CN108491953A - A kind of PM2.5 predictions and method for early warning and system based on nonlinear theory - Google Patents
A kind of PM2.5 predictions and method for early warning and system based on nonlinear theory Download PDFInfo
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Abstract
PM2.5 predictions and method for early warning and the system that the invention discloses a kind of based on nonlinear theory, model training step and model prediction step；It is divided into two groups for PM2.5 concentration time series datas, respectively as training time series data collection and test sequence training set；S grades of wavelet decompositions are carried out to the data of the trained time series data collection, carry out time frequency analysis, one-dimension information is extended to high dimensional information, extracts the implicit information of PM2.5 historical datas, obtain training timing indicator data set；Structure forecast model；Prediction model is trained；For test sequence training set, MLRC LSSVR model predictions are carried out, variance analysis is done to model prediction result, obtains the upper dividing value of confidence interval as final prediction result.The present invention is capable of providing the adjustable parameter of model, is worked by changing adjustable parameter to adapt to the prediction and warning of different regions PM2.5 concentration.
Description
Technical field
The present invention relates to Air Quality Forecasts and early warning field, more particularly to a kind of PM2.5 based on nonlinear theory
Prediction and method for early warning and system.
Background technology
The main component of haze is exactly PM2.5, and PM2.5 is the particulate matter that grain size is less than 2.5 μm, is a kind of colloid mixing
Object.The influence factor of PM2.5 is complicated, and concentration variation shows nonlinear characteristic.
Predict Model of Air Pollutant Density mainly has two class of statistical model and deterministic models at present.Wherein, mould is counted
Type is generally based on historical data and establishes correlation model between air quality and influence factor, the advantage is that input data
It is required that relatively low, but precision of prediction is relatively low, it is difficult to reflecting regional air quality and can not be given to Causes for Pollution and source etc.
Go out reasonable dismissal；Numerical model is then theoretical according to different scale atmospheric dynamics, couples atmospheric physics and chemical change process,
Multiple dimensioned type atmospheric pollutant diffusion model is established, by computer system predicting atmosphere pollutant concentration variation tendency and is moved
State distribution situation calculates accurately its advantage is that can be diagnosed to Causes for Pollution, can be to pollutant in region
It is predicted, is limited in that timeliness disposal of pollutants data acquisition is difficult, for model to data demand height, practical operation is difficult
It is larger.
It is higher in view of cost consumption needed for numerical forecast, there are more uncertain factor, model foundation process and data
Demand requires more complex, numerous research trend in using statistical model as main means development pollutant prediction, spy
It is not to have carried out a large amount of linguistic term for the forecast of single site statistical model.Many researchers by traditional statistical method with
Neural network model, ARMA model, multiple linear regression model, which are combined, obtains ideal prediction knot
Fruit.
And from the perspective of methodology, ARMA model and multiple linear regression model are linear moulds
Formula, certain nonlinear relationships are difficult accurately to be predicted, this defect embodies in certain case studies；Neural network
Model makes neural network model in fine particulates concentration prediction as a kind of nonlinear mapping method, Multilayer Perception pattern
Aspect has good effect.But the pace of learning of neural network method is usually slow, parameter tuning difficult, and is easily trapped into
Local optimum, Generalization Ability is poor, and forecasting efficiency is relatively low.The appearance of support vector machines (SVM) overcomes neural metwork training
Time is long, generalization ability is poor, easy the shortcomings of being absorbed in local minimum.Single-step Prediction works well, but when carrying out multi-step prediction,
Often step prediction is required for the output of last time prediction as input, and during this iteration, last prediction result can shadow
The prediction result at following time point is rung, error also will gradually accumulate to the last, and prediction effect gradually weakens.
In conclusion in the prior art for the forecasting problem of PM2.5, still lack effective solution scheme.
Invention content
In order to solve the deficiencies in the prior art, the PM2.5 predictions that the present invention provides a kind of based on nonlinear theory with it is pre-
Alarm method, this method are capable of providing the adjustable parameter of model, by changing adjustable parameter to adapt to different regions PM2.5 concentration
Prediction and warning work.
A kind of PM2.5 predictions and method for early warning based on nonlinear theory, including：
Model training step and model prediction step；
It is divided into two groups for PM2.5 concentration time series datas, respectively as training time series data collection and test sequence training set；
S grades of wavelet decompositions are carried out to the data of the trained time series data collection, time frequency analysis is carried out, one-dimension information is extended
For high dimensional information, the implicit information of PM2.5 historical datas is extracted, obtains training timing indicator data set；
Then construction is pre- based on the modified non-linear least square support vector regression (AMLRC-LSSVR) of multi-grade remnant
Survey model；
AMLRC-LSSVR models are trained；
For test sequence training set, MLRC-LSSVR model predictions are carried out, variance analysis is done to model prediction result, is obtained
To confidence interval upper dividing value as final prediction result.
Further, the prediction model adjustable parameter is：Wavelet decomposition number of plies s, least square method supporting vector machine return
Parameter, including kernel functional parameter and regularization parameter γ can be obtained by the methods of genetic algorithm come optimizing.
Further, it is based on modified non-linear least square support vector regression (MLRC-LSSVR) prediction of multi-grade remnant
Model is described as follows：
Training input：Training dataset (Xtrain,Ytrain)∈R(n-1)×2, wherein
Prediction output：The prediction concentrations of n+1 moment PM2.5 pollutants
Further, the model training step：
Step 1：X is concentrated to training datatrainCoifN wavelet transformations are carried out, m floor heights dimension input training matrix is obtained
X′train={ X 'Train, 1, X 'Train, 2... X 'Train, n-1, whereinI=1,
2 ... n-1, construction LSSVR model training data sets (X 'rain,Ytrain)∈R(n-1)×(m+2)；
Step 2：Based on training dataset (X 'train,Ytrain) LSSVR models are trained, training process is using search
The higher simplex methods of efficiency and 10 folding cross validations, the gaussian kernel function key parameter of Optimizing Search LSSVR, and obtain
LSSVR trains final value Y 'train；
Step 3：Calculate LSSVR training final values Y 'trainWith YtrainBetween R2Coefficient R2(Y′train,Ytrain)；
Step 4：If R2Coefficient R2(Y′train,Ytrain) it is less than preset R2Correlation coefficient threshold then calculates training
Residual vector simultaneously constructs residual error training dataset (X 'train,Ytrain=Ytrain-Y′train), and Step 2 and Step 3 is repeated, directly
Meet R to model2Correlation coefficient threshold, it is pre- by additional k-1 LSSVR residual errors to construct MLRC-LSSVR prediction models
Survey on-line synchronous amendment of the model realization to prediction residual, wherein k is MLRC-LSSVR prediction model levels.
Further, the work step of the model predictive process is described as follows：
Step 1：Reconstruct the predictive data set X at n momentpredict={ Xtrain,Xpredict, whereinIt is right
XpredictCoifN wavelet decompositions are carried out, the higher-dimension input prediction vector X ' at n moment is obtainedpredict=(Am,predict,
D1,predict,...Dm,predict)；
Step 2：By higher-dimension input prediction vector X 'predictMLRC-LSSVR prediction models are inputted, MLRC-LSSVR is obtained
Multistage prediction output { Y 'predict,RC1,predict,...RCk-1,predict, to obtainWherein, RCj,predictPrediction for j-th of LSSVR residual prediction model is defeated
Go out.
Step 3：Linear smoothing is carried out based on central limit theory and biasing is corrected, to residual error (RCk-1,train,
RCk-1,predict) variance evaluation is carried out, to obtain predicting top confidence limit YP accordinglypredict=Ypredict+RCPk-1,predict,
Wherein, RCPk-1,predictFor 97% confidence estimate variance of k-1 grades of residual errors；
The model predictive process of step 1-3 is repeated, the on-line prediction and confidence upper limit that PM2.5 prediction concentrations may be implemented are estimated
Meter.
In addition, with the continuous renewal of PM2.5 concentration sequential, in order to eliminate the redundancy of long history steady state bias information,
The AMLRC-LSSVR prediction models constructed can update the data in conjunction with time ordered interval and repeat at periodic or other desired above-mentioned training process, improve
The validity of model on-line prediction.
A kind of PM2.5 predictions and early warning system based on nonlinear theory, including：
Data processing unit, for PM2.5 concentration time series datas to be divided into trained time series data collection and test sequence training
Collection；
Wavelet decomposition unit, for carrying out S grades of wavelet decompositions to the data of the trained time series data collection, frequency division when progress
One-dimension information is extended to high dimensional information, extracts the implicit information of PM2.5 historical datas by analysis, obtains training timing indicator data
Collection；
Support vector regression predicting unit is based on the modified non-linear least square supporting vector of multi-grade remnant for constructing
Return the prediction model of (AMLRC-LSSVR)；AMLRC-LSSVR models are trained；For test sequence training set, into
Row MLRC-LSSVR model predictions do variance analysis to model prediction result, obtain the upper dividing value of confidence interval as final
Prediction result.
Compared with prior art, the beneficial effects of the invention are as follows：
The present invention provides the modified methods of multi-grade remnant, can avoid the cumulative effect of error, improve precision of prediction；This
Invention carries out variance analysis for prediction result, can avoid the uncertain problem of prediction；The present invention is capable of providing model
Adjustable parameter is worked by changing adjustable parameter to adapt to the prediction and warning of different regions PM2.5 concentration.
Description of the drawings
The accompanying drawings which form a part of this application are used for providing further understanding of the present application, and the application's shows
Meaning property embodiment and its explanation do not constitute the improper restriction to the application for explaining the application.
Fig. 1 is the flow chart of data processing figure of the present invention；
Fig. 2 wavelet decomposition schematic diagrames.
Specific implementation mode
It is noted that following detailed description is all illustrative, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific implementation mode, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singulative
It is also intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or combination thereof.
As background technology is introduced, the deficiency of PM2.5 prediction data inaccuracy exists in the prior art, in order to solve
Technical problem as above, the PM2.5 predictions and method for early warning that present applicant proposes a kind of based on nonlinear theory.
In a kind of typical embodiment of the application, as shown in Figure 1, providing a kind of based on nonlinear theory
PM2.5 predict and method for early warning, this it is a kind of based on nonlinear theory PM2.5 prediction be as follows with method for early warning：
Step 1：For PM2.5 time series datas, time frequency analysis is carried out using wavelet decomposition, one-dimension information is extended to higher-dimension
Information extracts the implicit information (tendency, the information such as randomness and periodicity) of PM2.5 historical datas.
Step 2：Build the non-linear least square support vector regression (AMLRC- based on adaptive multistage residual GM
LSSVR) prediction model, the step include parameter optimization, regression forecasting two parts, which refers to
The description of AMLRC-LSSVR；
Step 3：Variance analysis is done to model prediction result, obtains the upper dividing value of confidence interval as final prediction knot
Fruit.
Adjustable parameter is adjusted by parameter optimization unit, improves model to the universal adaptability of different zones, model can
Adjust parameter be：Wavelet decomposition number of plies s, s selection is main rule of thumb, after general decomposition variables A, that is, tendency part is smooth,
The parameter that least square method supporting vector machine returns includes kernel functional parameter and regularization parameter γ.
When choosing kernel function solving practical problems, the method for generally use has：First, the priori using expert is pre-
First select kernel function；Second is that using Cross-Validation methods, i.e., when carrying out kernel function selection, try out respectively different
Kernel function, the kernel function for concluding error minimum are exactly best kernel function, and the present invention is to conclude the minimum selection criteria of error, in detail
Thin operating procedure refers to the description of specific training process.
(1) wavelet decomposition and feature extraction
Wavelet decomposition is to characterize signal by zooming and panning using the waveform for having limit for length or rapid decay, is based on
The partial transformation of time and frequency, and then information is effectively extracted from signal (data), preferably extend Fourier
The application of transformation.Select with oscillating characteristic, can decay to rapidly zero mother wavelet function generating function race：
ψ in formulaa,τ(x) it is wavelet basis function；X is PM2.5 time series datas；τ translation parameters, a are scale parameter.
In practical engineering application, the characteristics of due to computer discrete sampling, discrete wavelet variation is mostly used, signal f is obtained
(x) wavelet transform WTf(p, q) and corresponding reconstruction formula：
In formula, p, q are scale factor and shift factor respectively；ψ*(x) complex conjugate function for being ψ (x)；C be with signal without
The constant of pass.
Understanding for wavelet analysis, it may be assumed that a signal S illustrates that decomposition tree is shown in Fig. 2 by three layers of decomposition.
During signal is analyzed, using different wavelet basis functions as handling implement, the result of gained has obviously
Difference, to obtain high-precision prediction result, it is necessary to select rational wavelet basis.At present in engineering field for wavelet basis
It chooses not there are one specific standard, mostly empirically or the purpose of signal processing chooses small echo.Generally grown in support
Degree, vanishing moment, tradeoff processing in regularity, it is contemplated that wavelet decomposition is applied to the feature extraction of PM2.5 concentration-time sequences
With prediction, the real-time and Time-Frequency Localization ability of feature extraction and prediction are comprehensive to divide herein in conjunction with the property of wavelet basis
Analysis, coifN small echos are with the obvious advantage：On vanishing moment, coifN small echos can carry out original signal by the less classification number of plies
It effectively decomposes, bearing length is shorter, and to which filter length is shorter, wavelet decomposition calculation amount is low, can meet to signal in this way
Process performance, and calculation amount can be reduced, help to improve on-line prediction efficiency.
(2) Least square support vector regression (LSSVR)
Least square support vector regression (LSSVR) is a kind of modeling method based on Statistical Learning Theory, has training
The feature that speed is fast, Generalization Capability good fit nonlinear function ability is strong.LSSVR is the one of Support vector regression (SVR)
A important branch, similar to Support vector regression, training algorithm is to solve convex double optimization problem, has globally unique solution, it
The input space is mapped to high-dimensional feature space by Nonlinear Mapping φ (x), highest possible priority function is sought in feature space.
LSSVR is SVR deformation algorithms, and inequality constraints is changed into equality constraint by Suykens, and function by error and is turned
Become quadratic sum, derivation algorithm is changed by convex double optimization problem solves system of linear equations problem, solves variable number by 2n+
1 is reduced to n+1, and n is training sample number, therefore LSSVR algorithms are low compared with SVR solutions difficulty, and training speed is fast.
If training dataset isInput xi∈Rd, export yi∈ R, then LSSVR can be expressed as：
s.t.yi=wTφ(xi)+b+ei, i=l ..., n (5)
φ (x) is Nonlinear Mapping of the input space to high-order feature space in formula；W is weight vector, the complexity of characterization model；
E=[e1,e2,…,en]TIt is error vector；γ∈R+It is regularization parameter.
In order to solve the problems, such as this constrained optimization, Lagrange functions and antithesis optimization are introduced, solution formula (6) institute is changed into
The unconstrained optimization problem shown.
Wherein α is Lagrangian, respectively to w, b, etAnd αtPartial derivative is sought, it is zero elimination w, e to enable partial derivativet, obtain
Following equation group：
Y=[y in formula1... ..., yn]；α=[α1... ..., αn]；L=[1 ..., 1]TIt is the matrixes of n × 1；InIt is n × n mono-
Bit matrix； Kij=κ (xi,xj)=φ (xi)Tφ(xj), i, j=1 ... ..., n；κ(xi,xj) it is kernel function.Kernel function is adopted
Optimizing is carried out with genetic algorithm, obtains optimal result.
It is as follows to finally obtain LSSVR model prediction functions for the algorithm provided according to Suykens：
Wherein αiFor Lagrangian, b constants can be obtained by the statistical regression to PM2.5 time series datas.
(3) structure is based on modified non-linear least square support vector regression (AMLRC-LSSVR) prediction of multi-grade remnant
Model
It can be with based on modified non-linear least square support vector regression (MLRC-LSSVR) prediction model of multi-grade remnant
It is described as follows：
Training input：Training dataset (Xtrain,Ytrain)∈R(n-1)×2, wherein For i-th of PM2.5 time series data.
Prediction output：The prediction concentrations of n+1 moment PM2.5 pollutants
Its operation principle includes mainly model training process and model predictive process two parts.
The work step of model training process is described as follows：
Step 1：X is concentrated to training datatrainCoifN wavelet transformations are carried out, m floor heights dimension input training matrix is obtained
X′train={ X 'Train, 1, X 'Train, 2... X 'Train, n-1, (X 'train,iFor i-th of PM2.5 time series dataBy small echo
Data acquisition system after decomposition) wherein,(wherein, A, D are the component after wavelet decomposition),
I=1,2 ... n-1, construction LSSVR model training data sets (X 'train,Ytrain)∈R(n-1)×(m+2)；
Step 2：Based on training dataset (X 'train,Ytrain) LSSVR models are trained, training process is using search
The higher simplex methods of efficiency and 10 folding cross validations, the gaussian kernel function key parameter of Optimizing Search LSSVR, and obtain
LSSVR trains final value Y 'train；
Step 3：Calculate LSSVR training final values Y 'trainWith YtrainBetween R2Coefficient R2(Y′train,Ytrain)；
Step 4：If R2Coefficient R2(Y′train,Ytrain) it is less than preset R2Correlation coefficient threshold then calculates training
Residual vector simultaneously constructs residual error training dataset (X 'train,Ytrain=Ytrain-Yt′rain), and Step 2 and Step 3 is repeated, directly
Meet R to model2Correlation coefficient threshold, it is pre- by additional k-1 LSSVR residual errors to construct MLRC-LSSVR prediction models
Survey on-line synchronous amendment of the model realization to prediction residual, wherein k is MLRC-LSSVR prediction model levels.
The work step of model predictive process is described as follows：
Step 1：Reconstruct the predictive data set X at n momentpredict={ Xtrain,Xpredict, whereinIt is right
XpredictCoifN wavelet decompositions are carried out, the higher-dimension input prediction vector X ' at n moment is obtainedtredict=(Am,predict,
D1,predict,...Dm,predict)；
Step 2：By higher-dimension input prediction vector X 'predictMLRC-LSSVR prediction models are inputted, MLRC-LSSVR is obtained
Multistage prediction output { Y 'predict,RC1,predict,...RCk-1,predict, to obtainWherein, RCj,predictPrediction for j-th of LSSVR residual prediction model is defeated
Go out.
Step 3：Linear smoothing is carried out based on central limit theory and biasing is corrected, to residual error (RCk-1,train,
RCk-1,predict) variance evaluation is carried out, to obtain predicting top confidence limit YP accordinglypredict=Ypredict+RCPk-1,predict,
Wherein, RCPk-1,predictFor 97% confidence estimate variance of k-1 grades of residual errors；
The model predictive process of step 1-3 is repeated, the on-line prediction and confidence upper limit that PM2.5 prediction concentrations may be implemented are estimated
Meter.In addition, with the continuous renewal of PM2.5 concentration sequential, in order to eliminate the redundancy of long history steady state bias information, constructed
AMLRC-LSSVR prediction models, can be updated the data in conjunction with time ordered interval and repeat at periodic or other desired above-mentioned training process, improve model
The validity of on-line prediction.
Data processing unit (splitting data into training dataset, test set two parts), wavelet decomposition list are covered in the invention
The units such as member and support vector regression prediction (including kernel function optimizing, residual computations and prediction etc.), and the adjustable of model is provided
Parameter (selection, Decomposition order of wavelet basis function etc.), by changing adjustable parameter to adapt to different regions PM2.5 concentration
Prediction and warning works.
The foregoing is merely the preferred embodiments of the application, are not intended to limit this application, for the skill of this field
For art personnel, the application can have various modifications and variations.Within the spirit and principles of this application, any made by repair
Change, equivalent replacement, improvement etc., should be included within the protection domain of the application.
Claims (6)
1. a kind of PM2.5 predictions and method for early warning based on nonlinear theory, characterized in that including：
Model training step and model prediction step；
It is divided into two groups for PM2.5 concentration time series datas, respectively as training time series data collection and test sequence training set；
S grades of wavelet decompositions are carried out to the data of the trained time series data collection, time frequency analysis is carried out, one-dimension information is extended to height
Information is tieed up, the implicit information of PM2.5 historical datas is extracted, obtains training timing indicator data set；
Then the prediction mould based on the modified non-linear least square support vector regression AMLRC-LSSVR of multi-grade remnant is constructed
Type；
AMLRC-LSSVR models are trained；
For test sequence training set, MLRC-LSSVR model predictions are carried out, variance analysis is done to model prediction result, is set
Believe the upper dividing value in section as final prediction result.
2. a kind of PM2.5 predictions and method for early warning based on nonlinear theory as described in claim 1, characterized in that described
Prediction model adjustable parameter is：Wavelet decomposition number of plies s, the parameter that least square method supporting vector machine returns, including kernel functional parameter
And regularization parameter γ, it can be obtained come optimizing by genetic algorithm.
3. a kind of PM2.5 predictions and method for early warning based on nonlinear theory as described in claim 1, characterized in that be based on
The modified non-linear least square support vector regression MLRC-LSSVR prediction models of multi-grade remnant are described as follows：
Training input：Training datasetWherein,
Prediction output：The prediction concentrations of n+1 moment PM2.5 pollutants
4. a kind of PM2.5 predictions and method for early warning based on nonlinear theory as described in claim 1, characterized in that described
Model training step：
Step 1：X is concentrated to training datatrainCoifN wavelet transformations are carried out, m floor heights dimension input training matrix x ' is obtainedtrain=
{X′Train, 1, X 'Train, 2... X 'Train, n-1Wherein,Construction
LSSVR model training data sets (X 'train,Ytrain)∈R(n-1)×(m+2)；
Step 2：Based on training dataset (X 'train,Ytrain) LSSVR models are trained, training process uses search efficiency
Higher simplex methods and 10 folding cross validations, the gaussian kernel function key parameter of Optimizing Search LSSVR, and obtain LSSVR
Training final value Y 'train；
Step 3：Calculate LSSVR training final values Y 'trainWith YtrainBetween R2Coefficient R2(Y′train,Ytrain)；
Step 4：If R2Coefficient R2(Y′train,Ytrain) it is less than preset R2Correlation coefficient threshold then calculates trained residual error
Vector simultaneously constructs residual error training dataset (X 'train,Ytrain=Ytrain-Y′train), and step 2 and step 3 are repeated, until model
Meet R2Correlation coefficient threshold passes through additional k-1 LSSVR residual prediction models to construct MLRC-LSSVR prediction models
Realize the on-line synchronous amendment to prediction residual, wherein k is MLRC-LSSVR prediction model levels.
5. a kind of PM2.5 predictions and method for early warning based on nonlinear theory as described in claim 1, characterized in that described
The work step of model predictive process is described as follows：
Step 1：Reconstruct the predictive data set X at n momentpredict={ Xtrain,Xpredict, wherein Xpredict=PM2.5n, to Xpredict
CoifN wavelet decompositions are carried out, the higher-dimension input prediction vector X ' at n moment is obtainedpredict=(Am,predict,D1,predict,
...Dm,predict)；
Step 2：By higher-dimension input prediction vector X 'predictMLRC-LSSVR prediction models are inputted, it is multistage pre- to obtain MLRC-LSSVR
Survey output { Y 'predict,RC1,predict,...RCk-1,predict, to obtainIts
In, RCj,predictFor the prediction output of j-th of LSSVR residual prediction model；
Step 3：Linear smoothing is carried out based on central limit theory and biasing is corrected, to residual error (RCk-1,train,RCk-1,predict) into
Row variance evaluation, to obtain predicting top confidence limit YP accordinglypredict=Ypredict+RCPk-1,predict, wherein
RCPk-1,predictFor 97% confidence estimate variance of k-1 grades of residual errors；
The model predictive process of step 1-3 is repeated, realizes on-line prediction and the confidence upper limit estimation of PM2.5 prediction concentrations.
6. a kind of PM2.5 predictions and early warning system based on nonlinear theory, characterized in that including
Data processing unit, for PM2.5 concentration time series datas to be divided into trained time series data collection and test sequence training set；
Wavelet decomposition unit carries out S grades of wavelet decompositions for the data to the trained time series data collection, carries out time frequency analysis,
One-dimension information is extended to high dimensional information, extracts the implicit information of PM2.5 historical datas, obtains training timing indicator data set；
Support vector regression predicting unit is based on the modified non-linear least square support vector regression of multi-grade remnant for constructing
The prediction model of AMLRC-LSSVR；AMLRC-LSSVR models are trained；For test sequence training set, MLRC- is carried out
LSSVR model predictions do variance analysis to model prediction result, obtain the upper dividing value of confidence interval as final prediction knot
Fruit.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109858696A (en) * | 2019-01-30 | 2019-06-07 | 山东万钢信息科技有限公司 | A kind of city environmental pollution prediction technique and system |
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| CN113532263A (en) * | 2021-06-09 | 2021-10-22 | 厦门大学 | Joint angle prediction method for flexible sensor time sequence performance change |
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