Adaptive Neural Network based Fault Detection ...

Adaptive Neural Network based Fault Detection Design for Unmanned Quadrotor under Faults and Cyber Attacks Alireza Abbaspour

Michael Sanchez

Arman Sargolzaei

Department of Electrical Engineering Florida International University Miam, FL, USA [email protected]

Department of Electrical Engineering Florida Polytechnic University, Lakeland, FL, USA

Department of Electrical Engineering Florida Polytechnic University, Lakeland, FL, USA

Kang Yen

Nalat Sornkhampan

Department of Electrical Engineering Florida International University Miam, FL, USA

Department of Electrical Engineering Florida International University Miam, FL, USA

Abstract—The occurrence of faults and failures in flight control systems of unmanned aerial vehicles (UAVs) can destabilize the system which could cause potential economic and life losses. Therefore, it’s necessary to detect faults and attacks in real time and modify the control system based on the occurred fault. In this paper, a neural network-based fault detection (NNFD) approach is introduced to detect and estimate the faults and false data injection (FDI) attacks on the sensor systems of a quadrotor in real time. An unmanned quadrotor is selected as our case study to demonstrate the effectiveness of our proposed NFDD strategy. The simulation results show that the applied NNFD method can detect the faults and FDI attacks on an unmanned quadrotor sensors with sufficient accuracy. Index Terms—Fault detection; False Data Injection; Sensor faults; Nonlinear system

I. I NTRODUCTION The application of Unmanned Aerial Vehicle (UAV) has increased in the past several years, and it is trending to increase significantly in the near future. The wide variety of the UAVs applications have provided a great comfortability to mankind by performing specific missions in hazardous environments without a human in the vehicles [1]. Since UAVs can be controlled and monitored remotely, there would not be a human decision to diagnose, troubleshoot, or repair instantaneously when an anomaly occurs. Nowadays, the applications of knowledge-based algorithms are very effective to detect faults in UAV. In this work, we investigate techniques to detect and diagnose potential anomalies in UAV systems based on the measured value from the system outputs. Generally, the sources of anomalies in UAV systems can be categorized into two main classes which are system faults and cyber-attacks [2]. System faults are anomalies

that usually occur in control systems unintentionally and they can cause serious damages to the vehicles. Therefore, system faults in UAVs have broadly been studied [3]–[5]. Heredia et al. studied potential faults in differential global positioning system (DGPS), inertial and vision sensors [3]. Fault detection (FD) and fault-tolerant in multi-rotor Micro Aerial Vehicles (MAVs) were investigated by Schneider [4]. An online FD approach in aircraft system was investigated by Lee et al. [5]. Different techniques have been proposed to linear and nonlinear systems to detect anomalies in the system. Each detection technique has its own advantages and disadvantages. Extended Kalman filter [6], [7], sliding mode observers [8], [9], and linear matrix inequality [10] have been used for fault detection in linear system; however, they cannot provide sufficient accuracy for fault detection in nonlinear systems. The ability of Neural Networks (NNs) to learn mathematical relationships between input variables and the corresponding output variables with a training data set has made them one of the best tools for system identification and FD in nonlinear systems [11]. Wong et al. used a multilayer perceptronbased NN approach with backpropagation algorithm to classify different types of aircraft failures theoretically and experimentally [12]. However, learning-based methods such as perceptron based NN, Bayesian Network (BN), and k-Nearest Neighbor (k-NN) have a common disadvantage. If their training data are too small, they may not effectively detect faults in the systems. On the other hand, if the training data are too large, computation time will be increased which will cause a significant delay in the fault detection systems [13]–[18]. For this reason, adaptive neural networks which are able to detect anomalies online have received a great

attention among the researchers [19]–[21]. Cyber-attacks are employed by intruders or adversaries that aim to disrupt computer communication, information, or network systems in the critical infrastructures [22]–[25]. In this work, we investigate the attacks that aimed the attitude sensors of the UAV. Attitude sensors in UAVs play an important role in obtaining attitude information of the body system which are used in the control and the navigation system. Intruders can penetrate to the control system of the UAV through different ways, e.g, hacking the cipher keys in the communication links of the UAV with ground station [26], and GPS spoofing [27]. In this work, we assume that the hackers are already penetrated to the control system, and try to insert false data to the attitude sensors to deceive the autopilot. Without a detection system, UAVs flight performance will be vulnerable to cyber-attacks which may cause serious damages to the UAVs and the desired missions [28]. Several types of research and experiments about cyber-attack detection algorithms in communication, control, and network systems have been conducted [29]–[33]. Shon et al. used a Support Vector Machine (SVM) approach to detect a cyberattack in a network system [30], Ye et al. introduced a robust Markov-Chain (MC) technique for cyber-attack detection on a computer and network systems [31], and Lokman et al. proposed a Neural Network based hyper-spectral imagery (HSI) for anomaly detection and target recognition in UAVs [32]. Sargolzaei et al. introduced a novel strategy for detection and compensation for time-delay switch (TDS) attack in power distributed control system [33]. In this paper, we developed a new NNFD structure for an unmanned quadrotor system which is able to detect faults and FDI attacks in the sensors of a quadrotor. Our contribution in this paper can be summarized as: 1) Introducing a new NNFD design based on the nonlinear dynamics; 2) Being able to detect sensor FDI attacks; 3) Using six degree-of-freedom (DoF) dynamic model to achieve an accurate simulation result. The paper organized as follows: In Section 2, we explained the dynamic model of the quadrotor is explained. The DI controller for quadrotor is presented in Section 3. Section 4 illustrates the proposed fault detection strategy. In Section 5, numerical simulation results show the effectiveness our proposed strategy. Finally, the conclusion and remarks are presented in Section 6. II. Q UADROTOR M ODEL To understand the dynamic of the quadrotor, a set of equations have been presented in this section. Figure 1 shows the model of the quadrotor coordinate system on a flat earth diagram. The forces created by this device come from four rotors in a cross structure. By using this rotor structure, the variations in the rotors spinning speed creates three moments roll, pitch, and yaw as well as lifting force. In order to create a model for flight conditions, we define the model on a flat-earth as a rigid body using the right-hand rule.

Fig. 1: Overall view of a Quadrotor: a dynamic system.

The following equations can help to understand the quadrotor body dynamic behavior and help to design a controller based on these dynamics [34]. Tp Ix − Iy + Ix Ix Tq Ix − Iz + r˙ = −pr Iy Iy Iy − Ix Tr r˙ = −pq + Iz Iz

p˙ = −qr

φ˙ = p + sin(φ) tan(θ)q + cos(φ) tan(θ)r θ˙ = cos(φ)1q − sin(φ)q

(1)

(2)

cos(φ) sin(φ) q+ r ψ˙ = cos(θ) cos(θ) u˙ = rv − qw + g sin(θ) v˙ = −ru + pw − g cos(θ) sin(φ) z w˙ = −qu − pv + Fmz − g cos(θ) cos(φ) + K1 (z1 −z)δ m

(3) where p, q, and r are components of the quadrotors angular velocity about x, y, z body axes [rad/s], respectively; Ix , Iy , and Iz are moments of inertia [kg/m2 ]; φ, θ and ψ are Euler angles in [rad] or [deg], which describe the roll, pitch and yaw angle in the body fix coordinate system, respectively; u, v, and w are the velocities [m/s] along the x, y and z body fix coordinate, respectively. K1 and z1 are the elastic coefficient and elastic deformation of the landing gear of the quadrotor on ground; Fz is the total thrust force; δ(z) is a threshold function that eliminates the elasticity effect of the landing gear during the flight because it disappears after taking off; Tp , Tq and Tr are the rolling, pitching and yawing torques, respectively, which are described in the following [34].  δ(z) = 

  Tp −Lkf  Tq  −Lkf  =  Tr   kt Fz kf

1 0

Lkf Lkf kt kf

z1 − z > 0 z1 − z 6 0 Lkf −Lkf −kt kf

  2 −Lkf ω1 ω22  Lkf    −kt  ω32  kf ω42

(4)

(5)

where ωi for i = 1, 2, 3, 4 are the angular velocity of each rotor of the quadrotor; L is the distance from the motor to the center of mass of the quadrotor; kf and kt are the aerodynamic force and anti-torque, respectively. III. C ONTROL S YSTEM D ESIGN In this section, we explain the proposed control strategy used for designing the attitude controller. Dynamic inversion (DI) controller is selected to be implemented in order to control the quadrotor attitude. This controller have been successfully implemented in many aircraft [34]–[36]. DI is a nonlinear control strategy based on feedback linearization that can be applied in several control loops in a system. Based on the time scale difference between the angular velocities and attitude angles in quadrotor body fixed frame, the control design is implemented in two control-loops as follows A. Inner loop Control The inner loop in the DI control system is the loop that its parameters vary with a higher rate. The angular velocities (p, q, r) changing frequency is 50 Hz while the attitude angle frequency (φ, θ, ψ) is 4 Hz; therefore, p, q, r are selected as the inner loop system. Using DI theory, angular velocities in Equations (1) can be transformed to [34]:       Tp pI ˙ x (Iz − Iy )qr Tq  = qI ˙ y  + (Ix − Iz )pr  (6) Tr rI ˙ z (Iy − Ix )pq In Equation (6), in order to maintain zero dynamics while angular velocity error is zero, the right side of this equation can be omitted. Therefore, the unmolded dynamics characteristics can be compensated through enhancing the DI as follows     Tp (p − pc )Ix Tq  = Kin  (q − qc )Iy  (7) Tr (r − rc )Iz where pc , qc , and rc are the commanded p, q, and r that are received from the outer loop controller. Kin is the inner loop control gain that can be tuned by designer to obtain the desired control response. B. Outer Loop Control In this loop, the attitude dynamics in Equation(2) can be organized as follows to obtain the desired angular velocities (p, q, r) [34]:   ˙    1 sin(φ) tan(θ) cos(φ) tan(θ) φ pc qc  = 0 cos(φ) − sin(φ)  +  θ˙  cos(φ) sin(φ) rc 0 ψ˙ cos(θ) cos(θ)   1 sin(φ) tan(θ) cos(φ) tan(θ) cos(φ) − sin(φ)  + = 0 sin(φ) cos(φ) 0 cos(θ)  cos(θ) φc − φ Kout  θc − θ  ψc − ψ (8)

where Kout is a control gain that can be tuned by the designer to obtain the desired system performance; φc , θc , and ψc are the commanded roll angle, pitch angle, and yaw angle which are produced by pilot or guidance system. C. Motor Speed Control In order to control the angular velocity of the quadrotor motors, the following relation can be extracted form the equation (5) :    2  Tp /(Lkf ) −0.25 −0.25 0.25 0.25 ω1c 2     ω2c 0.25 0.25 0.25   Tq /(Lkf )  2  =  0.25 ω3c   0.25 −0.25 −0.25 0.25   Tr /(Lkt )  2 Fz /kf −0.25 0.25 −0.25 0.25 ω4c (9) IV. FD D ESIGN In order to detect incoming faults and false data injection (FDI) attacks to the quadrotor sensors, we developed a new structure. This structure is a combination of a nonlinear observer (NO) and an NN observer which has the ability to detect the anomalies in the sensors. These anomalies can be faults, uncertainties or FDI attacks in the quadrotor sensors. In this section, the effects of faults and cyber-attacks on the aircraft attitude sensor system are described, then the proposed FD design is developed. A. Fault effect on the sensors Faults can occur in a system due to various reasons, i.e., a fall in a supply voltage or current of a sensor because it normally needs a separated power supply, interruptions in communication between the sensor and control, noise effect on the sensor (environmental noise like a magnetic field), denial of service for a period of time due to processor speed and network bandwidth, FDI attack, etc. [2]. Consider a nonlinear system with the following equations x(t) ˙ = f (x(t)) + g(x(t))u(t) y(t) = h(x(t)) + Fs

(10)

where x(t) is the state vector of the system; y(t) is the output state vector; u(t) is the control input state vector; f (x(t)) is a function that contains the states of the x(t) which are not directly related to the u(t); g(x(t)) is a state function that contains parameter directly related to the u(t); FS is the sensor fault. To show the effect of fault and cyber-attacks on the UAV’s control system, a step fault and a sinusoidal attack are selected to test on the quadrotor. Figure 2 shows the fault and the attack that are considered in this work. Figure 3 shows the fault effect on the inner loop controller of the quadrotor. Figure 4 shows the attack effect on the system inner loop controller of the quadrotor. It can be clearly seen that the conventional DI controller are susceptible against fault attack and their performance can be totally degraded as an intruder attack to the system. Thus, having an FD system is necessary to detect the fault and do further action, e.g., fault tolerant

control, reconfigurable control, etc, to compensate for the fault effect.

Fault & Attack Scenarios Sinsoidal Attack Step Fault

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Fig. 2: The fault and attack scenarios considered in this work.

C. NN Updating Laws This subsection presents the updating law of the NN observer to ensure the detection of the fault in the nonlinear system. The stability and convergence of the proposed updating law is discussed and demonstrated using Lyapunov’s direct method in Ref [19]. Considering the nonlinear observer in Equation (14), the NN updating laws can be presented as   ˆ ˆ˙ (t) = −γ1 ∂C − η1 k˜ y kW W ˆ ∂ W  (15) ˙ − η2 k˜ y kVˆ Vˆ (t) = −γ2 ∂∂C Vˆ where γ1 , γ2 > 0 are the NN learning coefficients; C = 0.5(˜ y T y˜) is the objective function of the NN, and η1 , η2 are small positive coefficients which can be tuned by designer to get optimum performance in NN. In order to obtain the NN updating laws (15), the derivative of the objective function can be calculated using static gradient approximation and chain rules [19], thus, we have
T T ˆ ˆ˙ (t) = −γ1 y˜T A−1 L1 − η1 k˜ y kW W c T  ˙ˆ ˆ − η2 k˜ y kVˆ V (t) = −γ2 y˜T A−1 c W L2

B. NN Observer Design Here, an NN-based observer for detection of faults in the sensors is presented. A feed forward NN structure which is shown by NN in conjunction with a nonlinear observer is used to construct a recurrent model which can detect Fs in Equation (10). The following model is used to develop our observer-based FD design: x ˆ˙ (t) = f (ˆ x(t)) + g(ˆ x(t))u(t) ˆ (ˆ yˆ(t) = cˆ x(t) + M x, u, W )

(11)

(12)

where W and V are the NN output layer and hidden layer weight matrices, respectively. Let x ¯ = [x, u]T , x ˜(t) = x(t) − x ˆ ≤ eM is the estimation error of the NN which is bounded by eM , and σ is a sigmoid activation function which represents the transfer function of the hidden layers [19] σi (V i x ¯) = 1+exp2−2V i x¯ − 1 (13) i = 1, 2, ..., N where N denotes the number of hidden layers, V i is the ith row of V , and the ith element of σ(V x ¯) is denoted by σi (V i x ¯). Now, based on Equations (11) and (12), the estimator model can be presented as x ˆ˙ (t) = f (ˆ x(t)) + g(ˆ x(t))u(t) ˆ σ(Vˆ x yˆ(t) = cˆ x(t)) + W ˆ)

where Ac = kn × I3 and kn is a small positive constant; L1 and L2 are be defined by ˆ¯) L1 = σ(Vˆ x ˆ¯) L2 = I − Γ(Vˆ x

(17)


ˆ¯) = diag L1 (i)2 , i = 1, 2, 3 Γ(Vˆ x

(18)

and

ˆ (ˆ where M x, u, W ) is the observed fault by the NN. It is already demonstrated that for a restricted set of x ∈ Rn and sufficient number of hidden layers of neurons, weights and threshold, a recurrent NN observer with the following structure will be stable [19] M (x, u, W ) = W σ(V x) + x ˜(t)

(16)

(14)

and L1 (i) denotes the ith element of L1 vector. D. Sensor FD Design In this subsection, the design procedure of an FD system using the proposed technique for the sensors of a quadrotor is illustrated. In this paper, we considered faults in the angular rates sensors (p, q, and r). Here, according to (11), an NO should be designed to estimate the sensor output based on system dynamics. However, this NO, which is based on nonlinear dynamic model, is not accurate enough since dynamic models have always uncertainties or some unmodeled dynamic. Therefore, NN is attached to this design to achieve a better observation of the system. An NO for the quadrotor angular rate sensors can be obtained based on Equation (1) Tp Ix − Iy + pˆ˙ = −ˆ q rˆ Ic Ix I − I T x z q rˆ˙ = −ˆ prˆ + (19) Iy Iy Iy − Ix Tr rˆ˙ = −ˆ pqˆ + Iz Iz The above equation helps to observe the sensor output based on the controller inputs (Tp , Tq , and Tr ). Using this NO in Equation (14) will lead to the proposed FD design which its structure is shown in Figure 5.

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DI p tracking in healthy DI p tracking with faulty sensor commanded p

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DI q tracking in healthy DI q tracking with faulty sensor commanded q

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Fig. 3: Fault effect on the DI controller of a quadrotor.

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Fig. 4: Attack effect on the DI controller of a quadrotor.

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Fault Detection System [ p, q, r ]T y

Detected Fault

+

yˆ

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Nonlinear Observer

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+

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Tp    Tq  T   r

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Sensors

Actuators

System Model Fig. 5: Block diagram of the NN-FD system for sensor fault detection in Quadrotor

V. S IMULATION R ESULTS

Fault Detection in p 1.2

In this section, numerous simulations are conducted to evaluate the performance of the proposed NNFD method in detection of the FDI attack and natural faults on UAVs sensors. The detailed parameters of the quadrotor can be found in [34], the NN parameters with 5 hidden layer are selected as follows: Ac = 3 × 10−3 × I3 , γ1 = γ2 = 0.5, η1 = η2 = 0.1, W0 is a 3 × 5 matrix which all of its elements are 0.2, and V0 is a 5 × 6 matrix with the same elements. The ability of the proposed NNFD is examined in two major scenarios which are discussed below.

1

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Scenario I: In this scenario, a step shaped fault is applied to each angular rate (p, q, and r), separately. Figures 6-8 show the performance of the proposed NNFD in detecting this fault scenario. As we see in these figures, the proposed NNFD is able to detect faults in real time with sufficient accuracy. This accurate fault detection helps to use this information to tackle the fault problem with further action, e.g, reconfigurable control strategies. Scenario II: In this case, FDI attack is considered as a potential threat to the quadrotor control system. Attackers send these false data to mislead the autopilot from its mission or even destabilize the aircraft [2]. There is no specific pattern for these kind of attack because the injected false data is unpredictable; thus, the detection system should be prepared for the faults with any shape and amplitude. In our design, we put a limiter with the amplitude of two radians to prevent

NN fault detection Real Fault

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Fig. 6: The proposed fault detection ability in sensor ’p’

false data with high amplitudes. A sinusoidal FDI attack is considered in this scenario. Figures (9-11) show the FDI attack detection of the proposed NNFD system for attacks in p, q, and r sensors, respectively. These figures show that our proposed strategy has sufficient accuracy for intrusion detection, and finding the location, time and the amplitude of the injected false data. Then, further actions can be done against the intrusion [33], [37]. VI. C ONCLUSION This paper investigated the impacts of FDI attacks and natural faults on UAVs sensors. An NNFD technique is

Fault Detection in q 1.2

Fault Detection in q 1.5

NN fault detection Real Fault

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Fig. 7: The proposed fault detection ability in sensor ’q’

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Fig. 10: The proposed fault detection ability in detecting FDI attack in sensor ’q’

Fault Detection in r 1.2

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Fig. 8: The proposed fault detection ability in sensor ’r’

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Fig. 11: The proposed fault detection ability in detecting FDI attack in sensor ’r’

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Fig. 9: The proposed fault detection ability in detecting FDI attack in sensor ’p’

applied to detect and estimate the FDI attack in real-time to alarm the system about the existence of attacks and faults in the system. The applied NNFD technique has been evaluated on a six-DoF quadrotor nonlinear model. The simulation results conclude that the applied method has the ability to successfully detect the sudden and smooth attacks in the sensors with sufficient accuracy. The detection method can be further used for fault tolerable control and emergency controller design to make the UAVs control system more robust against cyber-attacks and natural faults.

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