CN115562023A - Noise-tolerant zero-ization neural network model design and method based on fuzzy control - Google Patents

Abstract

The embodiment of the present disclosure provides a fuzzy control-based noise tolerance and zeroing neural network model design and method, which belongs to the field of computing technology, and specifically includes: Step 1, designing fuzzy control, wherein the fuzzy control includes a fuzzy interface, Rule base, database, fuzzy decision-making unit and defuzzification interface; Step 2, according to the evolution formula of the fuzzy control and the traditional zeroing neural network, obtain the fuzzy noise-tolerant zeroing neural network evolution formula; Step 3, combine with time-varying The specific form of the problem-related error matrix is substituted into the evolution formula of the fuzzy noise-tolerant zero neural network to obtain a fuzzy noise-tolerant zero neural network model for solving the time-varying problem. Through the solution disclosed in the present disclosure, a noise-tolerant and zeroing neural network model with a simple structure, better noise tolerance, global stability and limited time convergence can be designed.

Description

Design and method of neural network model for noise tolerance and zeroing based on fuzzy control

technical field

The embodiments of the present disclosure relate to the field of computing technology, and in particular to a design and method of a neural network model for noise tolerance and zeroing based on fuzzy control.

Background technique

At present, as a kind of artificial neural network with feedback structure, recurrent neural network has a very wide range of applications in the fields of protein structure prediction, cooperative control of manipulators, image caption generation, passive positioning and so on. The research on recurrent neural network can be traced back to the Hopfield neural network proposed by J.J. Hopfield in 1982, which clarified the relationship between neural network and dynamics for the first time. It is worth mentioning that recurrent neural networks with neurodynamic behavior have been deeply studied, among which gradient neural networks and zeroing neural networks are two well-known recurrent neural networks. In particular, due to the obvious advantages of nulling neural networks in solving time-varying problems, they are widely used in wireless sensor networks, dynamic positioning, chaotic sensor systems, and image object detection.

Convergence and robustness are two important indicators to evaluate the effectiveness of nulling neural networks in solving time-varying problems. Currently, researchers have studied these two characteristics from many aspects. For example, by introducing design parameters such as constant scalar, fuzzy scalar, and dynamic scalar, the convergence speed of the zeroing neural network can be improved; the convergence type of the zeroing neural network can usually be achieved by using a linear or nonlinear activation function. For example, the bipolar Sigmoid and power activation functions can make the zeroing neural network achieve exponential convergence and super-exponential convergence; the zeroing neural network activated by the Sign-bi-power function has finite time convergence. The zeroing neural network with finite time convergence can reach a stable state in a finite time, and its stable time is related to the initial value. Fixed-time convergence and predefined-time convergence of nulling neural networks were further developed when researchers applied some nonlinear activation functions. Previous studies have shown that the advantages of fixed time convergence and predefined time convergence are mainly reflected in the fact that the settling time has nothing to do with the initial value, which has great advantages over finite time convergence. Furthermore, compared to fixed-time convergence, the convergence time of predefined-time convergence is determined by only one or more parameters and thus can be easily pre-determined. In summary, these different types of convergence studies have important implications for the development of nulling neural networks and lead to more practical applications. In addition to the study of convergence, the researchers also conducted an in-depth study on the robustness of nulling neural networks. For example, Zhang et al. discussed the robustness of the zeroing neural network and calculated the upper bound of the residual; the two nonlinear activation functions proposed by Li et al. can not only improve the convergence of the zeroing neural network, but also tolerate Various noises, including large constant noise and dynamic noise; Jin and Zhang et al. proposed an integral design formula for deriving the anti-noise nulling neural network, which means that the nulling neural network has inherent anti-noise ability ; on this basis, Xiao et al. proposed a zeroing neural network algorithm with finite time convergence and inherent noise tolerance, in which the algorithm is mainly realized by an improved integral design formula. However, the above-mentioned studies on the convergence and robustness of the zeroing neural network have certain deficiencies: the model form of the zeroing neural network derived from the integral design formula is too complex to be realized; the types of noise that the zeroing neural network can resist are limited ; Nullifying neural networks cannot tolerate noise in finite time.

It can be seen that there is an urgent need for a noise-tolerant and nulling neural network model that can design a simple structure, noise tolerance, global stability, and finite time convergence.

Contents of the invention

In view of this, the embodiments of the present disclosure provide a design and method of a neural network model and method for noise tolerance and zeroing based on fuzzy control, which at least partially solve some problems existing in the prior art.

The embodiment of the present disclosure provides a fuzzy control-based noise tolerance and zeroing neural network model design and method, including:

Step 1, designing fuzzy control, wherein the fuzzy control includes a fuzzy interface, a rule base, a database, a fuzzy decision unit and a defuzzification interface;

Step 2, according to the fuzzy control and the evolution formula of the traditional zeroing neural network, obtain the fuzzy noise-tolerant zeroing neural network evolution formula;

Step 3, substituting the specific form of the error matrix related to the time-varying problem into the evolution formula of the fuzzy noise-tolerant zero neural network to obtain the fuzzy noise-tolerant zero neural network model for solving the time-varying problem.

According to a specific implementation manner of an embodiment of the present disclosure, the step 1 specifically includes:

Step 1.1, design a fuzzy interface that includes two clear inputs;

Step 1.2, establishing multiple if-then rules to form the rule base;

Step 1.3, designing membership functions corresponding to two inputs and outputs to form the database;

Step 1.4, designing the processing flow of the fuzzy decision-making unit;

Step 1.5, designing a defuzzification method for the defuzzification interface to obtain a clear output.

其中，p(t)＝vec(P(t))，e(t)＝vec(E(t))，v＝vec(V)，P(t)为误差矩阵，η为设计参数用于控制零化神经网络的的收敛速率，E(t)为外部噪声，V为模糊控制。According to a specific implementation of an embodiment of the present disclosure, the evolution formula of the fuzzy noise tolerance and zeroing neural network is

Wherein, p(t)=vec(P(t)), e(t)=vec(E(t)), v=vec(V), P(t) is an error matrix, and η is a design parameter for controlling The convergence rate of the zeroing neural network, E(t) is the external noise, and V is the fuzzy control.

According to a specific implementation manner of an embodiment of the present disclosure, the step 3 specifically includes:

Step 3.1, obtaining the time-varying Sylvester matrix equation;

Step 3.2, defining the error matrix;

Step 3.3, substituting the error matrix into the evolution formula of the fuzzy noise-tolerant and zeroing neural network to obtain the fuzzy noise-tolerant and zeroing neural network model and perform vectorization.

The fuzzy control-based noise tolerance and zeroing neural network model design scheme in the embodiment of the present disclosure includes: Step 1, designing fuzzy control, wherein the fuzzy control includes a fuzzy interface, a rule base, a database, a fuzzy decision-making unit and a regression Fuzzy interface; Step 2, according to the evolution formula of the fuzzy control and the traditional zeroing neural network, obtain the fuzzy noise-tolerant zeroing neural network evolution formula; Step 3, substitute the specific form of the error matrix related to the time-varying problem into the The evolution formula of fuzzy noise tolerance and zero neural network is described, and the fuzzy noise tolerance and zero neural network model for solving this time-varying problem is obtained.

The beneficial effects of the embodiments of the present disclosure are as follows: through the scheme of the present disclosure, 1) by introducing a new fuzzy control method into the zeroing neural network, a fuzzy noise-tolerant and zeroing neural network with simple structure and superior performance is proposed ; 2) The fuzzy control method is designed based on two kinds of error variations of the zeroing neural network, and the fuzzy control produced therein has inherent anti-noise ability; 3) Although there is noise interference, the fuzzy noise-tolerant zeroing neural network still has Global stability and finite (or fixed) time convergence; 4) The fuzzy noise-tolerant and nulling neural network effectively solves the time-varying Sylvester matrix equation problem.

Description of drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present disclosure. Those of ordinary skill in the art can also obtain other drawings based on these drawings without any creative effort.

FIG. 1 is a schematic flowchart of a fuzzy control-based noise tolerance and zeroing neural network model design method provided by an embodiment of the present disclosure;

Fig. 2 is the membership function of input p _i (t);

的隶属函数；Figure 3 is the input

membership function;

Fig. 4 is the realization block diagram of fuzzy noise-tolerant zeroing neural network;

Fig. 5 is the elemental error figure of traditional zeroing neural network and fuzzy noise tolerance zeroing neural network;

Fig. 6 is the trajectory of the solution of the fuzzy noise-tolerant zeroing neural network under the simple nonlinear activation function;

Figure 7 is the residual diagram of the traditional zeroing neural network and the fuzzy noise-tolerant zeroing neural network, where (a) is about the traditional zeroing neural network and the fuzzy noise-tolerant zeroing neural network, (b) is the fuzzy noise-tolerant ZNN, where TZNN means traditional zeroing neural network, and INT-ZNN means fuzzy noise-tolerant zeroing neural network;

Fig. 8 is the residual diagram of fuzzy noise-tolerant zeroing neural network under the effect of Sign-bi-power nonlinear activation function, wherein (a) is e(t)=sign(p(t)) (b) is e(t )=sign(p(t))|0.5cos(t)+0.5sin(t)|;

Fig. 9 is under the interference of noise, the residual error comparison of fuzzy control noise tolerance and zeroization neural network and integral control noise tolerance zeroization neural network, wherein, (a) is impulse noise: when t=2,4,6,8 , e(t)=100(b) is bounded noise: e(t)=0.2cos(10t)+0.2sin(10t)(c) is unbounded noise: e(t)=0.1t;

Fig. 10 is the denoising of synthetic image-1, wherein, (a) is the original image of 400×400, (b) is the noise image, and (c) is the restored image;

Fig. 11 is the composite image-2 denoising, wherein (a) is the original image of 400×400, (b) is the noise image, and (c) is the restored image;

Fig. 12 is a three-dimensional grid diagram for recovering a composite image, wherein (a) is a composite image-1, and (b) is a composite image-2;

Figure 13 is the residual error generated when the fuzzy noise-tolerant and zeroing neural network solves the synthetic image denoising, where (a) is the synthetic image-1, and (b) is the synthetic image-2;

Fig. 14 is medical brain image reconstruction, wherein, (a) is the original image, (b) is the 20% point-like missing image, and (c) is the reconstructed image;

Fig. 15 is medical cervical spine image reconstruction wherein, (a) is the original image, (b) is the 40% point-like missing image, and (c) is the reconstructed image;

Fig. 16 is the residual error generated when the fuzzy noise tolerance and zeroing neural network solves the medical image reconstruction, where (a) is a medical brain image, and (b) is a medical cervical spine image.

detailed description

Embodiments of the present disclosure will be described in detail below in conjunction with the accompanying drawings.

Embodiments of the present disclosure are described below through specific examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Apparently, the described embodiments are only some of the embodiments of the present disclosure, not all of them. The present disclosure can also be implemented or applied through different specific implementation modes, and various modifications or changes can be made to the details in this specification based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that, in the case of no conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in the present disclosure, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present disclosure.

It is noted that the following describes various aspects of the embodiments that are within the scope of the appended claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is illustrative only. Based on the present disclosure one skilled in the art should appreciate that an aspect described herein may be implemented independently of any other aspects and that two or more of these aspects may be combined in various ways. For example, any number of the aspects set forth herein can be used to implement an apparatus and/or practice a method. In addition, such an apparatus may be implemented and/or such a method practiced using other structure and/or functionality than one or more of the aspects set forth herein.

It should also be noted that the diagrams provided in the following embodiments are only schematically illustrating the basic ideas of the present disclosure, and only the components related to the present disclosure are shown in the drawings rather than the number, shape and shape of the components in actual implementation. Dimensional drawing, the type, quantity and proportion of each component can be changed arbitrarily during actual implementation, and the component layout type may also be more complicated.

Additionally, in the following description, specific details are provided to facilitate a thorough understanding of examples. However, it will be understood by those skilled in the art that the described aspects may be practiced without these specific details.

An embodiment of the present disclosure provides a method for designing a neural network model based on fuzzy control, and the method can be applied in an image processing process.

Referring to FIG. 1 , it is a schematic flowchart of a method for designing a neural network model for noise tolerance and zeroing based on fuzzy control provided by an embodiment of the present disclosure. As shown in Figure 1, the method mainly includes the following steps:

Step 1, designing fuzzy control, wherein the fuzzy control includes a fuzzy interface, a rule base, a database, a fuzzy decision unit and a defuzzification interface;

Further, the step 1 specifically includes:

Step 1.1, the design contains two fuzzy interfaces for clear input;

Step 1.2, establishing multiple if-then rules to form the rule base;

Step 1.3, designing membership functions corresponding to two inputs and outputs to form the database;

Step 1.4, designing the processing flow of the fuzzy decision-making unit;

Step 1.5, designing a defuzzification method for the defuzzification interface to obtain a clear output.

组成，其中v_j表示v的第j个元素。In concrete implementation, design fuzzy control. The fuzzy control consists of five parts: fuzzy interface, rule base, database, fuzzy decision-making unit, and defuzzification interface. fuzzy control v by v _j ,

Composition, where v _j represents the jth element of v.

其中p_j(t)和

分别是p(t)和

的第j个元素，并且p(t)表示零化神经网络中的误差函数，

表示传统零化神经网络中的设计公式。1) Fuzzy interface: Consider two clear inputs, p _j (t) and

where p _j (t) and

are p(t) and

The jth element of , and p(t) represents the error function in the zeroing neural network,

Represents the design formulation in traditional annihilating neural networks.

2) Rule base: establish the following six "if-then" rules.

is N_j1，then v_j1 is 0；Rule 1: if p _j (t) is M _j1 and

is N _j1 , then v _j1 is 0;

is N_j2，then v_j2 is p_j(t)；Rule 2: if p _j (t) is M _j1 and

is N _j2 ，then v _j2 is p _j (t);

is N_j3，then v_j3 is u_j；Rule 3: if p _j (t) is M _j1 and

is N _j3 ，then v _j3 is u _j ；

is N_j1，then v_j4 is -u_j；Rule 4: if p _j (t) is M _j2 and

is N _j1 , then v _j4 is -u _j ;

is N_j2，then v_j5 is p_j(t)；Rule 5: if p _j (t) is M _j2 and

is N _j2 ，then v _j5 is p _j (t);

is N_j3，then v_j6 is 0；Rule 6: if p _j (t) is M _j2 and

is N _j3 , then v _j6 is 0;

是规则的前件，v_j是规则的后件。在这些规则中，M_j1，M_j2，N_j1，N_j2和N_j3是模糊集，

即u_j是

的界。因此，v_j被定义为一个常数，即p_j(t)，u_j，-u_j或者0。where p _j (t) and

is the antecedent of the rule, and v _j is the consequent of the rule. In these rules, M _j1 , M _j2 , N _j1 , N _j2 and N _j3 are fuzzy sets,

i.e. u _j is

boundary. Therefore, v _j is defined as a constant, ie p _j (t), u _j , -u _j or 0.

的隶属函数如图2和图3所示，其中p_j(t)和

在各模糊集的隶属度分别为3) Database: design p _j (t) and

The membership function of is shown in Figure 2 and Figure 3, where p _j (t) and

The degree of membership in each fuzzy set is

M _j1 =1; M _j2 =1.

4) Fuzzy decision-making unit: based on the above-mentioned fuzzy relationship, connect fuzzy input and output, and make inferences according to fuzzy rules.

其中A_ji∈{N_j1，N_j2，N_j3}。最终，与p(t)以及

相关的模糊控制v可以通过v_j获得。5) Defuzzification interface: use Centroid defuzzification method to get clear output. Since M _j1 =1 and M _j2 =1, so

where A _ji ∈ {N _j1 , N _j2 , N _j3 }. Finally, with p(t) and

The related fuzzy control v can be obtained by v _j .

Step 2, according to the fuzzy control and the evolution formula of the traditional zeroing neural network, obtain the fuzzy noise-tolerant zeroing neural network evolution formula;

Further, the evolution formula of the fuzzy noise tolerance and zeroing neural network is

Wherein, p(t)=vec(P(t)), e(t)=vec(E(t)), v=vec(V), P(t) is an error matrix, and η is a design parameter for controlling The convergence rate of the zeroing neural network, E(t) is the external noise, and V is the fuzzy control.

In the specific implementation, based on the fuzzy control above, according to the evolution formula of the traditional zeroing neural network, the evolution formula of the fuzzy noise-tolerant and zeroing neural network is further proposed as follows:

As above, P(t) is the error matrix, which is determined by the specific time-varying problem; η is the design parameter used to control the convergence rate of the zeroing neural network; E(t) is the external noise; V is the fuzzy control used to improve the zeroing Noise Tolerance of Neural Networks. After adopting the vectorization operation, the following results are further obtained:

由此，我们也可以得到

where p(t)=vec(P(t)), e(t)=vec(E(t)), v=vec(V). make

From this, we can also get

是与模型相关的两个量，其通过模糊化、模糊决策以及退模糊化，最终得到模糊输出v。将该模糊输出v放入模型中，其可以有效抑制外部噪声e(t)。由此，被噪声干扰的模糊容噪零化神经网络依然可以有效解决时变问题。The implementation of the fuzzy noise tolerance and zeroing neural network is shown in Figure 4, where the content in the dashed box is the fuzzy control part, input p(t) and

are two quantities related to the model, through fuzzification, fuzzy decision-making and defuzzification, the fuzzy output v is finally obtained. This fuzzy output v is put into the model, which can effectively suppress the external noise e(t). Therefore, the fuzzy noise-tolerant neural network interfered by noise can still effectively solve the time-varying problem.

Step 3, substituting the specific form of the error matrix related to the time-varying problem into the evolution formula of the fuzzy noise-tolerant zero neural network to obtain the fuzzy noise-tolerant zero neural network model for solving the time-varying problem.

On the basis of the foregoing embodiments, the step 3 specifically includes:

Step 3.1, obtaining the time-varying Sylvester matrix equation;

Step 3.2, defining the error matrix;

Step 3.3, substituting the error matrix into the evolution formula of the fuzzy noise-tolerant and zeroing neural network to obtain the fuzzy noise-tolerant and zeroing neural network model and perform vectorization.

In the specific implementation, the specific form of the error matrix P(t) related to the time-varying problem is brought into the above evolution formula of the fuzzy noise-tolerant zero neural network, and the fuzzy noise-tolerant zero neural network model for solving the time-varying problem can be obtained . Next, we take the time-varying Sylvester matrix equation problem as an example to design a specific fuzzy noise-tolerant neural network model.

1) Consider the following time-varying Sylvester matrix equation:

H(t)X(t)+X(t)G(t)+R(t)＝0

表示已知的系数矩阵。

表示未知的待求解矩阵。in,

represents the known coefficient matrix.

Represents the unknown matrix to be solved.

2) Define the error matrix P(t): P(t)=H(t)X(t)+X(t)G(t)+R(t)

3) Bring the error matrix P(t) into the above evolution formula of the fuzzy noise tolerance and zeroing neural network, and further obtain the fuzzy noise tolerance and zeroing neural network model as follows:

After vectorizing the above model, we can get

e(t)＝vec(E(t))，r(t)＝vec(R(t))，并且v＝vec(V)。in

e(t)=vec(E(t)), r(t)=vec(R(t)), and v=vec(V).

The fuzzy control-based noise tolerance and zeroing neural network model design method provided in this embodiment, 1) introduces a new fuzzy control method into the zeroing neural network, and proposes a fuzzy noise tolerance with simple structure and superior performance 2) The fuzzy control method is designed based on two kinds of error changes of the NN, and the fuzzy control generated in it has inherent anti-noise ability; 3) Despite the noise interference, the fuzzy noise-tolerant NULL The neural network still has global stability and finite (or fixed) time convergence; 4) The fuzzy noise-tolerant and nulling neural network effectively solves the time-varying Sylvester matrix equation problem.

In order to further illustrate the effect of the fuzzy noise tolerance and zeroing neural network model designed by the method of the present application, a specific example will be described below.

1. First consider the evolution formula of the traditional zeroing neural network as follows:

是根据具体的时变问题F(X(t)，t)＝0定义的误差矩阵，其中F(·)：

是函数映射，X(t)是待求解的未知变量。P(t)＝F(X(t)，t)的作用是监测时变问题的变化。η为正参数，保证零化神经网络的收敛性。Ψ(·)：

是矩阵映射称为激活函数。in,

is the error matrix defined according to the specific time-varying problem F(X(t), t)=0, where F(·):

is a function mapping, and X(t) is the unknown variable to be solved. The function of P(t)=F(X(t), t) is to monitor the change of the time-varying problem. η is a positive parameter to ensure the convergence of the zeroing neural network. Ψ(·):

is the matrix mapping called the activation function.

2. By introducing fuzzy control, on the basis of the above-mentioned evolution formula of the traditional zeroing neural network, the evolution formula of the fuzzy noise-tolerant and zeroing neural network is further proposed, as follows:

Among them, E(t) is the external noise, and V is the fuzzy control used to improve the noise tolerance performance of the zeroing neural network. After adopting the vectorization operation, the following results are further obtained:

我们可以得到

模糊容噪零化神经网络的实现方式如图4所示，其中虚线框中的内容为模糊控制部分，输入p(t)和

是与模型相关的两个量，其通过模糊化、模糊决策以及退模糊化，最终得到模糊输出v。将该模糊输出v放入模型中，其可以有效抑制外部噪声e(t)。由此，被噪声干扰的模糊容噪零化神经网络依然可以有效解决时变问题。where p(t)=vec(P(t)), e(t)=vec(E(t)), v=vec(V). make

we can get

The implementation of the fuzzy noise tolerance and zeroing neural network is shown in Figure 4, where the content in the dashed box is the fuzzy control part, input p(t) and

are two quantities related to the model, through fuzzification, fuzzy decision-making and defuzzification, the fuzzy output v is finally obtained. This fuzzy output v is put into the model, which can effectively suppress the external noise e(t). Therefore, the fuzzy noise-tolerant neural network interfered by noise can still effectively solve the time-varying problem.

组成，其中v_j表示v的第j个元素。该模糊控制由以下5个部分组成。3. Next, we will detail the generation of the above fuzzy control v, which is mainly applied in the nulling neural network to resist noise. fuzzy control v by v _j ,

Composition, where v _j represents the jth element of v. The fuzzy control consists of the following 5 parts.

其中p_j(t)和

分别是p(t)和

的第j个元素。Fuzzy interface: consider two sharp inputs, p _j (t) and

where p _j (t) and

are p(t) and

The jth element of .

·Rule base: establish the following six "if-then" rules.

is N_j1，then v_j1 is 0；Rule 1: if p _j (t) is M _j1 and

is N _j1 , then v _j1 is 0;

is N_j2，then v_j2 is p_j(t)；Rule 2: if p _j (t) is M _j1 and

is N _j2 ，then v _j2 is p _j (t);

is N_j3，then v_j3 is u_j；Rule 3: if p _j (t) is M _j1 and

is N _j3 ，then v _j3 is u _j ；

is N_j1，then v_j4 is -u_j；Rule 4: if p _j (t) is M _j2 and

is N _j1 , then v _j4 is -u _j ;

is N_j2，then v_j5 is p_j(t)；Rule 5: if p _j (t) is M _j2 and

is N _j2 ，then v _j5 is p _j (t);

is N_j3，then v_j6 is 0；Rule 6: if p _j (t) is M _j2 and

is N _j3 , then v _j6 is 0;

是规则的前件，v_j是规则的后件。在这些规则中，M_j1，M_j2，N_j1，N_j2和N_j3是模糊集，

即u_j是

的界。因此，v_j被定义为一个常数，即p_j(t)，u_j，-u_j或者0。where p _j (t) and

is the antecedent of the rule, and v _j is the consequent of the rule. In these rules, M _j1 , M _j2 , N _j1 , N _j2 and N _j3 are fuzzy sets,

i.e. u _j is

boundary. Therefore, v _j is defined as a constant, ie p _j (t), u _j , -u _j or 0.

的隶属函数设计如图2和图3所示，其中p_j(t)和

在各模糊集的隶属度分别为Database: In this part, p _j (t) and

The membership function design of is shown in Figure 2 and Figure 3, where p _j (t) and

The degree of membership in each fuzzy set is

M _j1 =1; M _j2 =1.

·Fuzzy decision-making unit: This part is the core of fuzzy control method. It is based on fuzzy relations, connects fuzzy inputs and outputs, and makes inferences according to fuzzy rules.

其中A_ji∈{N_j1，N_j2，N_j3}。Defuzzification interface: We adopt Centroid defuzzification method to obtain clear output. Since M _j1 =1 and M _j2 =1, so

where A _ji ∈ {N _j1 , N _j2 , N _j3 }.

相关的模糊控制v最终可以通过v_j获得。Based on the above fuzzy control method, with p(t) and

The relevant fuzzy control v can finally be obtained by v _j .

4. Take the fuzzy noise-tolerant and nulling neural network as an example to solve the time-varying Sylvester matrix equation to verify its noise-tolerant performance. Consider the following time-varying Sylvester matrix equation:

H(t)X(t)+X(t)G(t)+R(t)＝0

表示已知的系数矩阵。

表示未知的待求解矩阵。in,

represents the known coefficient matrix.

Represents the unknown matrix to be solved.

In addition, in order to verify the finite-time convergence or fixed-time convergence of the fuzzy noise-tolerant and zeroing neural network, a simple nonlinear activation function is introduced in the numerical experiment:

ψ(p _j (t))=|p _j (t)| ^∈ sign(p _j (t)), 0<ε<1

With Sign-bi-power nonlinear activation function:

The coefficient matrices in the time-varying Sylvester matrix equation are

According to the design method introduced above, define the error matrix P(t)=H(t)X(t)+X(t)G(t)+R(t) to obtain the model as follows:

其中

e(t)＝vec(E(t))，r(t)＝vec(R(t))，并且v＝vec(V)。After vectorizing it, we can get

in

e(t)=vec(E(t)), r(t)=vec(R(t)), and v=vec(V).

Experiment 1: set η=5, the initial value of x(t) is x(0)=[0.01 0.01 0.01 0.01] ^T , and the time interval is [0, 10]. This experiment mainly shows that under the interference of external noise e(t)=[3sin(t) 3sin(2t) 3sin(3t) 3sin(4t)] ^T , the fuzzy noise-tolerant neural network and the traditional zeroing neural network Convergence effect comparison. In Fig. 5 and (a) of Fig. 7, we can observe that the traditional zeroing neural network model has no noise tolerance performance at all, and the element errors and residuals have obvious fluctuations. However, the elemental errors and residuals of the fuzzy noise-tolerant nulling neural network almost converge to zero, which indicates that the performance of the fuzzy noise-tolerant nulling neural network is more significant due to the application of fuzzy control.

Experiment 2: Set η=2, ∈=0.9, the initial value of x(t) is x(0)=[0.01 0.01 0.01 0.01] ^T , and the time interval is [0, 10]. This experiment mainly shows the comparison of the convergence effect of the fuzzy noise-tolerant neural network and the traditional zeroing neural network under the interference of external noise e(t)=sign(p(t))|20cos(10t)+1|. In Figure 6, the state solutions produced by the fuzzy noise-tolerant nulling neural network can be quickly traced back to the theoretical solution. And in (b) of Fig. 7, the residual error of the fuzzy noise-tolerant zeroing neural network can converge to zero within a limited time.

Experiment 3: set η=2, τ=0.5, time interval [0, 1]. In order to verify the convergence of the fuzzy noise tolerance and zeroing neural network activated by the Sign-bi-power nonlinear function under the interference of external noise, 12 groups of initial values of x(t) are considered, that is, the following initial values are respectively two groups: x (0)=0.01ones(4,1), x(0)=0.1ones(4,1), x(0)=0.02ones(4,1), x(0)=0.2ones(4,1) , x(0)=0.05ones(4,1), x(0)=0.5ones(4,1), where ones(4,1) represents a 4×1 unit vector. Observing (a) and (b) in Figure 8, no matter what the initial value is, the residual of the fuzzy noise tolerance and zeroing neural network always converges to zero within a fixed time.

Experiment 4: We compared the fuzzy noise-tolerant and nulling neural network with the integral control noise-tolerant and nulling neural network. Wherein the parameters are set as η ₁ =η ₂ =η=2, the time interval is [0,10], the initial value of x(t) is x(0)=[0.01 0.01 0.010.01] ^T , the experimental results are shown in Figure 9 Show. In this experiment, we considered three kinds of noise respectively, and it can be seen that no matter what kind of noise, the fuzzy noise-tolerant neural network has better anti-noise performance. This means that fuzzy control is better than integral control in terms of noise tolerance.

5. Apply the fuzzy noise tolerance and zeroing neural network to image processing, thus illustrating its potential practical application value.

The first is synthetic image denoising. The research shows that the algorithm based on the maximum posterior probability can effectively realize the image denoising task by solving the Sylvester equation. It is assumed that Y=X+Λ is a noise observation of an unknown image X, where Λ∼N(0, σ ² ) is random noise satisfying a Gaussian distribution. The image denoising problem is then described as the following Sylvester matrix equation:

_ΘN X(t)+X(t)ΘM ₊ D=0,

以及

(θ_N是纵向差分，θ_M是横向差分)，∑＝G/σ²意味着先验是全变差(G的第ij个元素是

考虑图10中(a)和图11中(a)所示的两幅合成图像，其中合成图像-1和合成图像-2都被加性高斯噪声干扰Λ～N(0，0.1²)，并且噪声图像如图10中(b)和图11中(b)所示。在该实验中，参数设置为η＝100，β＝1，α＝500，σ＝0.1，x(t)的初始值为x(0)＝[0.01 0.01 0.01 0.01]^T，时间区间[0，0.5]。利用模糊容噪零化神经网络解决这两个图像去噪问题，得到恢复图像如图10中(c)和图11中(c)所示，对应的三维网格模式如图12中(a)和图12中(b)所示。由这些实验结果可知，模糊容噪零化神经网络可以有效地解决图像去噪问题，特别是图像边缘得到了很好的保留。此外，从图13中(a)和图13中(b)可以看出，模糊容噪零化神经网络的残差可以快速收敛到零，这表明模糊容噪零化神经网络在解决图像去噪问题时具有优越的收敛性能。where Θ _N = β/2+2ασ ² Ω _N , Θ _M = β/2+2ασ ² Ω _M , and D = ∑⊙(X(t)-Y)-βX(t). As above, β is the conditional parameter , α is the prior parameter,

as well as

(θ _N is the vertical difference, θ _M is the horizontal difference), ∑=G/σ ² means that the prior is total variation (the ijth element of G is

Consider two synthetic images shown in (a) in Fig. 10 and (a) in Fig. 11, where both synthetic image-1 and synthetic image-2 are disturbed by additive Gaussian noise Λ∼N(0, 0.1 ² ), and The noise image is shown in (b) in Figure 10 and (b) in Figure 11. In this experiment, the parameters are set as η=100, β=1, α=500, σ=0.1, the initial value of x(t) is x(0)=[0.01 0.01 0.01 0.01] ^T , and the time interval is [0, 0.5]. Use the fuzzy noise tolerance and zeroing neural network to solve these two image denoising problems, and the restored images are shown in Figure 10 (c) and Figure 11 (c), and the corresponding three-dimensional grid pattern is shown in Figure 12 (a) And shown in (b) in Figure 12. From these experimental results, it can be known that the fuzzy noise-tolerant neural network can effectively solve the problem of image denoising, especially the edge of the image is well preserved. In addition, it can be seen from Figure 13(a) and Figure 13(b) that the residual of the fuzzy noise-tolerant and zeroing neural network can quickly converge to zero, which indicates that the fuzzy noise-tolerant and zeroing neural network is effective in solving image denoising It has excellent convergence performance when solving the problem.

被处理为向量

并且其每一个数据的位置记录为u_i，i＝1，2，...，mn，假设该图像被损坏，其中缺失数据的位置随机分布，并且记录为z_j，j＝1，2，...，l(l是缺失数据的总数)。假设y＝Υx是缺失图像的向量化形式。根据研究，图像重建问题可以描述为如下形式：The second is medical image reconstruction. when the image

is processed as a vector

And the position of each data is recorded as u _i , i=1, 2, ..., mn, assuming that the image is damaged, where the positions of missing data are randomly distributed, and recorded as z _j , j=1, 2, ..., l (l is the total number of missing data). Suppose y=Yx is the vectorized version of the missing image. According to the research, the image reconstruction problem can be described as the following form:

是先验参数，

以及

(θ_N是纵向差分，θ_M是横向差分)，in

is the prior parameter,

as well as

(θ _N is the vertical difference, θ _M is the horizontal difference),

首先考虑医学脑图像，损伤图像含20％的点样缺失率，如图14中(b)所示。然后，我们应用模糊容噪零化神经网络对受损图像进行重建并且进一步得到重建图像14中(c)。显然，模糊容噪零化神经网络能够有效地重建受损图像，尤其是重建后的图像细节表现得更加清晰。此外，图16中(a)的模糊容噪零化神经网络的残差收敛情况也表明了其有效性。其次考虑医学颈椎图像，损伤图像中点样缺失率为40％，如图15中(b)所示。然后，我们利用模糊容噪零化神经网络对受损图像进行重建，得到恢复图像如图15中(c)所示。图15中(c)和图16中(b)所示的实验结果，再次验证了模糊容噪零化神经网络在医学图像重建问题上的优越性能。Where χ _i (z _j )=χ(z _j -u _i ), when 0≤z _j -u _i ≤1, χ(·)=1, z _j -u _i >1, χ(·)=0. It is worth mentioning that the fuzzy noise tolerance and zeroing neural network proposed by the present invention is effective and feasible for the image reconstruction problem, despite the high dimensionality of the correlation matrix. This experiment uses two medical images in (a) in Figure 14 and (a) in Figure 15, and restores the damaged image through the fuzzy and noise-tolerant neural network, where the parameter is set to η=100,

Considering the medical brain image first, the damaged image contains 20% point loss rate, as shown in (b) in Fig. 14 . Then, we apply the fuzzy and noise-tolerant neural network to reconstruct the damaged image and further obtain the reconstructed image 14 (c). Obviously, the fuzzy and noise-tolerant neural network can effectively reconstruct the damaged image, especially the details of the reconstructed image are clearer. In addition, the residual convergence of the fuzzy noise-tolerant zeroing neural network in Fig. 16(a) also shows its effectiveness. Next, considering the medical cervical spine image, the missing point rate in the damaged image is 40%, as shown in (b) in Fig. 15 . Then, we use the fuzzy and noise-tolerant neural network to reconstruct the damaged image, and the restored image is shown in Figure 15(c). The experimental results shown in (c) in Figure 15 and (b) in Figure 16 have once again verified the superior performance of the fuzzy noise-tolerant and annihilating neural network on medical image reconstruction problems.

The units involved in the embodiments described in the present disclosure may be implemented by software or by hardware.

It should be understood that various parts of the present disclosure may be implemented in hardware, software, firmware or a combination thereof.

The above is only a specific implementation of the present disclosure, but the scope of protection of the present disclosure is not limited thereto, any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present disclosure, should be covered within the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be determined by the protection scope of the claims.

Claims (4)

1. A noise-tolerant zero-ization neural network model design method based on fuzzy control is characterized by comprising the following steps:

step 1, designing fuzzy control, wherein the fuzzy control comprises a fuzzification interface, a rule base, a database, a fuzzy decision unit and a defuzzification interface;

step 2, obtaining an evolution formula of the fuzzy noise-tolerant zero-ization neural network according to the evolution formula of the fuzzy control and the traditional zero-ization neural network;

and 3, substituting a specific form of an error matrix related to the time-varying problem into the fuzzy noise-tolerant zero neural network evolution formula to obtain a fuzzy noise-tolerant zero neural network model for solving the time-varying problem.

2. The method according to claim 1, wherein step 1 specifically comprises:

step 1.1, designing a fuzzification interface comprising two clear inputs;

step 1.2, establishing a plurality of if-then rules to form the rule base;

step 1.3, designing two membership functions corresponding to input and output to form the database;

step 1.4, designing a processing flow of the fuzzy decision unit;

and step 1.5, designing the defuzzification method of the defuzzification interface to obtain clear output.

3. The method of claim 2, wherein the fuzzy noise-tolerant zero-ized neural network evolution formula is

Wherein P (t) = vec (P (t)), E (t) = vec (E (t)), v = vecvec (V), P (t) is an error matrix, eta is a design parameter used for controlling the convergence rate of the zero-ization neural network, E (t) is external noise, and V is fuzzy control.

4. The method according to claim 3, wherein step 3 specifically comprises:

step 3.1, acquiring a time-varying Sylvester matrix equation;

step 3.2, defining the error matrix;

and 3.3, substituting the error matrix into the fuzzy noise-tolerant zero-ization neural network evolution formula to obtain the fuzzy noise-tolerant zero-ization neural network model and vectorizing the model.

Images