CN106920007B - PM based on second-order self-organizing fuzzy neural network2.5Intelligent prediction method - Google Patents

PM based on second-order self-organizing fuzzy neural network2.5Intelligent prediction method Download PDF

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CN106920007B
CN106920007B CN201710107408.2A CN201710107408A CN106920007B CN 106920007 B CN106920007 B CN 106920007B CN 201710107408 A CN201710107408 A CN 201710107408A CN 106920007 B CN106920007 B CN 106920007B
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乔俊飞
蔡杰
韩红桂
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Abstract

PM based on second-order self-organizing fuzzy neural network2.5The intelligent prediction method belongs to the field of environmental engineering and the technical field of detection. PM (particulate matter)2.5The prediction difficulty is large, and the neural network has better processing capability for highly nonlinear and seriously uncertain systems. The present invention is directed to PM2.5The problem difficult to predict is solved by adopting an air pollutant intelligent prediction method based on a second-order self-organizing fuzzy neural network, and the PM is extracted by utilizing a principal component analysis method2.5Then establishing characteristic variables and PM by using a second-order self-organizing fuzzy neural network2.5Soft measurement model in between, for PM after 24 hours2.5The concentration is predicted. The method obtains better prediction effect, provides timely and accurate atmospheric environment quality information for environmental management departments and the public, is favorable for preventing and treating air pollution in time, and improves the quality of life of the public.

Description

PM based on second-order self-organizing fuzzy neural network2.5Intelligent prediction method
Technical Field
The present invention relates to PM2.5The intelligent prediction method is an important branch in the technical field of advanced manufacturing, and belongs to the technical field of environmental engineering and detection. The intelligent prediction method is to establish a soft measurement model of the system by extracting the characteristics of the complex system and predict the future trend of the system. PM (particulate matter)2.5The prediction of the method has important significance for preventing and treating the air pollution. Applying intelligent prediction methods to PM2.5In the prediction of (2), the PM can be acquired in time2.5The concentration information is beneficial to strengthening the atmospheric environmental pollution control, and simultaneously, the air pollution monitoring cost can be saved. Therefore, PM2.5The application of the intelligent prediction method has profound practical significance.
Background
At present, the situation of air pollution in China is severe, and the air quality is accelerated by the air pollutants generated by the combustion of industrial waste gas, motor vehicle tail gas, biomass and coalChange to PM2.5The regional atmospheric environmental problems characterized by pollutants are increasingly prominent, harm the health of the public, influence the climate, influence the sustainable development of society and economy, and are not beneficial to the achievement of the stage target of basic thinking. Thus passing through to PM2.5Prevention of the occurrence of serious pollution has received a great deal of attention from society. However, PM2.5The concentration of the PM is simultaneously influenced by emission sources, pollutants, meteorological conditions and topographic features of a research area, and the atmospheric environment system has the characteristics of multivariable, nonlinearity, complex internal mechanism, incomplete information and the like, so that the PM is enabled to be generated2.5The prediction difficulty of (2) is large. Study of effective PM2.5Prediction method for PM2.5Accurate prediction becomes an urgent problem to be solved. Therefore, the research result of the invention has wide application prospect.
General PM2.5Predictive methods include process-based chemical modeling methods and data-based statistical methods. The chemical modeling method simulates the processes of generation, transportation, transformation and settlement of pollutants, but parameters such as model resolution, meteorological boundary conditions, a discharge source list and the like required by modeling are difficult to determine, and the calculation is complex. Statistical methods are classified into linear modeling methods based on linear regression and nonlinear modeling methods based on artificial neural networks. The linear regression model is not suitable for modeling an atmospheric environment system which is nonlinear per se; the artificial neural network has poor interpretability; compared with a neural network, the fuzzy neural network combining the neural network and a fuzzy system has stronger expression capability, but has the problem of structure determination. Therefore, novel PM is studied2.5The prediction method becomes an important subject of research in the field of air pollution prevention and control, and has important significance.
For the above PM2.5The invention provides a PM based on a second-order self-organizing fuzzy neural network2.5Provided is an intelligent prediction method. The second-order self-organizing fuzzy neural network determines the contribution rate of the neural output of the regularization layer of the fuzzy neural network to the network output by utilizing a model output sensitivity analysis method on a frequency domain, and increases and deletes the neural output of the regularization layer according to the contribution rate, so as to automatically adjust and deleteThe structure of the whole fuzzy neural network effectively solves the structural design problem of the fuzzy neural network, and is beneficial to analyzing and generating PM2.5The dynamic process of (2). Meanwhile, the parameters of the fuzzy neural network are trained by using the self-adaptive second-order gradient descent algorithm with rapid convergence and strong search capability, the defects of limited search capability and long search time of the genetic algorithm of the first-order gradient descent algorithm are avoided, and the PM after 24 hours of the fuzzy neural network is enhanced2.5Predicted performance of concentration. In order to remove redundant variables and reduce the computational complexity of the model, the invention extracts and PM by using a principal component analysis method2.5The characteristic variable with the maximum relevance can be obtained, the extracted characteristic variable and the research site PM2.5The concentration characteristics are matched, and then the second-order self-organizing fuzzy neural network is utilized to establish PM2.5Soft measurement model for PM2.5Accurate prediction of (2).
Disclosure of Invention
The invention obtains the PM based on the second-order self-organizing fuzzy neural network2.5The intelligent prediction method comprises the following steps: the method firstly extracts and PM from a plurality of groups of measurable variables by utilizing a principal component analysis method2.5The characteristic variable with the maximum relevance is established, and then the characteristic variable and the PM are established by utilizing a second-order self-organizing fuzzy neural network2.5Soft measurement model in between, for PM after 24 hours2.5The concentration is predicted, and the PM is solved2.5A problem that is difficult to predict.
PM based on second-order self-organizing fuzzy neural network2.5The design of the intelligent prediction method comprises the following steps:
(1) feature analysis determination of PM2.5The characteristic variables of (1).
An atmospheric background monitoring station (117 degrees 07 'from east longitude, 40 degrees 39' from north latitude and 287 meters from altitude) of the upper pasture area is selected as a research station. The station is located at the position of 100 kilometers in the northeast direction of the Beijing urban area, the square circle of the station has no dense population distribution and industrial area within 30 kilometers, and the PM of the station2.5The concentration is heavily influenced by the meteorological variables and is closely related to the optical thickness of the aerosol. The hour observation data of the county monitoring station from 14 days 1 month to 23 days 1 month in 2010 are taken as the experimental data of the invention, and the experimental data are obtained by the methodMeanwhile, the upper garden monitoring station had a cloudy weather from 1 month 16 to 1 month 19 of 2010. Will react with PM2.5Hourly data (including both ground and satellite observations) and PM after 24 hours for relevant meteorological variables and air pollutants and aerosol optical thickness2.5The concentration data are in one-to-one correspondence, and the PM which lacks the aerosol optical thickness data and does not have the correspondence is removed2.5And finally sorting L groups of data from the data of the observation value time period, wherein the value of L is 150-250, the amount of undersized data is insufficient, the contained information is incomplete, and the oversize calculation is too complex1,x2,…,x11]Wherein x is1,x2,…,x11Respectively representing temperature, relative humidity, wind speed, wind direction, air pressure, visibility, optical thickness of aerosol, CO and NO2、O3And SO2Data array of concentrations. Predicted variable PM2.5The data array of concentrations is denoted y. The temperature is given in units of C, the wind speed is given in units of m/s, the wind direction is given in units of C, the air pressure is given in units of hPa, the visibility is given in units of km, the CO is given in units of ppm, NO2、O3And SO2Has the unit of ppb, PM2.5Unit of (d) is [ mu ] g/m3Relative humidity is expressed as a percentage and aerosol optical thickness is in units. The principal component analysis method extracts and analyzes PM through the following steps2.5The most relevant characteristic variable:
① normalizing the variable data:
Figure RE-GDA0002383869430000031
wherein Z is a normalized observed data array, xijAnd zijRespectively the ith observed value of the jth variable before and after normalization,
Figure RE-GDA0002383869430000032
andjare respectively the mean and standard deviation of the jth variable before normalization, an
Figure RE-GDA0002383869430000033
②, calculating the Z correlation coefficient matrix R:
Figure RE-GDA0002383869430000034
③ solving the characteristic equation of 0, finding out the characteristic value of R, arranging in descending order, and marking as λ I-R |, where1,λ2,…,λ11The corresponding feature vector is denoted as γ1,γ2,…,γ11Applying the Schmidt orthogonalization method to gamma1,γ2,…,γ11Obtaining a unit orthogonal feature vector gamma'1,γ'2,…,γ'11。
④ calculating the characteristic value lambda1,λ2,…,λ11Cumulative contribution rate of (a)1,θ2,…,θ11：
Figure RE-GDA0002383869430000035
Wherein λ isαAnd λβα th eigenvalue and β th eigenvalue of the correlation coefficient matrix R after being arranged according to a descending order respectively, according to the given extraction efficiency theta, if thetaNMore than or equal to theta (N < 11), extracting N main components gamma'1,γ'2,…,γ'NWherein, the value of theta is between 85 and 95 percent, the undersize extraction information is incomplete, and the oversize dimensionality reduction effect is not obvious.
⑤ the data of the feature variable is obtained by calculating the projection of Z on the extracted unit orthogonal feature vector by equation (4).
Y＝Zγ' (4)
Wherein γ ═ γ'1,γ'2,…,γ'N]. Recording the selected characteristic variable as r ═ r1,r2,…,rN]Is the input of a second order self-organizing fuzzy neural network, PM2.5Concentration is taken as a prediction variable, the observed value of the concentration is the expected output of the second-order self-organizing fuzzy neural network,randomly ordering the observation data of the normalized characteristic variables and the normalized predictive variables, selecting the front I group data as a training sample and the back I ' group data as a test sample, so that the training sample and the test sample both comprise observation data of haze weather and observation data of non-haze weather, wherein I ' is L-I, I '<＝I。
(2) Designed for PM2.5An initial topology of the predicted second-order self-organizing fuzzy neural network. For PM2.5The predicted second-order self-organizing fuzzy neural network has four layers: an input layer, an RBF layer, a regularization layer, and an output layer. The input is the extracted characteristic variable and the output is PM2.5The predicted value of the concentration is denoted as p. Determining the initial connection mode of the second-order self-organizing fuzzy neural network N-M-M-1, namely the number of neurons in the input layer and the number of characteristic variables are both N, the number of neurons in the RBF layer is M, the number of neurons in the regularization layer is M, wherein M is a positive integer, and the value is 1,10]And the condition that the calculation load of the second-order self-organizing fuzzy neural network is overlarge due to overlarge M value is avoided, and the number of neurons in an output layer is 1. The initial values of the center, the width and the weight of the second-order self-organizing fuzzy neural network are set between (0,1), and the initial values can be randomly set, so that only the convergence speed of the network is influenced, and the prediction effect of the network is not influenced. The data of the characteristic variables of the kth set of training samples is denoted as r (k) ═ r1(k),r2(k),…,rN(k)](k is 1,2 …, I), when the second-order self-organizing fuzzy neural network is trained by using the kth group of training samples, the output of each layer is as follows:
① input layer this layer has N neurons:
ud(k)＝rd(k),d＝1,2,…,N (5)
wherein u isd(k) Is the output of the d-th neuron of the input layer whose input vector is r (k) ═ r1(k),r2(k),…,rN(k)]。
② RBF layer with M neurons and q-th neuron output
Figure RE-GDA0002383869430000051
Comprises the following steps:
Figure RE-GDA0002383869430000052
wherein, cdqAnd σdqThe center and width of the second order self-organizing fuzzy neural network, respectively.
③ regularization layer, the layer has the same number of neurons as the RBF layer, the output v of the l-th neuron of the layerl(k) Comprises the following steps:
Figure RE-GDA0002383869430000053
wherein,
Figure RE-GDA0002383869430000054
is the output of the first neuron in the RBF layer.
④ output layer with 1 neuron, the output of which represents PM2.5The predicted value of the concentration is shown as the following formula:
Figure RE-GDA0002383869430000055
wherein, wlIs the connection weight between the ith neuron and the output layer neuron of the regularization layer. The Root Mean Square Error (RMSE) of the training of the second-order self-organizing fuzzy neural network is:
Figure RE-GDA0002383869430000056
wherein, p (k) and o (k) are respectively the network output and the expected output when the kth training sample is used for training the second-order self-organizing fuzzy neural network, and the purpose of training the second-order self-organizing fuzzy neural network is to make the training RMSE defined by the formula (9) reach the expected value.
(3) And training a second-order self-organizing fuzzy neural network by using the training samples. In the training process, a method for analyzing the output sensitivity of a model on a frequency domain is utilizedDetermining the contribution rate of the neural output of the regularization layer of the fuzzy neural network to the network output, increasing and deleting the neural output of the regularization layer according to the contribution rate, thereby automatically adjusting the structure of the fuzzy neural network, analyzing and generating PM2.5The dynamic process of (2). At the same time, for PM after 24 hours2.5And (3) accurately predicting the concentration, and training the center, the width and the weight of the fuzzy neural network by using a self-adaptive second-order gradient descent algorithm. The method specifically comprises the following steps:
① the parameters for a given initial fuzzy neural network are trained using an adaptive second order gradient descent algorithm:
Φ(t+1)＝Φ(t)+(Q(t)+μ(t)I)-1g(t) (10)
wherein t is the current training step number, Φ (t +1) and Φ (t) are parameters of the fuzzy neural network when training to the t +1 th step and the t th step, respectively, and Φ (t) ═ c11(t)…cNM(t),σ11(t)…σNM(t),w1(t)…wM(t)]. μ (t) is a learning rate, and in order to avoid a fixed value of μ (t), μ (t) | | g (t) | | is adaptively changed in the training process. I is the identity matrix. The hessian matrix q (t) and the gradient vector g (t) are respectively expressed as:
Figure RE-GDA0002383869430000061
Figure RE-GDA0002383869430000062
wherein, Pk(t)、ηk(t)、Jk(t) and ekAnd (t) row vectors and errors of the sub-Hessian matrix, the sub-gradient vector and the Jacobian matrix corresponding to the kth training sample in the training step t are respectively. J. the design is a squarek(t) and ek(t) are respectively expressed as:
Figure RE-GDA0002383869430000063
ek(t)＝ok(t)-pk(t) (14)
wherein o isk(t) and pkAnd (t) respectively representing the observed value and the predicted value corresponding to the kth training sample when the kth training is reached. The I set of training samples was repeatedly trained using equation (10).
② training parameters of the fuzzy neural network by using an adaptive second-order gradient descent algorithm for ξ steps, and calculating the output v of the h neuron of the normalized layer in the frequency domain by using an equation (15)hContribution ratio ST to network output ph(h ═ 1,2, …, M), where ξ takes values between 5 and 15, too small acquisition of information from the neurons in the regularization layer of the fuzzy neural network is insufficient, and too large acquisition of information from the neurons reduces the efficiency of structural adjustment.
Figure RE-GDA0002383869430000064
Figure RE-GDA0002383869430000065
Wherein S ishIs vhTotal sensitivity to p, SnIs the output v of the nth neuron of the regularization layernTotal sensitivity to p, AωAnd BωAnd
Figure RE-GDA0002383869430000066
and
Figure RE-GDA0002383869430000067
fourier expansion f(s) of p at frequencies ω and ω, respectivelyhFourier coefficients of (A), and
Figure RE-GDA0002383869430000068
ωhis vhFundamental frequency of (d), max (ω)～h) Is to divide by vhTaking the maximum value of the fundamental frequencies output by all the regularization layer neurons except the regularization layer neurons as omegah＝2H max(ω～h) H is an interference factor, the value in the text is 4, too small Fourier amplitude cannot be fully extracted, too large Fourier amplitude increases algorithm complexity, and f(s) and v (v) arehExpressed by formula (17) and formula (18), respectively:
Figure RE-GDA0002383869430000069
Figure RE-GDA0002383869430000071
wherein, ahAnd bhAre each vhMinimum and maximum values of.
③ if STh>＝1Then the h-th neuron of the regularization layer is split, wherein,1＝0.3，1the too large result in uneven distribution of the output contribution rate of the neuron in the regularization layer, the too simple network structure and the too small result in the redundancy of the neuron in the regularization layer. In order to reduce the influence of the network structure adjustment on the network error, the initial parameters of the new neuron obtained by splitting are set by the following formula:
Figure RE-GDA0002383869430000072
of these, new1 and new2 are two new neurons, c.new1、σ.new1And wnew1The center vector, width vector and weight of neuron new1, respectively. c.new2、σ.new2And wnew2The center vector, width vector and weight of neuron new2, respectively. c.h(t)、σ.h(t) and whAnd (t) training the central vector, the width vector and the weight of the neuron h before the adjustment of the network structure in the t step, wherein tau is subjected to standard normal distribution.
If STh<2Deleting the neuron and adjusting network parameters at the same time, as shown in the following formula,2＝0.05，2too large results in too much pruning of the neurons in the regularization layer, and too small results in complex network structure.
Figure RE-GDA0002383869430000073
Wherein the neuron nea is the channel of the heartRegularization layer neurons with minimum Euclidean distance per h, and STnea>＝2，c.nea、σ.neaAnd wneaThe center vector, width vector and weight, c, of the network pruned neuron nea, respectively.nea(t)、σ.nea(t) and wnea(t) center vector, width vector and weight, w, of the pre-pruned neurons nea of the network trained to step t, respectivelyh(t) is the weight of the neuron h before training to the t-th step of network pruning, vh(t) and vnea(t) are the outputs of pre-net-pruning neuron h and neuron nea, respectively, trained to step t.
If it is not2＝<STh<1If the network structure is not changed, the network parameters are not adjusted.
④ the algorithm moves to step ① to continue training the parameters of the fuzzy neural network using the adaptive second-order gradient descent algorithm the computation stops when the training RMSE < > 0.01 or the algorithm iterates over 100 steps during a certain training step.
(4) And detecting the test sample. Testing the trained second-order self-organizing fuzzy neural network by using the test sample, wherein the output of the second-order self-organizing fuzzy neural network is PM2.5The predicted result of (1).
The invention is mainly characterized in that:
(1) the present invention is directed to PM2.5The concentration is difficult to predict, the traditional chemical modeling method is difficult to model and the like, and the PM based on the second-order self-organizing fuzzy neural network is provided2.5Provided is an intelligent prediction method. The second-order self-organizing fuzzy neural network can automatically adjust the structure according to a sensitivity analysis method, and is beneficial to analyzing PM2.5The generated dynamic process, and meanwhile, the parameters of the fuzzy neural network are adjusted by using a self-adaptive second-order gradient descent degree algorithm, so that the PM after 24 hours is enhanced2.5The prediction performance of the concentration solves the problem of PM2.5The concentration prediction difficulty is large.
(2) The invention takes pastures as research sites, the selected data comprises ground observation data and satellite observation data, and the selected data is based on principal component to remove redundant variablesAnalytical method extraction and PM2.5The characteristic variable with the maximum relevance, the finally extracted characteristic variable and the upper pasture PM2.5The concentration is matched with the characteristics closely related to the meteorological variables and the optical thickness of the aerosol.
Particular attention is paid to: the invention determines PM2.5Predicting the input variables of the method, so long as the relevant variables of the invention and the principle of the invention are adopted to carry out PM2.5Prediction is intended to be within the scope of the present invention.
Drawings
FIG. 1 is a PM of the present invention2.5Intelligent prediction method flow chart.
FIG. 2 is a satellite map of the present invention.
FIG. 3 is a PM of the present invention2.5The soft-measure model is a training RMSE variation graph for normalized data.
FIG. 4 is a PM of the present invention2.5And (3) a structural change graph of the soft measurement model in the training process.
FIG. 5 is a PM of the present invention2.5The soft measurement model trains a scatter plot.
FIG. 6 is a PM of the present invention2.5And (4) training an error map by using the soft measurement model.
FIG. 7 is a PM of the present invention2.5And testing the scatter diagram by using the soft measurement model.
FIG. 8 is a PM of the present invention2.5And testing an error map by using a soft measurement model.
Detailed Description
The invention obtains the PM based on the second-order self-organizing fuzzy neural network2.5Provided is an intelligent prediction method. The method uses PM2.5For output, the characteristic variable extracted by the principal component analysis method is used as input, and the second-order self-organizing fuzzy neural network is used for establishing PM2.5Soft measurement model for PM after 24 hours2.5The concentration is predicted. The flow chart of the intelligent prediction method is shown in fig. 1.
An atmospheric background monitoring station in the upper county area is selected as a research site, and a satellite map of the atmospheric background monitoring station is shown in figure 2. The hourly observation data from 1 month 14 to 1 month 23 of 2010 of the site are taken as experimental data. Removing the deficiency of the gasSol optical thickness data and lack of corresponding PM2.5Data for observation time period, weather variable and air pollutant and aerosol optical thickness hour data and PM after 24 hours2.5The concentration data are in one-to-one correspondence, 182 groups of data are arranged, L is 182, and the observation data array for characteristic analysis is marked as X (X)1,x2,…,x11]Wherein x is1,x2,…,x11Respectively representing temperature, relative humidity, wind speed, wind direction, air pressure, visibility, optical thickness of aerosol, CO and NO2、O3And SO2Data array of concentrations. Predicted variable PM2.5The data array of concentrations is denoted y.
PM based on second-order self-organizing fuzzy neural network2.5The design of the intelligent prediction method comprises the following steps:
(1) feature analysis determination of PM2.5The characteristic variables of (1). Principal component analysis was performed on the observed data array X using equations (1) to (4), and the value of extraction efficiency θ was set to 90%. The contribution rate and the cumulative contribution rate of each Principal Component (PC) are shown in table 1:
TABLE 1 principal component contribution rate and cumulative contribution rate
PC 1 2 3 4 5 6 7 8 9 10 11
Contribution ratio (%) 56.55 15.71 10.00 5.98 4.01 2.34 1.71 1.50 1.13 0.86 0.21
Cumulative contribution ratio (%) 56.55 72.26 82.26 88.24 92.25 94.59 96.30 97.80 98.93 99.79 100
As can be seen from table 1, the cumulative contribution rate of the first 5 principal components exceeds 90%, so 5 principal components are extracted, and the value of N is 5. Temperature, relative humidity, wind speed, wind direction, air pressure, visibility, aerosol optical thickness, CO, NO corresponding to 5 extracted main components2、O3And SO2The coefficient of concentration is as shown in equation (21):
Figure RE-GDA0002383869430000101
selecting the variable corresponding to the coefficient having the largest absolute value among the principal components expressed by the formula (21) to obtain the variable corresponding to PM2.5The most relevant characteristic variable: relative humidity, air pressure, aerosol optical thickness, wind speed, and wind direction. It can be seen that the extracted feature variables and the upper pasture PM2.5The concentration is matched with the characteristics closely related to the meteorological variable and the optical thickness of the aerosol. The extracted characteristic variable is recorded as r ═ r1,r2,…,r5]，PM2.5The observed value of the concentration as a predictive variable is the expected output of the second-order self-organizing fuzzy neural network and is marked as o. And randomly sequencing the normalized observed data of the characteristic variables and the predicted variables, selecting the first 130 groups of sequenced data as training samples, and selecting the second 52 groups of sequenced data as test samples (I is 130, and I' is 52).
(2) Initialization for PM2.5A predicted second-order self-organizing fuzzy neural network. The invention is used for PM2.5The predicted second-order self-organizing fuzzy neural network has four layers: an input layer, an RBF layer, a regularization layer, and an output layer. According to the extraction result of the characteristic variables, taking the relative humidity, the air pressure, the optical thickness of the aerosol, the wind speed and the wind direction as input, and taking PM2.5And determining the number of neurons of an input layer of the second-order self-organizing fuzzy neural network as 5, the number of neurons of an output layer as 1, and the number M of initial neurons of an RBF layer and a regularization layer as 3, namely the initial connection mode of the second-order self-organizing fuzzy neural network is 5-3-3-1. The center, the width and the weight of the second-order self-organizing fuzzy neural network are assigned with initial values of (0,1)) Is used. When training the second-order self-organizing fuzzy neural network by using the k (k is 1,2, …,130) th group training sample, the output of each layer is calculated according to the formula (5) to the formula (8),
(3) and training a second-order self-organizing fuzzy neural network by using the training samples. In the training process, a model output sensitivity analysis method on a frequency domain is utilized to determine the contribution rate of the neural output of the regularization layer of the fuzzy neural network to the network output, the neurons of the regularization layer with high contribution rate are split, the neurons of the regularization layer with low contribution rate are deleted, so that the structure of the fuzzy neural network is automatically adjusted, and the center, the width and the weight of the fuzzy neural network are trained by utilizing a self-adaptive second-order gradient descent algorithm. The method specifically comprises the following steps:
①, training the given initial fuzzy neural network by using training samples and an adaptive second-order gradient descent algorithm, and repeatedly updating the center, the width and the weight of the fuzzy neural network according to the formula (10).
② repeatedly training the parameters of fuzzy neural network by adaptive second-order gradient descent algorithm for 10 steps to find out the output v of each neuron in regulation layerhMaximum value of bhAnd a minimum value ahTaking the interference factor H as 4, and calculating v using equation (15)hContribution ratio ST to network output ph。
③ if STh>＝10.3, the h neuron of the regularization layer is split. To reduce the influence of the network structure adjustment on the network error, the centers, widths, and weights of two new neurons obtained by splitting are set by equation (19). If STh<2When the number of neurons is 0.05, the network parameters are adjusted by equation (20) while deleting the neuron. If it is not2＝<STh<1If the network structure is not changed, the network parameters are not adjusted.
④ the algorithm moves to step ① to continue training the parameters of the fuzzy neural network using the adaptive second-order gradient descent algorithm the computation stops when the training RMSE < > 0.01 or the algorithm iterates over 100 steps during a certain training step.
(4) And detecting the test sample. Using the test sample as the trained second-order self-organizationThe input of the fuzzy neural network is organized, and the output of the second-order self-organized fuzzy neural network is PM2.5The predicted result of (1).
FIG. 3 is PM2.5The soft-measurement model trains the RMSE variation graph. FIG. 4 is PM2.5And (3) training a process structure change diagram by using the soft measurement model. FIG. 5 is PM2.5Training a scatter diagram of a soft measurement model, wherein an X axis: PM (particulate matter)2.5Training observations (μ g/m)3) And the Y axis: PM (particulate matter)2.5Soft measurement model training prediction value (mu g/m)3). FIG. 6 is PM2.5And (4) training an error map by using the soft measurement model. FIG. 7 is PM2.5Soft measurement model test scatter plot, X-axis: PM (particulate matter)2.5Measurement of observed value (μ g/m)3) And the Y axis: PM (particulate matter)2.5Soft measurement model test prediction value (mu g/m)3). FIG. 8 is PM2.5And testing an error map by using a soft measurement model.
Tables 2-21 show experimental data for the present invention, and tables 2-7 show monitoring variables of temperature, visibility, CO, NO2、 O3And SO2Observed values of concentrations, tables 8-13 are training samples, and Table 14 is PM2.5Training prediction values for the soft measurement model, with tables 15-20 being test samples and table 21 being PM2.5And testing predicted values of the soft measurement model.
TABLE 2 observed values of monitoring variable temperature (. degree. C.)
Figure RE-GDA0002383869430000111
Figure RE-GDA0002383869430000121
TABLE 3 observed value (km) of visibility of monitoring variables
21.06 21.64 37.42 35.48 14.30 11.85 6.50 6.98 7.19 7.74 49.52 49.96 34.65 26.74 33.32
20.07 20.81 39.42 36.81 13.34 10.55 7.32 7.22 7.09 15.97 49.99 49.94 33.09 26.93 32.39
19.03 21.15 36.67 36.07 12.00 8.75 7.76 7.11 7.31 23.36 49.98 48.68 31.01 25.65 34.27
17.63 22.73 37.22 36.93 11.56 8.21 7.72 6.81 7.72 39.28 49.95 46.38 23.48 23.08 35.98
16.87 26.02 40.59 35.64 11.41 8.36 7.72 6.46 8.18 45.30 49.94 41.48 18.45 20.09 38.11
16.55 30.65 43.61 33.34 11.89 7.87 8.34 6.48 8.54 43.55 49.94 38.78 18.72 23.57 35.92
16.92 37.09 47.50 31.62 12.45 8.02 8.65 6.35 9.45 45.49 49.94 36.02 19.04 27.56 33.92
17.41 43.22 45.25 29.18 12.61 7.71 9.17 5.90 10.35 45.39 49.94 34.40 17.11 31.05 30.59
16.81 41.27 41.52 27.48 13.57 7.49 9.05 6.35 10.51 46.20 49.94 32.95 16.74 32.16 26.26
16.51 40.62 35.09 25.72 12.86 7.03 8.13 6.92 10.84 47.74 49.94 34.17 19.19 33.59 22.94
18.85 42.61 32.54 21.97 12.31 6.62 7.76 6.65 9.45 46.04 49.94 35.04 21.73 32.79 20.40
21.28 39.69 34.92 18.96 13.43 5.96 6.87 6.81 8.00 46.46 49.94 35.59 25.32 32.47 18.65
19.30 20.87
TABLE 4 observed values (ppm) of the monitoring variable CO
0.92 0.49 0.58 0.24 1.23 0.92 1.40 1.37 1.40 0.92 0.23 0.71 1.14 1.02 0.26
0.69 0.55 0.46 0.26 0.92 1.26 1.52 1.49 1.34 1.74 0.26 0.40 0.48 0.88 0.26
0.66 0.49 0.46 0.26 1.06 1.29 1.34 1.63 1.26 1.71 0.26 0.54 0.63 0.83 0.25
0.69 0.32 0.49 0.29 0.86 1.49 1.34 2.03 1.26 1.74 0.31 0.68 0.74 0.80 0.25
0.66 0.24 0.49 0.29 0.83 1.57 1.17 1.91 1.17 1.31 0.31 0.83 0.83 0.60 0.25
0.64 0.18 0.46 0.29 0.80 1.43 1.14 1.54 1.09 0.57 0.29 1.00 0.85 0.57 0.31
0.58 0.15 0.44 0.41 0.80 1.69 1.29 1.74 1.29 0.49 0.29 1.14 0.85 0.48 0.31
0.46 0.15 0.35 0.55 0.78 1.74 1.32 2.11 1.14 0.43 0.34 0.48 0.80 0.60 0.34
0.49 0.15 0.24 0.92 0.75 1.66 1.54 1.54 1.09 0.34 0.37 0.60 1.34 0.94 0.34
0.55 0.15 0.26 0.69 0.75 1.91 1.54 1.77 1.06 0.34 0.46 0.74 1.00 0.82 0.45
0.52 0.15 0.21 0.72 0.75 1.86 1.49 1.66 1.20 0.31 0.48 0.88 1.20 0.60 0.43
0.44 0.04 0.21 0.75 0.75 1.54 1.37 1.51 1.26 0.23 0.60 1.03 1.25 0.34 0.74
0.60 0.68
TABLE 5 monitoring variable NO2Observed value (ppb)
20.08 5.40 5.40 0.33 26.38 15.54 44.56 18.86 45.61 15.90 1.39 0.34 0.34 23.07 0.17
14.84 7.85 3.48 0.68 30.05 23.06 44.56 24.81 43.34 31.98 1.04 0.17 0.34 26.91 0.35
23.40 8.37 3.83 0.68 32.50 29.00 41.06 30.40 39.14 25.16 1.04 0.17 0.17 19.75 0.35
28.82 4.35 6.97 1.56 27.25 34.94 41.41 38.97 41.06 30.41 0.87 1.92 0.17 12.93 0.17
30.39 1.38 7.32 3.48 27.60 38.44 38.44 44.04 37.74 21.32 11.70 0.17 1.22 7.86 0.35
23.23 0.16 7.50 5.93 26.20 45.96 34.25 48.75 35.30 9.96 1.74 0.34 4.19 7.86 0.35
21.66 0.16 6.28 11.35 24.11 45.43 33.37 49.98 33.37 5.59 1.57 0.52 9.26 11.36 0.17
21.13 0.16 6.63 13.97 22.18 46.13 31.45 51.90 30.05 4.01 1.92 1.74 14.85 13.98 0.35
15.36 0.33 9.77 20.96 18.16 47.00 25.16 49.63 22.89 2.79 2.09 1.92 16.60 19.40 0.52
11.17 0.16 4.35 22.53 16.24 44.73 20.96 47.88 18.17 2.79 1.74 2.62 15.38 12.93 5.07
8.20 1.56 1.21 29.87 12.92 46.66 18.34 47.88 17.64 2.27 0.34 1.22 15.38 6.29 8.56
4.35 2.95 0.33 24.46 11.87 46.48 16.77 46.13 17.64 1.39 0.17 0.87 17.13 0.87 12.93
11.88 13.81
TABLE 6 monitoring variable O3Observed value (ppb)
15.40 33.22 32.52 39.85 6.82 25.86 2.62 26.03 3.13 28.12 40.51 39.46 37.36 11.32 38.75
18.19 33.39 34.96 39.85 4.37 26.21 2.09 27.43 3.31 16.57 41.04 39.63 38.41 7.30 39.10
13.48 32.87 33.91 40.55 3.67 28.31 3.14 26.73 4.71 21.64 41.56 39.98 39.11 14.29 39.27
11.55 36.19 30.59 40.20 6.82 25.69 2.44 22.88 2.61 18.15 41.21 39.98 39.63 22.33 39.45
9.46 38.99 29.02 38.10 6.47 18.17 4.36 16.42 3.48 20.24 40.86 40.33 39.11 27.74 39.80
12.95 40.73 30.07 31.29 7.17 8.39 6.11 7.85 4.01 35.27 40.69 37.89 36.48 26.34 39.45
14.00 41.08 30.59 26.22 8.57 7.16 6.11 5.06 4.18 39.29 39.46 37.71 27.22 21.45 39.27
13.82 40.91 30.24 21.33 10.14 4.37 6.63 3.66 6.10 40.69 38.59 35.44 21.63 19.00 39.45
17.84 38.81 31.99 14.34 13.46 2.97 10.65 2.26 11.52 40.69 38.06 34.56 19.01 12.71 39.10
21.51 38.46 33.39 12.24 15.55 3.32 14.32 4.18 16.06 39.29 37.71 33.69 17.26 19.18 31.23
25.18 36.71 37.76 5.60 20.10 2.79 18.34 3.13 19.91 40.16 39.81 35.26 16.91 28.26 25.99
31.82 34.26 39.15 8.92 24.64 2.27 22.71 3.66 23.93 40.16 39.81 36.66 15.16 36.13 22.32
22.32 20.92
TABLE 7 monitoring variables SO2Observed value (ppb)
Figure RE-GDA0002383869430000131
Figure RE-GDA0002383869430000141
Training a sample:
TABLE 8 training observations of the relative humidity of the characteristic variables (%)
26.86 26.82 22.00 27.72 41.41 72.67 64.86 22.17 73.98 37.24 73.79 65.22 45.71
45.00 52.99 31.78 20.10 65.60 39.25 28.72 27.86 60.29 67.28 27.75 69.23 46.33
57.79 63.60 43.62 57.94 72.34 40.32 77.96 36.21 41.10 41.00 26.58 47.69 33.64
31.54 54.43 71.63 24.78 34.63 26.82 46.94 25.97 69.45 37.71 59.99 43.58 68.27
64.44 33.11 24.82 51.48 71.48 75.40 75.12 51.84 20.81 68.68 35.74 76.54 36.17
75.50 75.02 37.73 24.32 27.86 40.42 36.20 30.87 43.37 41.71 48.09 29.39 75.00
75.00 22.67 73.98 39.20 29.31 28.46 35.79 29.60 27.86 31.64 61.59 72.63 29.83
51.68 45.61 72.63 78.85 67.00 75.40 61.97 43.28 43.52 72.03 31.86 32.43 43.15
50.06 37.24 48.79 59.91 64.92 31.97 66.78 19.27 52.08 53.02 62.99 37.08 32.99
30.17 56.23 25.92 29.74 37.57 33.20 51.08 49.01 45.19 44.72 33.59 28.19 23.47
TABLE 9 training observations (hPa) of the characteristic variables air pressure
1002.02 1000.53 999.62 997.11 993.40 999.18 996.91 1000.66 993.23 997.60 995.54 986.65 998.67
999.74 998.58 989.47 1000.20 990.64 994.49 1001.05 996.73 993.39 986.49 995.51 990.78 997.01
987.03 988.16 987.05 992.53 991.18 991.98 995.06 996.61 997.66 990.03 999.73 992.58 1002.41
995.74 990.06 993.17 1000.72 998.74 995.21 998.32 995.46 995.25 999.52 988.87 995.82 987.37
990.47 997.42 1001.73 987.23 996.98 990.94 991.13 989.83 997.13 996.91 997.79 994.53 995.45
995.02 995.22 997.67 1000.89 996.15 1002.22 985.65 998.36 993.35 989.65 1000.86 1000.13 991.19
991.49 996.02 998.95 997.68 1001.59 995.82 986.35 999.40 996.74 999.32 999.32 991.36 998.25
988.83 998.19 986.57 985.60 999.25 993.91 994.39 991.28 989.67 991.49 990.94 1001.18 998.27
993.16 1002.68 998.49 996.98 992.06 988.60 986.48 995.67 996.77 999.29 986.64 999.26 995.59
997.14 993.81 995.31 995.82 997.37 998.35 992.58 999.46 996.06 999.03 986.76 997.36 1000.05
TABLE 10 training observations of the characteristic variable Aerosol optical thickness
Figure RE-GDA0002383869430000142
Figure RE-GDA0002383869430000151
TABLE 11 training observations (m/s) of characteristic variable wind speed
2.51 4.21 3.17 1.71 5.08 0.38 1.92 2.18 2.39 1.78 0.56 1.15 2.73
4.66 2.76 3.86 2.16 1.04 5.91 3.78 4.88 2.55 1.76 3.49 1.36 3.11
2.18 0.54 2.92 3.31 2.57 5.89 1.99 5.54 1.32 1.70 4.54 2.63 4.51
2.04 0.68 1.24 3.73 2.68 3.83 0.96 3.27 0.34 3.15 0.82 3.77 3.99
1.64 1.49 3.31 2.58 0.67 2.24 2.62 0.59 3.18 1.19 0.57 2.91 2.10
2.07 0.94 1.09 2.56 4.63 3.20 3.36 4.84 2.53 1.27 3.99 4.07 1.99
1.44 1.00 0.32 1.16 3.28 2.53 3.17 2.69 4.91 2.61 1.15 1.94 5.67
5.76 1.00 2.32 1.70 0.59 3.10 2.00 2.30 6.34 2.36 4.66 4.87 2.17
2.13 3.99 1.98 2.78 2.97 2.97 1.48 1.95 2.38 0.86 1.92 1.85 2.35
4.32 1.81 3.64 1.92 1.40 4.89 3.59 4.15 1.89 3.28 2.87 6.25 3.85
TABLE 12 training observations (°) of characteristic variables wind direction
106.18 78.94 73.84 32.93 38.96 86.86 45.11 20.20 64.66 137.65 236.68 15.41 29.00
26.43 49.93 27.31 34.67 8.43 21.08 84.05 38.10 73.16 32.44 47.37 50.15 101.38
68.20 350.06 80.11 86.74 54.40 35.56 21.24 50.88 171.70 78.26 43.20 85.08 89.43
32.03 99.54 62.10 29.57 37.17 47.37 107.86 45.66 187.29 51.65 55.44 61.36 56.01
50.15 130.83 84.89 76.71 309.94 74.83 69.71 333.71 101.06 11.91 343.73 68.07 9.89
56.15 315.86 18.45 35.53 73.01 74.96 86.07 22.78 234.14 171.08 63.90 86.88 71.42
73.98 261.14 103.03 31.22 80.64 37.14 79.26 99.64 32.14 77.50 287.82 56.95 42.35
45.78 36.31 33.87 148.82 119.22 66.36 291.18 92.74 38.97 67.17 11.98 93.69 62.21
215.40 73.26 60.15 77.47 76.52 38.38 17.96 246.67 49.37 74.94 52.02 39.18 40.54
344.55 259.68 39.70 37.99 137.67 25.33 79.93 18.77 120.89 28.99 92.03 38.09 88.30
TABLE 13 prediction variables PM2.5Training observation value (μ g/m)3)
Figure RE-GDA0002383869430000152
Figure RE-GDA0002383869430000161
TABLE 14 prediction variables PM2.5Training prediction of (μ g/m)3)
24.48 17.73 18.05 12.62 10.03 57.04 67.14 9.77 63.19 28.11 77.53 0.29 22.53
16.18 28.42 11.59 12.87 141.62 8.55 24.38 10.66 60.37 4.78 9.63 161.28 33.72
9.35 10.15 6.88 186.54 173.66 4.19 50.61 12.02 35.25 56.50 13.61 59.33 21.28
13.35 96.08 55.72 13.69 21.43 9.32 37.73 12.58 62.09 23.94 19.96 19.11 9.78
134.80 21.44 19.77 9.12 80.47 164.20 171.35 79.49 13.33 50.09 16.24 56.80 9.36
63.56 69.92 21.39 13.98 11.77 30.86 1.76 13.75 59.57 61.98 31.10 19.58 171.34
165.33 10.60 72.17 25.34 33.69 13.66 1.94 29.80 8.87 30.53 68.19 173.68 13.24
0.29 14.74 9.64 13.81 55.70 62.12 79.06 42.68 2.03 174.72 12.90 19.50 24.04
67.51 25.06 27.54 72.10 175.93 2.83 1.50 10.42 59.35 43.69 7.69 26.54 13.18
10.43 75.14 9.74 15.68 43.21 14.98 220.75 18.06 64.13 21.72 2.59 14.31 16.12
Testing a sample:
TABLE 15 test observations of the relative humidity of the characteristic variables (%)
73.98 37.19 29.69 64.18 37.21 71.56 29.24 28.08 73.95 71.66
75.02 40.13 34.13 28.54 44.15 61.94 24.89 76.37 65.62 78.01
45.26 41.10 42.06 44.99 26.75 65.36 73.08 24.61 77.68 47.16
33.14 64.15 21.79 66.36 40.88 30.02 20.43 76.56 71.47 74.64
46.24 59.70 20.74 23.83 73.83 75.00 45.40 39.99 27.01 44.12
53.41 35.12
TABLE 16 test observations (hPa) of characteristic variable air pressure
992.86 993.45 997.76 999.26 997.82 990.95 999.03 996.22 992.82 988.33
998.15 990.28 985.53 999.68 997.80 988.61 1000.38 997.93 987.02 994.91
1000.57 997.50 994.87 991.04 995.72 994.81 991.68 1000.07 997.68 999.26
992.63 987.54 998.56 993.43 993.92 997.74 996.17 997.25 991.50 998.40
989.69 990.31 999.67 1001.04 997.09 995.43 999.26 994.79 996.59 1001.41
993.16 997.94
TABLE 17 measurement observations of the characteristic variable Aerosol optical thickness
Figure RE-GDA0002383869430000162
Figure RE-GDA0002383869430000171
TABLE 18 test observations (m/s) of characteristic variable wind speed
1.99 3.75 6.15 1.04 3.68 1.81 4.41 3.09 1.56 4.75
0.71 6.62 3.40 3.10 2.40 0.74 4.82 0.44 0.73 1.53
4.35 1.54 1.09 3.46 3.02 0.92 1.96 4.03 0.57 0.51
4.32 0.51 3.78 2.07 1.86 4.91 2.72 0.51 2.71 1.51
0.93 1.50 2.74 4.08 0.36 0.70 2.23 3.99 1.38 2.89
2.79 1.99
TABLE 19 test observations (°) of characteristic variables wind direction
68.06 48.59 38.94 40.88 299.42 52.70 43.20 3.95 72.32 72.18
187.33 52.59 77.56 51.11 80.09 104.83 52.56 50.23 12.86 68.92
40.06 165.76 157.50 74.81 31.18 123.43 67.17 75.54 13.62 275.90
28.16 144.85 92.55 79.12 229.88 28.74 230.49 166.89 75.67 40.87
172.78 41.64 50.85 79.78 269.92 119.17 57.61 59.66 286.69 65.60
74.01 279.00
TABLE 20 predicted variablesPM2.5Test observation value of (g/m)3)
54.27 37.98 19.76 71.64 2.28 160.71 19.48 2.00 53.25 4.81
63.05 3.51 3.95 66.94 33.03 9.59 29.41 58.68 10.92 62.13
28.68 11.28 54.78 195.92 6.55 101.93 168.60 4.05 54.60 67.40
17.84 11.49 2.48 56.03 67.48 1.65 4.38 52.71 173.29 69.18
74.30 104.23 1.27 2.18 54.90 78.60 7.49 22.08 5.42 26.06
52.40 6.34
TABLE 21 prediction variables PM2.5Test prediction value of (g/m)3)
54.93 28.94 13.54 47.19 18.30 152.09 15.35 7.52 48.42 1.27
91.60 3.81 2.58 21.34 42.25 32.44 15.08 55.01 1.27 53.17
25.58 58.96 46.86 151.35 13.79 49.18 110.90 19.48 43.00 46.38
51.95 20.04 16.10 62.44 50.05 7.93 13.96 81.43 138.07 66.37
79.98 96.85 23.09 17.75 67.78 45.68 40.06 17.48 17.83 37.31
47.99 36.47

Claims (1)

1. PM based on second-order self-organizing fuzzy neural network2.5The intelligent prediction method is characterized by comprising the following steps:
(1) feature analysis determination of PM2.5A characteristic variable of (d);
will react with PM2.5Hourly data for relevant meteorological variables and air pollutants and aerosol optical thickness and PM after 24 hours2.5The concentration data are in one-to-one correspondence, and the PM which lacks the aerosol optical thickness data and does not have the correspondence is removed2.5The data of the time section of the observed value is finally sorted out L groups of data, and the data are used for processing the observed valueL is between 150 and 250, and the observed data array for principal component analysis is X ═ X1,x2,…,x11]Wherein x is1,x2,…,x11Respectively representing temperature, relative humidity, wind speed, wind direction, air pressure, visibility, optical thickness of aerosol, CO and NO2、O3And SO2A data array of concentrations; predicted variable PM2.5The data array of the concentration is marked as y; the temperature is given in units of C, the wind speed is given in units of m/s, the wind direction is given in units of C, the air pressure is given in units of hPa, the visibility is given in units of km, the CO is given in units of ppm, NO2、O3And SO2Has the unit of ppb, PM2.5Unit of (d) is [ mu ] g/m3Relative humidity is expressed in percent, and aerosol optical thickness has no units; the principal component analysis method extracts and analyzes PM through the following steps2.5The most relevant characteristic variable:
① normalizing the variable data:
Figure FDA0002383869420000011
wherein Z is a normalized observed data array, xijAnd zijRespectively the ith observed value of the jth variable before and after normalization,
Figure FDA0002383869420000012
andjare respectively the mean and standard deviation of the jth variable before normalization and
Figure FDA0002383869420000013
②, calculating the Z correlation coefficient matrix R:
Figure FDA0002383869420000014
③ constructing characteristic equation | λ I-R | ═ 0, where I is unit matrix, solving the characteristic equation to obtain characteristic value of R, arranging in descending order, and recordingIs λ1,λ2,…,λ11The corresponding feature vector is denoted as γ1,γ2,…,γ11Applying the Schmidt orthogonalization method to gamma1,γ2,…,γ11Obtaining a unit orthogonal feature vector gamma'1,γ'2,…,γ'11；
④ calculating the characteristic value lambda1,λ2,…,λ11Cumulative contribution rate of (a)1,θ2,…,θ11：
Figure FDA0002383869420000015
Wherein λ isαAnd λβRespectively α th eigenvalue and β th eigenvalue of the correlation coefficient matrix R after being arranged according to descending order, according to the given extraction efficiency theta if theta is larger than thetaNMore than or equal to theta, N is less than 11, and N main components gamma are extracted'1,γ'2,…,γ′NWherein the value of theta is between 85 and 95 percent;
⑤ calculating the projection of Z on the extracted unit orthogonal feature vector by using the formula (4) to obtain the data of the feature variable;
Y＝Zγ' (4)
wherein γ ═ γ'1,γ'2,…,γ'N](ii) a Recording the selected characteristic variable as r ═ r1,r2,…,rN]Is the input of a second order self-organizing fuzzy neural network, PM2.5Randomly ordering the observation data of the normalized characteristic variables and the prediction variables, selecting front I group data after ordering as a training sample, and taking rear I 'group data as a test sample, wherein I' is L-I, I 'contains observation data under different weather conditions'<＝I；
(2) Designed for PM2.5An initial topology of a predicted second-order self-organizing fuzzy neural network; for PM2.5Predictive second-order self-organizing fuzzy neural networkFour layers in total: the system comprises an input layer, an RBF layer, a regularization layer and an output layer; the input is the extracted characteristic variable and the output is PM2.5The predicted value of the concentration is marked as p; determining the initial connection mode of the second-order self-organizing fuzzy neural network N-M-M-1, namely the number of neurons in the input layer and the number of characteristic variables are both N, the number of neurons in the RBF layer is M, the number of neurons in the regularization layer is M, wherein M is a positive integer, and the value is 1,10]Taking values, wherein the output layer is provided with a neuron; the initial values of the center, the width and the weight of the second-order self-organizing fuzzy neural network are randomly set between (0, 1); the data of the characteristic variables of the kth set of training samples is denoted as r (k) ═ r1(k),r2(k),…,rN(k)]When the second-order self-organizing fuzzy neural network is trained by using the kth training sample, the output of each layer is as follows:
① input layer this layer has N neurons:
ud(k)＝rd(k),d＝1,2,…,N (5)
wherein u isd(k) Is the output of the d-th neuron of the input layer whose input vector is r (k) ═ r1(k),r2(k),…,rN(k)]；
② RBF layer with M neurons and q-th neuron output
Figure FDA0002383869420000021
Comprises the following steps:
Figure FDA0002383869420000022
wherein, cdqAnd σdqThe center and the width of the second-order self-organizing fuzzy neural network respectively;
③ regularization layer, the layer has the same number of neurons as the RBF layer, the output v of the l-th neuron of the layerl(k) Comprises the following steps:
Figure FDA0002383869420000031
wherein,
Figure FDA0002383869420000032
is the output of the first neuron of the RBF layer;
④ output layer with a neuron, the output of which represents PM2.5The predicted value of the concentration is shown as the following formula:
Figure FDA0002383869420000033
wherein, wlIs the connection weight between the first neuron of the regularization layer and the neuron of the output layer; the training root mean square error RMSE of the second-order self-organizing fuzzy neural network is as follows:
Figure FDA0002383869420000034
wherein, p (k) and o (k) are respectively the network output and the expected output when the kth group of training samples are used for training the second-order self-organizing fuzzy neural network, and the purpose of training the second-order self-organizing fuzzy neural network is to enable the training RMSE defined by the formula (9) to reach the expected value;
(3) training a second-order self-organizing fuzzy neural network by using a training sample; in the training process, the model output sensitivity analysis method on the frequency domain is utilized to determine the contribution rate of the neural output of the regularization layer of the fuzzy neural network to the network output, and the neurons of the regularization layer are increased or deleted according to the contribution rate, so that the structure of the fuzzy neural network is automatically adjusted, and PM is generated through analysis2.5The dynamic process of (2); meanwhile, the center, the width and the weight of the fuzzy neural network are trained by using a self-adaptive second-order gradient descent algorithm, and the method specifically comprises the following steps:
① the parameters for a given initial fuzzy neural network are trained using an adaptive second order gradient descent algorithm:
Φ(t+1)＝Φ(t)+(Q(t)+μ(t)I)-1g(t) (10)
where t is the current training step number, Φ (t)+1) and Φ (t) are parameters of the fuzzy neural network trained to step t +1 and t, respectively, where Φ (t) ═ c11(t)…cNM(t),σ11(t)…σNM(t),w1(t)…wM(t)]，c11(t)…cNM(t)、σ11(t)…σNM(t) and w1(t)…wM(t) respectively representing the center, the width and the weight of the fuzzy neural network, and N and M respectively representing the number of the input layer neurons and RBF layer neurons of the fuzzy neural network; μ (t) is a learning rate, and in order to avoid a fixed value of μ (t), μ (t) | | g (t) | | is made to adaptively change in the training process; i is an identity matrix; the hessian matrix q (t) and the gradient vector g (t) are respectively expressed as:
Figure FDA0002383869420000035
Figure FDA0002383869420000036
wherein, Pk(t)、ηk(t)、Jk(t) and ek(t) row vectors and errors of the sub-Hessian matrix, the sub-gradient vector and the Jacobian matrix corresponding to the kth training sample set from the training step t are respectively obtained; t denotes transpose, Jk(t) and ek(t) are respectively expressed as:
Figure FDA0002383869420000041
ek(t)＝ok(t)-pk(t) (14)
wherein o isk(t) and pk(t) the observed value and the predicted value corresponding to the kth group of training samples from the training to the tth step are respectively obtained; c. C11(t)…cNM(t)、σ11(t)…σNM(t) and w1(t)…wM(t) respectively representing the center, the width and the weight of the fuzzy neural network, and N and M respectively representing the number of the input layer neurons and RBF layer neurons of the fuzzy neural network; utilization type (10)Repeatedly training the I group of training samples;
② training parameters of the fuzzy neural network by using an adaptive second-order gradient descent algorithm for ξ steps, and calculating the output v of the h neuron of the normalized layer in the frequency domain by using an equation (15)hContribution ratio ST to network output phH is 1,2, …, M, wherein ξ is between 5 and 15;
Figure FDA0002383869420000042
Figure FDA0002383869420000043
wherein S ishIs vhTotal sensitivity to p, SnIs the output v of the nth neuron of the regularization layernTotal sensitivity to p, AωAnd BωAnd
Figure FDA0002383869420000044
and
Figure FDA0002383869420000045
fourier expansion f(s) of p at frequencies ω and ω, respectivelyhAt s is an argument of the Fourier expansion at [ - π, π]In the range of (a) to (b),
Figure FDA0002383869420000046
ωhis vhFundamental frequency of (d), max (ω)～h) Is to divide by vhTaking the maximum value of the fundamental frequencies output by all the regularization layer neurons except the regularization layer neurons as omegah＝2H max(ω～h) H is an interference factor, and the value in the text is 4; f(s) and vhExpressed by formula (17) and formula (18), respectively:
Figure FDA0002383869420000047
Figure FDA0002383869420000048
wherein, ahAnd bhAre each vhMinimum and maximum values of;
③ if STh>＝1Then the h-th neuron of the regularization layer is split, wherein,10.3; in order to reduce the influence of the network structure adjustment on the network error, the initial parameters of the new neuron obtained by splitting are set by the following formula:
Figure FDA0002383869420000049
wherein new1 and new2 are two new neurons, c.new1、σ.new1And wnew1The central vector, width vector and weight of the neuron new 1; c. C.new2、σ.new2And wnew2The central vector, width vector and weight of the neuron new 2; c. C.h(t)、σ.h(t) and wh(t) training the central vector, the width vector and the weight of the neuron h before the adjustment of the network structure in the t step, wherein tau is subjected to standard normal distribution;
if STh<2Deleting the neuron and adjusting network parameters at the same time, as shown in the following formula,2＝0.05；
Figure FDA0002383869420000051
wherein the neuron nea is a regularized layer neuron with a minimum h Euclidean distance from the neuron, and STnea>＝2，c.nea、σ.neaAnd wneaThe center vector, width vector and weight of the network pruned neuron nea, c.nea(t)、σ.nea(t) and wnea(t) center vector, width vector and weight, w, of the pre-pruned neurons nea of the network trained to step t, respectivelyh(t) training to the tth step network pruning of the pre-neuronsWeight of h, vh(t) and vnea(t) outputs of the pre-net-pruning neuron h and the neuron nea trained to step t, respectively;
if it is not2＝<STh<1If the network structure is not changed, the network parameters are not adjusted;
④, the algorithm is shifted to step ① to continue to train parameters of the fuzzy neural network by using the adaptive second-order gradient descent algorithm, and when the training RMSE is 0.01 or the iteration of the algorithm exceeds 100 steps in the training process, the calculation is stopped;
(4) detecting the test sample; testing the trained second-order self-organizing fuzzy neural network by using the test sample, wherein the output of the second-order self-organizing fuzzy neural network is PM2.5The predicted result of (1).
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