turbofan engine is taken as the research object and semi-physical simulation experiments on fault-tolerant control are conducted on a semi-physical simulation test platform. Results show that the controller of this system can safely and reliably control the aero-engine without losing its control performance under the circumstance that there are faults in engine sensors. The purpose of fault-tolerant control is reached.


I. INTRODUCTION
With the continuous development of the modern aero-engine control technology, the continuous improvement of performance has led to the continuous upgrade of system complexity, and its requirements of safety and reliability have become more stringent [1]. To ensure that the engine's full authority digital electronic controller (FADEC) can still maintain stable, efficient and safe operation of related sensors and actuators in an extremely harsh working environment, reduce the probability of system failure and improve the performance of aero-engines stability and reliability requires a series of research on fault diagnosis and fault-tolerant control methods [2]. When the relevant functional components of the FADEC system fail, real-time and accurate diagnosis of the fault and corresponding fault-tolerant control strategies will be an effective way to improve the reliability and safety of the The associate editor coordinating the review of this manuscript and approving it for publication was Xiwang Dong. engine, and it is also a work of very important engineering significance.
At present, the development of intelligent fault diagnosis technology promotes the progress of fault-tolerant control technology. Since the 1970s, foreign countries have carried out a series of research work on aero-engine fault-tolerant control technology. For example, Wallhagen and Arpasi [7] performed fault diagnosis by comparing the response difference of the engine output between step input and normal control, and on this basis, the fault sensor signal is reconstructed by the resolution margin to realize the fault tolerance of the rotational speed closed-loop control loop; Napolitano and Silvestri [8] proposed a sensor fault diagnosis and fault-tolerant control method based on online BP(Back Propagation) neural network. In recent years, Ahmed et al. [9] designed an adaptive fault-tolerant controller based on the C-130 aircraft fuel tank model; Chen et al. [10] developed a fault-tolerant integral sliding mode control scheme based on a large civil Boeing 747 engine model, which is through effective use of actuator redundancy to retain the nominal (fault-free) closed-loop performance when the actuator fails or faults. Seo et al. [11] proposed a design method of single-engined aircraft fault-tolerant control system to deal with the problem of the gradual loss of reasoning over time. In China, many researchers have also conducted in-depth research on fault-tolerant control. Zhang et al. [12] and Li et al. [13] designed a corresponding output state feedback fault-tolerant control system for uncertain nonlinear systems; Wang et al. [14] aimed at the landing process of aircraft with damaged vertical tail for the fault-tolerant control problem, an improved state-space feedback controller with variable element linear quadratic regulator (LQR) is proposed. Wu et al. [15] developed an adaptive fault-tolerant tracking control strategy for actuator faults in nonlinear systems with non-strict feedback forms. Li [16] and Ma et al. [17] designed fuzzy fault-tolerant control systems for nonlinear systems. Liu et al. [18] designed an adaptive finite-time fault-tolerant control method based on neural network algorithm for strict feedback nonlinear system.
In summary, with the rapid development of intelligent algorithms, the application of machine learning algorithms to the fault-tolerant control of aero-engines has become a development trend. However, it is basically still in the digital simulation stage [19], [20], regarding its semi-physical simulation experiments and studies considering the actual application of engineering are rarely involved in the literature. Extreme learning machine is a simple and efficient single hidden layer feedforward neural network proposed by Huang et al. [21] in recent years. Different from the traditional neural network [22], [23], a large number of network training parameters need to be manually set, and then iteratively optimized, the network output weight of ELM(Extreme Learning Machine) is directly obtained by the Moore-Penrose generalized inverse matrix theory, which makes the training speed of ELM significant improvement, which is not easy to cause problems such as over-fitting. To make ELM have the ability of online training, literature [24] proposed an online sequential extreme learning machine(OS-ELM), which can calculate the current weight output by recursively according to the output weight of the previous step, thereby realizing online training. Later Zhou et al. [25] proposed a sensor fault diagnosis algorithm based on the selective updating regularized online sequential extreme learning machine (SROS-ELM) algorithm, and realized the semi-physical simulation test, but did not design the fault-tolerant control system, and in terms of real-time performance, the SROS-ELM algorithm slightly worse than the OS-ELM algorithm [26].
Hardware-in-the-loop(HIL) testing system has real I/O interfaces, controller and virtual subject [27]- [29]. As a validating method for control algorithm, it has a high confidence level. The semi-physical simulation platform based on HIL with real oil system and tubes, where the controller and hydraulic actuators, along with sensors can be tested and validated on, is closer to reality even than the HIL system. Besides, a semi-physical simulation test can introduce some real noise signals into control system in order to test if there is any designing flaw of the system, providing the control law design, parameter optimization, fault diagnosis and fault tolerant control with the most realistic testing platform. Therefore, this paper will start from the actual engineering application value, consider the algorithm complexity and real-time requirements, and design an aero-engine intelligent fault-tolerant control system based on the OS-ELM algorithm, while considering the traditional PID control robustness and poor anti-interference ability and other shortcomings, an improved global fast non-singular terminal sliding mode control(SMC) method [30]- [32] is used to obtain better control effects, effectively solve the uncertainty problem in aero-engine, and give full play to aero-engine performance. Finally, a fault-tolerant control simulation of a certain type of turbofan engine was carried out on the semi-physical simulation test platform to verify the effectiveness of the control system.

II. THE DESIGN OF AEROENGINE SENSOR FAULT DIAGNOSIS MODULE
∈ R m is output, the regression mathematical model for ELM with L hidden nodes and activation function g(x) can be written as: where w i = [w i1 w i2 · · · w in ] T is the weight vector connecting the ith hidden node and the input nodes, b i is the threshold for ith hidden node and β i = [β i1 β i2 · · · β im ] T is the weight vector connecting the ith hidden node and the output nodes. Rewrite (1) in matrix form: where H is called the hidden layer output matrix. The input weight w i and the bias b i are randomly selected. The weight vector β is one of the least-squares solutions of the general linear system (2): where H † is the Moore-Penrose inverse of matrix H. VOLUME 8, 2020 Suppose N ≥ L and rank (H) = L, then H T H is nonsingular matrix, Equation (6) can be solved by recursion. OS-ELM can be summarized as follows: Step 1: Randomly assign input weight w i and bias b i , i = 1, . . . , L; Step 2: Use initial training dataset to calculate the hidden layer output matrix: Step 3: Calculate the hidden layer output β k Update P k+1 and β k+1 by (9): Step 5: As new training sample arrives, let k = k + 1 and repeat Step 4; Step 6: End.

B. AERO-ENGINE FAULT DIAGNOSIS MODULE DESIGN BASED ON OS-ELM
A certain type of hybrid exhaust afterburner twin-shaft turbofan engine is the research object in this paper. Its components mainly include inlet, fan, compressor, combustor, high-pressure turbine, low-pressure turbine, afterburner, and nozzle. A schematic diagram of a typical mechanism and characteristic cross-section is shown in Fig.1. The proposed intelligent fault-tolerant control method based on OS-ELM is shown in Fig.2. There are six OS-ELM networks estimating the sensor signals for rotating speed of the low-pressure rotor n L , rotating speed of the high-pressure rotor n H , the temperature at outlet of the high-pressure compressor T t3 , the temperature at inlet of the low-pressure turbine T t45 , the pressure at outlet of the high-pressure compressor P t3 and the temperature at inlet of the low-pressure turbine P t45 . In addition to engine control variables, last m sensor signals are also sent to networks as inputs to achieve a better dynamic estimating accuracy: whered i k is the estimated output for ith sensor; y i is the input vector excluding ith sensor signal itself; u = W f , A 8 is the vector containing engine control variables, including fuel mass flow W f and throat area in nozzle A 8 ; m is the embedding dimension, set as 3 in this paper.
The sensor residual is defined as the absolute difference between estimated output and the measured output, which can be written as (11): where d i k represents the measured value of the ith sensor, r i k is the residual corresponding to the ith sensor. Let value D be the threshold of determining whether there is offset fault in sensors or not. If r i k <D, the sensor is working in normal condition without any malfunction. In which case, the outputd i k of fault diagnosis system is the value d i k measured by sensor; Otherwise, there is an offset fault happening in the sensor. The outputd i k from fault diagnosis system is the sensor estimated valued i k , which is fed back directly to controller. Fault tolerant control is achieved. Limited by the accuracy of online training algorithm, there is a high possibility of misdiagnosing for the remaining healthy sensors which could lead to a systematic crash, if the rest of the sensors took estimated value from the failed sensor. To tackle with this problem, the failed sensor signal is excluded from input vector y i and the fault diagnosis system is retrained.

III. IMPROVED GLOBAL FAST NONSINGULAR TERMINAL SLIDING MODE CONTROLLER DESIGN
The state space model of aero-engine is as follows: (12) In the design process of the sliding mode controller, the formula (12) needs to be augmented, after the augmentation is as followsẋ where For the above-mentioned aero-engine state space model, set the slip function as: where, G is the sliding mode coefficient matrix to be solved. The condition for the system to be stable in the sliding mode motion state is that the sliding function can reach the zero point in a finite time and remain unchanged after reaching the zero point. That is to meet the accessibility conditions: To improve the dynamic quality of the system's approaching motion, the approaching law method can be used for design [33]. At present, the three methods of approaching law of constant velocity approaching law, exponential approaching law, and power approaching law are the most commonly used, here are generally expressed as: Combining formula (13) and (14), the sliding mode control law is derived Since the sliding function expressed by formula (14) is linear, its tracking error cannot converge to zero in a finite time. To solve this problem, the sliding function of the global fast terminal sliding mode control introduces a nonlinear function, which is defined as follows: where, e(t) = x(t)−x r (t), C, is a diagonal positive definite matrix, and its diagonal elements are c i > 0, β i > 0 respectively, and p, q are positive odd numbers (1 > q/p > 0).
The power of formula(18) may appear negative in the process of derivation. The singularity problem will appear when e = 0, at which time the robustness of the system cannot be guaranteed. To ensure the robustness of the system, the power term when e = 0 is generally discarded.
The global fast non-singular terminal sliding mode control uses the following nonlinear sliding function: where, s 1 , s 2 are n-dimensional vectors, s 1i = t 0 e i (t)dt, s 2i = e i (t) = x i (t) − x ri (t), i = 1,2,. . . , n; C, is a diagonal positive definite matrix, and its diagonal elements are c i > 0, β i > 0 respectively, and p, q are positive odd numbers (2 > q/p > 0).
According to the (19) and (16): The control quantity is derived as: where, the power cannot be negative in the formula, so the singularity problem is effectively avoided. At the same time, literature [34] shows that the global fast non-singular terminal sliding mode control using exponential approaching law has a faster response and stronger robustness. Therefore, the approaching law in formula (21) takes the exponential approach Law, as shown in formula (22).
The control quantity expressed by the formula (21) exists a certain chattering, which is not allowed in engineering applications. To reduce the chattering generated by the sliding mode controller, a low-pass filter is connected in series based on the above-mentioned global fast non-singular terminal sliding mode controller. The structure of the improved controller is shown in Fig.3 below. Where, u the output of the global fast non-singular terminal sliding mode controller. The expression of the low-pass filter is as follows: where, λ > 0.
To verify the control effect of the designed sliding mode controller on the non-linear system, a simulation test is carried out for the rotational speed of the high-pressure rotor. Firstly, through debugging, the parameters p = 7, q = 5, c i = 2, β i = 2.5, i = 1,2 are set in formula (9); and in the exponential approaching law ε = 5, k = 10; in the low-pass filter λ = 20. Besides, since the above-mentioned controller is applied to the outer loop in the large closed-loop rotational speed of aero-engine and the output of the outer loop is the given position Lr of the metering valve, the given fuel quantity needs to be converted into Lr and then provided to the small closed-loop actuator position. Since the controller derivation process mentioned above is aimed at the design point state-space model in a large range, the output of this model is bound to be different from the output of the model and the nonlinear component-level model. There must be a difference between the model output and the model and the non-linear component-level model output. The difference can be considered to be caused by parameter perturbation and unknown interference. Finally, it is compared with the feedforward PID controller. The specific control loop is shown in Fig.3.  Fig.4 shows that compared to the feedforward PID controller, the improved global fast non-singular terminal sliding mode controller has good control effects in a large range, short adjustment time, and no obvious overshoot and steady-state error. There was basically no chattering phenomenon in the whole test process, indicating that the low-pass filter in series played a role in debounce. Also, the improved global fast non-singular terminal sliding mode controller has good dynamic and static performance in various ranges, which shows that the method is insensitive to parameter perturbation and interference, and effectively solves the uncertainty problem in aero-engines.

IV. THE DESIGN OF AEROENGINE FAULT TOLERANT CONTROL SYSTEM
In this paper, an intelligent fault-tolerant control system for aero-engines as shown in Fig.5 below is designed. Among them, the actuator circuit fault diagnosis module [35] is used to detect and distinguish the actuator and LVDT(Linear Variable Differential Transformer) faults. When the LVDT sensor is not faulty, the input of the airborne real-time model is the fuel W f 0 corresponding to the LVDT sensor. When the LVDT sensor fails, the input of the On-board real-time model is the estimated value W f 2 of the fuel inverse mapping model reflecting the real fuel. The sensor fault diagnosis module is constructed based on the above OS-ELM algorithm, which can detect sensor faults in time and estimate faulty sensor signals. Since the input and output signals of the two diagnostic modules are coupled, a fault isolation module is used to isolate the two. The output value d m of the airborne real-time model and the estimated valued of the sensor fault diagnosis module are fused through an adaptive weighting method to reconstruct an accurate sensor signal [36]. Switching logic is used when the sensor has no fault, and the sensor signal is directly provided to the improved global fast non-singular terminal sliding mode controller. Once a fault occurs, it is switched to the reconstructed sensor signal.

V. SEMI-PHYSICAL SIMULATION TEST
This paper considers a mixed exhaust afterburning turbofan engine as research subject. For a given altitude and Mach number, the engine model takes fuel mass flow and nozzle area as input variables and outputs rotating speeds for both high pressure and low-pressure rotors, and temperature and pressure at each section. To validate the feasibility of fault diagnosis carried out by the above mentioned intelligent fault tolerant system, a series of simulations were conducted on semi-physical testing platform.

A. BRIEF INTRODUCTION ON SEMI-PHYSICAL TESTING PLATFORM
The structure of the semi-physical testing platform is shown in Fig.6. It consists of a power system (which is driven by a small inertial motor), fuel system, PXI computer, interface simulator,and a rapid prototyping controller. The component level model(CLM) of the engine is running in PXI computer where the real-time simulation step is 20ms. The fuel mass flow measured by the turbine flowmeter is sent to the CLM to perform thermal calculations where parameters at each section of the engine can be withdrawn. The output card in PXI converts the rotating speed of the high-pressure rotor from a digital signal into an analog signal to drive the small inertial motor to simulate the high-pressure rotor in a real engine. Meanwhile, the motor functioning as an engine drives the fuel pump in the fuel regulator to provide the system with fuel. The rotating speed is measured by a rotating speed sensor and fed to a rapid prototyping controller. Other parameters in the engine, such as rotating speed of the low-pressure rotor, temperature, and pressure at each section are converted into analog signals by interface simulator and sent to a rapid prototyping controller. Rapid prototyping controller serves the purpose of giving commands and integrating fault diagnosis and tolerant control algorithms to ensure the safe and stable working of the engine. The fuel system provides a semi-physical testing platform with a physical simulation of the engine's main fuel cycle, including real actuators. As the main part of the semi-physical testing platform, its physical map is shown in Fig.7. The fuel system consists of a fuel tank, a booster pump, a fuel regulator (including main fuel pump), a turbine flowmeter, valves, tubes, sensors and corresponding readers. The cycle can be summarized as follows: clean fuel with a certain pressure is provided to fuel regulator through the fuel tank and booster pump. The main fuel pump in the fuel regulator will furtherly compress the fuel. The high-pressure fuel flow rate is controlled by a metering valve. The high-pressure fuel will circle back to the tank after flowing through the turbine flowmeter. The output position of the meter valve is controlled by an electro-hydraulic servo valve which is driven by a current signal output by a rapid prototyping controller. LVDT sensor picks up the position signal then feeds it back to rapid prototyping controller.

B. FAULT-TOLERANT CONTROL SIMULATION
Tests for the proposed intelligent fault tolerant control method were carried out on the above mentioned semi-physical testing platform with the subject of a certain turbofan engine model. Since the paper mainly concerns the change of engine states caused by the main fuel flow, the throat area of the nozzle is set to a constant. The threshold D for offset fault is set as 0.015 according to experiments. In this simulation, the number of nodes in the hidden layer is 30. Considering the steady-state error of the estimated model based on OS-ELM in above-mentioned fault diagnosis system is relatively small compared to a dynamic error, a dynamic threshold adjusting function is introduced to improve diagnosing accuracy. The threshold will decrease when the system is in steady state. While in the dynamic state, it will increase. The dynamic threshold adjusting function can be written as (24): where Ẇ f is the fuel flow rate and k is equal to 0.01. This paper mainly concerns the rotation speed closed-loop control on high-pressure rotor, thus a fault-tolerant control test on n H sensor failure is designed. The effectiveness of the VOLUME 8, 2020 given control method at altitude 0km and Mach number 0 is demonstrated in Fig.8 and Fig.9. Fig.8 simulates the steady-state process where a positive 3% bias is injected in 5s. Performance is shown in Fig.8(a) when the intelligent fault-tolerant control system is deactivated, while Fig.8(b) illustrates the change in rotation speed when the intelligent fault-tolerant system is activated. As observed from Fig.8(a), the rotation speed measured by the sensor will fall back to the original value as a result of closed-loop control, yet the actual rotation speed is down by roughly 2% comparing to the original one, leading to a decrease in aero-engine performance. On the other hand, the fault diagnosis system detects the sensor failure instantly and isolates it in the meantime. The reconstructed signal is sent to the controller. As a result, there is barely a change in rotation speed before and after the bias injection. The system regains stabilization in a very short time. Fig.9 shows test results of a dynamic process where a positive 3% bias is injected in 1s. It can be seen from Fig.9(a), without a fault-tolerant strategy, the actual rotation speed will deviate from command speed and stabilize at a lower value. While in the case of Fig.9(b), where fault-tolerant control is involved, the actual rotation speed follows the command speed closely without being affected by the injected bias, realizing the stable working of the engine.

VI. CONCLUSION
This paper proposed a design of an intelligent fault-tolerant control system based on OS-ELM from the perspective of engineering application and semi-physical simulations for fault-tolerant control against failures in the high-pressure rotor sensor were conducted. The conclusions can be drawn as follows:

(Yuan Liu and Qian Chen contributed equally to this work.)
(1) The designed online fault diagnosis system can detect and isolate sensor failures effectively in both steady-state and dynamic state. The accurate reconstructed sensor signals would guarantee the smooth operation of an aero-engine; (2) The proposed intelligent fault-tolerant control method has been validated through semi-physical simulations. Its excellent feasibility and fine real-time performance have tremendous help on improving the reliability of the system; (3) The intelligent fault-tolerant control method demonstrated good adaptability. It can be used to online diagnose the sensor failure on other types of aero-engines and reconstruct the signals.
In this paper, the research on related technologies is not enough and needs to be further improved and perfected. For example, the fault diagnosis system based on OS-ELM can learn and estimate online, which has good universality and real-time performance. However, due to the limitation of the number of fault sensors, this paper only carries out simulation test for single bias fault, and further theoretical and experimental research can be carried out for double fault and multi fault. The intelligent fault-tolerant control system in this paper is mainly realized by reconstructing the sensor signal, and the reconfigurable control law can be further considered for fault-tolerant control research. APPENDIX See Table 1.
QIAN CHEN received the B.S. degree in process equipment and control engineering from Anhui Polytechnic University, Anhui, China, in 2017. He is currently pursuing the Ph.D. degree in power machinery engineering with the Nanjing University of Aeronautics and Astronautics, Nanjing, China.
His research interests include aero-engine adaptive modeling method research, aero-engine fault diagnosis, and aero-engine surge margin control embedded software design. In 2019, he and his teacher (H. Sheng) has participated the International Aerial Robotics Competition (IARC) and received the World Championship.
SHENGYI LIU was born in Longyan, Fujian, China, in 1998. He received the bachelor's degree in aircraft power engineering from the Nanjing University of Aeronautics and Astronautics, where he is currently pursuing the master's degree in aerospace science and technology. His research interests include aero-engine control, combination of aero-engine, and deep learning.
HANLIN SHENG (Member, IEEE) received the B.S. degree in flight vehicle propulsion engineering and the Ph.D. degree in aerospace propulsion theory and engineering from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2009 and 2015, respectively. From 2015 to 2016, he was a Postdoctoral Fellow with Nanyang Technological University. He is currently an Assistant Professor with the School of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics. His research interests include aircraft and aeroengine modeling, simulation, and control.