CN109408896B - Multi-element intelligent real-time monitoring method for anaerobic sewage treatment gas production - Google Patents
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Abstract
The invention discloses a multi-element intelligent real-time monitoring method for the gas production of anaerobic sewage treatment, which comprises the following steps: (1) constructing a genetic-fuzzy wavelet neural network; determining the fuzzy rule number of the network; correcting and improving the network; (2) Programming a genetic-fuzzy wavelet neural network as a program and burning the program into an embedded anaerobic treatment monitoring system; (3) Inputting sewage data as training data into an embedded anaerobic treatment monitoring system, and keeping the trained network structure state in the system; (4) The trained embedded anaerobic treatment monitoring system is connected to a sewage treatment site for online measurement, and the system rapidly obtains gas production and methane content based on the improved genetic-fuzzy wavelet neural network; and (5) sampling every 30 minutes, and repeating the step (4). The invention intelligently monitors the sewage anaerobic treatment system by accurately predicting the gas production and the methane content, and promotes the efficient and stable operation of the sewage anaerobic treatment system.
Description
Technical Field
The invention relates to the field of sewage treatment, in particular to a multi-element intelligent real-time monitoring method for the gas production of anaerobic sewage treatment.
Background
The anaerobic treatment technology is a process of converting organic matters into methane and carbon dioxide by facultative anaerobe groups under anaerobic conditions, is an energy-saving and energy-yielding sewage treatment process, can treat high-concentration organic wastewater, can treat medium-low-concentration organic wastewater, and is widely applied worldwide.
In order to improve the anaerobic process treatment effect, ensure the water quality and simultaneously maximize the gas production, it is very necessary to establish an anaerobic treatment monitoring system. However, the anaerobic sewage treatment system is a complex system which relates to multiple subjects such as chemistry, physics, biology and the like, has complexity, time-varying property, nonlinearity and uncertainty, so that the nonlinear relation between the gas production and a plurality of parameters is presented, and a certain difficulty is brought to the establishment of a gas production prediction modeling technology. The intelligent method has strong learning ability and self-adaptive ability, is nonlinear, can simulate an object model by learning to achieve a required nonlinear shape, is suitable for a multiple-input multiple-output system, has great flexibility and self-adaptation to the problem that a large amount of original data cannot be described by rules or formulas, and can be used for simulating a dynamic variable anaerobic treatment system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a multi-element intelligent real-time monitoring method for the gas production of anaerobic sewage treatment. The invention organically combines wavelet analysis, fuzzy theory, genetic algorithm and neural network based on the interrelation among the GAs yield, water quality and system control parameters of the anaerobic sewage treatment system to construct a GA-FWNN GAs yield prediction model, and processes and analyzes the monitoring data by means of a cloud computing storage platform to predict GAs yield (Biogas) and methane Content (CH) 4 ) The sewage anaerobic treatment system is intelligently monitored, and the efficient and stable operation of the sewage anaerobic treatment system is promoted.
The aim of the invention can be achieved by the following technical scheme:
a sewage anaerobic treatment gas production multi-element intelligent real-time monitoring method comprises the following specific steps:
(1) Constructing a genetic-fuzzy wavelet neural network; determining the fuzzy rule number of the genetic-fuzzy wavelet neural network by adopting a self-adaptive fuzzy C-means clustering algorithm; correcting and improving the genetic-fuzzy wavelet neural network by adopting a genetic and gradient descent hybrid algorithm;
(2) The improved genetic-fuzzy wavelet neural network is compiled into a system program through a computer language, and the program is burnt in an embedded anaerobic treatment monitoring system;
(3) Inputting sewage data as training data into an embedded anaerobic treatment monitoring system, enabling an improved genetic-fuzzy wavelet neural network structure in the system to reach a network precision target, and keeping a trained network structure state in the system;
(4) The trained embedded anaerobic treatment monitoring system is accessed to a sewage treatment site for online measurement, site water sample data to be measured are collected in real time through a sensor and are input into the system, and the system rapidly obtains gas yield and methane content based on the improved genetic-fuzzy wavelet neural network;
(5) And (4) sampling every 30 minutes, and repeating the step (4).
Specifically, in the present invention, the chemical demand (COD), the organic load factor (OLR), the Hydraulic Retention Time (HRT), the pH value (pH) and the total carbonate Alkalinity (ALK) are selected as input values to produce gas (Biogas) and methane Content (CH) 4 ) As output.
Specifically, in step (1), the constructed genetic-fuzzy wavelet neural network (GA-FWNN) specifically includes a five-layer network structure, and the mapping relationship between the network input domain outputs is expressed as:
wherein wo j (t) is expressed as a connection weight function from the wavelet network layer node to the output layer, c ij Sum sigma ij Respectively expressed as membership functions (gaussian functions) X is the center and width of i (t) represents input node parameters j=1, 2, 3..18, i=1, 2,3,4,5.
Furthermore, the first layer of the GA-FWNN structure is an input layer and is responsible for receiving all input factors and distributing the input factors to the next layer of the network, and the first layer has five nodes, namely COD (t), HRT (t), OLR (t), pH (t) and ALK (t).
Furthermore, the second layer of the GA-FWNN structure is a fuzzification layer, and the second layer introduces a fuzzy set theory, so that the network can process semantic variables. The layer makes each node correspond to a fuzzy language respectively by fuzzifying each input. In the present invention, a gaussian function is chosen as the excitation function, and the output of each node is expressed as:
wherein c ij Sum sigma ij Represented as the center and width of the ith input variable gaussian function associated with the jth fuzzy rule, respectively. And carrying out fuzzy division on the network by adopting a self-adaptive fuzzy C-means clustering algorithm, and determining the fuzzy rule number.
Further, the third layer of the GA-FWNN structure is a fuzzy rule layer, the node number in the layer represents fuzzy rules and fuzzy segmentation number, and each node corresponds to one fuzzy rule. Using the operation of coincidence representation and, the fuzzy inference function is realized, the fuzzy rule base generated by the given data set, the output result of the layer is expressed as:
where n represents the number of fuzzy rules, specifically 18.
Further, the fourth layer of the GA-FWNN structure is a wavelet network layer (WNN layer), and the three-layer wavelet neural network is used as a back-piece part of the fuzzy rule, and the wavelet transformation local characteristic is utilized, and a wavelet basis function is used as an activation function of a neuron, and for the jth wavelet neuron, the method is specifically expressed as follows:
wherein,a ij 、b ij and w j Respectively represent the translation, expansion factor and weight of the wavelet function.
Further, the fifth layer of the GA-FWNN structure is an output layer, which is used to calculate the output result of the whole network. The layer mainly considers the analysis result of defuzzification of the output result of each wavelet network, and the output result is specifically expressed as follows:
wherein y is k The output of FWNN, i.e. the predicted gas production (Biogas) and methane content of the system, is used to monitor the operating status of the anaerobic system in real time.
Specifically, in the step (1), an adaptive fuzzy C-means clustering algorithm is adopted to determine the fuzzy rule number of the GA-FWNN, and the specific method is as follows:
fuzzy C-means clustering (FCM) is to obtain membership of each sample point to all class centers by optimizing an objective function, so that class of the sample points is determined to achieve the purpose of automatically classifying sample data. Let the sample set be x= { X 1 ,x 2 ,…,x q Dividing it into c fuzzy groups, so that the membership matrix U= [ U ] of the objective function J (U, V) ij ] c×q Reach minimum and get the cluster center v= { V 1 ,v 2 ,…,v c }。
d ij ＝||x j -v i || (9)
Wherein p represents the number of parameters, and is specifically 5; q represents the total number of samples, in particular 120 groups; c represents a cluster genus, h represents a fuzzy weighting index, d ij For data x j To the clustering center v i Is a euclidean distance of (c).
In order to improve the segmentation quality, a validity function B (C) is added into the FCM to form a self-adaptive fuzzy C-means clustering algorithm, which comprises the following specific steps:
(1-2-1) given iteration accuracy epsilon=0.001, k=0, c=2, fuzzy weighting index h=2, b (1) =0, select [0,1 ]]Uniformly distributed random numbers on the cluster as an initial cluster center V (0) ；
(1-2-2) calculating the membership matrix U of the kth step (k) The calculation formula is as follows:
(1-2-3) correction clustering center V (k+1) The expression is:
(1-2-4) if V (k+1) -V (k) If the I is less than or equal to epsilon, stopping iteration, otherwise, turning to the step (1-2-2), wherein k=k+1;
(1-2-5) calculating a validity function B (c), if B (c-1) > B (c-2) and B (c-1) > B (c) in case c >2 and c < n, ending the clustering process, otherwise setting c=c+1, proceeding to step (1-2-1).
Wherein the method comprises the steps ofRepresenting the center vector of the overall data sample.
Specifically, in the step (1), the FWNN is improved by adopting a genetic and gradient descent hybrid algorithm, and the specific steps are as follows:
(1-3-1) the genetic algorithm implementing the initialization process of the network structure;
during the initialization process, all parameters in the network are optimized, including regular middleware parameters (center of membership function c ij And width sigma ij ) And back-piece parameters (translation of wavelet function a ij Expansion factor b ij Sum weight w j )。
The invention takes the standard error between the expected value of the network and the actual output of the network as the fitness function of the model, and the expression method is as follows:
wherein y is dk Representing the desired output, y k Representing the actual output of the network, q represents the number of individuals in the population, and the output of the s-th chromosome in the network can be obtained by the following expression:
wherein,
thus the s-th chromosome is defined as:
wherein the method comprises the steps of
Thus, the initial parameters of FWNN can be obtained after three genetic operations (selection, crossover and mutation). The initial population N pop is 100, and the crossover probability P c 0.7, probability of variation P m 0.01 and a maximum number of iterations of 200.
(1-3-2) implementing a parameter correction process by a gradient descent method;
the FWNN initialized by the genetic algorithm has network parameters reaching the global optimum or the vicinity of the global optimum, and the gradient descent algorithm is utilized to adjust the network parameters in real time so as to obtain the parameter c of the FWNN ij 、σ ij 、a ij 、b ij And w j . The objective function of the gradient descent method is expressed as:
wherein y is d (t) represents a desired output, and y (t) represents a current output.
Parameter c of FWNN by objective function E and gradient descent method ij 、σ ij 、a ij 、b ij And w j Can be obtained by the following formula:
wherein, the learning rate eta is 0.02 and the momentum factor zeta is 0.5. Formulas (18) - (22) can be calculated from formulas (10) to (13):
wherein,
specifically, the invention adopts VC and Matlab language to jointly encode the GA-FWNN network structure, the self-adaptive fuzzy C-means clustering algorithm and the hybrid program of the improved multi-element algorithm.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention combines the advantages of wavelet analysis, fuzzy theory, genetic algorithm, neural network and other intelligent theory to construct GA-FWNN GAs production prediction model, which can accurately and rapidly realize GAs production (Biogas) and methane Content (CH) 4 ) Is provided.
2. The invention adopts a mixed algorithm of a genetic algorithm and a gradient descent method to optimize the neural network structure, solves the problem that the neural network is sunk into local optimum prematurely, has the advantages of short result lag time, small error, strong environment adaptability and the like, and can ensure that the anaerobic treatment system operates efficiently, stably and economically.
Drawings
FIG. 1 is a block diagram of a genetic-fuzzy wavelet neural network;
FIG. 2 is a schematic diagram of a sewage anaerobic treatment system monitored in real time according to the present invention;
FIG. 3 is a graph of training results of a genetic-fuzzy wavelet neural network model;
FIG. 4 is a graph of the results of gas production prediction for a genetic-fuzzy wavelet neural network.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but embodiments of the present invention are not limited thereto.
Examples
A sewage anaerobic treatment gas production multi-element intelligent real-time monitoring method comprises the following specific steps:
(1) Constructing a genetic-fuzzy wavelet neural network; determining the fuzzy rule number of the genetic-fuzzy wavelet neural network by adopting a self-adaptive fuzzy C-means clustering algorithm; and adopting a genetic and gradient descent hybrid algorithm to correct and improve the genetic-fuzzy wavelet neural network. In the invention, the chemical requirement (COD), the Organic Load Rate (OLR), the Hydraulic Retention Time (HRT), the pH value (pH) and the total carbonate Alkalinity (ALK) of the water are selected as input quantities, and the gas yield (Biogas) and the methane Content (CH) 4 ) As output.
Specifically, in step (1), the structure of the constructed genetic-fuzzy wavelet neural network (GA-FWNN) is shown in fig. 1, and specifically includes a five-layer network structure, where the mapping relationship between the network input domain outputs is expressed as:
wherein wo j (t) is expressed as a connection weight function from the wavelet network layer node to the output layer, c ij Sum sigma ij Respectively expressed as center and width of membership function (gaussian function), x i (t) represents input node parameters j=1, 2, 3..18, i=1, 2,3,4,5.
Furthermore, the first layer of the GA-FWNN structure is an input layer and is responsible for receiving all input factors and distributing the input factors to the next layer of the network, and the first layer has five nodes, namely COD (t), HRT (t), OLR (t), pH (t) and ALK (t).
Furthermore, the second layer of the GA-FWNN structure is a fuzzification layer, and the second layer introduces a fuzzy set theory, so that the network can process semantic variables. The layer makes each node correspond to a fuzzy language respectively by fuzzifying each input. In the present invention, a gaussian function is chosen as the excitation function, and the output of each node is expressed as:
wherein c ij Sum sigma ij Represented as the center and width of the ith input variable gaussian function, respectively, that is related first to the jth fuzzy rule. And carrying out fuzzy division on the network by adopting a self-adaptive fuzzy C-means clustering algorithm, and determining the fuzzy rule number.
Further, the third layer of the GA-FWNN structure is a fuzzy rule layer, the node number in the layer represents fuzzy rules and fuzzy segmentation number, and each node corresponds to one fuzzy rule. Using the operation of coincidence representation and, the fuzzy inference function is realized, the fuzzy rule base generated by the given data set, the output result of the layer is expressed as:
where n represents the number of fuzzy rules, specifically 18.
Further, the fourth layer of the GA-FWNN structure is a wavelet network layer (WNN layer), and the three-layer wavelet neural network is used as a back-piece part of the fuzzy rule, and the wavelet transformation local characteristic is utilized, and a wavelet basis function is used as an activation function of a neuron, and for the jth wavelet neuron, the method is specifically expressed as follows:
wherein the method comprises the steps of，a ij 、b ij And w j Respectively represent the translation, expansion factor and weight of the wavelet function.
Further, the fifth layer of the GA-FWNN structure is an output layer, which is used to calculate the output result of the whole network. The layer mainly considers the analysis result of defuzzification of the output result of each wavelet network, and the output result is specifically expressed as follows:
wherein y is k Representing the output of FWNN, predicting the gas production (Biogas) and methane content of the system for monitoring the operating status of the anaerobic system in real time.
Specifically, in the step (1), an adaptive fuzzy C-means clustering algorithm is adopted to determine the fuzzy rule number of the GA-FWNN, and the specific method is as follows:
fuzzy C-means clustering (FCM) is to obtain membership of each sample point to all class centers by optimizing an objective function, so that class of the sample points is determined to achieve the purpose of automatically classifying sample data. Let the sample set be x= { X 1 ,x 2 ,…,x q Dividing it into c fuzzy groups, so that the membership matrix U= [ U ] of the objective function J (U, V) ij ] c×q Reach minimum and get the cluster center v= { V 1 ,v 2 ,…,v c }。
d ij ＝||x j -v i || (9)
Wherein p represents the number of parameters, and is specifically 5; q represents the total number of samples, in particular 120 groups; c represents a cluster genus, h represents a fuzzy weighting index, d ij For data x j To the clustering center v i Is a euclidean distance of (c).
In order to improve the segmentation quality, a validity function B (C) is added into the FCM to form a self-adaptive fuzzy C-means clustering algorithm, which comprises the following specific steps:
(1-2-1) given iteration accuracy epsilon=0.001, k=0, c=2, fuzzy weighting index h=2, b (1) =0, select [0,1 ]]Uniformly distributed random numbers on the cluster as an initial cluster center V (0) ；
(1-2-2) calculating the membership matrix U of the kth step (k) The calculation formula is as follows:
(1-2-3) correction clustering center V (k+1) The expression is:
(1-2-4) if V (k+1) -V (k) If the I is less than or equal to epsilon, stopping iteration, otherwise, turning to the step (1-2-2), wherein k=k+1;
(1-2-5) calculating a validity function B (c), if B (c-1) > B (c-2) and B (c-1) > B (c) in case c >2 and c < n, ending the clustering process, otherwise setting c=c+1, proceeding to step (1-2-1).
Wherein the method comprises the steps ofRepresenting the center vector of the overall data sample.
Specifically, in the step (1), the FWNN is improved by adopting a genetic and gradient descent hybrid algorithm, and the specific steps are as follows:
(1-3-1) the genetic algorithm implementing the initialization process of the network structure;
during the initialization process, all parameters in the network are optimized, including regular middleware parameters (center of membership function c ij And width sigma ij ) And back-piece parameters (translation of wavelet function a ij Expansion factor b ij Sum weight w j ). In the present embodiment, specific values of the front piece parameter and the back piece parameter of the GA-FWNN model at the fuzzy rule number of 18 are shown in tables 1 and 2, respectively.
TABLE 1 front piece parameters of GA-FWNN model
TABLE 2 post-part parameters for GA-FWNN model
The invention takes the standard error between the expected value of the network and the actual output of the network as the fitness function of the model, and the expression method is as follows:
wherein y is dk Representing the desired inputGo, y k Representing the actual output of the network, q represents the number of individuals in the population, and the output of the s-th chromosome in the network can be obtained by the following expression:
wherein,
thus the s-th chromosome is defined as:
wherein the method comprises the steps of
Thus, the initial parameters of FWNN can be obtained after three genetic operations (selection, crossover and mutation). The initial population N pop is 100, and the crossover probability P c 0.7, probability of variation P m 0.01 and a maximum number of iterations of 200.
(1-3-2) implementing a parameter correction process by a gradient descent method;
the FWNN initialized by the genetic algorithm has network parameters reaching the global optimum or the vicinity of the global optimum, and the gradient descent algorithm is utilized to adjust the network parameters in real time so as to obtain the parameter c of the FWNN ij 、σ ij 、a ij 、b ij And w j . The objective function of the gradient descent method is expressed as:
wherein y is d (t) represents a desired output, and y (t) represents a current output.
Parameter c of FWNN by objective function E and gradient descent method ij 、σ ij 、a ij 、b ij And w j Can be obtained by the following formula:
/>
wherein, the learning rate eta is 0.02 and the momentum factor zeta is 0.5.
Formulas (18) - (22) can be calculated from formulas (10) to (13):
wherein,
(2) Programming the improved genetic-fuzzy wavelet neural network as a system program through VC and Matlab language, and burning the program into an embedded anaerobic treatment monitoring system;
(3) Inputting sewage data in the sewage anaerobic treatment system into the embedded anaerobic treatment monitoring system as training data, enabling the improved genetic-fuzzy wavelet neural network structure in the system to reach a network precision target, and keeping the trained network structure state in the system; the sewage anaerobic treatment system is shown in figure 2; the training results of the genetic-fuzzy wavelet neural network model are shown in fig. 3.
(4) The trained embedded anaerobic treatment monitoring system is accessed to a sewage treatment site for online measurement, site water sample data to be measured are collected in real time through a sensor and are input into the system, and the system rapidly obtains gas yield and methane content based on the improved genetic-fuzzy wavelet neural network;
(5) And (4) sampling every 30 minutes, and repeating the step (4). The gas production prediction result diagram of the genetic-fuzzy neural network model is shown in fig. 4.
As can be seen from FIG. 4, the model output curve tracks the actual output curve well, the error between the sample model output and the actual output is very small, and the correlation coefficients R and R are very small 2 And the GA-FWNN method is large, so that the rapid and accurate monitoring of the GAs production of anaerobic treatment can be realized.
The present invention was compared with Fuzzy Neural Networks (FNN), wavelet Neural Networks (WNN) and Neural Networks (NN), and the results are shown in table 3. Through calculation and analysis, the prediction performance of the invention is better than that of other three models, compared with the FNN, WNN and NN models, the square root error (RMSE) predicted by the GA-FWNN model has the minimum Mean Absolute Percentage Error (MAPE) and mean square error MSE, and the correlation coefficients R and R 2 Are all maximum. Thus, GA-FWNN is a good method for simulating the GAs production rate of anaerobic treatment.
Table 3 comparison of various model properties
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (1)
1. A multi-element intelligent real-time monitoring method for anaerobic sewage treatment gas production is characterized by comprising the following specific steps:
(1) Constructing a genetic-fuzzy wavelet neural network; determining the fuzzy rule number of the genetic-fuzzy wavelet neural network by adopting a self-adaptive fuzzy C-means clustering algorithm; correcting and improving the genetic-fuzzy wavelet neural network by adopting a genetic and gradient descent hybrid algorithm;
(2) The improved genetic-fuzzy wavelet neural network is compiled into a system program through a computer language, and the program is burnt in an embedded anaerobic treatment monitoring system;
(3) Inputting sewage data as training data into an embedded anaerobic treatment monitoring system, enabling an improved genetic-fuzzy wavelet neural network structure in the system to reach a network precision target, and keeping a trained network structure state in the system, wherein the chemical requirement of water inflow, an organic load rate, hydraulic retention time, pH value and total carbonate alkalinity are selected as input quantities, and gas production quantity and methane content are taken as output quantities;
(4) The trained embedded anaerobic treatment monitoring system is accessed to a sewage treatment site for online measurement, site water sample data to be measured are collected in real time through a sensor and are input into the system, and the system rapidly obtains gas yield and methane content based on the improved genetic-fuzzy wavelet neural network;
(5) Sampling every 30 minutes, and repeating the step (4);
in the step (1), an adaptive fuzzy C-means clustering algorithm is adopted to determine the fuzzy rule number of the GA-FWNN, and the specific method is as follows:
the fuzzy C-means clustering is to obtain membership of each sample point to all class centers by optimizing an objective function, so that class of the sample points is determined to achieve the purpose of automatically classifying sample data; let the sample set be x= { X 1 ,x 2 ,…,x q Dividing it into c fuzzy groups, so that the membership matrix U= [ U ] of the objective function J (U, V) ij ] c×q Reach minimum and get the cluster center v= { V 1 ,v 2 ,…,v c }；
d ij ＝||x j -v i || (9)
Wherein p represents the number of parameters; q represents the number of individuals in the population; c represents the number of fuzzy groups, h represents fuzzy weighting index, d ij For data x j To the clustering center v i Is the euclidean distance of (2);
in order to improve the segmentation quality, a validity function B (C) is added into the FCM to form a self-adaptive fuzzy C-means clustering algorithm, which comprises the following specific steps:
(1-2-0) given c=2;
(1-2-1) given iteration accuracy epsilon=0.001, w=0, fuzzy weighting index h=2, b (1) =0, select 0,1]Uniformly distributed random numbers on the cluster as an initial cluster center V (0) ；
(1-2-2) calculating the membership matrix U of the w th step (w) The calculation formula is as follows:
(1-2-3) correction clustering center V (w+1) The expression is:
(1-2-4) If V (w+1) -V (w) If the I is less than or equal to epsilon, stopping iteration, otherwise, turning to the step (1-2-2), wherein w=w+1;
(1-2-5) calculating a validity function B (c), if B (c-1) > B (c-2) and B (c-1) > B (c), if c >2 and c < q, ending the clustering process, otherwise setting c=c+1, turning to step (1-2-1);
wherein the method comprises the steps ofA center vector representing the overall data sample;
in the step (1), the GA-FWNN is improved by adopting a genetic and gradient descent mixing algorithm, and the specific steps are as follows:
(1-3-1) the genetic algorithm implementing the initialization process of the network structure;
during the initialization process, all parameters in the network are optimized, including regular precursor parameters, i.e. center c of membership function i'j' And width sigma i'j' And the back-piece parameter, i.e. translation of wavelet function a i'j' Expansion factor b i'j' Sum weight w j' ；
The standard error between the expected value of the network and the actual output of the network is used as the fitness function of the model, and the representation method is as follows:
wherein y is dk Representing the desired output, y k Representing the actual output of the network, q representing the number of individuals in the population, the output of the s-th chromosome in the network being expressed byThe formula is obtained:
wherein,
thus the s-th chromosome is defined as:
wherein the method comprises the steps of
Thus, the initial parameters of GA-FWNN are obtained after three genetic operations of selection, crossing and mutation; initial population Npop is 100, crossover probability P c 0.7, probability of variation P m 0.01 and a maximum number of iterations of 200;
(1-3-2) implementing a parameter correction process by a gradient descent method;
the GA-FWNN initialized by the genetic algorithm has network parameters reaching the global optimum or the vicinity of the global optimum, and the gradient descent algorithm is utilized to adjust the network parameters in real time so as to obtain the parameter c of the GA-FWNN i'j' 、σ i'j' 、a i'j' 、b i'j' And w j' The method comprises the steps of carrying out a first treatment on the surface of the The objective function of the gradient descent method is expressed as:
wherein y is d (t) represents a desired output, and y (t) represents a current output;
parameter c of GA-FWNN based on objective function E and gradient descent method i'j' 、σ i'j' 、a i'j' 、b i'j' And w j' Obtained by the following formula:
wherein, the learning rate eta is 0.02, and the momentum factor zeta is 0.5; formulas (18) - (22) are calculated from formulas (10) to (13):
wherein,
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