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

Water quality assessment Forecasting Methodology based on Fuzzy Wavelet Network Download PDF

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CN106529818B
CN106529818B CN201611034364.7A CN201611034364A CN106529818B CN 106529818 B CN106529818 B CN 106529818B CN 201611034364 A CN201611034364 A CN 201611034364A CN 106529818 B CN106529818 B CN 106529818B
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付立华
王刚
张晓玫
邓丽霞
李小魁
韩大伟
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Abstract

A kind of present invention offer water quality assessment Forecasting Methodology based on Fuzzy Wavelet Network, purpose is that solution BP neural network convergence rate when carrying out water quality prediction is slower, Approximation effect is poor, the problem of prediction result is not accurate, using known water quality analysis indexes number as, prediction index number, number of fuzzy rules build Fuzzy Wavelet Network forecast model, Fuzzy Wavelet Network forecast model include input layer, be subordinate to layer, fuzzy rule layer, wavelet layer, output layer conciliate obscuring layer；Membership function parameter, the wavelet parameter of wavelet layer are adjusted, and define cost function, the BP algorithm based on gradient descent method is used to carry out parameter adjustment, to avoid, convergence rate is slow, easily sinks into shake effect and local optimum, increase model stability, initial parameter is optimized using artificial bee colony algorithm, this patent method is mainly used in predicting water quality index.

Description

Water quality evaluation prediction method based on fuzzy wavelet neural network
Technical Field
The invention relates to the field of hydrological evaluation prediction, in particular to a water quality evaluation prediction method based on a fuzzy wavelet neural network.
Background
The water quality prediction is a technology for establishing a water area functional area in a water pollution control unit and obtaining target water quality information by utilizing the corresponding relation between water quality indexes and corresponding pollution sources of land areas. In the control of water environment and water pollution at home and abroad, the research and the application of a water quality model are greatly developed. The water quality prediction method mainly comprises a water quality simulation model, a mathematical statistics model and an artificial neural network model, and the application research of the traditional BP neural network model method in the aspects of water quality prediction and evaluation is greatly developed, but the traditional BP neural network model method has the defects of low convergence rate, poor generalization capability and insufficient prediction precision, and cannot achieve a satisfactory prediction result.
Disclosure of Invention
Aiming at the situation, the invention provides a water quality evaluation and prediction method based on a fuzzy wavelet neural network to overcome the defects of the prior art, and aims to solve the problems of low convergence rate, poor approximation effect and inaccurate prediction result of a BP neural network during water quality prediction.
The technical scheme is as follows:
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，…，xm；
The affiliation layer is used for calculating the affiliation value of each input variable, and the affiliation function is as follows:
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, cij、dijCenter and width of Gaussian membership function, ηj(xi) 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:
μj(x)＝ηj(x1)*ηj(x2)*…ηj(xm),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:
ψj(x) Formed by shifting and expanding a mother wavelet function ψ (x) where aj＝{a1j,a2j,…amj}，bj＝{b1j,b2j,…bmjAre respectively substitutedTable expansion and translation factors, the mother wavelet is taken as mexican strawboard wavelet as follows:
the jth wavelet network output of the wavelet layer is:
wherein,aij、bijis a wavelet parameter;
the output layer is the product of the fuzzy rule layer output and the wavelet layer network output,
Kj＝μj(x)*yj＝ηj(x1)*ηj(x2)*…ηj(xm)*ωjψj(z)，
the de-ambiguity layer is used to compute the output of the entire neural network, which is expressed as:
b. to membership function parameter cij、dijWavelet parameter omega of wavelet layerj、aij、bijAnd adjusting, and defining a cost function as:
whereinAnd uiRespectively 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 modelij、dij、ωj、aij、bij；
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 Xi＝[xi1,xi2,…,xiD]TThe randomly generated feasible solution is as follows:
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 a network model, and analyzing the water quality index, namely an input variable: x is the number of1，x2，…，xmAnd inputting the data into an input layer of the network model to obtain a predicted output value.
The invention replaces the linear function of the conclusion part of the traditional T-S type fuzzy neural network with the wavelet function, organically combines the wavelet transformation with the fuzzy neural network, ensures that the prediction network has the advantages of high convergence speed, strong approximation capability, capability of avoiding falling into local optimization and the like, optimizes the initial value of the parameter to be determined by utilizing the artificial bee colony algorithm, and avoids the defects of more parameters to be determined, large gradient calculation workload, great influence of the initial value and the like in the network, thereby improving the stability of the water quality evaluation prediction model.
Drawings
FIG. 1 is a topological diagram of a fuzzy wavelet neural network used in the water quality prediction method of the present invention.
FIG. 2 is a graph showing data comparison between the method and a conventional T-S type fuzzy neural network and a BP neural network under the condition that the absolute average error and the relative average error are used as evaluation indexes.
FIG. 3 is a graph of the water quality prediction result of the method of the present invention.
FIG. 4 is a graph of water quality prediction results of a T-S type fuzzy neural network.
FIG. 5 is a BP neural network water quality prediction result coordinate diagram.
FIG. 6 is a diagram of the network evolution process of the patent, a conventional T-S type fuzzy neural network and a BP neural network.
Detailed Description
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
In one embodiment: as shown in FIG. 1, the fuzzy neural network based on the T-S model is adopted, fuzzy logic has two types, namely a type I fuzzy logic and a type II fuzzy logic, and the traditional type I fuzzy system cannot process the uncertainty of the fuzzy rule, so that an effective and reasonable fuzzy rule cannot be established in the face of a complex system. The two-type fuzzy system mainly comprises a Mamdani type and a T-S type, wherein a T-S type fuzzy model uses IF-THEN fuzzy rules, the premise part of each rule comprises a premise variable and a fuzzy set, the function of the fuzzy set is to define a fuzzy subspace, and a conclusion part is generally a linear function. Research shows that the T-S type network is superior to the Mamdani network in the aspect of accurate learning. In the traditional wavelet neural network, a nonlinear Sigmoid function in a BP neural network is replaced by a nonlinear wavelet basis, and fitting of the nonlinear function is realized by linearly superposing the taken nonlinear wavelet basis, namely fitting by using a finite term of a wavelet series. In order to combine the advantages of fuzzy neural network and wavelet neural network, the invention uses waveletThe function replaces the linear function of the conclusion part of the traditional T-S type model to form a novel fuzzy wavelet neural network model, and the fuzzy rule of the fuzzy wavelet neural network model can be described as Rn：If x1is An1and x2is An2and…and xmis Anm,
Wherein x is1，x2，…，xmAs an input variable, y1，y2，…，ynAs output of a wavelet function, AijThe method is a Gaussian membership function and represents the ith rule of the jth input variable, and n is a fuzzy rule number; the wavelet of the fuzzy wavelet neural network model is defined as follows:
ψj(x) Formed by shifting and expanding a mother wavelet function ψ (x) where aj＝{a1j,a2j,…amj}，bj＝{b1j,b2j,…bmjThe mother wavelet is taken as Mexico straw hat wavelet as follows:
the output of the wavelet neural network can be expressed as:
wherein,ψj(x) The j unit wavelet function of the hidden layer, omegajThe Wavelet Neural Network (WNN) has better approximation capability for the weight coefficients of an input layer and a hidden layer, and has the characteristic of easy training compared with other types of multilayer perceptrons, radial basis networks and the like, meanwhile, the initial value of the wavelet neural network parameter has larger influence on the convergence speed of the wavelet neural network parameter, and the optimized initial parameter can increase the stability and the convergence speed of the network.
The influence of each wavelet function on the output of a fuzzy wavelet neural network model (FWNN) is shown by formula (1), and the fuzzy model in the IF-THEN rule form can be perfected by continuously learning and adjusting membership function parameters of a precondition part and expansion and translation factors of a conclusion part, so that the wavelet function can improve the calculation and approximation capability of the FWNN.
In the example, 6 indexes of water quality analysis are selected, namely ammonia nitrogen amount, dissolved oxygen, chemical oxygen demand, potassium permanganate index, total phosphorus and total nitrogen, the six indexes are used as input variables of the FWNN, the water quality grade is used as output of the FWNN, namely the number m of nodes of an input layer is 6, the number o of output nodes of a de-fuzzy layer is 1, meanwhile, the number n of fuzzy rules of a fuzzy rule layer is 4, a fuzzy wavelet neural network model is established in the MatlabR2010b environment, training samples are generated by adopting equivalent interpolation water quality index standard data, 350 training data are established, an Artificial Bee Colony (ABC) algorithm is used for optimizing initial parameters, and the ABC parameters are determined as follows: if SN is 40, Limit is 8, and maxCycle is 50, the number of parameters that the FWNN needs to optimize is (4m +1) × n is 100, and each solution is a 100-dimensional vector.
The initial values of the optimized Fuzzy Wavelet Neural Network (FWNN) are as follows:
step 1: initializing a bee population, wherein the total number of bees is 40, the number of the bee colonies and the number of the following bees are respectively 20, the maximum search frequency Limit is 8, the iteration frequency iter is 0, and the maximum iteration frequency maxCycle is 50; all bees are in a reconnaissance bee mode, and 40 feasible solutions are randomly generated;
step 2: initializing portions of a network modelSub-parameter cij、dij、ωj、aij、bij；
And step 3: assigning each parameter to a Fuzzy Wavelet Neural Network (FWNN);
and 4, step 4: training a Fuzzy Wavelet Neural Network (FWNN) using 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 real (i) >8, 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 more than 50, obtaining the initial value of the network model parameter after optimization, 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 Xi＝[xi1,xi2,…,xiD]TThe randomly generated feasible solution is as follows:
wherein i belongs to {1,2, …, SN }, and j belongs to {1,2, …, D };
then, assigning the initial values of the network parameters obtained by the artificial bee colony algorithm to a Fuzzy Wavelet Neural Network (FWNN), and analyzing the water quality indexes, namely input variables: x is the number of1，x2，…，xmAnd inputting the data into an input layer of the network model to obtain a predicted output value.
In order to verify the beneficial effect of the method, the absolute mean error (MAE) and the relative mean error (MAPE) are used as evaluation indexes:
the fuzzy wavelet neural network is compared with the traditional T-S type fuzzy neural network and the BP neural network, the test sample group number is 1-50, each group of data comprises 6 input variables, and the specific data and the group number are as follows:
constructing a traditional T-S type fuzzy neural network and a BP neural network with the same number of input nodes and the same number of output nodes, wherein the two network models and the Fuzzy Wavelet Neural Network (FWNN) have the same number of input nodes and the same number of output nodes, respectively inputting the 1-50 groups of data into each trained network model, taking the group number of a test sample as an abscissa and the network output index water quality grade as an ordinate to obtain figures 3-5, and making a table such as figure 2 according to the average error (MAE) and the relative average error (MAPE) output by each network, so that the fuzzy wavelet neural network can be obviously predicted to have more accurate prediction and have smaller error value.
The Fuzzy Wavelet Neural Network (FWNN) has the advantages that the traditional T-S type fuzzy neural network, BP neural network and Fuzzy Wavelet Neural Network (FWNN) models are required to be adjusted in parameters after being built, continuous iteration is required in the parameter adjusting process to obtain more optimized parameter values, therefore, the coordinates shown in the figure 6 are built according to the training errors and the iteration times of the parameter adjusting process in the building of the three network models, the training errors are vertical coordinates, the iteration times of the parameter optimizing process are horizontal coordinates, the Fuzzy Wavelet Neural Network (FWNN) has higher convergence speed, namely the process of obtaining the optimal parameters is faster and more convenient, and the fuzzy wavelet neural network is superior to the traditional T-S type 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，…，xm；
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, cij、dijCenter and width of Gaussian membership function, ηj(xi) 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:
μj(x)＝ηj(x1)*ηj(x2)*…ηj(xm),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>
ψj(x) Formed by shifting and expanding a mother wavelet function ψ (x) where aj＝{a1j,a2j,…amj}，bj＝{b1j,b2j,…bmjThe 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,aij、bijis a wavelet parameter;
the output layer is the product of the fuzzy rule layer output and the wavelet layer network output,
Kj＝μj(x)*yj＝ηj(x1)*ηj(x2)*…ηj(xm)*ωjψj(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 cij、dijWavelet parameter omega of wavelet layerj、aij、bijAnd 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 uiRespectively 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 modelij、dij、ωj、aij、bij；
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 Xi＝[xi1,xi2,…,xiD]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，…，xmAnd inputting the data into an input layer of the network model to obtain a predicted output value.
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