CN112765902A - RBF neural network soft measurement modeling method based on TentFWA-GD and application thereof - Google Patents
RBF neural network soft measurement modeling method based on TentFWA-GD and application thereof Download PDFInfo
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Abstract
The invention discloses a RBF neural network soft measurement modeling method based on Tent FWA-GD and application thereof, wherein a fitness variance method is adopted to carry out premature convergence analysis of an FWA algorithm, a Tent chaotic map is introduced to improve the FWA algorithm in order to avoid premature convergence of the FWA algorithm, and the global ergodicity of the Tent chaotic map is utilized to maintain the population diversity of the FWA; in order to improve the fitting precision and generalization capability of the RBF neural network, a Tent chaotic map, a FWA algorithm and a GD iteration method are organically fused to provide a Tent FWA-GD algorithm for training the RBF neural network to obtain optimal RBF neural network parameter values (namely c, delta and omega, wherein c is a central vector of a hidden layer RBF activation function, delta is a base width vector of the hidden layer RBF activation function, and omega is a connection weight from the hidden layer to an output layer). The RBF neural network based on TentFWA-GD is used for constructing 4 Benchmark function fitting models and a rural domestic sewage treatment process COD soft measurement model, has low function approximation error and high COD prediction precision, and achieves good application effect.
Description
Technical Field
The invention relates to the field of soft measurement modeling, in particular to a TentFWA-GD-based RBF neural network soft measurement modeling method and application thereof.
Background
With the development of rural economy, improvement of life and increase of population in China, the discharge amount of rural sewage is rapidly increased, and the rural domestic sewage is an important source of rural non-point source pollution. Strengthening rural sewage treatment has important significance for protecting rural water resources, improving living environment and promoting the construction of new ecotype rural areas. In the rural domestic sewage treatment process, Chemical Oxygen Demand (COD) is an important parameter for describing the content of organic matters in water and is a main index for measuring the water pollution degree. The timely and accurate measurement of water quality parameters such as COD (chemical oxygen demand) and the like has important significance for the optimal control of a sewage treatment system and the overall improvement of the sewage treatment quality. The traditional COD detection method mainly comprises a potassium dichromate method, a microwave seal digestion method, a spectrophotometry method and the like, various off-line detection methods have the advantages of good reproducibility, high detection precision and the like, but also have the defects of long digestion time, complicated operation process, serious secondary pollution and the like, and the timely detection of water quality parameters such as COD and the like and the real-time control of a sewage treatment process are difficult to realize.
The soft measurement technology based on the neural network achieves better effect in both theoretical research and practical application. In recent years, soft measurement methods for water quality parameters of sewage based on artificial neural networks such as BP neural network and RBF neural network are widely concerned by scholars at home and abroad. Compared with a BP neural network, the RBF neural network has the advantages of compact topological structure, high convergence rate, high approximation precision and the like, and is suitable for soft measurement modeling in a complex process.
When the RBF neural network is used for soft measurement modeling, a network model between an auxiliary variable which can be directly measured by adopting a conventional sensor and a main variable which is difficult to directly measure is constructed by utilizing the RBF neural network, so that the prediction of the main variable is realized; referring to fig. 1, a topology structure of an RBF network is generally composed of three layers, i.e., an input layer, a hidden layer, and an output layer, wherein 6 input layer nodes correspond to auxiliary variables of a soft measurement model, 1 output layer node corresponds to a dominant variable of the soft measurement model, and the number of hidden layer nodes is l; let input vector X ═ X1,x2,…,x6And the output vector is Y. The input layer non-linearly maps the input vector to the input of the hidden layer, and the output of the hidden layer is linearly mapped to the input of the output layer by the weight matrix. Using a Gaussian radial basis function as the implicit activation function, i.e.
Corresponding to the input vector X, the output Y of the RBF network is:
wherein j is 1,2, …, l, c is { c }1,c2,…,clδ and δ ═ δ1,δ2,…,δlIs the center vector and the base width vector of the hidden layer RBF activation function respectively, and omega is { omega ═ omega1,ω2,…,ωlThe connection weight from the hidden layer to the output layer. NetThe parameters c, delta and omega are important parameters of the soft measurement model, are directly related to the overall performance of the RBF neural network and the measurement precision and generalization performance of the soft measurement model, and have the problems that the key parameters of the RBF neural network are difficult to determine in practical application and the like. In order to improve the overall performance of the RBF neural network and the soft measurement model, the optimization and determination of the RBF neural network parameter values by using a group intelligent optimization algorithm such as Firework algorithm (FWA) and the like is an important task of soft measurement modeling.
In 2010, students such as Tan and Zhu propose a firework algorithm according to the phenomenon that sparks are generated due to firework explosion, and are widely concerned by students in different fields by virtue of strong robustness and global optimization capability. The method is successfully used for solving the problems of training of neural network weights, parameter optimization of continuous and discrete systems, solution of combined optimization problems and the like. In order to further improve the optimization performance of the algorithm, a plurality of scholars put forward a plurality of improved algorithms from different angles and perform mechanism analysis and comparative study, and all the improved algorithms achieve good results. The firework algorithm belongs to a guided randomness heuristic algorithm and has strong optimization problem solving capability. However, when a complex optimization problem is processed, the solution results may be different or a global optimal solution may not be found each time; the method has the defects of easy falling into local optimization, low convergence speed in the later evolution stage, poor robustness and the like.
The basic firework algorithm is realized by considering fireworks as a feasible solution in an optimal problem solution space, wherein the process of generating a certain amount of sparks by firework explosion is the process of searching an optimal solution in the neighborhood; the algorithm is described in detail as follows:
1) randomly generating N fireworks, namely randomly initializing N positions x in solving spaceiN initial solutions of the problem are characterized.
2) Calculating the fitness value of each firework, evaluating the quality of the fireworks and generating different quantities of sparks under different explosion radiuses; firework xiRadius of detonation RiAnd number of explosion sparks SiAre respectively formula (5) and formula (6), wherein y ismin＝min(f(xi) (i ═ 1,2, …, N) is the minimum value (optimal value) of fitness in the current firework population; y ismax＝max(f(xi) And (i ═ 1,2, …, N) is the maximum value (worst value) of the fitness in the current firework population. The constants R and M are used to adjust the explosion radius and the number of explosion sparks, respectively, and ε is a small quantity used to avoid zero operation.
In addition, in order to limit the number of spark particles generated at the firework position with better adaptability value and poorer adaptability value, the number of the generated sparks is limited as follows:
where a, b are two constants and round is a rounding function.
3) Generating an explosion spark, randomly selecting z dimensions to form a set DS, wherein the z dimension is round (D multiplied by rand (0,1)), and D represents a firework xiDimension number; round is a rounding function and rand is a function that yields uniformly distributed random numbers within the interval. Performing explosion operation on each dimension k of the DS according to the formula (8), and performing out-of-range processing on exikAnd storing in the explosive spark population.
exik＝xik+h，h＝Ri×rand(-1，1) (8)
Wherein h represents a position offset; x is the number ofikThe k dimension, ex, of the ith individual fireworkikRepresents xikExplosion spark after explosion operation.
4) Generating G Gaussian variant sparks, randomly selecting the sparks xiAnd randomly extracting z dimensions to form a set DS, wherein z is round (D multiplied by rand (0,1)), and D represents a firework member xiDimension (d) of (a). Performing Gaussian variation operation on each dimension k of DS according to formula (9), performing border crossing processing, and then performing mxikAnd preserving the strain in the Gaussian variant spark population.
mxik＝xik×e (9)
In the formula: e to N (1, 1), mxikIs xikA gaussian variant spark is generated after the gaussian variant.
5) Selecting N members from the three kinds of population members of fireworks, explosion sparks and Gaussian variation sparks to form a firework population for the next iterative operation. Setting a candidate set as S (including three types of population members), and setting the firework population scale as N; the individual with the optimal fitness value in the S is firstly determined as the next-generation firework member, the rest N-1 firework members are sequentially selected and generated from the S in a roulette mode, and the candidate xiProbability of being selected p (x)i) Comprises the following steps:
in the formula, R (x)i) Is xiAnd the sum of the distances from the individual entities in S. The higher the density of individuals in S, the lower the probability of being selected.
6) It is determined whether a termination condition is satisfied. If yes, stopping searching, otherwise, returning to the step 2).
Disclosure of Invention
Based on the above description, the invention organically integrates Tent chaotic mapping, FWA algorithm and GD iteration method to provide a TentFWA-GD algorithm for training RBF neural network to obtain optimal RBF neural network parameter value; the RBF neural network based on TentFWA-GD is used for constructing 4 Benchmark function fitting models and a rural domestic sewage treatment process COD soft measurement model, so that the function approximation error is low, the COD prediction precision is high, and a good application effect is achieved;
the adopted technical scheme is as follows:
the RBF neural network soft measurement modeling method based on TentFWA-GD organically integrates Tent chaotic mapping, a FWA algorithm and a GD iteration method to provide a TentFWA-GD hybrid algorithm for training an RBF neural network so as to obtain optimal RBF neural network parameter values c, delta and omega; c is a central vector of the hidden layer RBF activation function, delta is a base width vector of the hidden layer RBF activation function, and omega is a connection weight from the hidden layer to the output layer; the Tent chaotic mapping is Tent mapping or Tentmap, the FWA is a firework algorithm, and the GD iteration method is GradientDescent; adopting a fitness variance method to carry out premature convergence analysis on the FWA algorithm, introducing Tent chaotic mapping to improve the FWA algorithm in order to avoid premature convergence of the FWA algorithm, maintaining population diversity of the FWA by using global ergodicity of the Tent chaotic mapping, and guiding the FWA population to escape from a local optimal region to continue global search;
carrying out premature convergence analysis on the FWA algorithm by adopting a fitness variance method, and analyzing the overall change condition of the fitness values of the firework members in the iteration process of the FWA algorithm to serve as a judgment basis for local optimization of the FWA population; let N be the firework population size, f (x)i) And favgRespectively the fitness value of the ith member and the average fitness value of the current group, the variance sigma of the fitness values of the current group2Can be defined as:
variance σ of current population fitness value2The aggregation degree of firework members in a firework population is reflected, and the smaller the numerical value is, the more concentrated the distribution of the firework members in a solution space is, and the smaller the numerical value is, the more concentrated the distribution of the firework members in the solution space can be used as a measurement index of the FWA population diversity; in the FWA algorithm searching process, the fitness value of each firework member is gradually close along with the increase of the iteration number, and sigma is2The value of (c) is also decreased; when sigma is2And if the global optimal solution is smaller than the threshold H and the algorithm termination condition is not met, judging that the FWA algorithm is premature and converged.
Training an RBF neural network based on a TentFWA-GD hybrid algorithm, wherein an optimization mechanism combining global rough search and local fine exploration is adopted in the training process; in the first stage, searching is carried out by a FWA algorithm, and whether the local optimum is involved is judged by adopting a fitness variance method; in the second stage, when the FWA algorithm is trapped in a local optimal solution, on one hand, a Tent chaotic map is used for guiding a firework group to escape from a local optimal region and continue global search; on the other hand, an RBF neural network is trained by combining a GD iteration method, the local exploration capacity of the firework population is enhanced, and the accuracy of the optimal solution of the population is improved;
the specific process of the RBF neural network training process based on the TentFWA-GD hybrid algorithm is as follows:
1) carrying out random initialization on the firework population in the solution space according to preset parameters; the dimension of the firework member is the sum of the dimensions of parameters c, delta and omega to be optimized of the RBF neural network, and the fitness function is the mean square error of the neural network;
2) optimizing parameters of the RBF neural network based on the FWA algorithm, wherein the parameters comprise: calculating the information of each member of the firework population, the information of the optimal member of the population and the variance sigma of the population fitness value2(ii) a Judging whether the FWA falls into a local extreme value sigma2If not more than H, entering the step 3), otherwise, returning to the step 2); the information of each member of the firework population comprises a position and a fitness value; the information of the group optimal member comprises a group optimal position and a fitness value;
3) and further optimizing parameters of the RBF neural network by adopting a GD iteration method, wherein the parameters comprise: taking the position of the optimal firework member of the current group as the initial parameter value of the current RBF network, and calling a GD iteration method to adjust the network parameters; for each firework member, according to the probability PmPerforming Tent chaotic mapping in a chaotic search space, and calculating information of each member of the firework population, information of the optimal member of the population and the variance of the population fitness value;
4) and stopping searching by the algorithm when the training process reaches the maximum iteration times or the group optimal fitness value meets the precision requirement, and otherwise, turning to the step 2) to continue the iteration.
Tent chaotic mapping, setting system parameter alpha 2, Lyapunov exponent lambdamaxThe Tent chaotic mapping expression is as follows:
wherein z isnAnd zn+1Respectively representing the nth value and the (n + 1) th value of the iterative sequence.
A RBF neural network soft measurement modeling method based on TentFWA-GD is used for constructing 4 Benchmark function fitting models, and f is used for each of the 4 Benchmark functions1、f2、f3、f4It is shown that,
xiis the variable of 4 Benchmark functions;
the parameters are set as follows: f. of1The function corresponding RBF neural network has a structure of 2-7-1, f2The function corresponding RBF neural network has a structure of 3-6-1, f3The function corresponding RBF neural network has a structure of 5-10-1, f4The function corresponds to the structure 8-7-l of the RBF neural network; the solution space dimension D is the sum of the dimensions of parameters c, delta and omega to be optimized of the RBF neural network; the maximum training times of the RBF neural network is 1000, and the training target is 10-6(ii) a Generation of RBF neural network sample set: for 4 functions to be fitted, sample sets with the scale of 200 are randomly generated in the independent variable value range respectively, and the number of training samples and the number of testing samples are 150 and 50 respectively;
initialization of parameters of the FWA algorithm: the population scale M is 40, the explosion radius regulating coefficient R is 240, the explosion spark number regulating coefficient M is 200, the explosion spark number limiting coefficients a and b are 1 and 20 respectively, and the Gaussian variation spark number is 45; chaos transformation probability P of TentFWA-GD hybrid algorithmmIs 0.2, and the threshold H for the variance of the population fitness value is 0.01.
A soft measurement modeling method for COD concentration in rural domestic sewage treatment process based on a TentFWA-GD RBF neural network is characterized in that 6 auxiliary variables of inflow water flow Q, inflow water suspended solid concentration SS, inflow water total nitrogen TN, inflow water total phosphorus TP, inflow water temperature T and dissolved oxygen concentration DO are selected as input variables of a model, and COD concentration is an output variable of the model; i.e. vector X ═ X1,x2,…,x6]Corresponding to 6 auxiliary variables of different types, and taking the auxiliary variables as the input of the soft measurement model; y is a leading variable corresponding to COD concentration and is used as the output of the soft measurement model;
preprocessing water quality index data acquired from a field, and judging and removing abnormal values in a water quality index model database by using a Lett test method; secondly, considering that different water quality indexes have different dimensions and units, in order to eliminate dimension influence, the data are normalized and mapped to the range of [0,1], 200 groups of data are randomly selected from a water quality index model database to be used for training a soft measurement model, and the other 50 groups of data are used for testing the soft measurement model.
According to the method, a fitness variance method is adopted to analyze the premature convergence of the FWA algorithm, a Tent chaotic map is introduced to improve the FWA algorithm in order to avoid the premature convergence of the FWA algorithm, and the global ergodicity of the Tent chaotic map is utilized to maintain the population diversity of the FWA; in order to improve the fitting precision and generalization capability of the RBF neural network, a Tent chaotic map, an FWA firework algorithm and a GD iteration method (GD) are organically fused to provide a Tent FWA-GD hybrid algorithm which is used for training the RBF neural network to obtain optimal RBF neural network parameter values (namely c, delta and omega, wherein c is a central vector of an RBF activation function of a hidden layer, delta is a base width vector of the RBF activation function of the hidden layer, and omega is a connection weight from the hidden layer to an output layer). The RBF neural network based on TentFWA-GD is used for constructing 4 Benchmark function fitting models and a rural domestic sewage treatment process COD soft measurement model, has low function approximation error and high COD prediction precision, and achieves good application effect.
Drawings
FIG. 1 is a model of an RBF neural network;
FIG. 2 is a diagram showing the structure of a COD concentration soft measurement method;
FIG. 3 is the training results of the COD concentration soft measurement model;
fig. 4 is a prediction result of the COD concentration soft measurement model.
Detailed Description
The technical solution of the present invention is described in detail below. The embodiments of the present invention are provided only for illustrating a specific structure, and the scale of the structure is not limited by the embodiments.
The RBF neural network soft measurement modeling method based on TentFWA-GD organically integrates Tent chaotic mapping, a FWA algorithm and a GD iteration method to provide a TentFWA-GD hybrid algorithm for training an RBF neural network so as to obtain optimal RBF neural network parameter values c, delta and omega; c is a central vector of the hidden layer RBF activation function, delta is a base width vector of the hidden layer RBF activation function, and omega is a connection weight from the hidden layer to the output layer; the Tent chaotic mapping is Tent mapping or Tent map, the FWA is a firework algorithm, and the GD iteration method is Gradient Descent; adopting a fitness variance method to carry out premature convergence analysis on the FWA algorithm, introducing Tent chaotic mapping to improve the FWA algorithm in order to avoid premature convergence of the FWA algorithm, maintaining population diversity of the FWA by using global ergodicity of the Tent chaotic mapping, and guiding the FWA population to escape from a local optimal region to continue global search;
carrying out premature convergence analysis on the FWA algorithm by adopting a fitness variance method, and analyzing the overall change condition of the fitness values of the firework members in the iteration process of the FWA algorithm to serve as a judgment basis for local optimization of the FWA population; let N be the firework population size, f (x)i) And favgRespectively the fitness value of the ith member and the average fitness value of the current group, the variance sigma of the fitness values of the current group2Can be defined as:
variance σ of current population fitness value2Reflects the aggregation degree of firework members in the firework group, and the smaller the numerical value is, the more the firework member aggregation degree isThe more concentrated the distribution of the firework members in the solution space, the more concentrated the distribution of the firework members can be used as a measurement index of the FWA population diversity; in the FWA algorithm searching process, the fitness value of each firework member is gradually close along with the increase of the iteration number, and sigma is2The value of (c) is also decreased; when sigma is2And if the global optimal solution is smaller than the threshold H and the algorithm termination condition is not met, judging that the FWA algorithm is premature and converged.
Training an RBF neural network based on a TentFWA-GD hybrid algorithm, wherein an optimization mechanism combining global rough search and local fine exploration is adopted in the training process; in the first stage, searching is carried out by a FWA algorithm, and whether the local optimum is involved is judged by adopting a fitness variance method; in the second stage, when the FWA algorithm is trapped in a local optimal solution, on one hand, a Tent chaotic map is used for guiding a firework group to escape from a local optimal region and continue global search; on the other hand, an RBF neural network is trained by combining a GD iteration method, the local exploration capacity of the firework population is enhanced, and the accuracy of the optimal solution of the population is improved;
the specific process of the RBF neural network training process based on the TentFWA-GD hybrid algorithm is as follows:
1) carrying out random initialization on the firework population in the solution space according to preset parameters; the dimension of the firework member is the sum of the dimensions of parameters c, delta and omega to be optimized of the RBF neural network, and the fitness function is the mean square error of the neural network;
2) optimizing parameters of the RBF neural network based on the FWA algorithm, wherein the parameters comprise: calculating the information of each member of the firework population, the information of the optimal member of the population and the variance sigma of the population fitness value2(ii) a Judging whether the FWA falls into a local extreme value sigma2If not more than H, entering the step 3), otherwise, returning to the step 2); the information of each member of the firework population comprises a position and a fitness value; the information of the group optimal member comprises a group optimal position and a fitness value;
3) and further optimizing parameters of the RBF neural network by adopting a GD iteration method, wherein the parameters comprise: taking the position of the optimal firework member of the current group as the initial parameter value of the current RBF network, and calling a GD iteration method to adjust the network parameters; for each firework member, according to the probability PmTent chaotic mapping is carried out in the chaotic search space, and the respective composition of the firework population is calculatedMember information, information of the optimal members of the group and group fitness value variance;
4) and stopping searching by the algorithm when the training process reaches the maximum iteration times or the group optimal fitness value meets the precision requirement, and otherwise, turning to the step 2) to continue the iteration.
Tent chaotic mapping, setting system parameter alpha 2, Lyapunov exponent lambdamaxThe Tent chaotic mapping expression is as follows:
wherein z isnAnd zn+1Respectively representing the nth value and the (n + 1) th value of the iterative sequence.
In order to check the effectiveness of the improved algorithm, an RBF neural network function fitting model based on the TentFWA-GD algorithm is established, and four common Benchmark functions are used as test objects to perform function simulation and error analysis. In the simulation process, three function fitting models, namely a basic BP neural network, a basic RBF neural network and an RBF neural network based on an FWA-GD algorithm, are also constructed to form contrast. The 4 Benchmark functions are respectively expressed by f1、f2、f3、f4It is shown that,
xiis the variable of 4 Benchmark functions;
the parameters are set as follows: the solution space dimension D is the sum of the dimensions of parameters c, delta and omega to be optimized of the RBF neural network, the maximum training frequency of the neural network is 1000, and the training target is 10-6(ii) a Generation of neural network sample set: for 4 functions to be fitted, sample sets with the scale of 200 are randomly generated in the independent variable value range respectively, and the number of training samples and the number of testing samples are 150 and 50 respectively; initialization of parameters of the FWA algorithm: the population scale M is 40, the explosion radius regulating coefficient R is 240, the explosion spark number regulating coefficient M is 200, the explosion spark number limiting coefficients a and b are 1 and 20 respectively, and the number of the variable sparks is 45; chaos transformation probability P of TentFWA-GD algorithmm0.2, the threshold H of the variance of the population fitness value is 0.01; and selecting the number of hidden layer nodes of the neural network corresponding to the four functions, and determining that the neural network structures are 2-7-1, 3-6-1, 5-10-1 and 8-7-l respectively. Table 1 shows the fitting results of the four function fitting models, ER1 is the training mean square error, ER2 is the testing mean square error, ER3 is the training mean absolute error, and ER4 is the testing mean absolute error.
TABLE 1 comparison of fitting results of four neural network model functions
The comparison result of the table 1 shows that the fitting accuracy of the RBF-based neural network function fitting model is wholly better than that of the BP neural network function fitting model, and the training error and the inspection error are both reduced to a greater extent. The RBF network has better global approximation capability and can better solve the local optimal problem of the BP network; the RBF network parameters are optimized by adopting an FWA-GD algorithm and a TentFWA-GD algorithm, so that the function fitting precision of the model is further improved; the improved TentFWA-GD algorithm is used for optimizing RBF network parameters so as to obtain an optimal network structure, and the constructed RBF neural network function fitting model has optimal learning capacity and fitting performance.
Referring to fig. 1 to 4, the RBF neural network based on the TentFWA-GD algorithm is applied to a soft measurement model of the COD concentration in the sewage treatment process. Collecting sewage by using on-site DCS systemAnd (5) processing each original parameter information to establish a water quality index model database. The correlation between 6 process parameters such as inflow Q, inflow suspended solid concentration SS, inflow total nitrogen TN, inflow total phosphorus TP, inflow temperature T, dissolved oxygen concentration DO and the like and COD concentration is maximum by integrating field experience and PCA analysis. Defining an input auxiliary variable X ═ X for a soft measurement model1,x2,…,x6]And outputting a leading variable Y corresponding to parameters of inflow Q, inflow suspended solid concentration SS, inflow total nitrogen TN, inflow total phosphorus TP, inflow temperature T and dissolved oxygen concentration DO6, and establishing a RBF neural network soft measurement model corresponding to the effluent COD concentration. Some sample data are shown in table 2.
And preprocessing the actually measured water quality index data. Firstly, distinguishing and eliminating abnormal values in a water quality index model database by using a Latt test method; secondly, considering that different water quality indexes have different dimensions and units, in order to eliminate dimension influence, the data are normalized and mapped to the range of [0,1] interval. 200 sets of data are randomly selected from the model database for training the soft measurement model, and 50 sets of data are used for testing the soft measurement model.
TABLE 2 partial sample data
An RBF neural network sewage aeration process COD concentration on-line soft measurement model is constructed, wherein the three-layer network topology structure is 6-13-1, the number of network parameters c, delta and omega to be optimized is 39, and the training method is a TentFWA-GD algorithm. And comparing the model with models such as a basic BP neural network, a basic RBF neural network, an RBF neural network based on an FWA-GD algorithm and the like. The main parameters of the modeling process are as follows: the maximum number of training times is 5000; the FWA algorithm group size M is 40, the explosion radius regulating coefficient R is 200, the explosion spark number regulating coefficient M is 150, the explosion spark number limiting coefficients a and b are 1 and 20 respectively, and the variation spark number is 45; chaos transformation probability P of TentFWA-GD hybrid algorithmm0.2, the threshold H of the variance of the population fitness value is 0.015; the neural network structure is 6-13-1.
And taking 200 groups of preprocessed samples as training data of the neural network model, and storing the optimal c, delta and omega values for online prediction of COD concentration of the model after training. Table 3 shows the training and prediction results of four neural network models, ER1 and ER3 respectively represent the mean square error and mean absolute error of the training process, and ER2 and ER4 respectively represent the mean square error and mean absolute error of the testing process. FIGS. 3 and 4 show the training effect and the prediction result of the RBF neural network soft measurement model based on the TentFWA-GD algorithm, respectively.
TABLE 3 comparison of training and prediction results for four models
The comparative results in table 3 show that: compared with the other three neural network soft measurement models, the RBF neural network model based on the TentFWA-GD algorithm has the minimum training error and generalization error and shows stronger global approximation capability. As can be seen from the training results of FIG. 3, the RBF neural network is trained based on the improved combination training method, and the parameter optimization process adopts an optimization mechanism combining global rough search and local fine exploration, so that the training efficiency and the training precision are effectively improved. The deviation between the COD concentration actual value and the soft measurement model output value of 200 groups of training samples is small (the mean square error and the mean absolute error are respectively 0.18 and 0.25), and the training process meets the requirement. As can be seen from the prediction results in fig. 4, the COD concentration measurement accuracy of 50 test samples was high (mean square error and mean absolute error were 0.23 and 0.36, respectively). Training and testing results show that the soft measurement model constructed based on the method has good generalization performance and can better predict COD concentration.
Claims (5)
1. The RBF neural network soft measurement modeling method based on TentFWA-GD is characterized in that a Tent chaotic mapping, a FWA algorithm and a GD iteration method are organically integrated to provide a TentFWA-GD hybrid algorithm for training an RBF neural network so as to obtain optimal RBF neural network parameter values c, delta and omega; c is a central vector of the hidden layer RBF activation function, delta is a base width vector of the hidden layer RBF activation function, and omega is a connection weight from the hidden layer to the output layer; the Tent chaotic mapping is Tent mapping or Tentmap, the FWA is a firework algorithm, and the GD iteration method is Gradient Descent; adopting a fitness variance method to carry out premature convergence analysis on the FWA algorithm, introducing Tent chaotic mapping to improve the FWA algorithm in order to avoid premature convergence of the FWA algorithm, maintaining population diversity of the FWA by using global ergodicity of the Tent chaotic mapping, and guiding the FWA population to escape from a local optimal region to continue global search;
the method comprises the steps of adopting a fitness variance method to carry out premature convergence analysis on a FWA algorithm, analyzing the overall change condition of fitness values of firework members in the iteration process of the FWA algorithm, and using the overall change condition as a judgment basis for local optimization of FWA population; let N be the firework population size, f (x)i) And favgRespectively the fitness value of the ith member and the average fitness value of the current group, the variance sigma of the fitness values of the current group2Can be defined as:
variance σ of current population fitness value2The aggregation degree of firework members in a firework population is reflected, and the smaller the numerical value is, the more concentrated the distribution of the firework members in a solution space is, and the smaller the numerical value is, the more concentrated the distribution of the firework members in the solution space can be used as a measurement index of the FWA population diversity; in the FWA algorithm searching process, the fitness value of each firework member is gradually close along with the increase of the iteration number, and sigma is2The value of (c) is also decreased; when sigma is2And if the global optimal solution is smaller than the threshold H and the algorithm termination condition is not met, judging that the FWA algorithm is premature and converged.
2. The RBF neural network soft measurement modeling method based on TentFWA-GD as claimed in claim 1, wherein said TentFWA-GD hybrid algorithm trains RBF neural network, the training process employs an optimization mechanism combining global coarse search and local fine exploration; in the first stage, searching is carried out by a FWA algorithm, and whether the local optimum is involved is judged by adopting a fitness variance method; in the second stage, when the FWA algorithm is trapped in a local optimal solution, on one hand, a Tent chaotic map is used for guiding a firework group to escape from a local optimal region and continue global search; on the other hand, an RBF neural network is trained by combining a GD iteration method, the local exploration capacity of the firework population is enhanced, and the accuracy of the optimal solution of the population is improved;
the specific process of the RBF neural network training process based on the TentFWA-GD hybrid algorithm is as follows:
1) carrying out random initialization on the firework population in the solution space according to preset parameters; the dimension of the firework member is the sum of the dimensions of parameters c, delta and omega to be optimized of the RBF neural network, and the fitness function is the mean square error of the neural network;
2) optimizing parameters of the RBF neural network based on the FWA algorithm, wherein the parameters comprise: calculating the information of each member of the firework population, the information of the optimal member of the population and the variance sigma of the population fitness value2(ii) a Judging whether the FWA falls into a local extreme value sigma2If not more than H, entering the step 3), otherwise, returning to the step 2); the information of each member of the firework population comprises a position and a fitness value; the information of the group optimal member comprises a group optimal position and a fitness value;
3) and further optimizing parameters of the RBF neural network by adopting a GD iteration method, wherein the parameters comprise: taking the position of the optimal firework member of the current group as the initial parameter value of the current RBF network, and calling a GD iteration method to adjust the network parameters; for each firework member, according to the probability PmPerforming Tent chaotic mapping in a chaotic search space, and calculating information of each member of the firework population, information of the optimal member of the population and the variance of the population fitness value;
4) and stopping searching by the algorithm when the training process reaches the maximum iteration times or the group optimal fitness value meets the precision requirement, and otherwise, turning to the step 2) to continue the iteration.
3. A RBF neural network soft measurement modeling method based on TentFWA-GD is used for constructing 4 Benchmark function fitting models and is characterized in that f is used for 4 Benchmark functions respectively1、f2、f3、f4It is shown that,
xiis the variable of 4 Benchmark functions;
the parameters are set as follows: f. of1The function corresponding RBF neural network has a structure of 2-7-1, f2The function corresponding RBF neural network has a structure of 3-6-1, f3The function corresponding RBF neural network has a structure of 5-10-1, f4The function corresponds to the structure 8-7-l of the RBF neural network; the solution space dimension D is the sum of the dimensions of parameters c, delta and omega to be optimized of the RBF neural network; the maximum training times of the RBF neural network is 1000, and the training target is 10-6(ii) a Generation of RBF neural network sample set: for 4 functions to be fitted, sample sets with the scale of 200 are randomly generated in the independent variable value range respectively, and the number of training samples and the number of testing samples are 150 and 50 respectively;
initialization of parameters of the FWA algorithm: the population scale M is 40, the explosion radius regulating coefficient R is 240, the explosion spark number regulating coefficient M is 200, the explosion spark number limiting coefficients a and b are 1 and 20 respectively, and the Gaussian variation spark number is 45; chaos transformation probability P of TentFWA-GD hybrid algorithmmIs 0.2, and the threshold H for the variance of the population fitness value is 0.01.
4. A soft measurement modeling method for COD concentration in rural domestic sewage treatment process based on a TentFWA-GD RBF neural network is disclosedIs characterized in that 6 auxiliary variables of inflow Q, inflow suspended solid concentration SS, inflow total nitrogen TN, inflow total phosphorus TP, inflow temperature T and dissolved oxygen concentration DO are selected as input variables of a model, and COD concentration is an output variable of the model; i.e. vector X ═ X1,x2,…,x6]Corresponding to 6 auxiliary variables of inflow Q, inflow suspended solid concentration SS, inflow total nitrogen TN, inflow total phosphorus TP, inflow temperature T and dissolved oxygen concentration DO, and taking the auxiliary variables as the input of a soft measurement model; y is a leading variable corresponding to COD concentration and is used as the output of the soft measurement model;
preprocessing water quality index data acquired from a field, and judging and removing abnormal values in a water quality index model database by using a Lett test method; secondly, considering that different water quality indexes have different dimensions and units, in order to eliminate dimension influence, the data are normalized and mapped to the range of [0,1], 200 groups of data are randomly selected from a water quality index model database to be used for training a soft measurement model, and the other 50 groups of data are used for testing the soft measurement model.
5. The TentFWA-GD-based RBF neural network soft measurement modeling method according to claim 1, wherein the Tent chaotic map sets a parameter a ═ 2, Lyapunov exponent λmaxAnd alpha is a system parameter, and a Tent chaotic mapping expression is as follows:
wherein z isnAnd zn+1Respectively representing the nth value and the (n + 1) th value of the iterative sequence.
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