CN112115754B - Short-time traffic flow prediction model based on firework differential evolution hybrid algorithm-extreme learning machine - Google Patents
Short-time 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; carrying out phase space reconstruction, and determining key parameters of ELM network models such as time delay, embedded window width, embedded dimension and the like by using a C-C algorithm; the firework algorithm (FWA) and the differential evolution algorithm (DE) are organically combined to obtain a firework differential evolution (FWADE) hybrid optimization algorithm, so that the global convergence capacity and the robust performance of the basic algorithm are enhanced, and the overall optimization performance is improved; and using the FWADE algorithm to optimize the weight threshold of the ELM network, establishing a short-time traffic flow prediction model and evaluating. The short-time traffic flow prediction model has higher prediction precision and stronger 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-time traffic flow prediction model, in particular to a short-time traffic flow prediction model based on a firework differential 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 is a precondition for realizing real-time traffic control and guidance. The real-time accurate prediction of the short-time traffic flow plays an important role in road network traffic state analysis, traffic network planning and traffic optimization control; on the other hand, the continuous development of traffic data acquisition technology provides a technical means for acquiring road network traffic flow information in real time, and provides data guarantee for the research of short-time traffic flow prediction methods. 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 parameter method and a non-parameter method. The parameter method mainly comprises prediction methods such as historical average, linear and nonlinear parameter regression, kalman filtering, automatic regression, exponential smoothing and the like. The nonparametric method mainly comprises a nonparametric regression, an artificial neural network, a support vector machine and other prediction methods or a multi-model combined prediction method. The parameter method is characterized in that the model is easy to realize and has small calculated amount, but has the defects of insufficient model learning capability, difficulty in processing inherent uncertainty of the model, influence on prediction accuracy caused by abrupt change of traffic data and the like. The non-parameter method is to adopt methods such as data mining, artificial intelligence and the like to reveal a data change rule according to historical data so as to establish an input-output mapping relation; the method has the defects that the prediction accuracy is seriously dependent on the quantity and quality of historical data, and model parameters are difficult to select.
The actual urban traffic flow data has the characteristics of strong nonlinearity, time variability, susceptibility to random noise and the like, and is influenced by uncertain factors such as urban road traffic environment, weather conditions, road pedestrians and the like. The existing traffic flow prediction modeling method has the defects of difficult determination of model parameters, lower 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-time traffic flow prediction model based on a firework differential evolution hybrid algorithm-extreme learning machine, which adopts an SSA method to filter noise components contained in original traffic flow data, and trains an ELM neural network model by using the traffic flow data after noise reduction; carrying out phase space reconstruction, and determining key parameters of ELM network models such as time delay, embedded window width, embedded dimension and the like by using a C-C algorithm; the firework differential evolution (FWA) hybrid optimization algorithm is provided by organically combining a firework algorithm (FWA) and a differential evolution algorithm (DE) so as to enhance the global convergence capacity and the robust performance of the basic algorithm and improve the overall optimization performance; and using the FWADE algorithm to optimize the weight threshold of the ELM network, establishing a short-time traffic flow prediction model and evaluating. The short-time traffic flow prediction model has higher prediction precision and stronger generalization capability, and the fitting degree of the predicted value and the actual value is good.
The adopted technical scheme is as follows: the modeling method comprises the following steps of:
s1: taking the traffic flow data of a certain road section collected by the UTC/SCOOT system as original traffic flow time sequence data;
s2: adopting an SSA method to perform noise reduction treatment on the S1 data, and using the S1 data as modeling data of a traffic flow prediction model;
s3: reconstructing phase space, and estimating the width tau of an embedded window by adopting a C-C algorithm w Calculating an embedding dimension m and determining the structure of an ELM network model; the computational formula for embedding dimension m is as follows:
τ w ＝(m-)τ (1)
s4: generating training samples and test samples by using the traffic flow time sequence data after noise reduction and phase space reconstruction;
s5: taking the training sample in the S4 as the training sample of the ELM network; determining a connection weight between an ELM network input layer and an hidden layer and a threshold value of a hidden layer neuron 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 differential evolution algorithm (DE);
s6: saving the optimized ELM network connection weight and threshold value in the S5, and establishing an ELM network model for short-time traffic flow prediction;
s7: and S4, the test sample is untrained traffic flow time sequence data, is used as a test sample of the ELM network model, and evaluates the prediction performance of the optimized ELM network model.
Further, the SSA method is to filter noise components contained in the original traffic flow data, and collect the original traffic flow time sequence data Y containing the noise components on site N ＝[y 1 ,y 2 ,…,y N ]Converting into a track matrix X; for matrix XX T Singular value decomposition is carried out to obtain L characteristic values lambda 1 ≥λ 2 ≥…≥λ L Not less than 0 and corresponding feature vector; representative of each characteristic valueThe signals are analyzed and combined to reconstruct a new time sequence G= [ G ] 0 ,g 1 ,…,g N-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 N Conversion to trace matrix X, i.e
S22: singular value decomposition of matrix XX T Singular value decomposition is carried out to obtain L characteristic values lambda 1 ≥λ 2 ≥…≥λ L Not less than 0 and corresponding orthogonal feature vector U 1 ,…,U L Let d=max { i, λ i Not less than 0}, record
Singular value decomposition of matrix X into
X＝X 1 +…+X d (3)
wherein ,
is the singular value of matrix X, U i As the left eigenvector, V i Right feature vectors respectively;
s23: grouping, X is defined according to the extracted components i Divided into m different groups I 1 ,I 2 ,…,I m And adding the matrices contained in each group to form the I < th + > matrix J The subset comprised by the group is I J ＝{i 1 ,…,i p Then (V) is
X is correspondingly decomposed into
S24: reconstructing each component group
Reconstructing the sequence into a sequence G with the length of N; let matrix y= (Y) ij ) (i=1, …, L, j=1, …, K), defined as L * ＝min(L,K)，K * ＝max(L,K)，y * ij ＝y ij (if L<K) Or y * ij ＝y ji (if L is greater than or equal to K), reconstructing sequence G= [ G ] 0 ,…,g k ,…,g N-1 ]The method can be calculated by the following formula: />
The reconstruction process retains the first m larger singular value components in the original traffic flow time sequence, and discards those smaller singular value components caused by noise; the original traffic flow time sequence is filtered by SSA to obtain a reconstructed time sequence G after noise reduction, and the reconstructed time sequence G is used for building a short-time traffic flow prediction model.
Further, the FWADE hybrid optimization algorithm is adopted in the initial stage, a standard DE algorithm is adopted for searching, and for each target vector, a test vector is generated through mutation and crossover operation; if the adaptability of the test vector is better than 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 firework algorithm searching mechanism is utilized to generate new candidate solutions;
the FWADE algorithm comprises the following implementation steps:
s51: initializing an algorithm, and determining a population scale N according to a problem to be optimized 1 Maximum number of iterations N 2 Initial value X of individual member i (k) The method comprises the steps of carrying out a first treatment on the surface of the 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 high of an FWA algorithmThe initial value of the S-variation spark number G, the initial value of the scaling factor F and the crossover rate CR parameter of the DE algorithm; setting the iteration number k=1;
s52: according to the mathematical model of the problem to be optimized, calculating the fitness value f (X) i (k))；
S53: the DE algorithm searches for phase. The method comprises the following steps:
s531: performing mutation operation, namely randomly selecting two different individuals in the population, and referring to the principle of the DE algorithm for each target vector X in the population i (k) Performing mutation operation to generate a mutation vector V i (k)；
S532: cross operation, for each pair of target vectors X i (k) And corresponding variation vector V i (k) Performing cross operation to form a new test vector U i (k)；
S533: and selecting operation. Evaluating each test vector U according to a mathematical model of the problem to be optimized i (k) And corresponding target vector X i (k) Is used for the adaptation value f. If U is i (k) The fitness value of (2) is better, the solution is used as a candidate solution of the next iteration and the step S55 is carried out; otherwise, step S54 is entered, i.e. the FWA algorithm search phase.
S54: the FWA algorithm searches for phase. Searching the population by referring to an optimization mechanism of the FWA algorithm, calculating an adaptability value of the population, and preferentially generating a new candidate solution;
s55: the same is done for each individual in the population. Individual sequence number i=i+1, if i.ltoreq.N 1 Go to step S53, otherwise go to step S56;
s56: and updating the globally optimal solution and the iteration times. Evaluating the fitness value of each individual according to the newly generated candidate solution, updating the global optimal solution, and updating the iteration times k=k+1;
s57: algorithm termination conditions (i.e. optimal fitness value of population meets requirement or number of iterations reaches maximum number of iterations N 2 ) And (5) judging. If the termination condition is met, the step S58 is switched to, otherwise, the steps S53 to S57 are repeated;
s58: and outputting a global optimal solution of the FWADE algorithm.
Further, the training sample in S4 is used as a training sample of the ELM network, and parameters of the modeling process are set: 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 group members is 110, and the maximum iteration number is 5000; the explosion radius adjustment constant r=210, the explosion spark number adjustment constant m=220, the explosion spark number lower limit coefficient a=0.04, the explosion spark number upper limit coefficient b=0.8, and the gaussian variation spark number g=60 of the FWA algorithm; the hybridization parameter cr=0.6 of the DE algorithm and the scaling factor f=0.5.
The invention 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; carrying out phase space reconstruction, and determining key parameters of ELM network models such as time delay, embedded window width, embedded dimension and the like by using a C-C algorithm; the firework differential evolution (FWA) hybrid optimization algorithm is provided by organically combining a firework algorithm (FWA) and a differential evolution algorithm (DE) so as to enhance the global convergence capacity and the robust performance of the basic algorithm and improve the overall optimization performance; and using the FWADE algorithm to optimize the weight threshold of the ELM network, establishing a short-time traffic flow prediction model and evaluating. The short-time traffic flow prediction model has higher prediction precision and stronger generalization capability, and the fitting degree of the predicted value and the actual value is good.
Drawings
FIG. 1 is a block diagram of a 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 by way of examples with reference to the accompanying drawings, which are illustrative of the present invention and not limited to the following examples.
Referring to fig. 1 to 3, the short-time traffic flow prediction method based on the firework differential evolution hybrid algorithm-extreme learning machine is used for establishing a short-time traffic flow prediction model, performing experimental verification, and simultaneously comparing with three traffic flow prediction models of basic ELM, DE-ELM and FWA-ELM.
The experimental data is derived from the traffic flow data of a section of expressway with the length of about 12km in the city acquired by a UTC/SCOOT system of a certain city in China, and 3 basic traffic parameters such as flow, speed, time occupancy rate and the like are acquired through 95 main lines and 72 ramp ground induction coil detectors distributed on the road; the data acquisition time is 5 continuous monday of 7 months in 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 carrying out noise reduction processing on the original traffic flow time sequence data by adopting an SSA method, and setting L as 288 to correspond to the daily variation of the traffic flow time sequence. The singular spectrum analysis shows that the cumulative contribution rate of the reconstructed sequences 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%, and can be regarded as a noise component.
Reconstructing phase space, and calculating the width tau of the embedded window by adopting a C-C algorithm w Time delay τ=15, and the embedding dimension m=9 is obtained according to equation (1).
And taking the time sequence of the traffic flow (namely traffic flow data of four days of 7 months 1 day, 7 months 8 days, 7 months 15 days and 7 months 22 days) after noise reduction and 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 in 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 node number of the hidden layer of the model is finally set to be 11 after being weighted by a plurality of tests in the simulation process; the number of output layer nodes is 1, and the total weight threshold value required to be optimally adjusted in the learning process is 11× (9+1) =110 corresponding to the output value of the ELM network, namely the predicted value of traffic flow.
The weight threshold of the ELM network is optimized by adopting a basic DE algorithm, a basic FWA algorithm and the FWADE algorithm of the invention respectively, three traffic flow prediction models of DE-ELM, FWA-ELM and FWADE-ELM are constructed, and the traffic flow prediction models are compared with the basic ELM traffic flow prediction model. In the modeling process, the ELM network structure adopted by the four methods 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; DE. The population sizes of the FWA and FWADE algorithms are 40, the number of the group member dimensions (i.e. the number of ELM weight thresholds to be optimized) is 110, and the maximum iteration number is 5000. The other parameter setting conditions are as follows: explosion radius adjustment constant r=210, explosion spark number adjustment constant m=220, explosion spark number lower limit coefficient a=0.04, explosion spark number upper limit coefficient b=0.8, gaussian variation spark number g=60 in FWA and FWADE algorithm; hybridization parameter cr=0.6, scaling factor f=0.5 in DE algorithm.
The training ends and stores the optimal weight threshold for the ELM network model to predict traffic flow. In the implementation process, the influence of the number of hidden layer nodes of the traffic flow prediction model on the model prediction result is tested. Tables 1 to 3 are comparison of the prediction results of the four model traffic flows in the case that the hidden layer nodes are different in number (9, 11 and 13) and the remaining parameters are the same, respectively. Where RMSE represents root mean square error and MAPE represents mean absolute percentage error.
The test results in tables 1 to 3 show that: (1) The more nodes of the hidden layer are, 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 hidden layer nodes is more than 11, the training error and the generalization error of the prediction model are not obviously improved; (3) In contrast, the underlying layer node number has a greater impact on the underlying ELM model and a relatively smaller impact on the FWADE-ELM model. The number of hidden layer nodes is finally set to 11 after a plurality of experimental tradeoffs.
Fig. 2 and 3 are training and generalizing 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, which shows that the nonlinear fitting performance of the basic ELM can be improved by optimizing the weight threshold of the ELM by using an optimization algorithm; (2) Compared with three traffic flow prediction models of basic ELM, DE-ELM and FWA-ELM, the training error and the generalization error of the FWADE-ELM traffic flow prediction model are lower, the generalization capability is stronger, and the effectiveness of optimizing the ELM model by adopting the FWADE algorithm is demonstrated; (3) From fig. 2 and fig. 3, it can be seen that the training process of the FWADE-ELM model meets the requirements, and the model predicted value shown by the dotted line has a better fitting degree with the traffic flow actual value shown by the solid line, which indicates that the invented FWADE-ELM short-time traffic flow predicted model has higher prediction precision and stronger generalization capability.
Table 1 comparison of traffic flow prediction results for four models (hidden layer node number 9)
Table 2 comparison of traffic flow predictions for four models (hidden layer node count 11)
Table 3 comparison of traffic flow predictions for four models (hidden layer node count 13)
Claims (5)
1. The short-time 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: taking the traffic flow data of a certain road section collected by the UTC/SCOOT system as original traffic flow time sequence data;
s2: carrying out noise reduction treatment on the data obtained in the step S1 by adopting a singular spectrum analysis SSA method, and taking the data as modeling data of a traffic flow prediction model;
s3: reconstructing phase space, and estimating the width tau of an embedded window by adopting a C-C algorithm w Calculating an embedding dimension m and determining the structure of an ELM network model of the extreme learning machine; embedding typeThe computational formula for dimension m is as follows:
τ w ＝(m-1)τ (1)
s4: generating training samples and test samples by using the traffic flow time sequence data after noise reduction and phase space reconstruction;
s5: taking the training sample in the S4 as the training sample of the ELM network; determining a connection weight between an ELM network input layer and an hidden layer and a threshold value of a hidden layer neuron by adopting a firework differential evolution 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 differential evolution algorithm DE;
s6: saving the optimized ELM network connection weight and threshold value in the S5, and establishing an ELM network model for short-time traffic flow prediction;
s7: and S4, the test sample is untrained traffic flow time series data, is used as the test sample of the ELM network model, and evaluates the prediction performance of the optimized ELM network model.
2. The model for predicting short-term traffic flow based on Firework differential evolution hybrid algorithm-extreme learning machine as claimed in claim 1, wherein the SSA method is used for filtering noise components contained in the original traffic flow data, and collecting the original traffic flow time series data Y containing the noise components on site N ＝[y 1 ,y 2 ,…,y N ]Converting into a track matrix X; for matrix XX T Singular value decomposition is carried out to obtain L characteristic values lambda 1 ≥λ 2 ≥…≥λ L Not less than 0 and corresponding feature vector; analyzing and combining signals represented by each characteristic value to reconstruct a new time sequence G= [ G ] 0 ,g 1 ,…,g N-1 ]。
3. The model for predicting short-time traffic flow based on the firework differential evolution hybrid algorithm-extreme learning machine according to claim 1 or 2, wherein the data is subjected to noise reduction treatment by adopting an SSA method, and the treatment 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 N Conversion to trace matrix X, i.e
S22: singular value decomposition of matrix XX T Singular value decomposition is carried out to obtain L characteristic values lambda 1 ≥λ 2 ≥…≥λ L Not less than 0 and corresponding orthogonal feature vector U 1 ,…,U L Let d=max { i, λ i Not less than 0}, record
Singular value decomposition of matrix X into
X＝X 1 +…+X d (3)
wherein ,
is the singular value of matrix X, U i As the left eigenvector, V i Right feature vectors respectively;
s23: grouping, X is defined according to the extracted components i Divided into m different groups I 1 ,I 2 ,…,I m And adding the matrices contained in each group to form the I < th + > matrix J The subset comprised by the group is I J ＝{i 1 ,…,i p Then (V) is
X is correspondingly decomposed into
S24: reconstructing each component group
Reconstructing the sequence into a sequence G with the length of N; let matrix y= (Y) ij ) (i=1, …, L, j=1, …, K), defined as L * ＝min(L,K)，K * ＝max(L,K)，y * ij ＝y ij (if L<K) Or y * ij ＝y ji (if L is greater than or equal to K), reconstructing sequence G= [ G ] 0 ,…,g k ,…,g N-1 ]The method can be calculated by the following formula:
the reconstruction process retains the first m larger singular value components in the original traffic flow time sequence, and discards those smaller singular value components caused by noise; the original traffic flow time sequence is filtered by SSA to obtain a reconstructed time sequence G after noise reduction, and the reconstructed time sequence G is used for building a short-time traffic flow prediction model.
4. The model for predicting short-time traffic flow based on the firework differential evolution hybrid algorithm-extreme learning machine according to claim 1, wherein the FWADE hybrid optimization algorithm is characterized in that a standard DE algorithm is adopted for searching in the initial stage, and for each target vector, a test vector is generated through mutation and crossover operation; if the adaptability of the test vector is better than 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 firework algorithm searching mechanism is utilized to generate new candidate solutions;
the FWADE algorithm comprises the following implementation steps:
s51: initializing an algorithm, and determining a population scale N according to a problem to be optimized 1 Maximum number of iterations N 2 Initial value X of individual member i (k) The method comprises the steps of carrying out a first treatment on the surface of the Setting FWA algorithm explosionRadius adjusting constant R, explosion spark number adjusting constant M, explosion spark number lower limit coefficient a, explosion spark number upper limit coefficient b and Gaussian variation spark number G initial value, the scaling factor F of DE algorithm and crossover ratio CR parameter initial value; setting the iteration number k=1;
s52: according to the mathematical model of the problem to be optimized, calculating the fitness value f (X) i (k))；
S53: a DE algorithm searching stage; the method comprises the following steps:
s531: performing mutation operation, namely randomly selecting two different individuals in the population, and referring to the principle of the DE algorithm for each target vector X in the population i (k) Performing mutation operation to generate a mutation vector V i (k)；
S532: cross operation, for each pair of target vectors X i (k) And corresponding variation vector V i (k) Performing cross operation to form a new test vector U i (k)；
S533: selecting operation, and evaluating each test vector U according to a mathematical model of the problem to be optimized i (k) And corresponding target vector X i (k) The fitness value f of (a); if U is i (k) The fitness value of (2) is better, the solution is used as a candidate solution of the next iteration and the step S55 is carried out; otherwise, enter step S54, namely FWA algorithm searches the stage;
s54: in the FWA algorithm searching stage, searching is carried out on the population by referring to an optimization mechanism of the FWA algorithm, the fitness value of the population is calculated, and a new candidate solution is preferentially generated;
s55: the same operation is carried out on each individual in the population, the individual serial number i=i+1, if i is less than or equal to N 1 Go 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 according to the newly generated candidate solution, updating the global optimal solution, and updating the iteration times k=k+1;
s57: the algorithm termination condition is that the optimal fitness value of the group meets the requirement or the iteration number reaches the maximum iteration number N 2 Judging; if the termination condition is met, the step S58 is switched to, otherwise, the steps S53 to S57 are repeated;
s58: and outputting a global optimal solution of the FWADE algorithm.
5. The model for predicting short-time traffic flow based on the firework differential evolution hybrid algorithm-extreme learning machine according to claim 1, wherein the training sample in S4 is used as a training sample of an ELM network, and parameters of the modeling process are set 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 group members is 110, and the maximum iteration number is 5000; the explosion radius adjustment constant r=210, the explosion spark number adjustment constant m=220, the explosion spark number lower limit coefficient a=0.04, the explosion spark number upper limit coefficient b=0.8, and the gaussian variation spark number g=60 of the FWA algorithm; the hybridization parameter cr=0.6 of the DE algorithm and the scaling factor f=0.5.
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