CN106920007A - PM based on second order Self-organized Fuzzy Neural Network2.5Intelligent Forecasting - Google Patents

Abstract

PM based on second order Self-organized Fuzzy Neural Network_2.5Intelligent Forecasting both belongs to field of environment engineering, and detection technique field is belonged to again.PM_2.5Prediction difficulty it is larger, and neutral net has preferable disposal ability for nonlinearity and serious uncertain system.The present invention is directed to PM_2.5The problem predicted is difficult to, the air pollutants intelligent Forecasting based on second order Self-organized Fuzzy Neural Network is employed, PM is extracted first with principal component analytical method_2.5Characteristic variable, then set up characteristic variable and PM using second order Self-organized Fuzzy Neural Network_2.5Between soft-sensing model, to 24 hours PM afterwards_2.5Concentration is predicted.The method achieves preferable prediction effect, for environmental management department and the masses provide atmosphere quality information promptly and accurately, is conducive to preventing and treating air pollution in time, improves public life quality.

Description

PM based on second order Self-organized Fuzzy Neural Network2.5Intelligent Forecasting

Technical field

The present invention relates to PM_2.5Intelligent Forecasting, be the important branch in advanced manufacturing technology field, both belong to environment Engineering field, belongs to detection technique field again.Intelligent Forecasting is the feature by extracting complication system, sets up the soft of system Measurement model, the future trend to system is predicted.PM_2.5Prediction it is significant to prevention and cure of air pollution.Will intelligence Forecasting Methodology is applied to PM_2.5Prediction in, can in time obtain PM_2.5Concentration information, be conducive to strengthen air environmental pollution Control, while air pollution monitoring cost can be saved.Therefore, PM_2.5The application of intelligent Forecasting has far-reaching reality meaning Justice.

Background technology

The situation is tense for the atmosphere pollution of current China, the sky that industrial waste gas, motor-vehicle tail-gas, biomass and burning of coal are produced Gas pollutant accelerates the deterioration of air quality, causes with PM_2.5Etc. the regional atmospheric environment problem for being characterized pollutant increasingly Prominent, the harm public is healthy, influences weather, influence society and economic sustainable development, is unfavorable for《Basic ideas》Rank Section property target is reached.Therefore by PM_2.5Prediction, prevent severe contamination generation be subject to society extensive concern.So And, PM_2.5Concentration simultaneously influenceed by the features of terrain of emission source, pollutant, meteorological condition and survey region, and greatly compression ring Border system has the characteristics such as multivariable, non-linear, internal mechanism are complicated, information is incomplete, makes PM_2.5Prediction difficulty it is larger.Grind Study carefully effective PM_2.5Forecasting Methodology is to PM_2.5Carrying out accurately prediction becomes problem demanding prompt solution.As can be seen here, the present invention Achievement in research have broad application prospects.

Conventional PM_2.5Forecasting Methodology includes the chemistry modelization method and the statistical method based on data of Kernel-based methods.Chemistry Modeling method simulates generation, conveying, conversion and the infall process of pollutant, but models required model resolution, gas As the parameters such as boundary condition, emission inventory are difficult to determine, calculate complicated.Statistical method is divided into linearly building based on linear regression Mould method and the non-linear modeling method based on artificial neural network.Linear regression model (LRM) is not suitable for nonlinear big to itself Gas environmental system is modeled；Artificial neural network interpretation is poor；Compared to neutral net, combine neutral net and obscure The fuzzy neural network ability to express of system is stronger, but there is a problem of structure determination.Therefore, new PM is studied_2.5Prediction side Method has turned into the important topic of prevention and cure of air pollution area research, and significant.

For above PM_2.5Problem present in prediction, the present invention is proposed based on second order Self-organized Fuzzy Neural Network PM_2.5Intelligent Forecasting.The second order Self-organized Fuzzy Neural Network is true using the model output sensitivity analysis method on frequency domain Contribution rate of the fuzzy neural network regularization layer neuron output to network output is determined, according to contribution rate size additions and deletions regularization layer Neuron, the structure of adjust automatically fuzzy neural network is carried out with this, efficiently solves the Structure Designing Problem of fuzzy neural network, Analysis is contributed to produce PM_2.5Dynamic process.Meanwhile, rapid using convergence, the strong Adaptive Second-Order gradient of search capability declines The parameter of Algorithm for Training fuzzy neural network, it is to avoid First-order Gradient descent algorithm search capability is limited, during Genetic algorithm searching Between defect long, enhance fuzzy neural network to 24 hours PM afterwards_2.5The estimated performance of concentration.Become to remove redundancy The computational complexity of model is measured and reduces, the present invention is extracted and PM using principal component analytical method_2.5The maximum feature of relevance becomes Amount, it can be deduced that, the characteristic variable and research website PM of extraction_2.5The characteristics of concentration, matches, then using second order self-organizing mould Paste neural network PM_2.5Soft-sensing model, realizes to PM_2.5Accurate Prediction.

The content of the invention

Present invention obtains the PM based on second order Self-organized Fuzzy Neural Network_2.5Intelligent Forecasting：The method is sharp first Extracted and PM in multigroup measurable variable with principal component analytical method_2.5The maximum characteristic variable of relevance, then using second order certainly Tissue fuzzy neural network sets up characteristic variable and PM_2.5Between soft-sensing model, to the PM after 24 hours_2.5Concentration carries out pre- Survey, solve PM_2.5It is difficult to the problem predicted.

PM based on second order Self-organized Fuzzy Neural Network_2.5The design of intelligent Forecasting is comprised the following steps：

(1) signature analysis determines PM_2.5Characteristic variable.

Pasture regional atmospheric background monitoring station (117 ° 07 ' of east longitude, 40 ° 39 ' of north latitude, 287 meters of height above sea level) conduct is ground in selection Study carefully website.The website be located at the km of areas of Beijing northeastward 100 at, its circumference 30 kms in do not have intensive population distribution and Industrial area, the PM of the website_2.5Concentration is seriously influenceed by meteorological variables and is closely related with aerosol optical depth.With On January 14th, 2010 to the January 23 hour observation data of upper pasture monitoring station are experimental data of the invention, during this period, Upper pasture monitoring station occurs in that thick weather on 19th on January 16th, 2010 to January.Will be with PM_2.5Related meteorological variables and sky The hour data (not only including ground observation data but also including Satellite Observations) and 24 of gas pollutant and aerosol optical depth PM after hour_2.5Concentration data is corresponded, and rejects missing aerosol optical depth data and without corresponding PM_2.5Observation The data of the time period of value, finally sort out L group data, wherein, L values cross small data quantity not enough, bag between 150 to 250 Incomplete containing information, excessive calculating is excessively complicated.X=[x will be designated as the observation data matrix of principal component analysis₁,x₂,…, x₁₁], wherein x₁,x₂,…,x₁₁Represent that temperature, relative humidity, wind speed, wind direction, air pressure, visibility, aerosol optical are thick respectively Degree, CO, NO₂、O₃And SO₂The array of data of concentration.Predictive variable PM_2.5The array of data of concentration is designated as y.The unit of temperature is DEG C, the unit of wind speed is m/s, and the unit of wind direction is ° that the unit of air pressure is hPa, and the unit of visibility is km, and the unit of CO is Ppm, NO₂、O₃And SO₂Unit be ppb, PM_2.5Unit be μ g/m³, relative humidity represents with percentage, and aerosol optical is thick Spend no unit.Principal component analytical method is extracted and PM by following steps_2.5The maximum characteristic variable of relevance：

1. variable data is standardized：

Wherein, Z is the observation data matrix after standardization, x_ijAnd z_ijIt is respectively j-th i-th of variable before and after standardization Observation,And δ_jIt is respectively the average and standard deviation for standardizing preceding j-th variable, and

2. Z correlation matrixs R is calculated：

3. | the λ I-R |=0 that solve characteristic equation, obtain the characteristic value of R, and are arranged by descending order, are designated as λ₁,λ₂,…, λ₁₁, corresponding characteristic vector is designated as γ₁, γ₂,…,γ₁₁, Schmidt process is acted on into γ₁,γ₂,…,γ₁₁ To unit orthogonal eigenvectors γ '₁,γ'₂,…,γ'₁₁。

4. eigenvalue λ is calculated₁,λ₂,…,λ₁₁Accumulation contribution rate θ₁,θ₂,…,θ₁₁：

Wherein, λ_αAnd λ_βIt is respectively the α characteristic value and the β feature of correlation matrix R after being arranged according to descending Value.According to given extraction efficiency θ, if θ_N>=θ (N ＜ 11), then extract N number of principal component γ '₁,γ'₂,…,γ'_N, wherein, θ values are between 85%-95%, and too small extraction information is incomplete, excessive dimensionality reduction DeGrain.

5. the data that projections of the Z on the unit orthogonal eigenvectors for extracting obtains characteristic variable are calculated using formula (4).

Y=Z_γ' (4)

Wherein, γ '=[γ '₁,γ'₂,…,γ'_N].The characteristic variable of selection is designated as r=[r₁,r₂,…,r_N], it is two The input of rank Self-organized Fuzzy Neural Network, PM_2.5Used as predictive variable, its observation is second order Self-Fuzzy nerve to concentration The desired output of network, is designated as o.The observation data of the characteristic variable after standardization and predictive variable are randomly ordered, the row of selection , used as training sample, used as test sample, such training sample and test sample were both for rear I ' groups of data for preceding I groups data after sequence Observation data comprising thick weather include the observation data of non-thick weather again, wherein, I '=L-I, I '<=I.

(2) it is designed for PM_2.5The initial primary topology of the second order Self-organized Fuzzy Neural Network of prediction.For PM_2.5In advance Totally four layers of the second order Self-organized Fuzzy Neural Network of survey：Input layer, RBF layer, regularization layer and output layer.Input is the spy for extracting Variable is levied, output is PM_2.5The predicted value of concentration, is designated as p.Determine that the initial of second order Self-organized Fuzzy Neural Network N-M-M-1 connects Mode is connect, i.e. the number of input layer number and characteristic variable is both N, and RBF layers of neuron number is M, regularization layer neuron Number is M, and wherein M is positive integer, the value between [1,10], and avoid M values ambassador second order Self-organized Fuzzy Neural Network Calculated load is excessive, and output layer neuron number is 1.The center of second order Self-organized Fuzzy Neural Network, width and weights it is initial Value is set between (0,1), random setting, only influences the convergence rate of network, and the prediction effect of network is not influenceed.Kth The data of the characteristic variable of group training sample are expressed as r (k)=[r₁(k),r₂(k),…,r_N(k)] (k=1,2 ..., I), with During k groups training sample training second order Self-organized Fuzzy Neural Network, its each layer output is followed successively by：

1. input layer：The layer has N number of neuron：

u_d(k)=r_d(k), d=1,2 ..., N (5)

Wherein, u_dK () is the output of d-th neuron of input layer, the input vector of this layer is r (k)=[r₁(k),r₂ (k),…,r_N(k)]。

2. RBF layers：The Gaussian function that the layer choosing takes RBF neurons is carried out at obfuscation as membership function to input variable Reason.RBF layers has M neuron, the output of q-th neuron of this layerFor：

Wherein, c_dqAnd σ_dqIt is respectively center and the width of second order Self-organized Fuzzy Neural Network.

3. regularization layer：This layer of neuron number is identical with RBF layers, the output v of l-th neuron of this layer_lK () is：

Wherein,It is the RBF layers of output of l-th neuron.

4. output layer：The layer has 1 neuron, and the output of this layer represents PM_2.5The predicted value of concentration, is shown below：

Wherein, w_lIt is the connection weight between regularization l-th neuron of layer and output layer neuron.Second order self-organizing mould Paste neutral net training root-mean-square error (RMSE) be：

Wherein, p (k) and o (k) are respectively nets when second order Self-organized Fuzzy Neural Network is trained with kth group training sample Network is exported and desired output, and the purpose for training second order Self-organized Fuzzy Neural Network is that the training RMSE for defining formula (9) reaches Desired value.

(3) second order Self-organized Fuzzy Neural Network is trained using training sample.In the training process, using the mould on frequency domain Type output sensitivity analysis method determines contribution rate of the fuzzy neural network regularization layer neuron output to network output, according to Contribution rate size additions and deletions regularization layer neuron, the structure of adjust automatically fuzzy neural network is carried out with this, and parsing produces PM_2.5's Dynamic process.Meanwhile, in order to 24 hours PM afterwards_2.5Concentration carries out Accurate Prediction, is declined using Adaptive Second-Order gradient and calculated The center of method Training Fuzzy Neural Networks, width and weights.Specially：

1. the parameter of initial fuzzy neural network is given using the training of Adaptive Second-Order gradient descent algorithm：

Φ (t+1)=Φ (t)+(Q (t)+μ (t) I)^-1g(t) (10)

Wherein, t is current train epochs, and Φ (t+1) and Φ (t) is respectively that training obscures god when being walked to t+1 steps and t Through the parameter of network, and Φ (t)=[c₁₁(t)…c_NM(t),σ₁₁(t)…σ_NM(t),w₁(t)…w_M(t)].μ (t) is learning rate, In order to avoid the value of μ (t) is fixed, μ (t)=| | g (t) | | is made, make its adaptive change in the training process.I is unit matrix. Intend Hessian matrix Q (t) and gradient vector g (t) is expressed as：

Wherein, P_k(t)、η_k(t)、J_k(t) and e_k(t) respectively be training to t walk when corresponding to kth group training sample Sub- Hessian matrix, sub- gradient vector, the row vector of Jacobian matrix and error.J_k(t) and e_kT () is expressed as：

e_k(t)=o_k(t)-p_k(t) (14)

Wherein, o_k(t) and p_k(t) be respectively training to t walk when the corresponding observation of kth group training sample and predicted value. Repetition training is carried out to I groups training sample using formula (10).

2. using Adaptive Second-Order gradient descent algorithm to the parameter training of fuzzy neural network after ξ steps, using formula (15) in a frequency domain computation ruleization layer the h-th output v of neuron_hThe contribution rate ST of p is exported to network_h(h=1,2 ..., M), wherein, ξ values between 5-15 are too small inadequate to fuzzy neural network regularization layer neuron output information collection, excessive Structural adjustment efficiency can be reduced.

Wherein, S_hIt is v_hTo total susceptibility of p, S_nIt is total susceptibilitys of the regularization n-th output vn of neuron of layer to p, A_ωAnd B_ωAndWithIt is respectively Fourier expansion formula f (s) of p in frequencies omega and ω_hThe Fourier coefficient at place, andω_hIt is v_hFundamental frequency, max (ω_~h) it is except v_hIt The maximum of the fundamental frequency of outer strictly all rulesization layer neuron output, takes ω_h=2Hmax (ω_~h), H is interference factor, Wen Zhongqu Value is 4, and too small Fourier's amplitude extraction is not complete, and crossing conference increases algorithm complexity, f (s) and v_hFormula (17) and formula are used respectively (18) represent：

Wherein, a_hAnd b_hIt is respectively v_hMinimum value and maximum.

If 3. ST_h>=ε₁, then splitting ruleization layer h-th neuron, wherein, ε₁=0.3, ε₁It is excessive to cause regularization Layer neuron output contribution rate distribution is uneven, and network structure is excessively simplified, too small to cause regularization layer neuron redundancy.In order to drop Influence of the low network structure regulation to network error, the initial parameter of the new neuron obtained using following formula setting division：

Wherein, new1 and new2 are two new neurons, c._new1、σ._new1And w_new1Respectively in neuron new1 Heart vector, width vector sum weights.c._new2、σ._new2And w_new2It is respectively center vector, the width vector sum power of neuron new2 Value.c._h(t)、σ._h(t) and w_h(t) be respectively training to the center vector of neuron h, width before t step network structure regulations to Amount and weights, τ obey standardized normal distribution.

If ST_h<ε₂, the neuron is deleted, while being adjusted to network parameter, it is shown below, wherein, ε₂= 0.05, ε₂It is excessive to cause regularization layer neuron to be deleted excessively, it is too small to cause the complicated network structure.

Wherein, neuron nea is the regularization layer neuron minimum with neuron h Euclidean distances, and ST_nea>=ε₂, c._nea、σ._neaAnd w_neaIt is respectively center vector, the width vector sum weights, c. of neuron nea after network cut_nea(t)、σ._nea (t) and w_neaT () is respectively center vector, width vector sum weights, w of the training to neuron nea before t step network cuts_h T () is weights of the training to neuron h before t step network cuts, v_h(t) and v_neaT () is respectively that training is repaiied to t step networks Cut the output of preceding neuron h and neuron nea.

If ε₂=<ST_h<ε₁, then network structure is constant, and network parameter is not adjusted.

1. 4. algorithm branches step continued with the ginseng of Adaptive Second-Order gradient descent algorithm Training Fuzzy Neural Networks Number.RMSE is trained in training process is walked at certain<=0.01 or algorithm iteration stop calculating when having exceeded 100 step.

(4) test sample is detected.The second order Self-organized Fuzzy Neural Network for training is entered using test sample Row test, the output of second order Self-organized Fuzzy Neural Network is PM_2.5Predict the outcome.

Creativeness of the invention is mainly reflected in：

(1) present invention is directed to PM_2.5Concentration is difficult to predict, the problems such as traditional chemistry modelization Method Modeling is difficult, it is proposed that PM based on second order Self-organized Fuzzy Neural Network_2.5Intelligent Forecasting.The second order Self-organized Fuzzy Neural Network can basis Sensitivity analysis method automatic mechanism, helps to analyze PM_2.5The dynamic process of generation, meanwhile, using Adaptive Second-Order ladder The lower decreasing concentration algorithm of degree adjusts the parameter of fuzzy neural network, enhances to 24 hours PM afterwards_2.5The estimated performance of concentration, solution Determined PM_2.5The larger problem of concentration prediction difficulty.

(2) above pasture of the present invention is research website, and the data of selection had not only included ground observation data but also seen including satellite Data are surveyed, in order to remove redundant variables, is extracted based on principal component analytical method and PM_2.5The maximum characteristic variable of relevance, finally The characteristic variable of extraction and upper pasture PM_2.5The concentration characteristic closely related with meteorological variables and aerosol optical depth matches.

It is important to note that：Present invention determine that PM_2.5The input variable of Forecasting Methodology, as long as using related change of the invention Amount and principle of the invention carry out PM_2.5Prediction should all belong to the scope of the present invention.

Brief description of the drawings

Fig. 1 is PM of the invention_2.5Intelligent Forecasting flow chart.

Fig. 2 is the satellite map of upper pasture observation station of the invention.

Fig. 3 is PM of the invention_2.5Training RMSE variation diagram of the soft-sensing model for standardized data.

Fig. 4 is PM of the invention_2.5Soft-sensing model structure change figure in the training process.

Fig. 5 is PM of the invention_2.5Soft-sensing model trains scatter diagram.

Fig. 6 is PM of the invention_2.5Soft-sensing model training error figure.

Fig. 7 is PM of the invention_2.5Soft-sensing model tests scatter diagram.

Fig. 8 is PM of the invention_2.5Soft-sensing model test error figure.

Specific embodiment

Present invention obtains the PM based on second order Self-organized Fuzzy Neural Network_2.5Intelligent Forecasting.The method is with PM_2.5 It is output, is input with the characteristic variable extracted by principal component analytical method, is built using second order Self-organized Fuzzy Neural Network Vertical PM_2.5Soft-sensing model, to 24 hours PM afterwards_2.5Concentration is predicted.The flow chart of the intelligent Forecasting such as Fig. 1 institutes Show.

Regional atmospheric background monitoring station in pasture is research website in selection, and its satellite map is as shown in Figure 2.With the website The hour observation data on January 14th, 2010 to January 23 are experimental data.Reject missing aerosol optical depth data and lack Few corresponding PM_2.5The data of the time period of observation, by meteorological variables and air pollutants and aerosol optical depth hourage According to 24 hours PM afterwards_2.5Concentration data is corresponded, and 182 groups of data, L=182 are sorted out altogether.For signature analysis Observation data matrix is designated as X=[x₁,x₂,…,x₁₁], wherein x₁,x₂,…,x₁₁Temperature, relative humidity, wind speed, wind are represented respectively To, air pressure, visibility, aerosol optical depth, CO, NO₂、O₃And SO₂The array of data of concentration.Predictive variable PM_2.5Concentration Array of data is designated as y.

PM based on second order Self-organized Fuzzy Neural Network_2.5The design of intelligent Forecasting is comprised the following steps：

(1) signature analysis determines PM_2.5Characteristic variable.Principal component is carried out to observation data matrix X using formula (1)-formula (4) Analysis, the value for setting extraction efficiency θ is 90%.The contribution rate and accumulation contribution rate of each principal component (PC) are as shown in table 1：

The principal component contributor rate of table 1. and accumulation contribution rate

As can be drawn from Table 1, the accumulation contribution rate of preceding 5 principal components has exceeded 90%, therefore extracts 5 principal components, the value of N It is 5.The corresponding temperature of 5 principal components being extracted, relative humidity, wind speed, wind direction, air pressure, visibility, aerosol optical are thick Degree, CO, NO₂、O₃And SO₂Shown in the coefficient of concentration such as formula (21)：

Variable in the principal component that selection formula (21) is represented corresponding to the coefficient of maximum absolute value is obtained final product and PM_2.5Relevance Maximum characteristic variable：Relative humidity, air pressure, aerosol optical depth, wind speed and direction.As can be seen that the feature extracted becomes Amount and upper pasture PM_2.5The concentration characteristic closely related with meteorological variables and aerosol optical depth matches.The feature that will be extracted Variable is designated as r=[r₁,r₂,…,r₅], PM_2.5Used as predictive variable, its observation is second order Self-organized Fuzzy Neural Network to concentration Desired output, be designated as o.The observation data of the characteristic variable after standardization and predictive variable are randomly ordered, after choosing sequence Preceding 130 groups of data as training sample, 52 groups of data are used as test sample (I=130, I '=52) afterwards.

(2) initialize for PM_2.5The second order Self-organized Fuzzy Neural Network of prediction.The present invention is used for PM_2.5The two of prediction Totally four layers of rank Self-organized Fuzzy Neural Network：Input layer, RBF layer, regularization layer and output layer.Extraction knot according to characteristic variable Really, using relative humidity, air pressure, aerosol optical depth, wind speed and direction as input, PM_2.5Concentration determines two as output The input layer number of rank Self-organized Fuzzy Neural Network is 5, and output layer neuron number is that 1, RBF layers and regularization layer are initial Neuron number M is set as that the initial connected mode of 3, i.e. second order Self-organized Fuzzy Neural Network is 5-3-3-1.Second order self-organizing mould Center, width and the weights tax initial value for pasting neutral net are the pseudo random number on (0,1).With kth (k=1,2 ..., 130) group instruction When practicing sample training second order Self-organized Fuzzy Neural Network, the output of its each layer is calculated according to formula (5)-formula (8),

(3) second order Self-organized Fuzzy Neural Network is trained using training sample.In the training process, using the mould on frequency domain Type output sensitivity analysis method determines contribution rate of the fuzzy neural network regularization layer neuron output to network output, point The big regularization layer neuron of contribution rate is split, the small regularization layer neuron of contribution rate is deleted, the fuzzy god of adjust automatically is come with this Through the structure of network, and using the center of Adaptive Second-Order gradient descent algorithm Training Fuzzy Neural Networks, width and weights.Tool Body is：

1. initial fuzzy neural network is given using training sample and the training of Adaptive Second-Order gradient descent algorithm, according to formula (10) center to fuzzy neural network, width and weights are updated repeatedly.

2. found out after the step of parameter repetition training 10 using Adaptive Second-Order gradient descent algorithm to fuzzy neural network every One regularization layer neuron output v_hMaximum b_hWith minimum value a_h, interference factor H=4 is taken, calculate v using formula (15)_hIt is right Network exports the contribution rate ST of p_h。

If 3. ST_h>=ε₁=0.3, then line splitting is entered to regularization h-th neuron of layer.Adjusted to reduce network structure The whole influence to network error, two centers of new neuron, width and the weights obtained using formula (19) setting division.Such as Fruit ST_h<ε₂=0.05, the neuron is deleted, while adjusting network parameter using formula (20).If ε₂=<ST_h<ε₁, then network knot Structure is constant, and network parameter is not adjusted.

1. 4. algorithm branches step continued with the ginseng of Adaptive Second-Order gradient descent algorithm Training Fuzzy Neural Networks Number.RMSE is trained in training process is walked at certain<=0.01 or algorithm iteration more than 100 step when stop calculate.

(4) test sample is detected.Using test sample as the second order Self-organized Fuzzy Neural Network for training Input, the output of second order Self-organized Fuzzy Neural Network is PM_2.5Predict the outcome.

Fig. 3 is PM_2.5Soft-sensing model trains RMSE variation diagrams.Fig. 4 is PM_2.5Soft-sensing model training process structure change Figure.Fig. 5 is PM_2.5Soft-sensing model trains scatter diagram, X-axis：PM_2.5Training observation value (μ g/m³), Y-axis：PM_2.5Soft-sensing model Training predicted value (μ g/m³).Fig. 6 is PM_2.5Soft-sensing model training error figure.Fig. 7 is PM_2.5Soft-sensing model tests scatterplot Figure, X-axis：PM_2.5Test observation (μ g/m³), Y-axis：PM_2.5Soft-sensing model test predicted value (μ g/m³).Fig. 8 is PM_2.5Soft survey Amount model measurement Error Graph.

Table 2-21 is experimental data of the invention, and table 2-7 is monitored parameterses temperature, visibility, CO, NO₂、O₃And SO₂Concentration Observation, table 8-13 is training sample, and table 14 is PM_2.5The training predicted value of soft-sensing model, table 15-20 is test sample, Table 21 is PM_2.5The test predicted value of soft-sensing model.

The observation (DEG C) of the monitored parameterses temperature of table 2.

The observation (km) of the monitored parameterses visibility of table 3.

The observation (ppm) of the monitored parameterses CO of table 4.

The monitored parameterses NO of table 5.₂Observation (ppb)

The observation (ppb) of the monitored parameterses O3 of table 6.

The monitored parameterses SO of table 7.₂Observation (ppb)

Training sample：

The training observation value (%) of the characteristic variable relative humidity of table 8.

The training observation value (hPa) of the characteristic variable air pressure of table 9.

The training observation value of the characteristic variable aerosol optical depth of table 10.

The training observation value (m/s) of the characteristic variable wind speed of table 11.

Training observation value (°) of the characteristic variable wind direction of table 12.

The predictive variable PM of table 13._2.5Training observation value (μ g/m³)

The predictive variable PM of table 14._2.5Training predicted value (μ g/m³)

Test sample：

The test observation (%) of the characteristic variable relative humidity of table 15.

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

The test observation (hPa) of the characteristic variable air pressure of table 16.

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

The test observation of the characteristic variable aerosol optical depth of table 17.

0.95	0.24	0.18	0.32	0.11	0.59	0.16	0.10	1.03	1.08
										0.88	0.67	0.39	0.22	0.30	0.47	0.14	0.89	0.61	1.07
0.18	0.50	0.94	0.75	0.35	1.15	0.71	0.24	0.85	0.40
										0.33	0.63	0.20	0.86	0.83	0.99	0.23	0.80	0.73	1.03
1.00	1.29	0.57	0.13	0.87	1.18	0.25	0.21	0.36	0.15
										0.95	0.34

The test observation (m/s) of the characteristic variable wind speed of table 18.

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

Test observation (°) of the characteristic variable wind direction of table 19.

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

The predictive variable PM of table 20._2.5Test observation (μ g/m³)

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

The predictive variable PM of table 21._2.5Test predicted value (μ g/m³)

Claims (1)

1. the PM of second order Self-organized Fuzzy Neural Network is based on_2.5Intelligent Forecasting, it is characterised in that comprise the following steps：

(1) signature analysis determines PM_2.5Characteristic variable；

Will be with PM_2.5The hour data of related meteorological variables and air pollutants and aerosol optical depth and 24 hours are afterwards PM_2.5Concentration data is corresponded, and rejects missing aerosol optical depth data and without corresponding PM_2.5The time of observation The data of section, finally sort out L group data, wherein, L values are between 150 to 250；By for the observation number of principal component analysis X=[x are designated as according to battle array₁,x₂,…,x₁₁], wherein x₁,x₂,…,x₁₁Respectively represent temperature, relative humidity, wind speed, wind direction, air pressure, Visibility, aerosol optical depth, CO, NO₂、O₃And SO₂The array of data of concentration；Predictive variable PM_2.5The array of data of concentration It is designated as y；The unit of temperature is DEG C, and the unit of wind speed is m/s, and the unit of wind direction is ° that the unit of air pressure is hPa, the list of visibility Position is km, and the unit of CO is ppm, NO₂、O₃And SO₂Unit be ppb, PM_2.5Unit be μ g/m³, relative humidity percentage Represent, aerosol optical depth does not have unit；Principal component analytical method is extracted and PM by following steps_2.5Relevance maximum Characteristic variable：

1. variable data is standardized：

$Z={\left(z_{ij}\right)}_{L\&times;11}={\left(\frac{x_{ij}-{\stackrel{\&OverBar;}{x}}_j}{{\mathrm{\&delta;}}_j}\right)}_{L\&times;11},i=1,2,...,L;j=1,2,...,11---\left(1\right)$

Wherein, Z is the observation data matrix after standardization, x_ijAnd z_ijIt is respectively j-th i-th observation of variable before and after standardization Value,And δ_jBe respectively standardize preceding j-th variable average and standard deviation and

${\stackrel{\&OverBar;}{x}}_j=\frac{1}{L}{\mathrm{\&Sigma;}}_{i=1}^L{x}_{ij},{\mathrm{\&delta;}}_j=\sqrt{\frac{1}{L-1}{\mathrm{\&Sigma;}}_{i=1}^L{(x_{ij}-{\stackrel{\&OverBar;}{x}}_j)}^2};$

2. Z correlation matrixs R is calculated：

$R=\frac{1}{L}{Z}^{T}Z---\left(2\right)$

3. | the λ I-R |=0 that solve characteristic equation, obtain the characteristic value of R, and are arranged by descending order, are designated as λ₁,λ₂,…,λ₁₁, Corresponding characteristic vector is designated as γ₁,γ₂,…,γ₁₁, Schmidt process is acted on into γ₁,γ₂,…,γ₁₁Obtain list Position orthogonal eigenvectors γ '₁,γ'₂,…,γ′₁₁；

4. eigenvalue λ is calculated₁,λ₂,…,λ₁₁Accumulation contribution rate θ₁,θ₂,…,θ₁₁：

${\mathrm{\&theta;}}_i=\frac{{\mathrm{\&Sigma;}}_{\mathrm{\&alpha;}=1}^i{\mathrm{\&lambda;}}_{\mathrm{\&alpha;}}}{{\mathrm{\&Sigma;}}_{\mathrm{\&beta;}=1}^{11}{\mathrm{\&lambda;}}_{\mathrm{\&beta;}}},i=1,2,...,11---\left(3\right)$

Wherein, λ_αAnd λ_βIt is respectively the α characteristic value and the β characteristic value of correlation matrix R after being arranged according to descending；Root According to given extraction efficiency θ, if θ_N>=θ (N ＜ 11), then extract N number of principal component γ '₁,γ'₂,…,γ'_N, wherein, θ values Between 85%-95%；

5. the data that projections of the Z on the unit orthogonal eigenvectors for extracting obtains characteristic variable are calculated using formula (4)；

Y=Z γ ' (4)

Wherein, γ '=[γ '₁,γ'₂,…,γ'_N]；The characteristic variable of selection is designated as r=[r₁,r₂,…,r_N], be second order from Organize the input of fuzzy neural network, PM_2.5Used as predictive variable, its observation is second order Self-organized Fuzzy Neural Network to concentration Desired output, be designated as o；The observation data of the characteristic variable after standardization and predictive variable are randomly ordered, after choosing sequence Preceding I groups data as training sample, used as test sample, such training sample and test sample be not comprising for rear I ' groups of data With the observation data in the case of weather, wherein, I '=L-I, I '<=I；

(2) it is designed for PM_2.5The initial primary topology of the second order Self-organized Fuzzy Neural Network of prediction；For PM_2.5Prediction Totally four layers of second order Self-organized Fuzzy Neural Network：Input layer, RBF layer, regularization layer and output layer；Input is that the feature extracted becomes Amount, output is PM_2.5The predicted value of concentration, is designated as p；Determine the initial connection side of second order Self-organized Fuzzy Neural Network N-M-M-1 Formula, the i.e. number of input layer number and characteristic variable is both N, and RBF layers of neuron number is M, and regularization layer neuron number is M, wherein M are positive integers, and the value between [1,10], output layer neuron number is 1；In second order Self-organized Fuzzy Neural Network The initial value of the heart, width and weights is set between (0,1) at random；The data of the characteristic variable of kth group training sample are expressed as r (k)=[r₁(k),r₂(k),…,r_N(k)] (k=1,2 ..., I), train second order Self-Fuzzy nerve with kth group training sample During network, its each layer output is followed successively by：

1. input layer：The layer has N number of neuron：

u_d(k)=r_d(k), d=1,2 ..., N (5)

Wherein, u_dK () is the output of d-th neuron of input layer, the input vector of this layer is r (k)=[r₁(k),r₂(k),…, r_N(k)]；

2. RBF layers：The Gaussian function that the layer choosing takes RBF neurons carries out Fuzzy processing as membership function to input variable； RBF layers has M neuron, the output of q-th neuron of this layerFor：

Wherein, c_dqAnd σ_dqIt is respectively center and the width of second order Self-organized Fuzzy Neural Network；

3. regularization layer：This layer of neuron number is identical with RBF layers, the output v of l-th neuron of this layer_lK () is：

Wherein,It is the RBF layers of output of l-th neuron；

4. output layer：The layer has 1 neuron, and the output of this layer represents PM_2.5The predicted value of concentration, is shown below：

$p\left(k\right)={\mathrm{\&Sigma;}}_{l=1}^M{w}_l{v}_l\left(k\right),l=1,2,...,M---\left(8\right)$

Wherein, w_lIt is the connection weight between regularization l-th neuron of layer and output layer neuron；Second order Self-Fuzzy god Training root-mean-square error (RMSE) through network is：

$RMSE=\sqrt{\frac{{\mathrm{\&Sigma;}}_{k=1}^I{\left(p\right(k)-o(k\left)\right)}^2}{I}}---\left(9\right)$

Wherein, p (k) and o (k) are respectively to train network during second order Self-organized Fuzzy Neural Network defeated with kth group training sample Go out and desired output, the purpose for training second order Self-organized Fuzzy Neural Network is that the training RMSE for defining formula (9) reaches expectation Value；

(3) second order Self-organized Fuzzy Neural Network is trained with training sample；In the training process, exported using the model on frequency domain Sensitivity analysis method determines contribution rate of the fuzzy neural network regularization layer neuron output to network output, according to contribution rate Size additions and deletions regularization layer neuron, the structure of adjust automatically fuzzy neural network is carried out with this, and parsing produces PM_2.5Dynamic mistake Journey；Meanwhile, using the center of Adaptive Second-Order gradient descent algorithm Training Fuzzy Neural Networks, width and weights, specially：

1. the parameter of initial fuzzy neural network is given using the training of Adaptive Second-Order gradient descent algorithm：

Φ (t+1)=Φ (t)+(Q (t)+μ (t) I)^-1g(t) (10)

Wherein, t is current train epochs, and Φ (t+1) and Φ (t) is respectively training to fuzznet when t+1 steps and t steps The parameter of network, and Φ (t)=[c₁₁(t)…c_NM(t),σ₁₁(t)…σ_NM(t),w₁(t)…w_M(t)]；μ (t) is learning rate, in order to Avoid the value of μ (t) from fixing, make μ (t)=| | g (t) | |, make its adaptive change in the training process；I is unit matrix；Intend sea Gloomy matrix Q (t) and gradient vector g (t) are expressed as：

$Q\left(t\right)={\mathrm{\&Sigma;}}_{k=1}^I{P}_k\left(t\right),P_k\left(t\right)=J_k^T\left(t\right)J_k\left(t\right)---\left(11\right)$

$g\left(t\right)={\mathrm{\&Sigma;}}_{k=1}^I{\mathrm{\&eta;}}_k\left(t\right),{\mathrm{\&eta;}}_k\left(t\right)=J_k^T\left(t\right)e_k\left(t\right)---\left(12\right)$

Wherein, P_k(t)、η_k(t)、J_k(t) and e_k(t) respectively be training to t walk when corresponding to kth group training sample sub- Hai Sen Matrix, sub- gradient vector, the row vector of Jacobian matrix and error；J_k(t) and e_kT () is expressed as：

$J_k\left(t\right)=\&lsqb;\frac{\&part;e_k\left(t\right)}{\&part;c_{11}\left(t\right)}...\frac{\&part;e_k\left(t\right)}{\&part;c_{NM}\left(t\right)},\frac{\&part;e_k\left(t\right)}{\&part;{\mathrm{\&sigma;}}_{11}\left(t\right)}...\frac{\&part;e_k\left(t\right)}{\&part;{\mathrm{\&sigma;}}_{NM}\left(t\right)},\frac{\&part;e_k\left(t\right)}{\&part;w_1\left(t\right)}...\frac{\&part;e_k\left(t\right)}{\&part;w_M\left(t\right)}\&rsqb;---\left(13\right)$

e_k(t)=o_k(t)-p_k(t) (14)

Wherein, o_k(t) and p_k(t) be respectively training to t walk when the corresponding observation of kth group training sample and predicted value；Utilize Formula (10) carries out repetition training to I groups training sample；

2. the parameter training of fuzzy neural network after ξ steps, is existed using formula (15) using Adaptive Second-Order gradient descent algorithm The h-th output v of neuron of regularization layer is calculated in frequency domain_hThe contribution rate ST of p is exported to network_h(h=1,2 ..., M), wherein, ξ values between 5-15；

${\mathrm{ST}}_h=\frac{S_h}{{\mathrm{\&Sigma;}}_{n=1}^M{S}_n}---\left(15\right)$

$S_h=\frac{A_{{\mathrm{\&omega;}}_h}^2+B_{{\mathrm{\&omega;}}_h}^2}{\left(A_{{\mathrm{\&omega;}}_h}^2+B_{{\mathrm{\&omega;}}_h}^2\right)+{\mathrm{\&Sigma;}}_{\mathrm{\&omega;}=1}^{\max \left({\mathrm{\&omega;}}_{~h}\right)}\left(A_{\mathrm{\&omega;}}^2+B_{\mathrm{\&omega;}}^2\right)}---\left(16\right)$

Wherein, S_hIt is v_hTo total susceptibility of p, S_nIt is the n-th output v of neuron of regularization layer_nTo total susceptibility of p, A_ωWith B_ωAndWithIt is respectively Fourier expansion formula f (s) of p in frequencies omega and ω_hThe Fourier coefficient at place, andω_hIt is v_hFundamental frequency, max (ω_~h) it is except v_hIt The maximum of the fundamental frequency of outer strictly all rulesization layer neuron output, takes ω_h=2Hmax (ω_~h), H is interference factor, Wen Zhongqu Value is 4；F (s) and v_hRepresented with formula (17) and formula (18) respectively：

$f\left(s\right)={\mathrm{\&Sigma;}}_{\mathrm{\&omega;}=-\mathrm{\&infin;}}^{\mathrm{\&infin;}}\left(A_{\mathrm{\&omega;}}cos\right(\mathrm{\&omega;}s)+B_{\mathrm{\&omega;}}sin(\mathrm{\&omega;}s\left)\right)---\left(17\right)$

$v_h\left(s\right)=\frac{b_h+a_h}{2}+\frac{b_h-a_h}{\mathrm{\&pi;}}\arcsin \left(sin\right({\mathrm{\&omega;}}_{h}s)---\left(18\right)$

Wherein, a_hAnd b_hIt is respectively v_hMinimum value and maximum；

If 3. ST_h>=ε₁, then splitting ruleization layer h-th neuron, wherein, ε₁=0.3；In order to reduce network structure regulation Influence to network error, the initial parameter of the new neuron obtained using following formula setting division：

$\left\{\begin{array}{c}{c}_{\&CenterDot;new1}=c_{\&CenterDot;new2}=c_{\&CenterDot;h}\left(t\right)\\ {\mathrm{\&sigma;}}_{\&CenterDot;new1}={\mathrm{\&sigma;}}_{\&CenterDot;new2}={\mathrm{\&sigma;}}_{\&CenterDot;h}\left(t\right)\\ w_{new1}={\mathrm{\&tau;w}}_h\left(t\right),w_{new2}=(1-\mathrm{\&tau;})w_h\left(t\right)\end{array}\right.---\left(19\right)$

Wherein, new1 and new2 are two new neurons, c._new1、σ._new1And w_new1Be respectively neuron new1 center to Amount, width vector sum weights；c._new2、σ._new2And w_new2It is respectively center vector, the width vector sum weights of neuron new2； c._h(t)、σ._h(t) and w_hT () is respectively center vector, width vector of the training to neuron h before t step network structure regulations And weights, τ obedience standardized normal distributions；

If ST_h<ε₂, the neuron is deleted, while being adjusted to network parameter, it is shown below, wherein, ε₂=0.05；

$\left\{\begin{array}{c}{c}_{\&CenterDot;nea}=c_{\&CenterDot;nea}\left(t\right)\\ {\mathrm{\&sigma;}}_{\&CenterDot;nea}={\mathrm{\&sigma;}}_{\&CenterDot;nea}\left(t\right)\\ w_{nea}=w_{nea}\left(t\right)+w_h\left(t\right)v_h\left(t\right)/v_{nea}\left(t\right)\end{array}\right.---\left(20\right)$

Wherein, neuron nea is the regularization layer neuron minimum with neuron h Euclidean distances, and ST_nea>=ε₂, c._nea、 σ._neaAnd w_neaIt is respectively center vector, the width vector sum weights, c. of neuron nea after network cut_nea(t)、σ._nea(t) and w_neaT () is respectively center vector, width vector sum weights, w of the training to neuron nea before t step network cuts_hT () is instruction Practice the weights of the neuron h to before t step network cuts, v_h(t) and v_neaT () is respectively training to nerve before t step network cuts The output of first h and neuron nea；

If ε₂=<ST_h<ε₁, then network structure is constant, and network parameter is not adjusted；

1. 4. algorithm branches step continued with the parameter of Adaptive Second-Order gradient descent algorithm Training Fuzzy Neural Networks；When RMSE is trained in certain step training process<=0.01 or algorithm iteration stop calculating when having exceeded 100 step；

(4) test sample is detected；The second order Self-organized Fuzzy Neural Network for training is surveyed using test sample Examination, the output of second order Self-organized Fuzzy Neural Network is PM_2.5Predict the outcome.