CN101539030A - Method for forecasting gas by adopting sparse coefficient auto-regression model - Google Patents

Abstract

The invention discloses a method for forecasting gas by adopting a sparse coefficient auto-regression model, which carries out the ex ante forecast of gas condition according to gas monitoring data of a tunnel, thereby overcoming the defect that the forecast can not be realized in the past. The method converts gas concentration data which is monitored by a sensor of a monitoring point into electrical signals which are transmitted to a sub-station, carries out analysis treatment to the data in the sub-station, transmits a treatment result to a computer, collects the graph data of a gas concentration time curve in the computer and then carries out the abnormal mutation forecast of the gas monitoring data by calling the sparse coefficient auto-regression model in the computer, thereby achieving the purpose of carrying out the ex ante forecast of the gas according to the on-site gas monitoring data. The method provides a reference basis for making technical measures for preventing and controlling the gas and simultaneously ensures the safety of construction staff, thereby having great significance for safe construction of the gas tunnel.

Description

Adopt the method for sparse coefficient autoregressive model prediction gas

Technical field

The present invention relates to the tunnel construction technology field, especially a kind of method that adopts sparse coefficient autoregressive model prediction gas.

Background technology

Prediction to gas still is an ex post forecasting at present, and promptly gas density transfinites and just reports to the police, and does not have forecast function in advance.For this reason,, how to utilize the field monitoring data of methane monitoring system to carry out effective gas abnormity early warning prediction, become one of focus of current research along with popularizing of methane monitoring system.

Summary of the invention

The purpose of this invention is to provide a kind of method that adopts sparse coefficient autoregressive model prediction gas, concrete is exactly to carry out the gas density early warning prediction that suddenlys change unusually according to the field monitoring data characteristic of gas density in the gas tunnel, overcomes the influence of the unsafe factor that ex post forecasting brings.

The method of the employing sparse coefficient autoregressive model prediction gas among the present invention, be to lay computer in ground central station, data communication interface and substation, face in the tunnel, lining cutting, add the broadband and monitoring point, return air inlet place is laid the face sensor respectively, the lining cutting sensor, add broadband sensor and return air inlet sensor, described four monitoring points are laid left arch springing sensor respectively, right arch springing sensor and dome sensors, all the sensors is connected with substation by communication cable, substation is connected with data communication interface by the transmission data wire, data communication interface is connected with computer, it is characterized in that, comprise the steps:

(1) in described computer, sets up the sparse coefficient autoregression model;

(2) described various sensor is transformed into the signal of telecommunication to the gas density that is monitored and is transferred to described substation;

(3) described substation carries out analyzing and processing respectively to the gas density data that difference detects the position, simultaneously gas density is passed to described computer;

(4) computer is drawn the time graph figure according to gas density, determines 3 important abnormity point positions in the curvilinear figure: unusual starting point, slowly rise to the slow rising of fast rise/be climbed to/slowly drop to fast rise/drop to fast turning point, the peak point of slow decline;

(5) computer is determined the parameter of sparse coefficient autoregression technology model according to described time graph figure and abnormity point position, calls sparse coefficient autoregression technology model trend prediction is carried out in the unusual sudden change of gas density in future.

At gas Forecasting Methodology sparse coefficient autoregression model of the present invention:

$Y_t={\widehat{\mathrm{\α}}}_0+{\widehat{\mathrm{\α}}}_1{Y}_{t-1}+{\widehat{\mathrm{\α}}}_2{Y}_{t-2}+\·\·\·+{\widehat{\mathrm{\α}}}_p{Y}_{t-p}+{\mathrm{\ϵ}}_t,$ In the formula

Subscript be 1,2,3,4 ... the subclass of P}, P makes BIC criterion function BIC _P=log (σ _ε(P)) ²+ [Plog (N-n) ²The value of]/(N-n) (n 〉=P 〉=0) extreme value minimum, this moment, model was best forecasting model.

The present invention is by carrying out the gas prediction to the gas monitor data, by sparse coefficient autoregression forecast model the unusual early warning of greatly may carrying out constantly of the outstanding preceding appearance of gas is predicted, provide reference frame for formulating control gas technical measures, simultaneously, guarantee constructor's safety, therefore, the present invention is significant to the gas tunnel construction safety.

Description of drawings

The present invention will illustrate by example and with reference to the mode of accompanying drawing, wherein:

Fig. 1 is a basic skills logic block-diagram of the present invention.

The specific embodiment

Disclosed all features in this manual, or the step in disclosed all methods or the process except mutually exclusive feature and/or step, all can make up by any way.

Disclosed arbitrary feature in this manual (comprising any accessory claim, summary and accompanying drawing) is unless special narration all can be replaced by other equivalences or the alternative features with similar purpose.That is, unless special narration, each feature is an example in a series of equivalences or the similar characteristics.

Preferred embodiment: sparse coefficient autoregression forecast model

The principle of this model is:

If temporal model is

Y _t＝α ₀+α ₁Y _t-1+α ₂Y _t-2+…+α _pY _t-p+ε _t(1)

In the formula: p---model order; ε _t---the model residual error.

In order to try to achieve the α in (1) formula ₀, α ₁, α ₂..., α _p, must at first set up matrix and find the solution.Concrete grammar is as follows:

At first make p=n (n is the maximum amount of lagging, i.e. the model top step number).Can get following equation group according to the principle of least square:

$\left\{\begin{array}{c}{B}_{11}{A}_{1}l+B_{12}{A}_{2}l+\·\·\·+B_{1n}{A}_{n}l=B_{10}\\ B_{21}{A}_{1}l+B_{22}{A}_{2}l+\·\·\·+B_{2n}{A}_{n}l=B_{20}\\ .\\ .\\ .\\ B_{n1}{A}_{1}l+B_{n2}{A}_{2}l+\·\·\·+B_{\mathrm{nn}}{A}_{n}l=B_n\end{array}\right.---\left(2\right)$

In the formula: $B_{\mathrm{ij}}=\frac{A_{\mathrm{ij}}}{\sqrt{A_{\mathrm{ii}}}\sqrt{A_{\mathrm{jj}}}},$ $B_{i0}=\frac{A_{i0}}{\sqrt{A_{\mathrm{ii}}}\sqrt{A}}$

$A=\underset{t=n+1}{\overset{N}{\mathrm{\Σ}}}{Y}_t^2-(N-n){\left(\stackrel{\‾}{Y}\right)}^2;$ $A_{i0}=\underset{t=n+1}{\overset{N}{\mathrm{\Σ}}}{Y}_{t-i}{Y}_t-(N-n)\stackrel{\‾}{Y_i}\stackrel{\‾}{Y};$

Wherein:

$A_{\mathrm{ij}}=\underset{t=n+1}{\overset{N}{\mathrm{\Σ}}}{Y}_{t-i}{Y}_{t-j}-(N-n)\stackrel{\‾}{Y_i}\stackrel{\‾}{Y_j}=A_{\mathrm{ji}}$

$\stackrel{\‾}{Y_i}=\underset{t=n+1}{\overset{N}{\mathrm{\Σ}}}{Y}_{t-i}/(N-n),$ $\stackrel{\‾}{Y}=\underset{t=n+1}{\overset{N}{\mathrm{\Σ}}}{Y}_t/(N-n),(1\≤i,j\≤n)$

After solving Al from (2) formula, related parameter arranged in must (1) formula:

α ₀＝Y-(α ₁Y ₁+α ₂Y ₂+…+α _nY _n) ${\mathrm{\α}}_i={\mathrm{Al}}_i\sqrt{A/A_{\mathrm{ii}}},(1\≤i\≤n)$

Selecting variable in order to the equation (1) that last method is obtained without BIC criterion, also is not the time series forecasting equation of an optimum.For trying to achieve optimal models, must set up bordered matrix S.Make S _Ij=B _Ij, X _i=B _I0(1≤i, j≤n)

$S=\left[\begin{array}{ccccc}{S}_{11}& S_{12}& \·\·\·& S_{1n}& X_1\\ S_{21}& S_{22}& \·\·\·& S_{2n}& X_2\\ .& .& & .& .\\ .& .& & .& .\\ .& .& & .& .\\ S_{n1}& S_{n2}& \·\·\·& S_{\mathrm{nn}}& X_n\\ X_1& X_2& \·\·\·& X_n& X_0\end{array}\right]---\left(3\right)$

X herein ₀=1.Following formula is carried out stepwise regression analysis, and find out with BIC criterion and to make the minimum model of criterion function value as best forecasting model.

So-called BIC criterion is exactly a value of calculating following formula, makes it the standard of accepting or rejecting as model.

BIC _P＝log(σ _ε(P)) ²+[Plog(N-n) ²]/(N-n)(n≥P≥0)

(δ in the formula _ε(P)) ²Match residual error variance for P rank model.Concrete treatment step to (3) formula is as follows:

At first (3) formula is carried out continuous n cancellation conversion, can get preceding n element X of n+1 row after the conversion ₁, X ₂... X _n, these are exactly the parameter of n rank standardized model.Final reduction formula is:

${\mathrm{\α}}_i={\mathrm{Al}}_i\sqrt{A/A_{\mathrm{jj}}},$ (σ _ε(n)) ²＝A·Y ₀/(N-n)

BIC _n＝log(σ _ε(n)) ²+[n·log(N-n) ²]/(N-n)

A _JjThe i row of expression s-matrix to the A of strain capacity j in the A matrix _JjValue, Y ₀It is the lower right corner element of the s-matrix after the conversion.

In order to delete the parameter item less to regression effect contribution, existing with following formula as the standard of whether deleting:

$P_{n-1}^{\left(i\right)}=X_i^2/S_{\mathrm{ii}},(1\≤i\≤n)$

Get $P_{n-1}^{\mathrm{in}}=\underset{1\≤i\≤n}{\min }{P}_{n-1}^{\left(i\right)},(1\≤\mathrm{in}\≤n)$

Following formula has illustrated that the regression effect of in variable is the poorest, should delete it.The method of deletion is that the in the matrix capable (row) is transferred to outermost layer, drag then with (n=1, n=1) cancellation conversion, result of variations with regard to cancellation the variable of desire deletion, and preceding n-1 element X being listed as of matrix n ₁, X ₂..., X _N-1Be exactly the parameter of that model of the residual sum of squares (RSS) minimum of n-1 rank standardized model, (n, n) element is exactly the residual sum of squares (RSS) of this model to S.Calculate the BIC value of n-1 rank model, and calculate P _N-2 ⁽ⁱ⁾(1≤i≤n-1), the decision deletion is what variable, and then carries out the adjustment of matrix ranks, carries out (n, n) cancellation conversion.And the like, until the zeroth order model.Relatively the BIC value of each rank model is minimum as the BIC value of P rank model, just determine that so the P rank are best model, relevant parameters is

And model is

$Y_t={\widehat{\mathrm{\α}}}_0+{\widehat{\mathrm{\α}}}_1{Y}_{t-1}+{\widehat{\mathrm{\α}}}_2{Y}_{t-2}+\·\·\·+{\widehat{\mathrm{\α}}}_p{Y}_{t-p}+{\mathrm{\ϵ}}_t---\left(4\right)$

In the formula

Subscript normally 1,2,3,4 ... the subclass of P}.

Here the monitored data with certain tunnel tunnel face sensor is an example, utilizes the dynamic data processing method of sparse coefficient autoregression forecast that its " the unusual very big possibility that occurs constantly " carried out analyzing and processing.This face sensor passes to substation to the gas density data that monitored, in substation, gas density is carried out analyzing and processing with analysis software, simultaneously analysis processing result is formed gas density time graph figure in computer, computer gathers the initial data in the curvilinear figure as follows automatically:

Computer gathers the initial data in the curvilinear figure as follows automatically:

The sequence data of after original data processing, setting up:

i	1	2	3	4	5	6	7	8	9	10	11	12
													Y i	6	12	2	7	9	12	9	8	4	5	6	15
i	13	14	15	16	17	18	19	20	21	22
													Y i	11	6	2	6	15	12	11	2	3	4

In order to make time series data meet the characteristics of sparse coefficient model, time interval Y _iThe unit of sequence is the sky.

Get n=9, by computer program to Y _iTime series is carried out analyzing and processing, model order P and corresponding BIC value result:

P	BIC	P	BIC
				9	0.3584E+01	4	0.2466E+01
8	0.3207E+01	3	0.2657E+01
				7	0.2831E+01	2	0.2754E+01
6	0.2459E+01	1	0.2494E+01
				5	0.2178E+01	0	0.2942E+01

What the BIC value was minimum is the autoregression model of P=5.Determine model parameter Be respectively: 41.702 ,-0.953 ,-1.167 ,-1.659 ,-0.792,0.334; Variable of selecting and corresponding order: 3,9,6,8,1.So forecasting model is:

${\hat{Y}}_i=41.702-0.953Y_{i-3}-1.167Y_{i-9}-1.659Y_{i-6}-0.792Y_{i-8}+0.334Y_{i-1}+{\mathrm{\ϵ}}_t$

Final prognostic equation is:

${\hat{Y}}_i=41.702-0.953Y_{i-3}-1.167Y_{i-9}-1.659Y_{i-6}-0.792Y_{i-8}+0.334Y_{i-1}$

In order to check the effect of prognostic equation, below done concrete prediction:

${\hat{Y}}_{23}=41.702-0.953Y_{20}-1.167Y_{14}-1.659Y_{17}-0.792Y_{15}+{0.334Y}_{22}$

${\hat{Y}}_{23}=7.12$

According to predicted value, the 23rd time gas density takes place is unusually after 7.121 days, and (be Y this 25 days October in 2007 with reality ₂₃=6) the gas density maximum value is 1.34% (Y ₂₄=15) compare, precision of forecasting model is reliable.Therefore be feasible unusually with sparse coefficient autoregressive model prediction gas.

The present invention is not limited to the aforesaid specific embodiment.The present invention expands to any new feature or any new combination that discloses in this manual, and the arbitrary new method that discloses or step or any new combination of process.

Claims (2)

1. method that adopts sparse coefficient autoregressive model prediction gas, lay computer in ground central station, data communication interface and substation, face in the tunnel, lining cutting, add the broadband and monitoring point, return air inlet place is laid the face sensor respectively, the lining cutting sensor, add broadband sensor and return air inlet sensor, described four monitoring points are laid left arch springing sensor respectively, right arch springing sensor and dome sensors, all the sensors is connected with substation by communication cable, substation is connected with data communication interface by the transmission data wire, data communication interface is connected with computer, it is characterized in that, comprise the steps:

(1) in described computer, sets up the sparse coefficient autoregression model;

(2) described various sensor is transformed into the signal of telecommunication to the gas density that is monitored and is transferred to described substation;

(3) described substation carries out analyzing and processing respectively to the gas density data that difference detects the position, simultaneously gas density is passed to described computer;

(4) computer is drawn time graph according to gas density, determines 3 important abnormity point positions in the curvilinear figure: unusual starting point, slowly rise to the slow rising of fast rise/be climbed to/slowly drop to fast rise/drop to fast turning point, the peak point of slow decline;

(5) computer is determined the parameter of sparse coefficient autoregression technology model according to described time graph figure and abnormity point position, calls the sparse coefficient autoregression model trend prediction forecast is carried out in the unusual sudden change of gas density in future.

2. the method for employing sparse coefficient autoregressive model prediction gas according to claim 1 is characterized in that described sparse coefficient autoregression model is $Y_t={\widehat{\mathrm{\α}}}_0{\widehat{\mathrm{\α}}}_1{Y}_{t-1}+{\widehat{\mathrm{\α}}}_2{Y}_{t-2}+...+{\widehat{\mathrm{\α}}}_p{Y}_{t-p}+{\mathrm{\ϵ}}_t$ , in the formula

Subscript be 1,2,3,4 ... the subclass of P}, P makes BIC criterion function BIC _P=log (σ _ε(P)) ²+ [Plog (N-n) ²The value that]/(N-n) (n 〉=P 〉=0) value is extremely minimum, this moment, model was best forecasting model.

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