CN112115754A - Short-term traffic flow prediction model based on firework differential evolution hybrid algorithm-extreme learning machine - Google Patents
Short-term traffic flow prediction model based on firework differential evolution hybrid algorithm-extreme learning machine Download PDFInfo
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Abstract
The invention discloses a short-time traffic flow prediction model based on a firework differential evolution hybrid algorithm-extreme learning machine, which adopts a Singular Spectrum Analysis (SSA) method to filter noise components contained in original traffic flow data and trains an Extreme Learning Machine (ELM) neural network model by using the traffic flow data after noise reduction; performing phase space reconstruction, and determining key parameters of the ELM network model such as time delay, embedding window width and embedding dimension by using a C-C algorithm; the firework differential evolution (FWADE) hybrid optimization algorithm is obtained by organically combining a firework algorithm (FWA) and a differential evolution algorithm (DE), so that the overall convergence capability and the robustness of a basic algorithm are enhanced, and the overall optimization performance is improved; and (3) using the FWADE algorithm to optimize the weight threshold value of the ELM network, establishing a short-time traffic flow prediction model and evaluating the short-time traffic flow prediction model. The short-term traffic flow prediction model has high prediction precision and strong generalization capability, and the fitting degree of the predicted value and the actual value is good.
Description
Technical Field
The invention relates to a short-term traffic flow prediction model, in particular to a short-term traffic flow prediction model based on a firework difference evolution hybrid algorithm-extreme learning machine.
Background
The intelligent traffic leads the construction of intelligent cities, traffic flow prediction occupies an important position in an intelligent traffic system, and the premise of realizing real-time traffic control and guidance is provided. The real-time accurate prediction of the short-time traffic flow plays an important role in the analysis of the traffic state of a road network, the planning of the traffic network and the optimization control of the traffic; on the other hand, the continuous development of traffic data acquisition technology provides a technical means for the real-time acquisition of road network traffic flow information and provides data guarantee for the research of a short-time traffic flow prediction method. The traffic flow prediction modeling method has important theoretical value and practical significance.
According to different principles, the existing traffic flow prediction modeling methods can be divided into two types, namely a parametric method and a non-parametric method. The parameter method mainly comprises prediction methods such as historical average, linear and nonlinear parameter regression, Kalman filtering, autoregression, exponential smoothing and the like. The nonparametric method mainly comprises nonparametric regression, artificial neural networks, support vector machines and other prediction methods or multi-model combined prediction methods. The parameter method has the characteristics that the model is easy to realize and the calculated amount is small, but the defects of insufficient learning capability of the model, difficulty in processing the internal uncertainty of the model, influence on the prediction accuracy due to sudden change of traffic data and the like exist. The nonparametric method adopts methods such as data mining, artificial intelligence and the like to reveal the data change rule according to historical data so as to establish an input-output mapping relation; the method has the defects that the prediction precision depends on the quantity and quality of historical data seriously, and the selection of model parameters is difficult.
Influenced by uncertain factors such as urban road traffic environment, weather conditions, roads and pedestrians, and the like, and the actual urban traffic flow data has the characteristics of strong nonlinearity, time-varying property, susceptibility to random noise and the like. The existing traffic flow prediction modeling method has the defects of difficult determination of model parameters, low prediction precision, poor generalization capability and the like, and is difficult to meet the short-time traffic flow prediction requirement under complex conditions.
Disclosure of Invention
Based on the problems, the invention provides a short-term traffic flow prediction model based on a firework differential evolution hybrid algorithm-extreme learning machine, noise components contained in original traffic flow data are filtered by adopting an SSA method, and an ELM neural network model is trained by using the traffic flow data after noise reduction; performing phase space reconstruction, and determining key parameters of the ELM network model such as time delay, embedding window width and embedding dimension by using a C-C algorithm; the firework differential evolution (FWADE) hybrid optimization algorithm is provided by organically combining a firework algorithm (FWA) and a differential evolution algorithm (DE), so that the global convergence capability and the robustness of a basic algorithm are enhanced, and the overall optimization performance is improved; and (3) using the FWADE algorithm to optimize the weight threshold value of the ELM network, establishing a short-time traffic flow prediction model and evaluating the short-time traffic flow prediction model. The short-term traffic flow prediction model has high prediction precision and strong generalization capability, and the fitting degree of the predicted value and the actual value is good.
The adopted technical scheme is as follows: the short-term traffic flow prediction model based on the firework differential evolution hybrid algorithm-extreme learning machine comprises the following modeling steps:
s1: using the vehicle flow data of a certain road section collected by the UTC/SCOOT system as the time series data of the original traffic flow;
s2: noise reduction processing is carried out on the S1 data by adopting an SSA method, and the noise reduction processing is used as modeling data of a traffic flow prediction model;
s3: performing phase space reconstruction, and estimating the embedding window width tau by using C-C algorithmwCalculating an embedding dimension m and determining the structure of the ELM network model by time delay tau; the formula for the embedding dimension m is as follows:
τw＝(m-1)τ (1)
s4: generating a training sample and a test sample by using the traffic flow time sequence data after noise reduction and phase space reconstruction;
s5: taking the training sample in the S4 as a training sample of the ELM network; determining a connection weight between an input layer and a hidden layer of the ELM network and a threshold value of a neuron of the hidden layer by adopting a FWADE hybrid optimization algorithm; the FWADE hybrid optimization algorithm is a firework differential evolution hybrid optimization algorithm obtained by organically combining a firework algorithm (FWA) and a firework differential evolution algorithm (DE);
s6: saving the optimized ELM network connection weight and threshold in S5, and establishing an ELM network model for short-term traffic flow prediction;
s7: the test sample in S4 is untrained time-series data of the traffic flow, and is used as a test sample of the ELM network model to evaluate the prediction performance of the optimized ELM network model.
Furthermore, the SSA method is to filter noise components contained in the original traffic flow data, and is to collect the original traffic flow time series data Y containing the noise components on siteN＝[y1,y 2,…,yN]Converting into a track matrix X; for matrix XXTPerforming singular value decomposition to obtain L eigenvalues lambda1≥λ2≥…≥λLMore than or equal to 0 and corresponding feature vectors; analyzing and combining the signals represented by each characteristic value to reconstruct a new time sequence G-G0,g1,…,gN-1]。
The processing process comprises four steps of embedding, singular value decomposition, grouping and reconstruction;
s21: embedding, selecting window length L (1)<L<N, K ═ N-L +1), data Y is combinedNInto a trajectory matrix X, i.e.
S22: singular value decomposition, for matrix XXTPerforming singular value decomposition to obtain L eigenvalues lambda1≥λ2≥…≥λLNot less than 0 and corresponding orthogonal feature vector U1,…,ULLet d equal max { i, λiGreater than or equal to 0}, remember
The singular values of the matrix X are decomposed into
X＝X1+…+Xd (3)
wherein ,
being singular values of the matrix X, UiIs a left eigenvector, ViRespectively as right eigenvectors;
s23: grouping, based on the difference of the extracted components, XiDivided into m different groups I1,I2,…,ImAnd adding the matrices contained in each group, setting the IJThe subset of the set is IJ＝{i1,…,ip}, then
X is correspondingly decomposed into
S24: reconstructing each component group
Reconstructing the sequence G with the length of N; let matrix Y ═ Yij) (i-1, …, L, j-1, …, K), L is defined*＝min(L,K)，K*＝max(L,K)，y* ij＝yij(if L)<K) Or y* ij＝yji(if L ≧ K), the reconstructed sequence G ═ G0,…,gk,…,gN-1]The calculation can be obtained by the following formula:
in the reconstruction process, the first m components with larger singular values in the original traffic flow time sequence are reserved, and the components with smaller singular values caused by noise are discarded; and filtering the original traffic flow time sequence by SSA to obtain a reconstructed time sequence G after noise reduction, and using the reconstructed time sequence G to establish a short-time traffic flow prediction model.
Further, in the FWADE hybrid optimization algorithm, a standard DE algorithm is adopted for searching in an initial stage, and for each target vector, a test vector is generated through variation and cross operation; if the fitness of the test vector is superior to that of the target vector, the test vector is used as a next generation candidate solution; otherwise, the algorithm enters a FWA algorithm searching stage, and a new candidate solution is generated by utilizing a firework algorithm searching mechanism;
the FWADE algorithm is implemented as follows:
s51: initializing an algorithm, and determining the population size N according to a problem to be optimized1Maximum number of iterations N2Initial value X of individual Memberi(k) (ii) a Setting an explosion radius adjusting constant R, an explosion spark number adjusting constant M, an explosion spark number lower limit coefficient a, an explosion spark number upper limit coefficient b and a Gaussian variation spark number G initial value of a FWA algorithm, and setting a scaling factor F and a crossing rate CR parameter initial value of a DE algorithm; setting the iteration number k to be 1;
s52: calculating the fitness value f (X) of each individual member according to the mathematical model of the problem to be optimizedi(k))；
S53: the DE algorithm searches for a phase. The method comprises the following steps:
s531: performing mutation operation, randomly selecting two different individuals in the population, and performing mutation operation on each target vector X in the population according to the DE algorithm principlei(k) Performing mutation operation to generate a mutation vector Vi(k)；
S532: cross operation, for each pair of target vectors Xi(k) And corresponding variation vector Vi(k) Performing cross operation to form new test vector Ui(k)；
S533: and (6) selecting operation. Evaluating each test vector U according to the mathematical model of the problem to be optimizedi(k) With corresponding target vector Xi(k) The fitness value f. If U isi(k) If the fitness value is more optimal, the solution is taken as a candidate solution of the next iteration and the process goes to step S55; otherwise, step S54, i.e., FWA algorithm search phase, is entered.
S54: FWA algorithm search phase. Searching the population by referring to an optimization mechanism of a FWA algorithm, calculating the fitness value of the population, and preferentially generating a new candidate solution;
s55: the same procedure was performed for each individual in the population. The individual serial number i is i +1, if i is less than or equal to N1Go to step S53, NoGo to step S56;
s56: and updating the global optimal solution and the iteration times. According to the newly generated candidate solution, evaluating the fitness value of each individual and updating the global optimal solution, wherein the iteration number k is k + 1;
s57: algorithm termination condition (i.e. the optimal fitness value of the population meets the requirement or the number of iterations reaches the maximum number of iterations N2) And (6) judging. If the termination condition is met, turning to the step S58, otherwise, repeating the steps S53-S57;
s58: and outputting the global optimal solution of the FWADE algorithm.
Further, the training sample in S4 is used as a training sample of the ELM network, and the parameter setting condition of the modeling process is as follows: the ELM network structure is 9-11-1, and the activation function is a Sigmoid function; the fitness function of the ELM weight threshold optimization algorithm is the Root Mean Square Error (RMSE) calculated from the training samples; the population scale of the FWADE algorithm is 40, the dimension of the population member is 110, and the maximum iteration time is set to be 5000 times; the explosion radius regulating constant R of the FWA algorithm is 210, the explosion spark number regulating constant M is 220, the lower limit coefficient a of the explosion spark number is 0.04, the upper limit coefficient b of the explosion spark number is 0.8, and the Gaussian variation spark number G is 60; the hybridization parameter CR of the DE algorithm is 0.6 and the scaling factor F is 0.5.
The invention adopts a Singular Spectral Analysis (SSA) method to filter noise components contained in original traffic flow data, and trains an Extreme Learning Machine (ELM) neural network model by using the traffic flow data after noise reduction; performing phase space reconstruction, and determining key parameters of the ELM network model such as time delay, embedding window width and embedding dimension by using a C-C algorithm; the firework differential evolution (FWADE) hybrid optimization algorithm is provided by organically combining a firework algorithm (FWA) and a differential evolution algorithm (DE), so that the global convergence capability and the robustness of a basic algorithm are enhanced, and the overall optimization performance is improved; and (3) using the FWADE algorithm to optimize the weight threshold value of the ELM network, establishing a short-time traffic flow prediction model and evaluating the short-time traffic flow prediction model. The short-term traffic flow prediction model has high prediction precision and strong generalization capability, and the fitting degree of the predicted value and the actual value is good.
Drawings
FIG. 1 is a block diagram of the modeling flow of the present invention;
FIG. 2 is a training result of the FWADE-ELM traffic flow prediction model of the present invention;
FIG. 3 is a generalized result of the FWADE-ELM traffic flow prediction model of the present invention.
Detailed Description
The present invention will be described in further detail below by way of examples with reference to the accompanying drawings, which are illustrative of the present invention and the present invention is not limited to the following examples.
Referring to fig. 1 to 3, the short-term traffic flow prediction method based on the firework differential evolution hybrid algorithm-extreme learning machine is used for establishing a short-term traffic flow prediction model, performing experimental verification and comparing with three basic traffic flow prediction models, namely an ELM model, a DE-ELM model and a FWA-ELM model.
The experimental data is from traffic flow data of a section of express way with the length of about 12km acquired by a UTC/SCOOT system of a certain city traffic administration in China, and 3 basic traffic parameters such as flow, vehicle speed, time occupancy rate and the like are acquired through 95 main lines and 72 ramp ground induction coil detectors arranged on the road; the data acquisition time is 5 mondays in succession in 7 months of 2013, namely 7 months 1 day, 7 months 8 days, 7 months 15 days, 7 months 22 days and 7 months 29 days, the data acquisition time interval is 5 minutes, and 288 groups of traffic flow data can be obtained every day.
And performing noise reduction on the original traffic flow time sequence data by adopting an SSA method, setting L as 288, and corresponding to the daily change of the traffic flow time sequence. Singular spectrum analysis shows that the cumulative contribution rate of the reconstruction sequence corresponding to the first 37 singular values reaches 98.78%; the cumulative contribution rate of the reconstructed sequence corresponding to the last 251 singular values is only 1.22%, which can be regarded as a noise component.
Performing phase space reconstruction, and calculating the width tau of the embedding window by using C-C algorithmw123 and 15 for the time delay τ, the embedding dimension m is 9 according to equation (1).
And (3) taking the traffic flow time sequence (namely traffic flow data of four days including 7 months 1 day, 7 months 8 days, 7 months 15 days and 7 months 22 days) after the noise reduction and the phase space reconstruction as a training sample of the ELM network, and taking the original traffic flow data of 7 months 29 days as a test sample of the ELM network. Determining that the topological structure of the ELM network is 9-11-1 during traffic flow prediction modeling, namely the number of nodes of an input layer is 9, and corresponding to the embedding dimension 9 of the traffic flow time sequence after phase space reconstruction; the number of nodes of the hidden layer of the model is set to be 11 finally after being balanced by a plurality of tests in the simulation process; the number of nodes in the output layer is 1, and the total number of weight threshold values to be optimized and adjusted in the learning process is 11 × (9+1) to 110 corresponding to the output value of the ELM network, namely the predicted value of the traffic flow.
And respectively optimizing weight threshold values of the ELM network by adopting a basic DE algorithm, a basic FWA algorithm and the FWADE algorithm, constructing three traffic flow prediction models of DE-ELM, FWA-ELM and FWADE-ELM, and comparing the traffic flow prediction models with the basic ELM traffic flow prediction model. In the modeling process, the ELM network structures adopted by the four methods are all 9-11-1, and the activation function is a Sigmoid function; the fitness function of the ELM weight threshold optimization algorithm is the Root Mean Square Error (RMSE) calculated from the training samples; DE. The population sizes of the FWA and FWADE algorithms are both 40, the population member dimension (i.e., the number of ELM weight thresholds to be optimized) is 110, and the maximum iteration number is set to 5000. The rest parameter setting conditions are as follows: in the FWA and FWADE algorithms, an explosion radius regulating constant R is 210, an explosion spark number regulating constant M is 220, an explosion spark number lower limit coefficient a is 0.04, an explosion spark number upper limit coefficient b is 0.8, and a gaussian variation spark number G is 60; in the DE algorithm, the hybridization parameter CR is 0.6 and the scaling factor F is 0.5.
And after training, storing the optimal weight threshold value for predicting the traffic flow by the ELM network model. The influence of the number of hidden layer nodes of the traffic flow prediction model on the model prediction result is tested in the implementation process. Tables 1 to 3 show the comparison of the traffic flow prediction results of the four models when the number of hidden layer nodes is different (9, 11 and 13) and the other parameters are the same. Where RMSE represents the root mean square error and MAPE represents the mean absolute percentage error.
The test results of tables 1 to 3 show that: (1) the more the number of nodes of the hidden layer is, the more complex the structure of the prediction model is and the smaller the error is; (2) when the number of hidden layer nodes is less than 11, the training error and the generalization error of the prediction model have large changes. When the number of nodes of the hidden layer is more than 11, the training error and the generalization error of the prediction model are not obviously improved; (3) in contrast, the number of hidden layer nodes has a greater impact on the basic ELM model, while the impact on the FWADE-ELM model is relatively small. The number of hidden layer nodes is finally set to be 11 after being weighed by a plurality of tests.
Fig. 2 and 3 show the training and generalization results (hidden layer node number 11) of the FWADE-ELM traffic flow prediction model.
The test results of tables 1 to 3 and fig. 2 to 3 show that: (1) the short-time traffic flow prediction effects of the DE-ELM model, the FWA-ELM model and the FWADE-ELM model are all superior to those of the basic ELM model, and the optimization algorithm is used for optimizing the weight threshold of the ELM, so that the nonlinear fitting performance of the basic ELM can be improved; (2) compared with three basic traffic flow prediction models of ELM, DE-ELM and FWA-ELM, the FWADE-ELM traffic flow prediction model has lower training error and generalization error and stronger generalization capability, and shows the effectiveness of optimizing the ELM model by adopting a FWADE algorithm; (3) as can be seen from fig. 2 and 3, the training process of the FWADE-ELM model meets the requirements, the degree of fitting between the model prediction value shown by the dotted line and the actual traffic flow value shown by the solid line is better, which indicates that the FWADE-ELM short-term traffic flow prediction model of the invention has higher prediction accuracy and stronger generalization capability.
TABLE 1 comparison of traffic flow prediction results for four models (hidden layer node number 9)
TABLE 2 four model traffic flow prediction result comparison (hidden layer node number 11)
TABLE 3 comparison of traffic flow prediction results for four models (hidden layer node number 13)
Claims (5)
1. The short-term traffic flow prediction model based on the firework differential evolution hybrid algorithm-extreme learning machine is characterized in that: the modeling steps are as follows:
s1: using the vehicle flow data of a certain road section collected by the UTC/SCOOT system as the time series data of the original traffic flow;
s2: noise reduction processing is carried out on the data obtained in the S1 by adopting a Singular Spectrum Analysis (SSA) method, and the noise reduction processing is used as modeling data of a traffic flow prediction model;
s3: performing phase space reconstruction, and estimating the embedding window width tau by using C-C algorithmwCalculating an embedding dimension m and determining the structure of an Extreme Learning Machine (ELM) network model by using the time delay tau; the formula for the embedding dimension m is as follows:
τw＝(m-1)τ (1)
s4: generating a training sample and a test sample by using the traffic flow time sequence data after noise reduction and phase space reconstruction;
s5: taking the training sample in the S4 as a training sample of the ELM network; determining a connection weight between an input layer and a hidden layer of the ELM network and a threshold value of a neuron of the hidden layer by adopting a firework differential evolution (FWADE) mixed optimization algorithm; the FWADE hybrid optimization algorithm is a firework differential evolution hybrid optimization algorithm obtained by organically combining a firework algorithm (FWA) and a firework differential evolution algorithm (DE);
s6: saving the optimized ELM network connection weight and threshold in S5, and establishing an ELM network model for short-term traffic flow prediction;
s7: the test sample in S4 is untrained time-series data of the traffic flow, and is used as a test sample of the ELM network model to evaluate the prediction performance of the optimized ELM network model.
2. The short-term traffic flow prediction model based on firework difference evolution hybrid algorithm-limit learning machine as claimed in claim 1, wherein the SSA method is adopted to filter noise components contained in original traffic flow data, and original traffic flow time series data Y containing the noise components are collected on siteN＝[y1，y2，...，yN]Converting into a track matrix X;for matrix XXTPerforming singular value decomposition to obtain L eigenvalues lambda1≥λ2≥...≥λLMore than or equal to 0 and corresponding feature vectors; analyzing and combining the signals represented by each characteristic value to reconstruct a new time sequence G-G0，g1，...，gN-1]。
3. The short-term traffic flow prediction model based on the firework difference evolution hybrid algorithm-extreme learning machine as claimed in claim 1 or 2, wherein the SSA method is adopted to perform noise reduction processing on data, and the processing process comprises four steps of embedding, singular value decomposition, grouping and reconstruction;
s21: embedding, selecting window length L (L is more than 1 and less than N, K is N-L +1), and embedding data YNInto a trajectory matrix X, i.e.
S22: singular value decomposition, for matrix XXTPerforming singular value decomposition to obtain L eigenvalues lambda1≥λ2≥...≥λLNot less than 0 and corresponding orthogonal feature vector U1，...，ULLet d equal max { i, λiGreater than or equal to 0}, remember
The singular values of the matrix X are decomposed into
X＝X1+...+Xd (3)
wherein ,
being singular values of the matrix X, UiIs a left eigenvector, ViRespectively as right eigenvectors;
s23: grouping, according to the difference of the extracted components,mixing XiDivided into m different groups I1，I2，...，ImAnd adding the matrices contained in each group, setting the IJThe subset of the set is IJ＝{i1，...，ip}, then
X is correspondingly decomposed into
S24: reconstructing each component group
Reconstructing the sequence G with the length of N; let matrix Y ═ Yij) (i 1., L, j 1., K), defines L*＝min(L，K)，K*＝max(L，K)，y* ij＝yij(if L < K) or y* ij＝yji(if L ≧ K), the reconstructed sequence G ═ G0，…，gk，…，gN-1]The calculation can be obtained by the following formula:
in the reconstruction process, the first m components with larger singular values in the original traffic flow time sequence are reserved, and the components with smaller singular values caused by noise are discarded; and filtering the original traffic flow time sequence by SSA to obtain a reconstructed time sequence G after noise reduction, and using the reconstructed time sequence G to establish a short-time traffic flow prediction model.
4. The short-term traffic flow prediction model based on the firework differential evolution hybrid algorithm-limit learning machine as claimed in claim 1, wherein the FWADE hybrid optimization algorithm is initially searched by a standard DE algorithm, and for each target vector, a test vector is generated through mutation and intersection operation; if the fitness of the test vector is superior to that of the target vector, the test vector is used as a next generation candidate solution; otherwise, the algorithm enters a FWA algorithm searching stage, and a new candidate solution is generated by utilizing a firework algorithm searching mechanism;
the FWADE algorithm is implemented as follows:
s51: initializing an algorithm, and determining the population size N according to a problem to be optimized1Maximum number of iterations N2Initial value X of individual Memberi(k) (ii) a Setting an explosion radius adjusting constant R, an explosion spark number adjusting constant M, an explosion spark number lower limit coefficient a, an explosion spark number upper limit coefficient b and a Gaussian variation spark number G initial value of a FWA algorithm, and setting a scaling factor F and a crossing rate CR parameter initial value of a DE algorithm; setting the iteration number k to be 1;
s52: calculating the fitness value f (X) of each individual member according to the mathematical model of the problem to be optimizedi(k))；
S53: the DE algorithm searches for a phase. The method comprises the following steps:
s531: performing mutation operation, randomly selecting two different individuals in the population, and performing mutation operation on each target vector X in the population according to the DE algorithm principlei(k) Performing mutation operation to generate a mutation vector Vi(k)；
S532: cross operation, for each pair of target vectors Xi(k) And corresponding variation vector Vi(k) Performing cross operation to form new test vector Ui(k)；
S533: selecting operation, and evaluating each test vector U according to the mathematical model of the problem to be optimizedi(k) With corresponding target vector Xi(k) The fitness value f; if U isi(k) If the fitness value is more optimal, the solution is taken as a candidate solution of the next iteration and the process goes to step S55; otherwise, entering step S54, namely, FWA algorithm searching phase;
s54: in the FWA algorithm searching stage, searching the population by referring to an optimization mechanism of the FWA algorithm, calculating the fitness value of the population, and preferentially generating a new candidate solution;
s55: to the populationThe same operation is carried out on each individual, and the individual serial number i is i +1, if i is less than or equal to N1Go to step S53, otherwise go to step S56;
s56: updating the global optimal solution and the iteration times, evaluating the fitness value of each individual and updating the global optimal solution according to the newly generated candidate solution, wherein the updating iteration times k are k + 1;
s57: algorithm termination condition (i.e. the optimal fitness value of the population meets the requirement or the number of iterations reaches the maximum number of iterations N2) And (6) judging. If the termination condition is met, turning to the step S58, otherwise, repeating the steps S53-S57;
s58: and outputting the global optimal solution of the FWADE algorithm.
5. The short-time traffic flow prediction modeling method based on firework differential evolution hybrid algorithm-extreme learning machine as claimed in claim 1, wherein the training sample in S4 is used as the training sample of ELM network, and the parameter setting condition of the modeling process is as follows: the ELM network structure is 9-11-1, and the activation function is a Sigmoid function; the fitness function of the ELM weight threshold optimization algorithm is the Root Mean Square Error (RMSE) calculated from the training samples; the population scale of the FWADE algorithm is 40, the dimension of the population member is 110, and the maximum iteration time is set to be 5000 times; the explosion radius regulating constant R of the FWA algorithm is 210, the explosion spark number regulating constant M is 220, the lower limit coefficient a of the explosion spark number is 0.04, the upper limit coefficient b of the explosion spark number is 0.8, and the Gaussian variation spark number G is 60; the hybridization parameter CR of the DE algorithm is 0.6 and the scaling factor F is 0.5.
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