CN112765902B - Soft measurement modeling method for COD concentration in rural domestic sewage treatment process based on TentFWA-GD RBF neural network - Google Patents
Soft measurement modeling method for COD concentration in rural domestic sewage treatment process based on TentFWA-GD RBF neural network Download PDFInfo
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Abstract
The invention discloses a RBF neural network soft measurement modeling method based on TentFWA-GD and application thereof, which adopts an adaptability variance method to perform premature convergence analysis of FWA algorithm, introduces Tent chaotic mapping to improve the FWA algorithm in order to avoid premature convergence of the FWA algorithm, and maintains population diversity of FWA by utilizing global ergodic nature of the Tent chaotic mapping; in order to improve the fitting precision and generalization capability of the RBF neural network, a TentFWA-GD algorithm is provided by organically integrating a Tentchaotic mapping, a FWA algorithm and a GD iteration method and 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 an hidden layer, delta is a basic width vector of the RBF activation function of the hidden layer, and omega is a connection weight value from the hidden layer to an output layer). The RBF neural network based on the TentFWA-GD is used for constructing 4 Benchmark function fitting models and a rural domestic sewage treatment process COD soft measurement model, has lower function approximation error and higher 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 Radial Basis Function (RBF) neural network soft measurement modeling method based on TentFWA-GD and application thereof.
Background
With the development of rural economy, improvement of life and population increase of China, rural sewage discharge presents a rapidly growing situation, and rural domestic sewage is an important source of rural non-point source pollution. The enhanced rural sewage treatment has important significance for protecting rural water resources, improving living environment and promoting ecological new rural construction. In the rural domestic sewage treatment process, chemical oxygen demand (Chemical Oxygen Demand, COD) is not only an important parameter for describing the content of organic matters in water, but also a main index for measuring the pollution degree of water. The timely and accurate measurement of COD and other water quality parameters has important significance for the optimal control of a sewage treatment system and the integral improvement of sewage treatment quality. The traditional COD detection method mainly comprises a potassium dichromate method, a microwave sealing digestion method, a spectrophotometry method and the like, and the 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 are difficult to realize the timely detection of water quality parameters such as COD and the like and the real-time control of the sewage treatment process.
The soft measurement technology based on the neural network achieves good results in theoretical research and practical application. In recent years, sewage quality parameter soft measurement methods based on BP neural network, RBF neural network and other artificial neural networks are widely paid attention to domestic and foreign scholars. Compared with BP neural network, RBF neural network has advantages of compact topological structure, fast convergence speed, high approximation accuracy, etc., and is suitable for soft measurement modeling of complex process.
When the RBF neural network is used for soft measurement modeling, the RBF neural network is utilized to construct a network model between an auxiliary variable which can be directly measured by adopting a conventional sensor and a dominant variable which is difficult to directly measure, so that the prediction of the dominant variable is realized; referring to fig. 1, the topology structure of the rbf network is generally composed of three layers, i.e., an input layer, an hidden layer, an output layer, etc., wherein 6 input layer nodes correspond to each auxiliary variable of the soft measurement model, 1 output layer node corresponds to the dominant variable of the soft measurement model, and the number of hidden layer nodes is l; let the input vector x= { X 1 ,x 2 ,…,x 6 And 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 through the weight matrix. Using Gaussian radial basis functions as hidden layer activation functions, i.e
The output Y of the RBF network, corresponding to the input vector X, is:
where j=1, 2, …, l, c= { c 1 ,c 2 ,…,c l Sum delta = { delta 1 ,δ 2 ,…,δ l The central vector and the base width vector of the RBF activation function of the hidden layer are respectively, and omega= { omega 1 ,ω 2 ,…,ω l And the connection weight value from the hidden layer to the output layer. The network parameters c, delta and omega are important parameters of the soft measurement model, and directly relate to the overall performance of the RBF neural network, the measurement precision and generalization performance of the soft measurement model, and the problems that the key parameters of the RBF neural network are difficult to determine in practical application exist. To improve the overall performance of RBF neural network and soft measurement model, firework algorithm (Fireworks algorithm, FWA) and the like are appliedThe optimization of the group intelligent optimization algorithm to determine the RBF neural network parameter value is an important task of soft measurement modeling.
In 2010, students such as Tan and Zhu put forward a firework algorithm according to the phenomenon that spark is generated by firework explosion, and the strong robustness and global optimizing capability of the firework algorithm are widely focused by students in different fields. The method is successfully used for solving the problems of training of the weight of the neural network, parameter optimization of continuous and discrete systems, solving of combined optimization problems and the like. In order to further improve the optimization performance of the algorithm, a plurality of scholars propose a plurality of improved algorithms from different angles and perform mechanism analysis and comparison research, so that good results are obtained. The firework algorithm belongs to a guided random heuristic algorithm and has strong optimization problem solving capability. However, when complex optimization problems are processed, the solution results may be different or the global optimal solution may not be found each time; the method has the defects of easy sinking into local optimum, slow convergence speed in the later period of evolution, poor robustness and the like.
The implementation thinking of the basic firework algorithm at present is that fireworks are regarded as a feasible solution in an optimization problem solution space, and the process that a certain amount of sparks are generated by firework explosion is the process that the optimal solution is searched in the neighborhood; the algorithm is specifically described as follows:
1) Randomly generating N fireworks, i.e. initializing N positions x randomly in solution space i The N initial solutions to the problem are characterized.
2) Calculating the fitness value of each firework, evaluating the quality of the firework and generating different numbers of sparks under different explosion radiuses; firework x i Explosion radius R of (2) i And the number of explosion sparks S i The calculation formulas of (a) are respectively formula (5) and formula (6), wherein y min ＝min(f(x i ) (i=1, 2, …, N) is the fitness minimum (optimum) in the current fireworks population; y is max ＝max(f(x i ) (i=1, 2, …, N) is the maximum (worst) fitness value in the current fireworks population. The constants R and M are used to adjust the radius of the explosion and the number of sparks generated, respectively, epsilon being a small amount to avoid zero operation.
In addition, in order to limit the number of spark particles generated at the positions of the fireworks where the fitness value is good and the fitness value is poor, the number of spark generation 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, z=round (D×rand (0, 1)), wherein D represents firework x i Dimension number; round is a rounding function and rand is a function that generates random numbers that obey uniform distribution within an interval. Performing explosion operation on each dimension k of DS according to the reference formula (8), and performing ex after boundary crossing processing ik Stored in the explosive spark population.
ex ik ＝x ik +h，h＝R i ×rand(-1,1) (8)
Wherein h represents a positional offset; x is x ik The kth dimension, ex, representing the ith individual firework ik Represents x ik Explosion spark after explosion operation.
4) Generating G Gaussian variation sparks, randomly selecting sparks x i And randomly extracting z dimensions to form a set DS, let z=round (d×rand (0, 1)), D representing the dimension of the firework member xi. Performing Gaussian variation operation on each dimension k of DS according to reference formula (9), and performing mx after boundary crossing treatment ik Stored in gaussian variant spark populations.
mx ik ＝x ik ×e (9)
Wherein: e-N (1, 1), mx ik Is x ik Gaussian variation spark generated after gaussian variation.
5) From fireworks, explosion sparks and Gaussian variation sparksSelecting N members from the population members to form the firework population for the next iterative operation. Setting a candidate set as S (comprising three types of population members), and setting the firework population scale as N; the individual with the optimal fitness value in S is firstly determined as the next generation firework member, the rest N-1 firework members are sequentially selected from S to generate by a roulette mode, and the candidate x is selected i Probability of being selected p (x i ) The method comprises the following steps:
wherein R (x) i ) Is x i And the sum of the distances between the two bodies 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 fuses the Tent chaotic map, the FWA algorithm and the GD iterative method to provide a Tent FWA-GD algorithm which is used for training the RBF neural network so as to obtain the optimal RBF neural network parameter value; the RBF neural network based on the TentFWA-GD is used for constructing 4 Benchmark function fitting models and a rural domestic sewage treatment process COD soft measurement model, has lower function approximation error and higher COD prediction precision, and obtains good application effect;
the technical scheme adopted is as follows:
according to the RBF neural network soft measurement modeling method based on the TentFWA-GD, a TentFWA-GD hybrid algorithm is organically integrated with a Tentchaotic mapping method, a FWA algorithm and a GD iterative method and is used for training the RBF neural network so as to obtain optimal RBF neural network parameter values c, delta and omega; wherein c is a central vector of an RBF activation function of the hidden layer, delta is a basic width vector of the RBF activation function of the hidden layer, and omega is a connection weight value from the hidden layer to the output layer; the Tent chaotic map is Tent map or Tent map, the FWA is firework algorithm, and the GD iteration method is Gradent device; the method comprises the steps of adopting an fitness variance method to conduct early-maturing convergence analysis of an FWA algorithm, introducing a Tent chaotic map to improve the FWA algorithm in order to avoid early-maturing convergence of the FWA algorithm, maintaining population diversity of the FWA by utilizing global ergodic property of the Tent chaotic map, and guiding the FWA population to escape from a local optimal area to continue global search;
the early maturity convergence analysis of the FWA algorithm is carried out by adopting an adaptability variance method, and the overall change condition of the adaptability value of the firework member is analyzed in the iteration process of the FWA algorithm and is used as a judging basis for the partial optimum of the FWA population trapping; setting N as the firework population scale, f (x) i ) And f avg Fitness value of ith member and average fitness value of current group, variance sigma of fitness value of current group 2 Can be defined as:
current population fitness value variance sigma 2 The aggregation degree of the firework members in the firework group is reflected, the smaller the numerical value is, the more concentrated the firework members are distributed in the solution space, and the firework members can be used as a measurement index of FWA population diversity; in the FWA algorithm searching process, the fitness value of each firework member gradually approaches with the increase of iteration times, sigma 2 The value of (2) decreases as well; when sigma is 2 And if the value is smaller than the threshold value H and the global optimal solution does not meet the algorithm termination condition, judging that the FWA algorithm is premature and converged.
Training RBF neural network based on TentFWA-GD hybrid algorithm, wherein the training process adopts a optimizing mechanism combining global rough search and local fine exploration; the first stage is to search by FWA algorithm and judge whether to fall into local optimum by adopting adaptability variance method; when the FWA algorithm falls into a local optimal solution, on one hand, the Tent chaotic map is utilized to guide the firework group to escape from the local optimal area and continue global search; on the other hand, the RBF neural network is trained by combining with a GD iteration method, so that the local exploration capacity of the firework population is enhanced, and the precision of the optimal solution of the population is improved;
the training process of the RBF neural network based on the TentFWA-GD hybrid algorithm comprises the following specific procedures:
1) Carrying out random initialization of firework population in a solution space according to preset parameters; the dimension of the firework member is the sum of the dimension of the 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 comprises: calculating information of each member of the firework population, information of the optimal member of the population and variance sigma of the fitness value of the population 2 The method comprises the steps of carrying out a first treatment on the surface of the Judging whether FWA falls into local extremum or not, sigma 2 If H is less than or equal to H, entering the step 3), otherwise returning to the step 2); the information of each member of the firework population comprises a position and an adaptability value; the information of the optimal group members comprises optimal group positions and fitness values;
3) Further optimizing parameters of the RBF neural network by adopting a GD iteration method, comprising the following steps: taking the position of the current group optimal firework member as an initial parameter value of the current RBF network, and calling a GD iteration method to adjust network parameters; for each firework member, according to probability P m Performing Tent chaotic mapping in the chaotic search space, and calculating information of each member of the firework population, information of the optimal member of the population and variance of the population fitness value;
4) And (3) stopping searching by the algorithm when the training process reaches the maximum iteration times or the optimal fitness value of the group meets the precision requirement, otherwise, turning to the step 2) to continue iteration.
Tent chaotic mapping, setting system parameters a=2 and Lyapunov index lambda max =ln2, tent chaotic map expression is:
wherein z is n And z n+1 Respectively representing the nth value and the n+1th 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 the 4 Benchmark functions are respectively used with f 1 、f 2 、f 3 、f 4 The representation is made of a combination of a first and a second color,
x i variables that are 4 Benchmark functions;
the parameters were set as follows: f (f) 1 The structure of the RBF neural network corresponding to the function is 2-7-1, f 2 The structure of the RBF neural network corresponding to the function is 3-6-1, f 3 The structure of the RBF neural network corresponding to the function is 5-10-1, f 4 The function corresponds to the structure 8-7-1 of the RBF neural network; the dimension D of the solution space 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 RBF neural network is 1000, and the training target is 10 -6 The method comprises the steps of carrying out a first treatment on the surface of the Generation of RBF neural network sample set: for 4 functions to be fitted, randomly generating sample sets with the scale of 200 in the independent variable value range, wherein the number of training and testing samples is 150 and 50 respectively;
FWA algorithm parameter initialization: the population scale M is 40, the explosion radius adjusting coefficient R is 240, the explosion spark number adjusting 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; chaotic transformation probability P of TentFWA-GD hybrid algorithm m The threshold H for the variance of population fitness values was 0.01, which was 0.2.
A soft measurement modeling method of 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 the COD concentration is an output variable of the model; i.e. in the directionQuantity x= [ X ] 1 ,x 2 ,…,x 6 ]Corresponding to 6 auxiliary variables of different types, and taking the auxiliary variables as input of a soft measurement model; y is a dominant variable, corresponds to COD concentration and is used as the output of a soft measurement model;
preprocessing water quality index data acquired from the site, and firstly, judging and eliminating abnormal values in a water quality index model database by using a Lyte test method; secondly, considering that different water quality indexes have different dimensions and units, in order to eliminate the influence of the dimensions, data are normalized and mapped to a range of a [0,1] interval, 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.
The invention adopts the fitness variance method to carry out the premature convergence analysis of the FWA algorithm, introduces the Tent chaotic map to improve the FWA algorithm in order to avoid the premature convergence of the FWA algorithm, and maintains the population diversity of the FWA by utilizing the global ergodic property of the Tent chaotic map; in order to improve the fitting precision and generalization capability of the RBF neural network, a TentFWA-GD hybrid algorithm is provided by organically integrating a Tentchaotic map, a FWA firework algorithm and a GD iterative method (GD), and 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 an hidden layer, delta is a basic width vector of the RBF activation function of the hidden layer, and omega is a connection weight value from the hidden layer to an output layer). The RBF neural network based on the TentFWA-GD is used for constructing 4 Benchmark function fitting models and a rural domestic sewage treatment process COD soft measurement model, has lower function approximation error and higher COD prediction precision, and achieves good application effect.
Drawings
FIG. 1 is an RBF neural network model;
FIG. 2 is a diagram showing a structure of a COD concentration soft measurement method;
FIG. 3 is training results of a COD concentration soft measurement model;
fig. 4 is a prediction result of the COD concentration soft measurement model.
Detailed Description
The technical scheme of the present invention is described in detail below. The embodiments of the present invention are merely illustrative of specific structures, and the scale of the structures is not limited by the embodiments.
According to the RBF neural network soft measurement modeling method based on the TentFWA-GD, a TentFWA-GD hybrid algorithm is organically integrated with a Tentchaotic mapping method, a FWA algorithm and a GD iterative method and is used for training the RBF neural network so as to obtain optimal RBF neural network parameter values c, delta and omega; wherein c is a central vector of an RBF activation function of the hidden layer, delta is a basic width vector of the RBF activation function of the hidden layer, and omega is a connection weight value from the hidden layer to the output layer; the Tent chaotic map is Tent map or Tent map, the FWA is firework algorithm, and the GD iteration method is Gradent device; the method comprises the steps of adopting an fitness variance method to conduct early-maturing convergence analysis of an FWA algorithm, introducing a Tent chaotic map to improve the FWA algorithm in order to avoid early-maturing convergence of the FWA algorithm, maintaining population diversity of the FWA by utilizing global ergodic property of the Tent chaotic map, and guiding the FWA population to escape from a local optimal area to continue global search;
the early maturity convergence analysis of the FWA algorithm is carried out by adopting an adaptability variance method, and the overall change condition of the adaptability value of the firework member is analyzed in the iteration process of the FWA algorithm and is used as a judging basis for the partial optimum of the FWA population trapping; setting N as the firework population scale, f (x) i ) And f avg Fitness value of ith member and average fitness value of current group, variance sigma of fitness value of current group 2 Can be defined as:
current population fitness value variance sigma 2 The aggregation degree of the firework members in the firework group is reflected, the smaller the numerical value is, the more concentrated the firework members are distributed in the solution space, and the firework members can be used as a measurement index of FWA population diversity; in the FWA algorithm searching process, the fitness value of each firework member gradually approaches with the increase of iteration times, sigma 2 The value of (2) decreases as well; when sigma is 2 And if the value is smaller than the threshold value H and the global optimal solution does not meet the algorithm termination condition, judging that the FWA algorithm is premature and converged.
Training RBF neural network based on TentFWA-GD hybrid algorithm, wherein the training process adopts a optimizing mechanism combining global rough search and local fine exploration; the first stage is to search by FWA algorithm and judge whether to fall into local optimum by adopting adaptability variance method; when the FWA algorithm falls into a local optimal solution, on one hand, the Tent chaotic map is utilized to guide the firework group to escape from the local optimal area and continue global search; on the other hand, the RBF neural network is trained by combining with a GD iteration method, so that the local exploration capacity of the firework population is enhanced, and the precision of the optimal solution of the population is improved;
the training process of the RBF neural network based on the TentFWA-GD hybrid algorithm comprises the following specific procedures:
1) Carrying out random initialization of firework population in a solution space according to preset parameters; the dimension of the firework member is the sum of the dimension of the 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 comprises: calculating information of each member of the firework population, information of the optimal member of the population and variance sigma of the fitness value of the population 2 The method comprises the steps of carrying out a first treatment on the surface of the Judging whether FWA falls into local extremum or not, sigma 2 If H is less than or equal to H, entering the step 3), otherwise returning to the step 2); the information of each member of the firework population comprises a position and an adaptability value; the information of the optimal group members comprises optimal group positions and fitness values;
3) Further optimizing parameters of the RBF neural network by adopting a GD iteration method, comprising the following steps: taking the position of the current group optimal firework member as an initial parameter value of the current RBF network, and calling a GD iteration method to adjust network parameters; for each firework member, according to probability P m Performing Tent chaotic mapping in the chaotic search space, and calculating information of each member of the firework population, information of the optimal member of the population and variance of the population fitness value;
4) And (3) stopping searching by the algorithm when the training process reaches the maximum iteration times or the optimal fitness value of the group meets the precision requirement, otherwise, turning to the step 2) to continue iteration.
Tent chaotic mapping, setting system parameters alpha=2 and Lyapunov index lambda max =ln2, tent chaotic map expression is:
wherein z is n And z n+1 Respectively representing the nth value and the n+1th value of the iterative sequence.
In order to check the effectiveness of the improved algorithm, an RBF neural network function fitting model based on a TentFWA-GD algorithm is established, and four commonly used Benchmark functions are used as test objects for function simulation and error analysis. In the simulation process, three function fitting models of a basic BP neural network, a basic RBF neural network and an RBF neural network based on a FWA-GD algorithm are also constructed to form comparison. The 4 Benchmark functions are each applied with f 1 、f 2 、f 3 、f 4 The representation is made of a combination of a first and a second color,
x i variables that are 4 Benchmark functions;
the parameters were set as follows: the dimension D of the solution space 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 The method comprises the steps of carrying out a first treatment on the surface of the Generating a neural network sample set: for 4 functions to be fitted, randomly generating sample sets with the scale of 200 in the independent variable value range, training andthe number of test samples was 150 and 50, respectively; FWA algorithm parameter initialization: the population scale M is 40, the explosion radius adjusting coefficient R is 240, the explosion spark number adjusting coefficient M is 200, the explosion spark number limiting coefficients a and b are 1 and 20 respectively, and the variation spark number is 45; chaotic transformation probability P of TentFWA-GD algorithm m A threshold H of 0.2 for the variance of population fitness values of 0.01; and selecting the hidden layer node numbers of the neural network corresponding to the four functions, and determining the neural network structures to be 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 test mean square error, ER3 is the training mean absolute error, and ER4 is the test mean absolute error.
Table 1 comparison of the results of the four neural network model function fits
The comparison result of table 1 shows that based on the RBF neural network function fitting model, the fitting accuracy is overall better than that of the BP neural network function fitting model, and the training error and the inspection error are reduced to a greater extent. The RBF network has better global approximation capability, and can better solve the problem of local optimization of the BP network; the RBF network parameters are optimized by adopting a 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 ability and fitting performance.
Referring to fig. 1 to 4, the RBF neural network based on the tenfwa-GD algorithm is applied to a soft measurement model of COD concentration in a sewage treatment process. And collecting various original parameter information in the sewage treatment process by using a site DCS system to construct a water quality index model database. And (3) combining site experience and PCA analysis to determine that 6 process parameters such as inflow water flow Q, inflow water suspended solid concentration SS, inflow water total nitrogen TN, inflow water total phosphorus TP, inflow water temperature T, dissolved oxygen concentration DO and the like have the largest correlation with COD concentration. Input auxiliary variable x= [ X ] defining soft measurement model 1 ,x 2 ,…,x 6 ]And outputting a dominant variable Y corresponding to 6 parameters of water inflow Q, water inflow suspended solid concentration SS, water inflow total nitrogen TN, water inflow total phosphorus TP, water inflow temperature T and dissolved oxygen concentration DO, and establishing an RBF neural network soft measurement model corresponding to water outflow COD concentration. Some of the 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 Lyte test method; secondly, considering that different water quality indexes have different dimensions and units, in order to eliminate the influence of the dimensions, the data are normalized and mapped to the [0,1] interval range. 200 sets of data were randomly selected from the model database for training the soft measurement model, and 50 additional sets of data were used to test the soft measurement model.
TABLE 2 partial sample data
And (3) constructing an online soft measurement model of COD concentration in the sewage aeration process of the RBF neural network, 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 with models such as a basic BP neural network, a basic RBF neural network, an RBF neural network based on FWA-GD algorithm and the like. The main parameters of the modeling process are as follows: the maximum training frequency is 5000; the group size M of the FWA algorithm is 40, the explosion radius adjustment coefficient R is 200, the explosion spark number adjustment 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; chaotic transformation probability P of TentFWA-GD hybrid algorithm m A threshold H of 0.015 for a population fitness value variance of 0.2; the neural network structure is 6-13-1.
And taking the preprocessed 200 groups of samples as training data of a neural network model, and storing optimal c, delta and omega values for on-line prediction of COD concentration of the model after training. Table 3 shows training and predicting results of four neural network models, ER1 and ER3 respectively represent mean square error and mean absolute error of the training process, and ER2 and ER4 respectively represent mean square error and mean absolute error of the testing process. Fig. 3 and fig. 4 are training effects and prediction results of RBF neural network soft measurement model based on tenfwa-GD algorithm, respectively.
TABLE 3 training and prediction results comparison of four models
The comparison results in table 3 show that: compared with the other three neural network soft measurement models, the training error and the generalization error of the RBF neural network model based on the TentFWA-GD algorithm are minimum, and the RBF neural network model has stronger global approximation capability. From the training results of fig. 3, it can be seen that the RBF neural network is trained based on the improved combined training method, and the parameter optimization process adopts the optimizing mechanism combining global rough search and local fine search, so that the training efficiency and the training precision are effectively improved. The deviation between the COD concentration actual value of the training samples of the 200 groups and the output value of the soft measurement model is smaller (mean square error and average absolute error are respectively 0.18 and 0.25), and the training process meets the requirements. As can be seen from the prediction results of fig. 4, the COD concentration measurement accuracy of 50 groups of test samples is high (mean square error and average absolute error are 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 (4)
1. A soft measurement modeling method of COD concentration in rural domestic sewage treatment process based on a RBF neural network of TentFWA-GD is characterized in that based on a TentFWA-GD mixing algorithm, 6 auxiliary variables of water inflow Q, water inflow suspended solid concentration SS, water inflow total nitrogen TN, water inflow total phosphorus TP, water inflow temperature T and dissolved oxygen concentration DO are selected as input variables of a model, and the COD concentration is an output variable of the model; i.e. vector x= [ X ] 1 ,x 2 ,…,x 6 ]Corresponding to 6 auxiliary variables of water inflow Q, water inflow suspended solid concentration SS, water inflow total nitrogen TN, water inflow total phosphorus TP, water inflow temperature T and dissolved oxygen concentration DO, and taking the auxiliary variables as input of a soft measurement model; y is the dominant variable corresponding to COD concentrationAs output of the soft measurement model;
preprocessing water quality index data acquired from the site, and firstly, judging and eliminating abnormal values in a water quality index model database by using a Lyte test method; secondly, considering that different water quality indexes have different dimensions and units, in order to eliminate the influence of the dimensions, carrying out normalization processing on the data and mapping the data to a range of a [0,1] interval, randomly selecting 200 groups of data from a water quality index model database for training a soft measurement model, and testing the soft measurement model by the other 50 groups of data;
the TentFWA-GD mixing algorithm organically combines the Tentchaotic mapping, the FWA algorithm and the GD iteration method to provide a TentFWA-GD mixing algorithm which is used for training the RBF neural network to obtain optimal RBF neural network parameter values c, delta and omega; wherein c is a central vector of an RBF activation function of the hidden layer, delta is a basic width vector of the RBF activation function of the hidden layer, and omega is a connection weight value from the hidden layer to the output layer; the Tent chaotic map is Tent map or Tent map, the FWA is firework algorithm, and the GD iteration method is Gradent device; the method comprises the steps of adopting an fitness variance method to conduct early-maturing convergence analysis of an FWA algorithm, introducing a Tent chaotic map to improve the FWA algorithm in order to avoid early-maturing convergence of the FWA algorithm, maintaining population diversity of the FWA by utilizing global ergodic property of the Tent chaotic map, and guiding the FWA population to escape from a local optimal area to continue global search;
the early maturity convergence analysis of the FWA algorithm is carried out by adopting the fitness variance method, and the overall change condition of the fitness value of the firework member is analyzed in the iteration process of the FWA algorithm and is used as a judgment basis for the partial optimum of the FWA population trapping; setting N as the firework population scale, f (x) i ) And f avg Fitness value of ith member and average fitness value of current group, variance sigma of fitness value of current group 2 Can be defined as:
current population fitness value variance sigma 2 Reflecting the members of fireworks in the fireworks groupThe smaller the value is, the more concentrated the distribution of firework members in the solution space is, and the firework members can be used as a measure index of FWA population diversity; in the FWA algorithm searching process, the fitness value of each firework member gradually approaches with the increase of iteration times, sigma 2 The value of (2) decreases as well; when sigma is 2 And if the value is smaller than the threshold value H and the global optimal solution does not meet the algorithm termination condition, judging that the FWA algorithm is premature and converged.
2. The soft measurement modeling method of COD concentration in rural domestic sewage treatment process of RBF neural network based on TentFWA-GD according to claim 1, wherein the TentFWA-GD mixing algorithm is used for training the RBF neural network, and the training process adopts an optimizing mechanism combining global rough search and local fine search; the first stage is to search by FWA algorithm and judge whether to fall into local optimum by adopting adaptability variance method; when the FWA algorithm falls into a local optimal solution, on one hand, the Tent chaotic map is utilized to guide the firework group to escape from the local optimal area and continue global search; on the other hand, the RBF neural network is trained by combining with a GD iteration method, so that the local exploration capacity of the firework population is enhanced, and the precision of the optimal solution of the population is improved;
the training process of the RBF neural network based on the TentFWA-GD hybrid algorithm comprises the following specific procedures:
1) Carrying out random initialization of firework population in a solution space according to preset parameters; the dimension of the firework member is the sum of the dimension of the 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 comprises: calculating information of each member of the firework population, information of the optimal member of the population and variance sigma of the fitness value of the population 2 The method comprises the steps of carrying out a first treatment on the surface of the Judging whether FWA falls into local extremum or not, sigma 2 If H is less than or equal to H, entering the step 3), otherwise returning to the step 2); the information of each member of the firework population comprises a position and an adaptability value; the information of the optimal group members comprises optimal group positions and fitness values;
3) Further optimizing parameters of the RBF neural network by adopting a GD iteration method, comprising the following steps: as the followingThe position of the front group optimal firework member is used as an initial parameter value of the current RBF network, and a GD iteration method is called to adjust network parameters; for each firework member, according to probability P m Performing Tent chaotic mapping in the chaotic search space, and calculating information of each member of the firework population, information of the optimal member of the population and variance of the population fitness value;
4) And (3) stopping searching by the algorithm when the training process reaches the maximum iteration times or the optimal fitness value of the group meets the precision requirement, otherwise, turning to the step 2) to continue iteration.
3. The soft measurement modeling method of COD concentration in rural domestic sewage treatment process based on TentFWA-GD RBF neural network as set forth in claim 1, wherein the RBF neural network soft measurement modeling method of TentFWA-GD is used for constructing 4 Benchmark function fitting models, and the 4 Benchmark functions are respectively implemented by f 1 、f 2 、f 3 、f 4 The representation is made of a combination of a first and a second color,
x i variables that are 4 Benchmark functions;
the parameters were set as follows: f (f) 1 The structure of the RBF neural network corresponding to the function is 2-7-1, f 2 The structure of the RBF neural network corresponding to the function is 3-6-1, f 3 Function corresponds to RBF neural networkThe structure is 5-10-1, f 4 The function corresponds to the structure 8-7-l of the RBF neural network; the dimension D of the solution space 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 RBF neural network is 1000, and the training target is 10 -6 The method comprises the steps of carrying out a first treatment on the surface of the Generation of RBF neural network sample set: for 4 functions to be fitted, randomly generating sample sets with the scale of 200 in the independent variable value range, wherein the number of training and testing samples is 150 and 50 respectively;
FWA algorithm parameter initialization: the population scale M is 40, the explosion radius adjusting coefficient R is 240, the explosion spark number adjusting 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; chaotic transformation probability P of TentFWA-GD hybrid algorithm m The threshold H for the variance of population fitness values was 0.01, which was 0.2.
4. The soft measurement modeling method of COD concentration in rural domestic sewage treatment process based on TentFWA-GD RBF neural network according to claim 1, wherein the Tentchaotic mapping is characterized in that the parameters alpha=2 and Lyapunov index lambda are set max =ln2, a is a system parameter, and the Tent chaotic mapping expression is:
wherein z is n And z n+1 Respectively representing the nth value and the n+1th value of the iterative sequence.
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