CN106529818B - Water quality assessment Forecasting Methodology based on Fuzzy Wavelet Network - Google Patents

Abstract

The present invention provides a water quality evaluation and prediction method based on fuzzy wavelet neural network. The purpose is to solve the problems of slow convergence speed, poor approximation effect and inaccurate prediction results of BP neural network in water quality prediction. Based on the known water quality analysis index The number is, the number of prediction indicators, and the number of fuzzy rules to construct a fuzzy wavelet neural network prediction model, which includes an input layer, a membership layer, a fuzzy rule layer, a wavelet layer, an output layer and a defuzzification layer; the membership function parameters Adjust the wavelet parameters of wavelet layer and wavelet layer, and define the cost function, and use the BP algorithm based on the gradient descent method to adjust the parameters. The worker bee colony algorithm optimizes the initial parameters, and the patented method is mainly used to predict water quality indicators.

Description

Water Quality Evaluation and Prediction Method Based on Fuzzy Wavelet Neural Network

technical field

The invention relates to the field of hydrological evaluation and prediction, in particular to a water quality evaluation and prediction method based on fuzzy wavelet neural network.

Background technique

Water quality prediction is a technology to establish water functional areas in water pollution control units, and use the corresponding relationship between water quality indicators and corresponding pollution sources in land areas to obtain target water quality information. In the water environment and water pollution control at home and abroad, the research and application of water quality models have made great progress. Water quality prediction methods mainly include water quality simulation models, mathematical statistics models and artificial neural network models. The traditional BP neural network model method has made great progress in the application research of water quality prediction and evaluation, but there are slow convergence speed and generalization ability. Poor, the prediction accuracy is not high enough, and the satisfactory prediction results cannot be achieved.

Contents of the invention

For above-mentioned situation, in order to overcome the defective of prior art, the present invention provides a kind of water quality evaluation prediction method based on fuzzy wavelet neural network, the purpose is to solve BP neural network when carrying out water quality prediction, convergence speed is relatively slow, approximation effect is poor, and prediction The problem of inaccurate results.

Its technical solution is:

A, with the number of known water quality analysis indicators as m, the number of prediction indicators as o, and the number of fuzzy rules as n to build a fuzzy wavelet neural network prediction model, the fuzzy wavelet neural network prediction model includes an input layer, a subordinate layer, and fuzzy rules layer, wavelet layer, output layer and defuzzification layer;

The input layer is used to input known water quality analysis indicators, that is, input variables: x ₁ , x ₂ , . . . , x _m ;

The membership layer is used to calculate the membership degree value of each input variable, and the membership function is:

Among them, m is the number of input variables, n is the number of fuzzy rules, that is, the number of neurons in the hidden layer of the third layer, the center and width of the Gaussian membership functions of c _ij and d _ij , η _j ( _xi ) is the relative value of the i-th language variable Membership function of rule j;

Its node number of described fuzzy rule layer corresponds to fuzzy rule number n, and each node represents a fuzzy rule, and each node fuzzy rule layer output represents as follows:

μ _j (x)=η _j (x ₁ )*η _j (x ₂ )*…η _j (x _m ),j=1,2,…,n;

Described wavelet layer introduces wavelet function, utilizes wavelet function to improve the computation of network model and approximation capability, and wavelet is defined as follows:

ψ _j (x) is formed by the translation and extension of the mother wavelet function ψ(x), where a _j ＝{a _1j ,a _2j ,…a _mj }, b _j ＝{b _1j ,b _2j ,…b _mj } represent Scaling and translation factors, the mother wavelet is taken as the Mexican sombrero wavelet as follows:

The jth wavelet network output of the wavelet layer is:

in, a _ij and b _ij are wavelet parameters;

The output layer is the product of fuzzy rule layer output and wavelet layer network output,

K _j =μ _j (x)*y _j =η _j (x ₁ )*η _j (x ₂ )*...η _j (x _m )*ω _j ψ _j (z),

The defuzzification layer is used to calculate the output of the whole neural network, which is expressed as:

b. Adjust the membership function parameters c _ij , d _ij , wavelet parameters ω _j , a _ij , b _ij of the wavelet layer, and define the cost function as:

in and u _i are the expected output and actual output of the network respectively, o is the number of output variables, and the parameters are adjusted using the BP algorithm based on the gradient descent method. Stability, using the artificial bee colony algorithm to optimize the initial parameters, including the following steps:

Step 1: Initialize the bee population, the total number of bees is SN, the collecting bees and the following bees each account for SN/2, the maximum number of searches is Limit, the number of iterations iter=0, the maximum number of iterations is maxCycle; all bees are scout bees, and SN is randomly generated a feasible solution;

Step 2: Initialize the parameters c _ij , d _ij , ω _j , a _ij , b _ij of each part of the network model;

Step 3: assign each parameter to the network model;

Step 4: Use the training samples to train the network model;

Step 5: Calculate the fitness value, divide the bee colony into two kinds of honey bees and follower bees, initialize the flag vector trial (i)=0, record the number of consecutive stays of the honey bees in the same nectar source;

Step 6: The honey bees search locally for a new honey source, and calculate the fitness value. If it is better than the current honey source, then update the current honey source location where the bees are located, and set trial(i)=0, otherwise update trial(i)=trial(i) +1;

Step 7: Calculate the selection probability of the follower bees, each follower bee looks for a new honey source with this probability, and transforms into a bee harvesting bee for neighborhood search, calculates the fitness value, judges whether to keep the honey source, and updates trial(i);

Step 8: If trial(i)>Limit, go to step 9, otherwise go to step 10;

Step 9: The i-th honeybee abandons the current nectar source and is called a scout bee, and randomly generates a new nectar source in the solution space;

Step 10: Record the global optimal solution currently found by all bees, iter=iter+1;

Step 11: If iter>maxCycle, get the initial value of network model parameter optimization, otherwise return to step 4;

In the algorithm, each nectar source represents a solution of the search space. For a problem with D variables, the position of the i-th nectar source is X ⁱ =[x _i1 ,x _i2 ,…,x _iD ] ^T , and the randomly generated feasible solution is as follows :

Among them, i∈{1,2,…,SN}, j∈{1,2,…,D};

C. Assign the initial value of the parameters obtained by optimization to the network model, and input the water quality analysis indicators, namely input variables: x ₁ , x ₂ ,..., x _m , into the input layer of the network model to obtain the predicted output value.

The present invention replaces the linear function of the conclusion part of the traditional T-S fuzzy neural network with the wavelet function, and organically combines the wavelet transform with the fuzzy neural network, so that the prediction network has the advantages of fast convergence speed, strong approximation ability, and avoiding falling into local optimum. The artificial bee colony algorithm is used to optimize the initial values of the parameters to be determined, avoiding defects such as the large number of parameters to be determined in the network, the heavy workload of gradient calculation, and the large influence of the initial values, which improves the stability of the water quality evaluation prediction model.

Description of drawings

Fig. 1 is a topological diagram of the fuzzy wavelet neural network used in the water quality prediction method of the present invention.

Figure 2 is the comparison data between this method and the traditional T-S fuzzy neural network and BP neural network when the absolute average error and relative average error are used as evaluation indicators.

Fig. 3 is a coordinate diagram of the water quality prediction result of the method of the present invention.

Figure 4 is a coordinate diagram of the water quality prediction results of the T-S fuzzy neural network.

Fig. 5 is the coordinate diagram of the water quality prediction result of BP neural network.

Fig. 6 is a network evolution process diagram of this patent, traditional T-S type fuzzy neural network and BP neural network.

detailed description

The specific implementation manners of the present invention will be described in further detail below in conjunction with the accompanying drawings.

In an embodiment: as shown in Figure 1, this paper uses a fuzzy neural network based on the TS model. There are two types of fuzzy logic, type I and type II. The traditional type I fuzzy system cannot handle the uncertainty of fuzzy rules, so in the face of Complex systems cannot establish effective and reasonable fuzzy rules. Type II fuzzy systems mainly include Mamdani type and TS type. The TS type fuzzy model uses IF-THEN fuzzy rules. The premise part of each rule includes premise variables and fuzzy sets. Its function is to define a fuzzy subspace, and the conclusion part is usually a linear function. Studies have shown that TS-type networks are better than Mamdani networks in terms of learning accuracy. In the traditional wavelet neural network, the nonlinear Sigmoid function in the BP neural network is replaced by a nonlinear wavelet basis, and the fitting of the nonlinear function is realized by linear superposition with the nonlinear wavelet basis taken, that is, using the wavelet series Finite term fitting. In order to combine the advantages of fuzzy neural network and wavelet neural network, the present invention replaces the linear function of the conclusion part of the traditional TS type model with wavelet function to form a new fuzzy wavelet neural network model. The fuzzy rule of this fuzzy wavelet neural network model can be described as R _n : If x ₁ is A _n1 and x ₂ is A _n2 and…and x _m is A _nm ,

Among them, x ₁ , x ₂ ,..., x _m are the input variables, y ₁ , y ₂ ,..., y _n are the output of the wavelet function, A _ij is the Gaussian membership function, representing the i-th rule of the j-th input variable , n is the number of fuzzy rules; the wavelet of the above fuzzy wavelet neural network model is defined as follows:

ψ _j (x) is formed by the translation and extension of the mother wavelet function ψ(x), where a _j ＝{a _1j ,a _2j ,…a _mj }, b _j ＝{b _1j ,b _2j ,…b _mj } represent Scaling and translation factors, the mother wavelet is taken as the Mexican sombrero wavelet as follows:

The output of the wavelet neural network can be expressed as:

in, ψ _j (x) is the jth unit wavelet function of the hidden layer, ω _j is the weight coefficient of the input layer and the hidden layer, the wavelet neural network (WNN) has better approximation ability, compared with other types of multi-layer perceptron and radial basis network have the characteristics of easy training. At the same time, the initial value of wavelet neural network parameters has a great influence on its convergence speed. The optimized initial parameters can increase the stability and convergence speed of the network.

Formula (1) shows the influence of each wavelet function on the output of the fuzzy wavelet neural network model (FWNN). The fuzzy model in the form of IF-THEN rules can adjust the membership function parameters of the premise part, the expansion and translation of the conclusion part through continuous learning. factor, so the wavelet function can improve the calculation and approximation ability of FWNN.

In this example, six indicators of water quality analysis are selected, namely ammonia nitrogen, dissolved oxygen, chemical oxygen demand, potassium permanganate index, total phosphorus, and total nitrogen. The above six indicators are used as input variables of FWNN, and the water quality level is As the output of FWNN, that is, the number of nodes in the input layer m=6, the number of output nodes in the defuzzification layer o=1, and the number of fuzzy rules in the fuzzy rule layer n=4, the fuzzy wavelet neural network model is established under the MatlabR2010b environment, And use the equivalent interpolation water quality index standard data to generate training samples, construct 350 training data, and use the artificial bee colony (ABC) algorithm to optimize the initial parameters. The ABC parameters are determined as: SN=40, Limit=8, maxCycle=50, Then the number of parameters to be optimized by FWNN is (4m+1)×n=100, and each solution is a 100-dimensional vector.

The initial value of the optimized fuzzy wavelet neural network (FWNN) is as follows:

Step 1: Initialize the bee population, the total number of bees is 40, the number of bees collecting and following bees each account for 20, the maximum number of searches Limit = 8, the number of iterations iter = 0, the maximum number of iterations maxCycle = 50; all bees are scout bees, random Generate 40 feasible solutions;

Step 2: Initialize the parameters c _ij , d _ij , ω _j , a _ij , b _ij of each part of the network model;

Step 3: Assign each parameter to the fuzzy wavelet neural network (FWNN);

Step 4: use the training samples to train the fuzzy wavelet neural network (FWNN);

Step 5: Calculate the fitness value, divide the bee colony into two kinds of honey bees and follower bees, initialize the flag vector trial (i)=0, record the number of consecutive stays of the honey bees in the same nectar source;

Step 6: The honey bees search locally for a new honey source, and calculate the fitness value. If it is better than the current honey source, then update the current honey source location where the bees are located, and set trial(i)=0, otherwise update trial(i)=trial(i) +1;

Step 7: Calculate the selection probability of the follower bees, each follower bee looks for a new honey source with this probability, and transforms into a bee harvesting bee for neighborhood search, calculates the fitness value, judges whether to keep the honey source, and updates trial(i);

Step 8: If trial(i)>8, go to step 9, otherwise go to step 10;

Step 9: The i-th honeybee abandons the current nectar source and is called a scout bee, and randomly generates a new nectar source in the solution space;

Step 10: Record the global optimal solution currently found by all bees, iter=iter+1;

Step 11: If iter>50, get the initial value of the optimized network model parameters, otherwise return to step 4;

In the algorithm, each nectar source represents a solution of the search space. For a problem with D variables, the position of the i-th nectar source is X ⁱ =[x _i1 ,x _i2 ,…,x _iD ] ^T , and the randomly generated feasible solution is as follows :

Among them, i∈{1,2,…,SN}, j∈{1,2,…,D};

Then assign the initial value of the network parameters obtained by the artificial bee colony algorithm to the fuzzy wavelet neural network (FWNN), and input the water quality analysis indicators, namely input variables: x ₁ , x ₂ ,..., x _m , into the input layer of the network model , to get the predicted output value.

In order to verify the beneficial effect of the patented method, this article uses the absolute mean error (MAE) and relative mean error (MAPE) as evaluation indicators:

The fuzzy wavelet neural network is compared with the traditional T-S type fuzzy neural network and BP neural network. The test sample group numbers are 1-50, and each group of data contains 6 input variables. The specific data and group numbers are as follows:

Construct the traditional T-S type fuzzy neural network and BP neural network with the same number of input nodes and the same number of output nodes. The above two network models have the same number of input nodes and output nodes as the fuzzy wavelet neural network (FWNN), and the above 1- 50 sets of data were input into the trained network models respectively, with the group number of the test sample as the abscissa, and the network output index water quality level as the ordinate to obtain Figures 3 to 5, and according to the average error (MAE) output by each network , The relative average error (MAPE) is made into a table as shown in Figure 2. It can be clearly concluded that the fuzzy wavelet neural network has a more accurate prediction, and its error value is smaller.

After the traditional T-S type fuzzy neural network, BP neural network, and fuzzy wavelet neural network (FWNN) models are established, parameters need to be adjusted. During the parameter adjustment process, continuous iterations are required to obtain more optimal parameter values. The training error and the number of iterations of the above three network models are constructed as coordinates in Figure 6, where the training error is the ordinate, and the number of iterations is the abscissa when the parameters are optimized. It can be seen that the fuzzy wavelet neural network (FWNN) has more The fast convergence speed, that is, the process of obtaining the optimal parameters is faster and more convenient, which is better than the traditional T-S fuzzy neural network and BP neural network.

Claims (1)

1. The water quality evaluation and prediction method based on the fuzzy wavelet neural network is characterized by comprising the following steps of:

a. constructing a fuzzy wavelet neural network prediction model by taking the known water quality analysis index number as m, the prediction index number as o and the fuzzy rule number as n, wherein the fuzzy wavelet neural network prediction model comprises an input layer, an affiliation layer, a fuzzy rule layer, a wavelet layer, an output layer and a de-fuzzification layer;

the input layer is used for inputting known water quality analysis indexes, namely input variables: x is the number of₁，x₂，…，x_m；

The affiliation layer is used for calculating the affiliation value of each input variable, and the affiliation function is as follows:

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;eta;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>d</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>m</mi> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>n</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>

where m is the number of input variables, n is the number of fuzzy rules, i.e. the number of cryptic neurons in the third layer, c_ij、d_ijCenter and width of Gaussian membership function, η_j(x_i) Membership functions for the ith linguistic variable relative to the jth rule;

the node number of the fuzzy rule layer corresponds to the fuzzy rule number n, each node represents a fuzzy rule, and the output of each node fuzzy rule layer is represented as follows:

μ_j(x)＝η_j(x₁)*η_j(x₂)*…η_j(x_m),j＝1,2,…,n；

the wavelet layer introduces a wavelet function, the calculation and approximation capability of the network model is improved by utilizing the wavelet function, and the wavelet is defined as follows:

<mrow> <msub> <mi>&amp;psi;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <mo>|</mo> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>|</mo> </mrow> </msqrt> </mfrac> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>x</mi> <mo>-</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> </mrow> <msub> <mi>a</mi> <mi>j</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>&amp;NotEqual;</mo> <mn>0</mn> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> </mrow>

ψ_j(x) Formed by shifting and expanding a mother wavelet function ψ (x) where a_j＝{a_1j,a_2j,…a_mj}，b_j＝{b_1j,b_2j,…b_mjThe mother wavelet is taken as Mexico straw hat wavelet as follows:

<mrow> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <mo>|</mo> <mi>a</mi> <mo>|</mo> </mrow> </msqrt> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>-</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </msup> <mo>,</mo> </mrow>

the jth wavelet network output of the wavelet layer is:

<mrow> <msub> <mi>y</mi> <mi>j</mi> </msub> <mo>=</mo> <msub> <mi>&amp;omega;</mi> <mi>j</mi> </msub> <msub> <mi>&amp;psi;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&amp;psi;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </msubsup> <mfrac> <mn>1</mn> <msqrt> <mrow> <mo>|</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>|</mo> </mrow> </msqrt> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mn>2</mn> </mfrac> </mrow> </msup> <mo>,</mo> </mrow>

wherein,a_ij、b_ijis a wavelet parameter;

the output layer is the product of the fuzzy rule layer output and the wavelet layer network output,

K_j＝μ_j(x)*y_j＝η_j(x₁)*η_j(x₂)*…η_j(x_m)*ω_jψ_j(z)，

<mrow> <msub> <mi>&amp;psi;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </msubsup> <mfrac> <mn>1</mn> <msqrt> <mrow> <mo>|</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>|</mo> </mrow> </msqrt> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msubsup> <mi>z</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mn>2</mn> </mfrac> </mrow> </msup> <mo>,</mo> </mrow>

the de-ambiguity layer is used to compute the output of the entire neural network, which is expressed as:

<mrow> <mi>u</mi> <mo>=</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msub> <mi>&amp;mu;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <msub> <mi>y</mi> <mi>j</mi> </msub> <mo>/</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msub> <mi>&amp;mu;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow>

b. to membership function parameter c_ij、d_ijWavelet parameter omega of wavelet layer_j、a_ij、b_ijAnd adjusting, and defining a cost function as:

<mrow> <mi>E</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>o</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>u</mi> <mi>i</mi> <mi>d</mi> </msubsup> <mo>-</mo> <msub> <mi>u</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow>

whereinAnd u_iRespectively an expected output and an actual output of a network, o is an output variable number, a BP algorithm based on a gradient descent method is used for parameter adjustment, and in order to avoid slow convergence, easy collapse of a concussion effect and local optimization and increase model stability, an artificial bee colony algorithm is adopted to optimize initial parameters, and the method comprises the following steps:

step 1: initializing a bee population, wherein the total number of the bees is SN, the number of collected bees and the number of following bees respectively account for SN/2, the maximum search time Limit, the iteration time iter is 0, and the maximum iteration time maxCycle; all bees are in a reconnaissance bee mode, and SN feasible solutions are generated randomly;

step 2: initializing partial parameters c of a network model_ij、d_ij、ω_j、a_ij、b_ij；

And step 3: assigning each parameter to a network model;

and 4, step 4: training a network model by using the training samples;

and 5: calculating a fitness value, dividing a bee colony into a bee collecting part and a bee follower part, initializing a mark vector (i) to be 0, and recording the continuous residence times of the bee collecting part in the same bee source;

step 6: searching a new honey source locally by the bees, calculating a fitness value, if the fitness value is better than the current honey source, updating the position of the honey source where the current honey bees are located, and enabling the triel (i) to be 0, otherwise updating the triel (i) to be (i) + 1;

and 7: calculating the selection probability of the following bees, searching a new honey source by each following bee according to the probability, converting the new honey source into a bee collection for neighborhood search, calculating a fitness value, judging whether the honey source is reserved or not, and updating the deal (i);

and 8: if the trial (i) > Limit, executing the step 9, otherwise, executing the step 10;

and step 9: the ith honey bee abandons the current honey source called a reconnaissance bee, and randomly generates a new honey source in a solution space;

step 10: recording the global optimal solution found by all the bees currently, wherein iter is iter + 1;

step 11: if iter is greater than maxCycle, obtaining a network model parameter optimization initial value, otherwise, returning to the step 4;

in the algorithm, each honey source represents a solution of a search space, and for a problem containing D variables, the ith honey source position is X^i＝[x_i1,x_i2,…,x_iD]^TThe randomly generated feasible solution is as follows:

<mrow> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>X</mi> <mi>j</mi> <mi>min</mi> </msubsup> <mo>+</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>j</mi> <mi>max</mi> </msubsup> <mo>-</mo> <msubsup> <mi>X</mi> <mi>j</mi> <mi>min</mi> </msubsup> <mo>)</mo> </mrow> </mrow>

wherein i belongs to {1,2, …, SN }, and j belongs to {1,2, …, D };

c. assigning the initial value of the parameter obtained by optimization to the network model, and assigning the initial value of the parameter to the network modelWater quality analysis indicators, i.e. input variables: x is the number of₁，x₂，…，x_mAnd inputting the data into an input layer of the network model to obtain a predicted output value.