CN108491953B - PM2.5 prediction and early warning method and system based on nonlinear theory - Google Patents

Abstract

The invention discloses a PM2.5 prediction and early warning method and a system based on a nonlinear theory, and the method comprises a model training step and a model prediction step; dividing PM2.5 concentration time sequence data into two groups which are respectively used as a training time sequence data set and a test time sequence training set; performing S-level wavelet decomposition on the data of the training time sequence data set, performing time-frequency analysis, expanding one-dimensional information into high-dimensional information, and extracting implicit information of PM2.5 historical data to obtain a training time sequence index data set; constructing a prediction model; training the prediction model; and (3) performing MLRC-LSSVR model prediction aiming at the test time sequence training set, and performing variance analysis on the model prediction result to obtain an upper bound value of a confidence interval as a final prediction result. The invention can provide the adjustable parameters of the model, and is suitable for the prediction and early warning work of PM2.5 concentration in different regions by changing the adjustable parameters.

Description

PM2.5 prediction and early warning method and system based on nonlinear theory

Technical Field

The invention relates to the field of air quality prediction and early warning, in particular to a PM2.5 prediction and early warning method and system based on a nonlinear theory.

Background

The main component of haze is PM2.5, and PM2.5 is particulate matter with the particle size of less than 2.5 μm and is a colloid mixture. The influence factors of PM2.5 are complex, and the concentration change of the PM presents nonlinear characteristics.

At present, the atmospheric pollutant concentration prediction method mainly comprises two types, namely a statistical model and a deterministic model. The statistical model is generally a correlation model between the air quality and the influence factors established based on historical data, and has the advantages that the requirement on input data is relatively low, but the prediction precision is low, the regional air quality is difficult to reflect, and reasonable explanations on pollution causes, sources and the like cannot be given; the numerical model is based on the theory of atmospheric dynamics of different scales, couples the atmospheric physical and chemical change processes, establishes a multi-scale type atmospheric pollutant diffusion model, and forecasts the change trend and the dynamic distribution condition of the atmospheric pollutant concentration by a computer system.

In view of the high cost consumption required by numerical prediction, the existence of more uncertain factors, the complex requirements on the model establishment process and the data requirements, the prediction of the concentration of the atmospheric pollutants tends to be carried out by taking a statistical model as a main means through a plurality of researches, and particularly, a plurality of improvement researches are carried out aiming at the single-site statistical model prediction. Many researchers combine the traditional statistical method with a neural network model, an autoregressive moving average model and a multiple linear regression model to obtain a more ideal prediction result.

From the point of methodology, the autoregressive moving average model and the multiple linear regression model are linear modes, and some nonlinear relations are difficult to accurately predict, which is reflected in some example researches; as a nonlinear mapping method, the neural network model has a good effect on predicting the concentration of fine particulate matters through a multilayer perception mode. However, the learning speed of the neural network method is generally slow, the parameter setting is difficult, the neural network method is easy to fall into local optimization, the popularization capability is poor, and the prediction efficiency is low. The Support Vector Machine (SVM) overcomes the defects of long training time of a neural network, poor generalization capability, easy falling into local minimum and the like. The single-step prediction effect is good, but when multi-step prediction is carried out, each step of prediction needs the output of the previous prediction as the input, in the iteration process, the prediction result of the previous time can influence the prediction result of the next time point, errors can be gradually accumulated until the last time, and the prediction effect is gradually weakened.

In summary, the prior art lacks an effective solution to the PM2.5 prediction problem.

Disclosure of Invention

In order to solve the defects of the prior art, the invention provides a PM2.5 prediction and early warning method based on a nonlinear theory, the method can provide adjustable parameters of a model, and the prediction and early warning work of the PM2.5 concentration in different regions can be adapted by changing the adjustable parameters.

A PM2.5 prediction and early warning method based on a nonlinear theory comprises the following steps:

a model training step and a model prediction step;

dividing PM2.5 concentration time sequence data into two groups which are respectively used as a training time sequence data set and a test time sequence training set;

performing S-level wavelet decomposition on the data of the training time sequence data set, performing time-frequency analysis, expanding one-dimensional information into high-dimensional information, and extracting implicit information of PM2.5 historical data to obtain a training time sequence index data set;

then constructing a prediction model of nonlinear least squares support vector regression (AMLRC-LSSVR) based on multi-stage residual correction;

training an AMLRC-LSSVR model;

and (3) performing MLRC-LSSVR model prediction aiming at the test time sequence training set, and performing variance analysis on the model prediction result to obtain an upper bound value of a confidence interval as a final prediction result.

Further, the adjustable parameters of the prediction model are as follows: the wavelet decomposition layer number s and the regression parameters of the least square support vector machine, including the kernel function parameters and the regularization parameters gamma, can be obtained by optimizing through methods such as a genetic algorithm and the like.

Further, a multi-stage residual correction based nonlinear least squares support vector regression (MLRC-LSSVR) prediction model is described as follows:

training input: training data set (X)_train,Y_train)∈R^(n-1)×2Wherein, in the step (A),

and (3) prediction output: predicted concentration of PM2.5 contaminants at time n +1

Further, the model training step:

step 1: for X in the training data set_trainCarrying out coifN wavelet transformation to obtain m-layer high-dimensional input training matrix X'_train＝{X′_train，1，X′_train，2，...X′_train，n-1And (c) the step of (c) in which,

n-1, constructing an LSSVR model training dataset (X'_rain,Y_train)∈R^(n-1)×(m+2)；

Step 2: based on training data set (X'_train,Y_train) Training an LSSVR model, wherein a Simplex method with higher search efficiency and 10-fold cross validation are adopted in the training process, Gaussian kernel function key parameters of the LSSVR are optimally searched, and an LSSVR training final value Y 'is obtained'_train；

And step 3: calculating LSSVR training final value Y'_trainAnd Y_trainR between²Coefficient of correlation R²(Y′_train,Y_train)；

And 4, step 4: if R is²Coefficient of correlation R²(Y′_train,Y_train) Less than a predetermined value R²Calculating a training residual vector and constructing a residual training data set (X ') according to the correlation coefficient threshold value'_train,Y_train＝Y_train-Y′_train) And repeating Step 2 and Step 3 until the model satisfies R²And (4) constructing an MLRC-LSSVR prediction model by using a correlation coefficient threshold, and realizing online synchronous correction of the prediction residual by additionally k-1 LSSVR residual prediction models, wherein k is the MLRC-LSSVR prediction model level.

Further, the working steps of the model prediction process are described as follows:

step 1: reconstructing a prediction data set X at time n_predict＝{X_train,X_predictTherein of

To X_predictPerforming coifN wavelet decomposition to obtain a high-dimensional input prediction vector X 'at n time'_predict＝(A_m,predict,D_1,predict,...D_m,predict)；

Step 2: inputting a high dimensional prediction vector X'_predictInputting the MLRC-LSSVR prediction model to obtain MLRC-LSSVR multi-stage prediction output { Y'_predict,RC_1,predict,...RC_k-1,predictIs thus obtained

Wherein, RC_j,predictIs the prediction output of the jth LSSVR residual prediction model.

And step 3: linear smoothing and bias correction based on the central limit theory, for residual error (RC)_k-1,train,RC_k-1,predict) Performing variance estimation to obtain corresponding prediction confidence upper bound YP_predict＝Y_predict+RCP_k-1,predictWherein, RCP_k-1,predictEstimate variance for 97% confidence of k-1 level residuals;

and (3) repeating the model prediction process of the steps 1-3, and realizing the online prediction and the upper confidence limit estimation of the PM2.5 predicted concentration.

In addition, with the continuous updating of the PM2.5 concentration time sequence, in order to eliminate the redundancy of long-term historical steady-state bias information, the constructed AMLRC-LSSVR prediction model can be combined with the time sequence interval updating data to repeat the training process periodically, so that the effectiveness of model online prediction is improved.

A PM2.5 prediction and early warning system based on a nonlinear theory comprises:

the data processing unit is used for dividing the PM2.5 concentration time sequence data into a training time sequence data set and a test time sequence training set;

the wavelet decomposition unit is used for performing S-level wavelet decomposition on the data of the training time sequence data set, performing time-frequency analysis, expanding one-dimensional information into high-dimensional information, and extracting implicit information of PM2.5 historical data to obtain a training time sequence index data set;

a support vector regression prediction unit for constructing a prediction model of nonlinear least squares support vector regression (AMLRC-LSSVR) based on multi-stage residual correction; training an AMLRC-LSSVR model; and (3) performing MLRC-LSSVR model prediction aiming at the test time sequence training set, and performing variance analysis on the model prediction result to obtain an upper bound value of a confidence interval as a final prediction result.

Compared with the prior art, the invention has the beneficial effects that:

the invention provides a method for correcting multi-stage residual errors, which can avoid the cumulative effect of errors and improve the prediction precision; according to the invention, variance analysis is carried out on the prediction result, so that the problem of uncertainty of prediction can be avoided; the invention can provide the adjustable parameters of the model, and is suitable for the prediction and early warning work of PM2.5 concentration in different regions by changing the adjustable parameters.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.

FIG. 1 is a data processing flow diagram of the present invention;

fig. 2 is a schematic diagram of wavelet decomposition.

Detailed Description

It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

As introduced by the background art, the prior art has the defect that the PM2.5 prediction data is inaccurate, and in order to solve the technical problems, the application provides a PM2.5 prediction and early warning method based on a nonlinear theory.

In a typical embodiment of the present application, as shown in fig. 1, a PM2.5 prediction and early warning method based on a non-linear theory is provided, and the specific steps of the PM2.5 prediction and early warning method based on the non-linear theory are as follows:

step 1: and aiming at PM2.5 time series data, performing time-frequency analysis by using wavelet decomposition, expanding one-dimensional information into high-dimensional information, and extracting implicit information (information such as trend, randomness, periodicity and the like) of PM2.5 historical data.

Step 2: constructing a nonlinear least squares support vector regression (AMLRC-LSSVR) prediction model based on self-adaptive multistage residual correction, wherein the step comprises two parts of parameter optimization and regression prediction, and the specific operation steps of the part are detailed in the description of AMLRC-LSSVR;

and step 3: and carrying out variance analysis on the model prediction result to obtain an upper bound value of the confidence interval as a final prediction result.

The adjustable parameters can be adjusted through the parameter optimizing unit, the general adaptability of the model to different areas is improved, and the adjustable parameters of the model are as follows: the wavelet decomposition layer number s and s is selected mainly according to experience, a general decomposition variable A is obtained after the trend part is smoothed, and the regression parameters of the least square support vector machine comprise kernel function parameters and regularization parameters gamma.

When a kernel function is selected to solve an actual problem, the commonly adopted method includes: firstly, a kernel function is preselected by using the prior knowledge of an expert; secondly, a Cross-Validation method is adopted, namely different kernel functions are tried respectively when kernel function selection is carried out, the kernel function with the minimum induction error is the best kernel function, the minimum induction error is taken as a selection standard, and detailed operation steps are detailed in the description of a specific training process.

(1) Wavelet decomposition and feature extraction

The wavelet decomposition is characterized in that signals are represented by scaling and shifting by adopting oscillation waveforms with finite length or fast attenuation, and information is effectively extracted from the signals (research data) based on local transformation of time and frequency, so that the application of Fourier transformation is well expanded. Selecting a family of parent wavelet function generating functions having an oscillatory characteristic capable of rapidly decaying to zero:

in the formula psi_a,τ(x) Is a wavelet basis function; x is PM2.5 time series data; τ translation parameter, a is the scale parameter.

In practical engineering application, discrete wavelet transform WT for obtaining signal f (x) is mostly realized by adopting discrete wavelet transform due to the characteristic of computer discrete sampling_f(p, q) and corresponding reconstruction formula:

wherein p and q are a scale factor and a translation factor, respectively; psi^*(x) A complex conjugate function of ψ (x); c is a constant independent of the signal.

For an understanding of the wavelet analysis, it can be assumed that a signal S is illustrated by a three-layer decomposition, see fig. 2.

In the process of signal analysis, different wavelet basis functions are adopted as processing tools, the obtained results have obvious difference, and reasonable wavelet basis must be selected to obtain a high-precision prediction result. At present, no clear standard exists for selecting wavelet base in the engineering field, and wavelets are selected according to experience or the purpose of signal processing. Generally, the support length, the vanishing moment and the regularity are subjected to balance processing, and in consideration of the application of wavelet decomposition to feature extraction and prediction of a PM2.5 concentration time sequence, the real-time performance and the time-frequency localization capability of the feature extraction and prediction are considered, the coifN wavelet has obvious advantages by combining the properties of wavelet basis and comprehensively analyzing: on the vanishing moment, the coifN wavelet can effectively decompose the original signal through fewer hierarchical layers, the supporting length is shorter, the filter length is shorter, and the calculation amount of wavelet decomposition is low, so that the signal processing performance can be met, the calculation amount can be reduced, and the online prediction efficiency can be improved.

(2) Least Squares Support Vector Regression (LSSVR)

Least Squares Support Vector Regression (LSSVR) is a modeling method based on a statistical learning theory, and has the characteristics of high training speed and good generalization performance and strong capability of fitting a nonlinear function. The LSSVR is an important branch of support vector machine regression (SVR), is similar to the support vector machine regression, is a solution convex quadratic optimization problem with a globally unique solution, maps an input space to a high-dimensional feature space through nonlinear mapping phi (x), and finds an optimal priority function in the feature space.

LSSVR is SVR deformation algorithm, Suykens converts inequality constraint into equality constraint, functions are converted from error sum into square sum, solving algorithm is converted from convex quadratic optimization problem into solving linear equation set problem, the number of solving variables is reduced from 2n +1 to n +1, and n is the number of training samples, so that LSSVR algorithm is lower in solving difficulty and higher in training speed than SVR. Let the training data set be

Input x_i∈R^dOutput y_iE R, then LSSVR can be expressed as:

s.t.y_i＝w^Tφ(x_i)+b+e_i，i＝l，…，n (5)

where phi (x) is from input space to high-order feature spaceNonlinear mapping; w is a weight vector characterizing the complexity of the model; e ═ e₁,e₂,…,e_n]^TIs an error vector; gamma epsilon R⁺Is a regularization parameter.

In order to solve the constraint optimization problem, Lagrange function and dual optimization are introduced, and the problem is converted into an unconstrained optimization problem shown in a solving formula (6).

Where α is Lagrangian, for w, b, e respectively_tAnd alpha_tCalculating partial derivative, making partial derivative zero to eliminate w, e_tThe following system of equations is obtained:

wherein y is [ y ]₁,……，y_n]；α＝[α₁,……，α_n]；L＝[1,……,1]^TIs an n × 1 matrix; i is_nIs an n × n identity matrix; k_ij＝κ(x_i,x_j)＝φ(x_i)^Tφ(x_j)，i,j＝1,……,n；κ(x_i,x_j) Is a kernel function. And optimizing the kernel function by adopting a genetic algorithm to obtain an optimal result.

According to the algorithm given by Suykens, the LSSVR model prediction function is finally obtained as follows:

wherein alpha is_iB constants, which are lagrange operators, are obtained by statistical regression of the PM2.5 timing data.

(3) Constructing a nonlinear least squares support vector regression (AMLRC-LSSVR) prediction model based on multi-stage residual correction

The multi-stage residual correction based nonlinear least squares support vector regression (MLRC-LSSVR) prediction model can be described as follows:

training input: training data set (X)_train,Y_train)∈R^(n-1)×2Wherein, in the step (A),

is the ith PM2.5 time series data.

And (3) prediction output: predicted concentration of PM2.5 contaminants at time n +1

The working principle of the method mainly comprises a model training process and a model prediction process.

The working steps of the model training process are described as follows:

step 1: for X in the training data set_trainCarrying out coifN wavelet transformation to obtain m-layer high-dimensional input training matrix X'_train＝{X′_train，1，X′_train，2，...X′_train，n-1}，(X′_train,iFor the ith PM2.5 time series data

A data set after wavelet decomposition) of which,

(wherein A, D is a wavelet decomposed component), i ═ 1, 2.. n-1, and an LSSVR model training data set (X'_train,Y_train)∈R^(n-1)×(m+2)；

Step 2: based on training data set (X'_train,Y_train) Training the LSSVR model by using a simple method with higher search efficiency and 10And performing cross validation, optimally searching key parameters of Gaussian kernel function of LSSVR (least squares support vector regression) and obtaining an LSSVR training final value Y'_train；

And step 3: calculating LSSVR training final value Y'_trainAnd Y_trainR between²Coefficient of correlation R²(Y′_train,Y_train)；

And 4, step 4: if R is²Coefficient of correlation R²(Y′_train,Y_train) Less than a predetermined value R²Calculating a training residual vector and constructing a residual training data set (X ') according to the correlation coefficient threshold value'_train,Y_train＝Y_train-Y_t′_rain) And repeating Step 2 and Step 3 until the model satisfies R²And (4) constructing an MLRC-LSSVR prediction model by using a correlation coefficient threshold, and realizing online synchronous correction of the prediction residual by additionally k-1 LSSVR residual prediction models, wherein k is the MLRC-LSSVR prediction model level.

The working steps of the model prediction process are described as follows:

step 1: reconstructing a prediction data set X at time n_predict＝{X_train,X_predictTherein of

To X_predictPerforming coifN wavelet decomposition to obtain a high-dimensional input prediction vector X 'at n time'_tredict＝(A_m,predict,D_1,predict,...D_m,predict)；

Step 2: inputting a high dimensional prediction vector X'_predictInputting the MLRC-LSSVR prediction model to obtain MLRC-LSSVR multi-stage prediction output { Y'_predict,RC_1,predict,...RC_k-1,predictIs thus obtained

Wherein, RC_j,predictIs the prediction output of the jth LSSVR residual prediction model.

And step 3: linear smoothing and bias correction based on the central limit theory, for residual error (RC)_k-1,train,RC_k-1,predict) Performing variance estimation to obtain corresponding prediction confidence upper bound YP_predict＝Y_predict+RCP_k-1,predictWherein, RCP_k-1,predictEstimate variance for 97% confidence of k-1 level residuals;

and (3) repeating the model prediction process of the steps 1-3, and realizing the online prediction and the upper confidence limit estimation of the PM2.5 predicted concentration. In addition, with the continuous updating of the PM2.5 concentration time sequence, in order to eliminate the redundancy of long-term historical steady-state bias information, the constructed AMLRC-LSSVR prediction model can be combined with the time sequence interval updating data to repeat the training process periodically, so that the effectiveness of model online prediction is improved.

The method comprises a data processing unit (dividing data into a training data set and a test set), a wavelet decomposition unit, a support vector regression prediction unit (including kernel function optimization, residual calculation, prediction and the like), and the like, provides adjustable parameters of a model (selection of wavelet basis functions, the number of decomposition layers and the like), and adapts to prediction and early warning work of PM2.5 concentrations in different regions by changing the adjustable parameters.

The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (4)

1. A PM2.5 prediction and early warning method based on a nonlinear theory is characterized by comprising the following steps:

a model training step and a model prediction step;

for PM_2.5The concentration time sequence data are divided into two groups which are respectively used as a training time sequence data set and a test time sequence training set;

performing S-level wavelet decomposition on the data of the training time sequence data set, performing time-frequency analysis, expanding one-dimensional information into high-dimensional information, and extracting PM_2.5Implicit information of historical data is obtained to obtain a training time sequence index data set;

then constructing a prediction model of nonlinear least square support vector regression (MLRC-LSSVR) based on multi-stage residual correction;

training an MLRC-LSSVR model; the model training step comprises:

step 1: for X in the training data set_trainCarrying out coifN wavelet transformation to obtain m-layer high-dimensional input training matrix X'_train＝{X′_train，1，X′_train，2，...X′_train，n-1And (c) the step of (c) in which,

constructing an LSSVR model training dataset (X'_train,Y_train)∈R^(n-1)×(m+2)；

Step 2: based on training data set (X'_train,Y_train) Training an LSSVR model, wherein a Simplex method with higher search efficiency and 10-fold cross validation are adopted in the training process, Gaussian kernel function key parameters of the LSSVR are optimally searched, and an LSSVR training final value Y 'is obtained'_train；

And step 3: calculating LSSVR training final value Y'_trainAnd Y_trainR between²Coefficient of correlation R²(Y′_train,Y_train)；

And 4, step 4: if R is²Coefficient of correlation R²(Y′_train,Y_train) Less than a predetermined value R²Calculating a training residual vector and constructing a residual training data set (X ') according to the correlation coefficient threshold value'_train,Y_train＝Y_train-Y′_train) And repeating the steps 2 and 3 until the model satisfies R²Constructing an MLRC-LSSVR prediction model by a correlation coefficient threshold, and realizing online synchronous correction of prediction residuals through additional k-1 LSSVR residual prediction models, wherein k is the level of the MLRC-LSSVR prediction model;

performing MLRC-LSSVR model prediction aiming at the test time sequence training set, and performing variance analysis on a model prediction result to obtain an upper bound value of a confidence interval as a final prediction result; the working steps of the model prediction process are described as follows:

step 1: reconstructing a prediction data set X at time n_predict＝{X_train,X_predictTherein of

To X_predictPerforming coifN wavelet decomposition to obtain a high-dimensional input prediction vector X 'at n time'_predict＝(A_m,predict,D_1,predict,...D_m,predict)；

Step 2: inputting a high dimensional prediction vector X'_predictInputting the MLRC-LSSVR prediction model to obtain MLRC-LSSVR multi-stage prediction output { Y'_predict,RC_1,predict,...RC_k-1,predictIs thus obtained

Wherein, RC_j,predictIs the prediction output of the jth LSSVR residual prediction model;

and step 3: linear smoothing and bias correction based on the central limit theory, for residual error (RC)_k-1,train,RC_k-1,predict) Performing variance estimation to obtain corresponding prediction confidence upper bound YP_predict＝Y_predict+RCP_k-1,predictWherein, RCP_k-1,predictEstimate variance for 97% confidence of k-1 level residuals;

repeating the model prediction process of the step 1-3 to realize PM_2.5Online prediction of predicted concentration and upper confidence limit estimation.

2. The PM2.5 prediction and early warning method based on the nonlinear theory as claimed in claim 1, wherein the adjustable parameters of the prediction model are as follows: the wavelet decomposition layer number s, the regression parameters of the least square support vector machine, including the kernel function parameters and the regularization parameters gamma, can be obtained through optimization by a genetic algorithm.

3. The PM2.5 prediction and early warning method based on the non-linear theory as claimed in claim 1, wherein the model for predicting and early warning based on the multi-stage residual correction of the nonlinear least squares support vector regression MLRC-LSSVR is described as follows:

training input: training data set (X)_train,Y_train)∈R^(n-1)×2Wherein, in the step (A),

and (3) prediction output: time PM of n +1_2.5Predicted concentration of contaminant

4. A PM2.5 prediction and early warning system based on a nonlinear theory is characterized by comprising

A data processing unit for processing PM_2.5The concentration time sequence data is divided into a training time sequence data set and a test time sequence training set;

a wavelet decomposition unit for performing S-level wavelet decomposition on the data of the training time sequence data set, performing time-frequency analysis, expanding one-dimensional information into high-dimensional information, and extracting PM_2.5Implicit information of historical data is obtained to obtain a training time sequence index data set;

the support vector regression prediction unit is used for constructing a prediction model of nonlinear least square support vector regression (MLRC-LSSVR) based on multi-stage residual correction; training an MLRC-LSSVR model; the model training step comprises:

step 1: for X in the training data set_trainCarrying out coifN wavelet transformation to obtain m-layer high-dimensional input training matrix X'_train＝{X′_train，1，X′_train，2，...X′_train，n-1And (c) the step of (c) in which,

constructing an LSSVR model training dataset (X'_train,Y_train)∈R^(n-1)×(m+2)；

Step 2: based on training data set (X'_train,Y_train) Training an LSSVR model, wherein a Simplex method with higher search efficiency and 10-fold cross validation are adopted in the training process, Gaussian kernel function key parameters of the LSSVR are optimally searched, and an LSSVR training final value Y 'is obtained'_train；

And step 3: calculating LSSVR training final value Y'_trainAnd Y_trainR between²Coefficient of correlation R²(Y′_train,Y_train)；

And 4, step 4: if R is²Coefficient of correlation R²(Y′_train,Y_train) Less than a predetermined value R²Calculating a training residual vector and constructing a residual training data set (X ') according to the correlation coefficient threshold value'_train,Y_train＝Y_train-Y′_train) And repeating the steps 2 and 3 until the model satisfies R²Constructing an MLRC-LSSVR prediction model by a correlation coefficient threshold, and realizing online synchronous correction of prediction residuals through additional k-1 LSSVR residual prediction models, wherein k is the level of the MLRC-LSSVR prediction model;

performing MLRC-LSSVR model prediction aiming at the test time sequence training set, and performing variance analysis on a model prediction result to obtain an upper bound value of a confidence interval as a final prediction result; the working steps of the model prediction process are described as follows:

step 1: reconstructing a prediction data set X at time n_predict＝{X_train,X_predictTherein of

To X_predictPerforming coifN wavelet decomposition to obtain a high-dimensional input prediction vector X 'at n time'_predict＝(A_m,predict,D_1,predict,...D_m,predict)；

Step 2: inputting a high dimensional prediction vector X'_predictInputting the MLRC-LSSVR prediction model to obtain MLRC-LSSVR multi-stage prediction output { Y'_predict,RC_1,predict,...RC_k-1,predictIs thus obtained

Wherein, RC_j,predictIs the prediction output of the jth LSSVR residual prediction model;

and step 3: linear smoothing and bias correction based on the central limit theory, for residual error (RC)_k-1,train,RC_k-1,predict) Performing variance estimation to obtain corresponding prediction confidence upper bound YP_predict＝Y_predict+RCP_k-1,predictWherein, RCP_k-1,predictEstimate variance for 97% confidence of k-1 level residuals;

repeating the model prediction process of the step 1-3 to realize PM_2.5Online prediction of predicted concentration and upper confidence limit estimation.

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