CN106126909A - PM2.5 concentration prediction method based on Unscented kalman neutral net - Google Patents

Abstract

The invention provides a kind of PM2.5 concentration prediction method based on Unscented kalman neutral net, comprise the steps: to obtain the historical data of PM2.5 concentration, recurrence calculation is carried out based on Unscented kalman neutral net, MATLAB simulation software is utilized to program, constantly carry out on-line prediction, constantly revise weights and threshold value, set up the Dynamic Evolution Model of PM2.5 concentration prediction, on the basis of obtaining Dynamic Evolution Model and prediction data, set up figure and regard change early warning, to reach the forewarning function after data prediction.For based on BP neural net model establishing, based on Unscented kalman neural net model establishing on predicting the outcome more accurate, error is less.

Description

PM2.5 concentration prediction method based on unscented Kalman neural network

Technical Field

The invention relates to the technical field of air quality prediction, in particular to a PM2.5 concentration prediction method based on an unscented Kalman neural network (UKFNN for short).

Background

PM2.5, fine particulate matter, is particulate matter having an aerodynamic equivalent diameter of less than or equal to 2.5 microns in ambient air, also known as respirable lung particulate matter. It can be suspended in air for a long time, and the higher its concentration in air, the more serious the air pollution. Compared with the atmospheric particulate matters with larger diameters, PM2.5 has small particle size, large surface area, strong activity, easy attachment of toxic and harmful substances, longer retention time in the atmosphere, long conveying distance and larger influence on human health and atmospheric environment. It can cause diseases of bronchus, cardiovascular and respiratory tract, damage the oxygen conveying capacity of hemoglobin, even cause pathological changes in human body and induce cancer. Simultaneously, because the particulate matter in the atmosphere is to the scattering and the absorption of light, can show to weaken light signal, reduce effective stadia by a wide margin to make visibility in the air reduce, produce haze weather, bring inconvenience and harm to people's daily life. Therefore, monitoring of PM2.5 and studying of the concentration change thereof are important.

Disclosure of Invention

The application provides a PM2.5 concentration prediction method based on an unscented Kalman neural network, so as to solve the technical problems of inaccurate PM2.5 concentration prediction and large error in the prior art.

In order to solve the technical problems, the application adopts the following technical scheme:

a PM2.5 concentration prediction method based on an unscented Kalman neural network comprises the following steps:

s1: acquiring historical data of PM2.5 concentration;

s2: carrying out recursion operation by using an unscented Kalman neural network, and circularly correcting the weight and the threshold of the neural network by continuously carrying out online prediction to realize prediction of the PM2.5 concentration chaotic time sequence so as to establish a dynamic evolution model for predicting the PM2.5 concentration:

is provided with an N-layer forward neural network, and the number of neurons in each layer is S_k(k is 1,2, …, N), the input layer is the first layer, the output layer is the nth layer, and the connection weights for the k layer neurons are(i＝1,2,…,S_k-₁，j＝1,2,…,S_k) Taking the weight w and the threshold b of the neural network as state variables of unscented kalman filtering, taking the output of the neural network as a measurement variable of the unscented kalman filtering, and forming a state vector by all the weights and the thresholds in the neural network:

$X={\[w_{11}^1...w_{s_1{s}_2}^1{w}_{11}^2...w_{s_1{s}_2}^2{b}_{11}^1{w}_{11}^{N-1}...w_{s_1{s}_2}^{N-1}{b}_1^1....b_{s_1}^1{b}_1^2....b_{s_2}^2{b}_1^{N-1}....b_{s_{n-1}}^{N-1}\]}^T,$

the state equation and observation equation for the system can be expressed as:

$\left\{\begin{array}{c}{X}_k=X_{k-1}\\ Y_{ek}=h(W_k,X_k)+V_k=F^N(W_k^N,F^{N-1}(W_k^{N-1}...F^2(W_k^2,X_k)\left)\right)+V_k\end{array}\right.$

in the formula, h (-) is a nonlinear transformation, F^NIs the N layer transfer function of the neural network, Y_ekTo desired output, X_kAs an input vector, V_kTo observe noise, it is random white noise, set to 0 in unscented kalman neural network;

the time is updated as: predicted state variable X from time k-1 to time k_k/k-1＝AX_kA^TPrediction error covariance matrix P from time k-1 to time k_k/k-1＝AP_kA^TWherein A is [1 ]]，P_kThe covariance matrix at the k moment;

the measurement is updated as: computing kalman filter gainIn the formula, K_kA filter gain matrix for time k, P_k/k-1Is a prediction error mean square error matrix from time k-1 to time k, H_kIs the observation matrix at time k, R_kVariance matrix of the measured noise sequence at time k, R_k＝[0.01]；

Updating state variable X with measured values_k＝X_k/k-1+K_k(y(k)^T-H_k) In the formula, y (k)^TTo the desired output, H_kOutputting for network training;

updating an error covariance matrix P_k＝(I-K_kH_k)P_k/k-1Wherein, the identity matrix I ═ diag (1);

s3: and predicting the concentration of the PM2.5 by using a dynamic evolution model of the concentration value of the PM 2.5.

In order to clearly and vividly display the predicted PM2.5 concentration value, as a preferred technical solution, the present invention further includes step S4: the PM2.5 concentration predicted in step S3 is displayed by a table and/or a map visualization warning map.

Compared with the prior art, the technical scheme that this application provided, the technological effect or advantage that have are: the method predicts the concentration of the PM2.5 particles, enables people to know the distribution of the PM2.5 particles in advance, brings convenience to travel and life of people, and has extremely important significance in preventing and treating air pollution and preventing diseases of people.

Drawings

FIG. 1 is a comparative graph of the actual value of a PM2.5 concentration prediction dynamic evolution model based on UKFNN and a training value;

FIG. 2 is an error curve diagram of prediction of a UKFNN-based PM2.5 concentration prediction dynamic evolution model;

FIG. 3 is a graph of the error percentage predicted by a UKFNN-based PM2.5 concentration prediction dynamic evolution model;

FIG. 4 is a graph showing the comparison between the true values and the training values of the UKFNN model and the BPNN model;

FIG. 5 is a graph of the comparison of training errors in the UKFNN model and the BPNN model;

fig. 6 is a PM2.5 concentration warning diagram.

Detailed Description

The embodiment of the application provides a PM2.5 concentration prediction method based on an unscented Kalman neural network, so as to solve the technical problems of inaccuracy in PM2.5 concentration prediction and large error in the prior art.

In order to better understand the technical solutions, the technical solutions will be described in detail below with reference to the drawings and specific embodiments.

Examples

A PM2.5 concentration prediction method based on an unscented Kalman neural network comprises the following steps:

s1: acquiring historical data of PM2.5 concentration;

s2: carrying out recursion operation by using an unscented Kalman neural network, and circularly correcting the weight and the threshold of the neural network by continuously carrying out online prediction to realize prediction of the PM2.5 concentration chaotic time sequence so as to establish a dynamic evolution model for predicting the PM2.5 concentration:

is provided with an N-layer forward neural network, and the number of neurons in each layer is S_k(k is 1,2, …, N), the input layer is the first layer, the output layer is the nth layer, and the connection weights for the k layer neurons are(i＝1,2,…,S_k-1，j＝1,2,…,S_k) Taking the weight w and the threshold b of the neural network as state variables of unscented kalman filtering, taking the output of the neural network as a measurement variable of the unscented kalman filtering, and forming a state vector by all the weights and the thresholds in the neural network:

$X={\[w_{11}^1...w_{s_1{s}_2}^1{w}_{11}^2...w_{s_1{s}_2}^2{b}_{11}^1{w}_{11}^{N-1}...w_{s_1{s}_2}^{N-1}{b}_1^1....b_{s_1}^1{b}_1^2....b_{s_2}^2{b}_1^{N-1}....b_{s_{n-1}}^{N-1}\]}^T,$

the state equation and observation equation for the system can be expressed as:

$\left\{\begin{array}{c}{X}_k=X_{k-1}\\ Y_{ek}=h(W_k,X_k)+V_k=F^N(W_k^N,F^{N-1}(W_k^{N-1}...F^2(W_k^2,X_k)\left)\right)+V_k\end{array}\right.$

in the formula, h (-) is a nonlinear transformation, F^NIs the N layer transfer function of the neural network, Y_ekTo desired output, X_kAs an input vector, V_kTo observe noise, it is random white noise, set to 0 in unscented kalman neural network;

the time is updated as: predicted state variable X from time k-1 to time k_k/k-1＝AX_kA^TPrediction error covariance matrix P from time k-1 to time k_k/k-1＝AP_kA^TWherein A is [1 ]]，P_kThe covariance matrix at the k moment;

the measurement is updated as: computing kalman filter gainIn the formula, K_kA filter gain matrix for time k, P_k/k-1Is a prediction error mean square error matrix from time k-1 to time k, H_kIs the observation matrix at time k, R_kVariance matrix of the measured noise sequence at time k, R_k＝[0.01]；

Updating state variable X with measured values_k＝X_k/k-1+K_k(y(k)^T-H_k) In the formula, y (k)^TTo the desired output, H_kOutputting for network training;

updating an error covariance matrix P_k＝(I-K_kH_k)P_k/k-1Wherein, the identity matrix I ═ diag (1);

s3: and predicting the concentration of the PM2.5 by using a dynamic evolution model of the concentration value of the PM 2.5.

In order to clearly and vividly display the predicted PM2.5 concentration value, as a preferred technical solution, the present invention further includes step S4: the PM2.5 concentration predicted in step S3 is displayed by a table and/or a map visualization warning map.

In this embodiment, training models of PM2.5 concentration values of 13 regions, west ampere city between 14 days 1 month and 3 months 11 days 3 months 2013 are established, and a learning training process and a simulation result are described by taking a grassland region as an example.

1) PM2.5 concentration prediction based on unscented Kalman neural network

And taking the weight value and the threshold value of the neural network as state variables of the UKF, and taking the output of the neural network as measurement variables of the UKF. And (3) forming a state vector by all weights and thresholds in the neural network:

$X={\[w{1}_{s_{1}1}...w{1}_{s_1{s}_2}b{1}_{1s_1}w{2}_{s_{1}1}b{2}_{11}\]}^T,(s_1=6,s_2=1)---\left(1\right)$

wherein,

$w1=\left[\begin{array}{ccc}-1.6810& -0.2834& 0.4875\\ 1.6035& -0.3082& 1.5307\\ 2.1457& -0.8814& 0.2406\\ -2.3426& -0.7667& -1.1243\\ 2.8476& -0.3048& 0.5918\\ 0.8294& -0.6096& -0.2993\end{array}\right],w2=\left[\begin{array}{cccccc}-0.9656& 0.8364& 0.2417& -0.3390& 0.4409& 0.1224\end{array}\right]$

b1＝[-1.1071 -0.3188 -0.7754 -1.6647 1.1671 -1.8766]^T,b2＝[-0.6239]

the state equation and observation equation for the system can be expressed as:

$\left\{\begin{array}{c}{X}_k=X_{k-1}\\ Y_{ek}=h(W_k,X_k)+V_k=F^N(W_k^N,F^{N-1}(W_k^{N-1}...F^2(W_k^2,X_k)\left)\right)+V_k\end{array}\right.---\left(2\right)$

in the formula, F^NIs the N layer transfer function of the neural network, Y_ekTo desired output, X_kAs an input vector, V_kTo observe noise, it is random white noise, set to 0 in unscented kalman neural network;

the Kalman algorithm operates as follows:

the time is updated as: predicted state variable X from time k-1 to time k_k/k-1＝AX_kA^TPrediction error covariance matrix P from time k-1 to time k_k/k-1＝AP_kA^TWherein A is [1 ]]，P_kThe covariance matrix at the k moment;

X＝[-1.6810 1.6035 2.1457 -2.3426 2.8476 0.8294 -0.2834 -0.3082 -0.8814 -0.7667 -0.3048 -0.6096 0.4875 1.5307 0.2406 -1.1243 0.5918 -0.2993 -1.1071 -0.3188 -0.7754 -1.6647 1.1671 -1.8766 -0.9656 0.8364 0.2417 -0.33900.4409 0.1224 -0.6239]^T；

the measurement is updated as: computing kalman filter gainIn the formula, K_kA filter gain matrix for time k, P_k/k-1Is a prediction error mean square error matrix from time k-1 to time k, H_kIs the observation matrix at time k, R_kVariance matrix of the measured noise sequence at time k, R_k＝[0.01]；

K＝[-0.1424 0.1184 0.2102 -0.1627 0.5129 0.1188 -0.6120 0.5076 1.0498-0.8239 1.2770 0.4568 -0.1038 0.1177 0.1747 -0.1864 0.3739 0.0877 -0.15040.1165 0.3069 -0.5505 0.5667 0.3761 0.1098 0.0274 0.0347 0.1938 0.0229 0.07660.2119]^T

Updating state variable X with measured values_k＝X_k/k-1+K_k(y(k)^T-H_k) In the formula, y (k)^TTo the desired output, y (k)^T＝[0.038]，H_kFor network training output, H_k＝[0.2419]；

Updating an error covariance matrix P_k＝(I-K_kH_k)P_k/k-1In the formula, the identity matrix I is diag (1)

H＝[-0.0320 0.0444 0.0121 -0.0044 0.0115 0.0028 -0.0489 0.0678 0.0185-0.0067 0.0175 0.0044 -0.0334 0.0463 0.0127 -0.0046 0.0120 0.0030 -0.14820.2053。0.0561 -0.0204 0.0531 0.0132 0.1894 0.5674 0.36630.0643 0.8600 0.12280.10]

After the program is operated, an output result of a dynamic evolution model for predicting the PM2.5 concentration is obtained, and a comparison curve graph of an actual value and a training value of a beach zone is obtained and is shown in figure 1, figure 2 is an error curve graph, and figure 3 is an error percentage curve graph.

2) PM2.5 concentration prediction based on unscented Kalman neural network (AFNN) and PM2.5 concentration prediction based on BP neural network (BPNN) are compared

For clearer comparison of the PM2.5 concentration training results of the UKFNN and the BPNN on the beach area, respectively, fig. 4 is a comparison graph of the true value and the training value of the dynamic PM2.5 concentration evolution model based on the UKFNN and the BPNN, and fig. 5 is an error comparison graph of the dynamic PM2.5 concentration evolution model based on the UKFNN and the BPNN. As can be seen from fig. 4 and 5, the training values of UKFNN are closer to the true values and generate smaller errors than BPNN. In order to compare the training effects of the two models more conveniently, a part of data in the output values of the training of the concentration of PM2.5 in the beach area is selected to be compared with the real values, and a data table is listed, as shown in the table 1.

TABLE 1 comparison table of training output values and true values of two models in grassland and beach area

In order to make people know the concentration of PM2.5 in the next few days more directly and clearly so that people can take corresponding preventive measures in life and production, the embodiment predicts the concentration of PM2.5 in the next seven days of 13 regions in the city of sienna based on UKFNN, obtains corresponding predicted values as shown in table 2, and performs graphical early warning on the predicted concentration. The graph visualization early warning has the main function that after the concentration predicted value of PM2.5 is obtained, the obtained data is displayed on the corresponding area graph, so that the effect of simply and conveniently forecasting and reminding residents in each area is achieved. Fig. 6 shows a PM2.5 concentration warning map of 13 regions in west ampere city, 24 days 4 and 24 months in 2013, and table 3 shows an environmental quality grade table of 13 regions. As can be seen from fig. 6 and table 3: 2013-4-24, wherein the environmental quality grade of a high and new area, a city sports office, a Hades area and a poling area is good; the Xingqing district, the Changan district, the Yangjiang culture group, the textile city and the Jingkai district belong to light pollution; the small village and the wide Tan belong to moderate pollution; high-pressure plant switching and the grass beach are serious pollution.

Seven days PM2.5 concentrations (μ g/m) in 213 regions in Table³) Prediction value

Table 32013-4-2413 area PM2.5 environmental quality grade table

In the foregoing embodiment of the present application, a PM2.5 concentration prediction method based on an unscented kalman neural network is provided, including the following steps: acquiring historical data of PM2.5 concentration, carrying out recursive calculation based on an unscented Kalman neural network, programming by using MATLAB simulation software, continuously carrying out online prediction, continuously correcting weight and threshold, establishing a dynamic evolution model for predicting PM2.5 concentration, and establishing visualization early warning on the basis of obtaining the dynamic evolution model and prediction data so as to achieve the early warning effect after data prediction. Compared with the modeling based on the BP neural network, the modeling based on the unscented Kalman neural network is more accurate in prediction result and has smaller error.

It should be noted that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make variations, modifications, additions or substitutions within the spirit and scope of the present invention.

Claims (2)

1. A PM2.5 concentration prediction method based on an unscented Kalman neural network is characterized by comprising the following steps:

s1: acquiring historical data of PM2.5 concentration;

s2: carrying out recursion operation by using an unscented Kalman neural network, and circularly correcting the weight and the threshold of the neural network by continuously carrying out online prediction to realize prediction of the PM2.5 concentration chaotic time sequence so as to establish a dynamic evolution model for predicting the PM2.5 concentration:

is provided with an N layers of forward neural networks, each layer of neuronsNumber S_k(k is 1,2, …, N), the input layer is the first layer, the output layer is the nth layer, and the connection weights for the k layer neurons are(i＝1,2,…,S_k-1，j＝1,2,…,S_k) Taking the weight w and the threshold b of the neural network as state variables of unscented kalman filtering, taking the output of the neural network as a measurement variable of the unscented kalman filtering, and forming a state vector by all the weights and the thresholds in the neural network:

$X={\[w_{11}^1...w_{s_1{s}_2}^1{w}_{11}^2...w_{s_1{s}_2}^2{b}_{11}^1{w}_{11}^{N-1}...w_{s_1{s}_2}^{N-1}{b}_1^1\mathrm{....}{b}_{s_1}^1{b}_1^2\mathrm{....}{b}_{s_2}^2{b}_1^{N-1}\mathrm{....}{b}_{s_{k-1}}^{N-1}\]}^T,$

the state equation and observation equation for the system can be expressed as:

$\left\{\begin{array}{c}{X}_k=X_{k-1}\\ Y_{ek}=h(W_k,X_k)+V_k=F^N(W_k^N,F^{N-1}(W_k^{N-1}...F^2\left(W_k^2,X_k\right)\left)\right)+V_k\end{array}\right.$

in the formula, h (-) is a nonlinear transformation, F^NIs the N layer transfer function of the neural network, Y_ekTo desired output, X_kAs an input vector, V_kTo observe noise, it is random white noise, set to 0 in unscented kalman neural network;

the time is updated as: predicted state variable X from time k-1 to time k_k/k-1＝AX_kA^TPrediction error covariance matrix P from time k-1 to time k_k/k-1＝AP_kA^TWherein A is [1 ]]，P_kThe covariance matrix at the k moment;

the measurement is updated as: computing kalman filter gainIn the formula, K_kA filter gain matrix for time k, P_k/k-1Is a prediction error mean square error matrix from time k-1 to time k, H_kIs the observation matrix at time k, R_kVariance matrix of the measured noise sequence at time k, R_k＝[0.01]；

Updating state variable X with measured values_k＝X_k/k-1+K_k(y(k)^T-H_k) In the formula, y (k)^TTo the desired output, H_kOutputting for network training;

updating an error covariance matrix P_k＝(I-K_kH_k)P_k/k-1Wherein, the identity matrix I ═ diag (1);

s3: and predicting the concentration of the PM2.5 by using a dynamic evolution model of the concentration value of the PM 2.5.

2. The method for predicting the concentration of PM2.5 based on the unscented kalman network according to claim 1, further comprising the step S4: the PM2.5 concentration predicted in step S3 is displayed by a table and/or a map visualization warning map.