Neural Network-Based Sensor Fault Accommodation in Flight Control System

General Terms

A,B,C,D:

State space matrices specifications of aircraft longitudinal model. x is the state.

x:

[q Nz δe]^T; q – pitch rate (rad), Nz – normal acceleration (ft/s²), δe – elevator position (rad).

u:

input; elevator command (rad)

y:

output, [2 × 1]; [q, Nz]^T

SFDA:

sensor fault detection and accommodation.

1 Introduction

Sensor fault detection and isolation is a major concern in any reliable automatic and pilot-in-loop flight control system. It is crucial for aircraft flight control because of the significant number of incidents that have occurred because of such failures and their serious consequences [1].

Sensor failures need to be identified quickly so that reconfiguration of the failed sensor can be autonomously attempted online to minimize damage. Many researchers have worked in this area with different approaches. A wide variety of conventional approaches exist for the detection and identification of failures in dynamic systems. A failure detection system can employ either a hardware or an analytical redundancy technique. However, hardware redundancy results in higher cost, increased power consumption, and increase in volume and weight. Analytical redundancy implies the use of a validated mathematical model to generate signals that would otherwise be produced by redundant hardware. These redundant techniques employ state estimation, adaptive filtering, statistical decision theory, Kalman filters, and observers. Frank [1] gives various such techniques for fault diagnosis in a dynamic system in his survey paper.

In recent years, neural networks have become very popular in many areas, including fault diagnosis systems. They have an attractive property of learning and adaptation. As neural networks have an inherent parallel architecture with multiple input and output nodes, they can be implemented in high-speed parallel hardware with multivariable input and output.

There can be two approaches to using a neural network: model-based approach and knowledge-based approach. A model-based approach is where neural networks can be used to provide analytical redundancy for fault detection purposes. A knowledge-based approach deals with training a neural network to recognize faults on the basis of certain features. Seema and Rama Murthy [11] dealt with sensor fault detection based on the knowledge-based approach of a neural network (KBNNFD) and proved it to be better than the conventional algorithmic approach. This work is an extension to the previous study by employing another neural network model that uses the model-based approach of a neural network (MBNN). MBNN is used for reconfiguration of failed sensor. It provides analytical redundancy similar to Kalman filters and Luenberger observers, which have been used by many researchers [9, 10]. The sensor fault detection and accommodation (SFDA) system developed in this article has these both neural network-based models.

KBNNFD and MBNN will be able to detect and reconfigure the faults of sensors in either lateral or longitudinal axes; however, for the purpose of demonstrating the utility of the technique, Nz sensor failure is considered. The results are better when compared with the algorithmic method of sensor failure detection on the whole. KBNNFD follows the gradient descent back propagation algorithm [11] and MBNN follows GRNN, which uses radial basis function.

Napolitano et al. [8] also showed the advantages of the neural network-based method for sensor fault detection in an aircraft control system over the Kalman filter-based approach. Napolitano et al. [7] used neural networks for sensor and actuator fault detection. They could detect sensor and actuator faults for a non-linear model of aircraft using neural networks. Judd and Smith [3] stated that “the perfect model scenario is a fiction; in practice all models are imperfect.” Neural network algorithms are inherently capable of handling linear or non-linear dynamic systems without any approximation. This is because a neural network deals with real data of an input–output pair of any system. The output data set may be non-linearly dependent on the input data set. A neural network is capable of approximating any complex relation between input and output [4].

The novelty of this work lies in the use of a neural network as a two-way approach for sensor fault accommodation in a flight control system, which is not documented in the literature. KBNNFD and MBNN together make a robust sensor fault-tolerant control system that proves to work faster, and detect and reconfigure faults near the steady state. It works successfully for accommodation of a fault in the transient state and also for intermittent faults. In this application, the neural network is trained for sensor fault detection in an F8 aircraft model with a C-Star controller. Further, A, B, C, D matrices are randomly varied, and the validity of the proposed method tested. It was found that the method still accommodates the Nz sensor fault. This explains the usefulness of the method for model imperfections, which is similar to some of the non-linearities.

2 Aircraft Model and C-Star Controller

2.1 F8 Aircraft Model

A short-period approximation of the longitudinal dynamics of the F-8 aircraft has been taken as the model for the flight control system. The model of the aircraft is given in state space form in Eqs. (1) and (2):

The values of matrices A, B, C, D at flight condition (altitude of 6096 m and Mach no. 0.67) [2] are given in Eq. (3):

These equations form the “aircraft short-period dynamics” subsystem in the main simulation model shown in Figure 1.

Figure 1

Simulink Model for Sensor Fault Accommodation.

2.2 C-Star Controller

The model of C-Star controller [6] is shown in Figure 2. This forms the controller subsystem in the main simulation model shown in Figure 1. It was postulated that the pilot responds to a mix of q and Nz. The variable controlled is known as C-Star, which was defined to specify the handling qualities of the aircraft. The variable C-Star is composed of the weighted sum of Nz at the pilot’s position and q as shown in Eq. (4). Nz and q sensor values are fed back to the C-Star controller as shown in the Simulink model of Figure 1.

Figure 2

Simulink Model of C-Star Controller.

Flight envelope indicates the limits within which the aircraft can be operated safely based on conditions such as altitude and Mach number. A criterion based on the envelope of the time trajectory of the response of a composite dimensionless variable, C-Star, to a step input was proposed:

Here, Vco is the value where the contributions to C-Star from Nz and q become equal. The handling quality requires that C-Star lie within a specific bound in its time trajectory. For a healthy simulation model, the C-Star value remains close to “1.”

3 Neural Network Models

The neural network refers to the interconnections between the neurons in the different layers of each system. For example, Figure 3 shows a system with three layers. The first layer has input neurons, which send data via synapses to the second (hidden) layer of neurons. Thereafter, the data are sent via more synapses to the third layer of output neurons. More complex systems will have more layers of neurons with some having increased layers of input neurons and output neurons. The synapses store parameters called “weights” that manipulate the data in the calculations. Figure 3 shows weight matrix [v] between the input and hidden layers and weight matrix [w] between the hidden and output layers. Training of the neural network updates these weights. Supervised training is used for both the KBNNFD and MBNN models. An artificial neural network is typically defined by following three types of parameters [12]:

• The interconnection pattern between different layers of neurons. It deals with the number of inputs, outputs, and hidden layers in the structure.

• The learning process for updating the weights of the interconnections. KBNNFD uses the gradient descent back propagation algorithm and MBNN uses GRNN. The GRNN architecture is shown in Figure 4.

• The activation function that converts a neuron’s weighted input to its output activation. KBNNFD uses a hyperbolic tangent sigmoid function for the hidden layer and linear function for the output layer. MBNN uses a radial basis function for the hidden layer and a linear function for the output layer. The hidden layer is named as Layer 1 and the output layer is named as Layer 2 in Figure 5, which shows the Simulink model of MBNN. Both functions of MBNN are shown in more detail in Figure 6.

Figure 3

Neural Network Model with One Hidden Layer.

Figure 4

GRNN Architecture [5].

Figure 5

Simulink Model of MBNN.

Figure 6

Radial Basis and Purelin Function Used in GRNN [5].

4 Simulation Set-up and Fault Induction

Simulation has been carried out for sensor fault accommodation for the F8 aircraft model using Simulink [5]. The output of the aircraft short-period dynamic model consists of Nz and q, as shown in Figure 1. Fault is introduced in the Nz sensor of the aircraft model, which will be successfully detected and reconfigured using KBNNFD and MBNN, respectively. A stuck fault is considered where a sensor gets stuck at one position and erroneously gives a constant output. This output is the last value of the sensor at the time instant when it failed. Stuck fault induction is done with the help of an N-sample switch [5], as shown in Figure 1. A stuck fault of “–0.3” is induced at 6 s in the model as one of the fault cases. Induction of stuck fault is done at 10 s, as shown below.

It is explained with the if–else statement below:

If t < 6 s, output = left input port (healthy signal),

else   output = right input port (stuck signal).

The N-sample switch block outputs the signal connected to the left input port during the first N-sample times after the simulation begins, where N is specified in the switch count parameter. Beginning with output sample N + 1, the block outputs the signal connected to the specified constant input until the end of the simulation. The sample time is 20 ms in the model and N = 300 in the N-sample switch. Figure 1 shows the Nz sensor stuck at value of “–0.3” at 6 s, i.e., (0.02 * 300). This forces the Nz sensor value to get stuck at “–0.3” at t ≥ 6 s. A stuck fault can be introduced at any time and for any value using this N-sample switch block of Simulink.

5 Discussion of Results

The fault considered for the simulation study is the Nz sensor fault. A sensor can fail at any point of time. Stuck faults are induced at various time instants for the Nz sensor. A pitch-up command for an elevator is given to the model as a step input along with noise that has uniform distribution. The model generates the steady value of “–0.67 ft/s²” for the Nz sensor output. It is assumed that while moving from 0 to the steady-state value of “–0.67,” the Nz sensor can get stuck at any value. Various cases of stuck fault at values ranging from “0” to “–0.45” are considered. Figures 7–13 show various cases of stuck faults, including intermittent faults and faults occurring in the transient state. Each figure shows the Nz sensor output of the aircraft model, which also shows where the fault is introduced. Trained neural networks accommodate fault at any value of time, t, and for any stuck value up to “–0.45 ft/s²”.

Figure 7

SFDA for Stuck Fault of “0” at 6 s.

Figure 8

SFDA for Stuck Fault of “–0.1” at 6 s.

Figure 9

SFDA for Stuck Fault of “–0.25” at 4 s.

Figure 10

SFDA Stuck Sensor Fault of “–0.35” at 2 s.

Figure 11

SFDA for Stuck Sensor Fault of “–0.45” at 8 s.

Figure 12

SFDA for Stuck Sensor Fault of “–0.45” at 1 s (Transient State Fault).

Figure 13

SFDA for Stuck Sensor Fault of “–0.4” from 6 to 10 s (Intermittent Fault).

The system is under continuous observation and fault monitoring is done every 20 ms. If the fault disappears, the output of the fault indicator will be less than the threshold value and the Nz sensor will switch back in feedback. This is the case where the fault occurs intermittently. It is important for the system that actual sensor feedback should replace the reconfigured feedback if the fault is cleared. This is shown in Figure 13. Figure 14 clearly shows how reconfiguration is done only for 4 s when the fault occurred from 6 to 10 s. As the fault clears at 10 s, the Nz sensor switches back and continues to be in feedback. Furthermore, it is important that the output of the fault indicator is above the threshold until the fault is cleared. Only at time instants when the fault is indicated by KBNNFD, reconfiguration is done using MBNN. Generally, it is difficult to accommodate a fault if it occurs in a transient state. The proposed fault accommodation technique has also shown to work satisfactorily for the case where a fault occurs in a transient state, as shown in Figure 12.

Figure 14

SFDA for Intermittent Stuck Sensor Fault; Nz Switching Back as Fault is Cleared at 10 s.

The SFDA system is capable of handling model imperfections to a certain extent. The aircraft model’s A, B, C, D matrices were randomly varied up to ± 10%. It was found that the SFDA system still accommodates the Nz sensor fault. This explains the usefulness of the method for model imperfections, which is similar to some of the non-linearities.

To summarize, the fault accommodation system developed in this article is better in the following ways:

• Faults near steady state can also be accommodated.

• Accommodation of fault in the transient state.

• Accommodation of intermittent stuck faults.

• Capable of handling aircraft model parameter variations to a certain extent.