Research on fault tolerant control system based on optimized neural network algorithm

Abstract

Due to the strict personnel control measures in COVID-19 epidemic, the control system cannot be maintained and managed manually. This puts forward higher requirements for the accuracy of its fault-tolerant performance. The control system plays an increasingly important role in the rapid development of industrial production. When the sensor in the system fails, the system will become unstable. Therefore, it is necessary to accurately and quickly diagnose the faults of the system sensors and maintain the system in time. This paper takes the control system as the object to carry out the fault diagnosis and fault-tolerant control research of its sensors. A network model of wavelet neural network is proposed, and an improved genetic algorithm is used to optimize the weights and thresholds of the neural network model to avoid the deficiencies of traditional neural network algorithms. For the depth sensor of a certain system, an online fault diagnosis scheme based on RBF (Radial Basis Function) neural network and genetic algorithm optimized neural network was designed. The disturbance fault, “stuck” fault, drift fault and oscillation fault of the depth sensor are simulated. Simulation experiments show that both online fault diagnosis schemes can accurately identify sensor faults and the genetic algorithm optimized neural network is superior to RBF neural network in both recognition accuracy and training time under the influence of COVID-19.

Keywords

Fault diagnosis COVID-19 fault-tolerant control neural network genetic algorithm optimization

1 Introduction

The novel corona virus pneumonia is the most widespread global epidemic disease that mankind has suffered in the past hundred years. It is a serious crisis and severe test for the whole world. Human life safety and health are facing a major threat. Due to the strict personnel control measures in COVID-19 epidemic, the control system cannot be maintained and managed manually. This puts forward higher requirements for the accuracy of its fault-tolerant performance.

The requirements for performance and maintainability have also gradually increased, so failure detection and fault tolerance control have received increasing attention [1 –4]. The fault detection and diagnosis technology has a profound theoretical foundation, and the technologies of system theory, information theory, cybernetics, and nonlinear science have been widely used [5]. The technology is mainly based on analytical redundancy. The fault detection and diagnosis technology mainly includes fault detection, prediction, identification, isolation and decision-making [6].

The fault detection method based on parameter estimation refers to the purpose of fault detection by identifying the system model parameters or corresponding physical parameters [7]. It combines modeling theory and parameter identification to describe the fault by comparing the significant jump of the identified parameter with the fault threshold [8]. Compared with other fault detection methods, the parameter estimation method can better achieve fault separation and corresponding fault-tolerant control, but the parameter estimation method requires accurate modeling, and the corresponding relationship between model parameters and physical parameters must be found, and the parameter estimation usually requires continuous excitation of the system, which is generally not allowed by industrial or chemical processes [9, 10]. So it limits the use of parameter estimation methods. The state filter method is an important part of the fault diagnosis method. The key is to use the system state and output to construct the fault residual sequence. By filtering out non-fault signals (control input and interference signals), the fault-related information is obtained. The corresponding filter construction methods are output feedback filter, Kalman filter, wavelet filter, etc [11]. The filter method can effectively separate the fault signal from the external interference signal to ensure the accuracy and real-time performance of fault detection. It directly obtains the fault signal, it can also predict and track the fault signal. However, because the filter method needs to cancel non-fault signals, it usually needs a more accurate system model, and at the same time, it needs to set an appropriate fault threshold to increase its robustness [12]. Combining the filter with the neural network can also increase the self-learning ability of the filter method for new faults, and can more accurately detect sudden faults [13].

Relevant scholars have applied fuzzy to the analysis of system models, which has better dealt with the problem of inaccurate modeling and realized the residual design with modeling errors [14, 15]. The artificial neural network has powerful simulation and learning functions. By learning it, the fault can be automatically identified and classified, and timely and accurate fault diagnosis can be performed. Due to this characteristic of neural networks, it has been used for fault diagnosis of nonlinear systems [16]. However, neural networks still have the disadvantages of slow convergence and poor real-time performance, which requires expert systems to give qualitative diagnosis conclusions in advance. As a result, the fault detection method combining fuzzy and neural network has attracted the interest of many experts as soon as it was proposed [17, 18]. Scholars applied fuzzy neural network to the fault detection of a class of nonlinear systems, and successfully achieved fault separation [19]. The researchers used adaptive controller reconstruction technology and introduced Kalman filters to estimate parameters online, and realized fault-tolerant control of a class of actuator failure systems [20]. Scholars apply the estimated information scheduling strategy to fault-tolerant control, which enhances the system’s fault-tolerant margin and performance indicators [21]. However, due to the use of information estimation, this method requires very accurate fault detection information. Scholars have introduced linear quadratic robust control methods into discrete linear guaranteed cost control to ensure that when a fault occurs, the system’s secondary control performance index still meets the control requirements [22].

Through research on common methods, this paper determines the fault diagnosis method based on genetic algorithm optimized wavelet neural network and the fault-tolerant control method based on linear time-varying parameter state observer. A network model of wavelet neural network is proposed, and the genetic algorithm with global search capability is used to optimize the weights and thresholds of the neural network model to avoid the deficiencies of traditional neural network algorithms. Based on RBF (Radial Basis Function) and genetic algorithm optimized neural network, an online fault diagnosis model with dynamic changes of training samples was established respectively. On this basis, an online fault diagnosis scheme for the depth sensor of a product was designed, and the actual flight data of the product was used. We perform simulation experiments for training samples. The results show that the scheme is effective and feasible, and can accurately identify multiple failure modes of the sensor.

2 Related theories of fault diagnosis and fault-tolerant control

2.1 Fault diagnosis under neural network

Signal collection is the basis for fault diagnosis, and its purpose is to obtain useful information that can be collected in real time and is sensitive to changes in working status. Signal analysis and processing is to extract the characteristic values of the representative signals in the signal for processing. Status recognition is at the core of the fault diagnosis process. The extracted feature vectors are continuously compared with thresholds or normal values to identify the operating state of the system to be diagnosed, thereby determining the type of fault. The general fault diagnosis system is shown in Fig. 1.

Fig. 1

Fault diagnosis system.

Neural network solves the problem of difficult to build mathematical models of complex systems, so it has a clear advantage in the research of fault diagnosis. The diagnosis process is shown in Fig. 2.

Fig. 2

The diagnosis process diagram based on neural network.

The diagnosis process is roughly divided into two steps. First, you select a reasonable number of training sample sets and input to the neural network for training to obtain the desired network with diagnostic functions. Second, you input the pre-diagnosed test sample set into the trained system for diagnosis. Before training, the data needs to be processed, such as normalization and feature extraction, the purpose is to provide more appropriate diagnostic input and training samples for the diagnostic network, thereby improving the accuracy of the diagnosis.

2.2 State observer

In most modern control theory research processes, most of the controlled objects are described using state space expressions, especially for the linear system studied in this paper. The correct system state and control quantity are obtained and correct implementation has an inseparable relationship. Therefore, obtaining the state of the system is very important for the control system.

The state observer is described by differential equations as follows: ${\begin{matrix} \tilde{x} = f (x, t) \\ y = g (x, t) \end{matrix}$ (1)

Suppose the research object is the following linear system: ${\begin{matrix} \tilde{x} = Ax + Bu \\ y = Cx \end{matrix}$ (2)

In the formula, the state vector is x, the input vector is u, the output vector is y, A, B, and C are real matrices, and the initial state is x (0)=x₀.

We construct a full-dimensional state observer: $\vec{x} = y - C \overset{⌣}{x} + Bu + A \overset{⌣}{x}$ (3)

In the formula, $\overset{⌣}{x}$ represents the observed state.

2.3 Principle analysis of fault-tolerant control of control system

The basic idea of fault-tolerant control of the system is that on the basis of the fault diagnosis of the sensor, the fault value can be estimated by the fault value of the sensor, and then the true value of the fault value can be estimated from the fault value. The actual value estimated by this is used as a feedback amount to realize control. Therefore, even if the sensor fails, the system can well achieve the expected control purpose.

Since the system state cannot be directly measured when the system fails, a state observer is used to estimate the state of the system. Specifically, the fault state of the system can be estimated based on the state observer. The original controller no longer uses the estimated state to implement control based on the measured value of the sensor. At this time, the controller is called a state controller. This is the principle of fault tolerance.

It must be noted that in the choice of state observer, whether it is a full-dimensional state observer or a reduced-dimensional state observer, the system must be observable.

Assuming that the system satisfies considerable conditions, a system can be designed: ${\begin{matrix} \vec{x} = Bu (t) + A (θ) \ddot{x} (t) \\ \vec{y} = C \ddot{x} (t) \end{matrix}$ (4)

In the formula, $\vec{x} (t)$ is the state vector of the construction system, and $\vec{y} (t)$ is its output vector.

The purpose of the state observer is to realize the state observation and tracking of the original closed-loop system.

When the sensor fails, the state observer is used to observe the failure state, and the controller uses the observation value obtained by the observer to control the system, rather than using the system state measured by the faulty sensor, so as to eliminate the failure during the control. This is the principle of fault-tolerant control based on the observer method.

3 Wavelet neural network model based on genetic algorithm optimization

3.1 Fault diagnosis of wavelet neural network

The structure proposed in this paper is shown in Fig. 3. Generally speaking, wavelet neural network (WNN) has simpler structure, faster convergence speed and higher accuracy. $x_{h} = ψ (x_{h} - b_{h}) - ψ (a_{h})$ (5)

Fig. 3

WNN structure.

The a_h and b_h are the wavelet’s scaling factor and translation factor, respectively. We define the error function according to the gradient descent method: $E = \sum_{p = 0}^{P - 1} \sum_{j = 0}^{J - 1} (y_{j} - {\bar{y}}_{j})^{2}$ (6)

The training algorithm of WNN is used to update the connection weights between neurons, wavelet expansion and translation factors, where η is the learning rate of BP algorithm and α is the momentum factor of BP algorithm. $Δ α_{h} = - η (\partial E / \partial α_{h})$ (7)

We perform fault diagnosis based on the established WNN model. Using the above WNN as a prototype to diagnose sensor faults, the sensor data sequence at the first k times is the input, and the predicted value of the sensor data at the k + 1th time is the output. Therefore, taking k as the input node of the WNN, the output node is 1.

Although there may be a sudden change in the sensor signal caused by environmental noise and other factors, it is considered to be abnormal data caused by a sensor failure. It is found that the average value of the error within Δt for a period of time after that time. On the contrary, it is considered that the sensor has not failed, and continues to add the current sampling value to the sample, overwrite the previous sample, and predict and train the network. Among them, Δt is determined according to experiment and actual experience, and is related to the number of sampling points.

To use such a network to diagnose faults, it is necessary to adjust the weights of the proposed network. The BP algorithm is commonly used for training, but the BP algorithm cannot guarantee the global optimal solution of the network.

3.2 Genetic algorithm optimized neural network

The study of learning algorithm is mainly based on the proposed model to find an adjustment neural network. Because genetic algorithms are robust, and can search for global optimal solutions, using genetic algorithms to optimize neural networks can not only exert the generalized mapping capabilities of neural networks, but also improve the convergence speed and learning of neural networks.

Genetic algorithm is an optimization algorithm that performs robust search in complex space. It absorbs the evolutionary thinking of “survival of the fittest and survival of the fittest” of natural biological systems, and provides a new way to solve many problems that traditional optimization methods are difficult to solve. In the genetic algorithm, the problem is first solved into genotypes, and the fitness function is used to evaluate the pros and cons of each individual, so as to select the population, and then perform crossover and mutation operations on the newly generated population. The purpose is to make the individuals in the population have diversity and prevent falling into the local optimal solution.

Using genetic algorithm to replace the traditional learning algorithm in neural network can weigh the BP network. The value and threshold are optimized to obtain the global optimal solution, which can not only ensure convergence at the global minimum point, but also ensure the convergence speed.

The S function is used as the activation function of the neuron, and the unipolar S function is the output layer. The coding methods commonly used in genetic algorithms are binary coding and real coding. However, when solving this problem, binary coding cannot intuitively reflect the structural characteristics of the problem itself. Real number coding describes the problem intuitively, without the process of encoding and decoding, which can improve the accuracy and speed of the solution.

In this paper, real number coding is used. A real number is used to represent each connection weight or threshold. The weights and thresholds of the network are compiled into a long string in order to form an individual chromosome.

The length of the chromosome is 70, and each chromosome is composed of 4 parts (output layer and hidden layer weights, output layer threshold, input layer and hidden layer weights, hidden layer threshold). Threshold values are put together.

The block diagram is shown in Fig. 4.

Fig. 4

Genetic algorithm program block diagram.

4 Simulation experiment and result analysis

In order to verify the effectiveness of RBF neural network and genetic algorithm optimization, the sensor data of a certain type of product are used for simulation experiments. As shown in Fig. 5, the data of 3000 time points of the depth sensor is selected, and the real-time tracking prediction is performed by the RBF neural network prediction model and the genetic algorithm optimization neural network prediction model. It can be seen from the figure that the RBF neural network has large fluctuations at certain times, but the overall stability is stable. It can track the rising and falling trends of the data well, and can effectively predict the sensor data in real time. The genetic algorithm optimized neural network model does not show large fluctuations, can generally track the data up and down trend, and has strong real-time prediction ability. Therefore, the prediction ability of the neural network optimized by genetic algorithm is better.

Fig. 5

WNN structure.

Figure 6 (a) reflects the mean square error of the predicted output of the RBF neural network and the actual output of the sensor, and Fig. 6 (b) reflects the mean square error of the genetic algorithm optimized single hidden layer neural network’s predicted output and the actual output of the sensor. The analysis and comparison of the two figures show that the prediction error of the genetic algorithm optimized neural network from the first time point to the 2800th time point is relatively stable, and the prediction error value of the RBF neural network has a large range during this time. It can be seen that the genetic algorithm optimized neural network has smaller prediction errors than the RBF neural network and has better stability, so the genetic algorithm optimized prediction ability is better.

Fig. 6

Neural network tracking prediction error graph.

When the system is running, the data at 3000 times is selected, and after the 1500th time point, the fault is injected artificially. The output value of the sensor is abruptly changed during this period to simulate the sensor disturbance failure. Figure 7 shows the experiment results.

Fig. 7

Neural network fault prediction diagram.

As shown in Fig. 8, the mean square error curves of the two prediction models also showed large fluctuations near the 1500th time point, and the mean square error values were all consecutive time points greater than the threshold. Therefore, RBF neural network and genetic algorithm optimization neural network prediction model can determine the sensor failure.

Fig. 8

Neural network fault prediction error graph.

The selection of the threshold value is also a problem that cannot be ignored. The selection of the threshold value is reasonable or not, which directly affects the accuracy of the fault judgment. If it is set too small, the slight disturbance will be mistaken as a fault. It may not be detected. In the simulation process, after many experiments, the threshold was finally selected as 0.01. After this value was selected, the two neural network fault diagnosis models were relatively reasonable and accurate when determining the fault.

The fault is artificially injected from the selected 1000th time point, the output value of the sensor is set to a constant value during this period, and the output information of the analog sensor remains unchanged, that is, a “stuck” fault. As shown in Fig. 9. The system is in the dive state at this time, the predicted output curve of the RBF neural network begins to fluctuate violently at the 1000th point, and the mean square error also fluctuates greatly, and the values are greater than the set threshold from the 1000th time point. Therefore, the RBF neural network prediction model determines that the sensor is malfunctioning.

Fig. 9

RBF neural network fault prediction and prediction error.

As shown in Fig. 10, when the system dives, the sensor output during the period after the 600th time point is set to a constant value to simulate the sensor’s “stuck” fault. It can be seen from the figure that the predicted output curve of the genetic algorithm optimized neural network starts to fluctuate at the 600th point and is consistent with the sensor output. The mean square error also fluctuates greatly at this moment. Therefore, the genetic algorithm optimized neural network prediction model can determine the failure of the sensor.

Fig. 10

Genetic algorithm optimization Neural network fault prediction and prediction error.

When the left thruster of the system fails, the torque generated on the horizontal plane will no longer be balanced, and the system will deflect to the left. The changes of its motion parameters are shown in Fig. 11. It can be seen from the figure that after the left propeller of the system fails, the torque balance is still achieved under the balance of the vertical rudder, but its navigation direction has changed greatly, which is impossible in the actual operation of the system. Because the vertical rudder has reached the limit in the control process, the system has not entered the cycle because the limit value is not set in the simulation.

Fig. 11

System speed components and system displacement components.

At this time, there are two fault-tolerant control strategies. One is to reduce the thrust of the right thruster to make it equal to the thrust of the left thruster. The thrust of the propeller does not need to be reduced to be equal to that of the left propeller, but only needs to be reduced to the range that the vertical rudder can compensate. The other is to increase the thrust of the right thruster and find the compensation rudder angle of the vertical rudder according to the system loss torque, so that the vertical torque of the system can be balanced again.

5 Conclusion

This paper studies the method of sensor fault diagnosis based on neural network, mainly introduces the basic theory of artificial neural network and the theory of neural network fault diagnosis method, and studies the related theory of state observer. It provides a sufficient theoretical basis for fault diagnosis and fault tolerance control. In order to improve the convergence speed of the neural network and avoid falling into the local optimum, an improved genetic algorithm is proposed to optimize the weights and thresholds of the neural network. The genetic algorithm can perform a global search and use genetically optimized WNN to simulate sensor data. The simulation results show that the genetic algorithm-optimized neural network sensor fault diagnosis method and the RBF neural network fault diagnosis method can accurately identify the system sensor fault, and the genetic algorithm optimization is more excellent in diagnosis accuracy and training time. This provides a certain reference value for promoting the reliability of unattended control system.

Footnotes

Acknowledgments

This paper is supported by the National Science Foundation of China under Grants (61603262), “Liaoning BaiQianWan Talents Program, Natural Science Foundation of Liaoning Province (20180550418), i5 Intelligent Manufacturing Institute Fund of Shenyang Institute of Technology (i5201701). Thanks for their help.

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