CN101493392A - CFB furnace tube longevity assessment method based on gray prediction theory - Google Patents

Abstract

The invention discloses a life evaluation method of a CFB furnace tube based on grey prediction theory. The life evaluation method helps solve the problems of hard life evaluation and the like of the current furnace tube and does not need to consider factors which thins wall thickness, such as complex wear, even corrosion and the like; and the life evaluation method has the advantages of requiring fewer raw data, convenient computation and high precision, and can be used in actual engineering practice and the like. The life evaluation method comprises the following steps: (1) measuring a set of wear data; (2) adopting the measured data and a method for weighting processing on time interval in the process of accumulating and reducing the raw data to establish an unequal time interval GM (1,1) prediction model based on the CFB furnace tube wear of the measured wearing capacity data; (3) computing the wearing capacity, that is, wall thickness reduction amount by the established prediction model; (4) comparing a computation result with a measurement result, and optimizing the model; (5) obtaining a specific prediction model of the furnace tube wall thickness reduction amount of a boiler; and (6) predicting the subsequent wear capacity according to the specific prediction model, thus computing the residual life of the furnace tube.

Description

Lifetime estimation method based on the CFB boiler tube of gray prediction theory

Technical field

The present invention relates to a kind of lifetime estimation method of the CFB boiler tube based on gray prediction theory.

Background technology

The life appraisal of recirculating fluidized bed (CFB) generator tube is to instructing boiler design and operation significant.The wall thickness reduction of boiler tube, particularly water screen tube mainly is because wearing and tearing cause.Because operating mode complexity in the CFB boiler furnace, the wearing and tearing of water screen tube belong to high temperature wear (fire box temperature is between 840 ℃～900 ℃), the factor of influence wearing and tearing is numerous, particularly can be used for difficult foundation of forecast model of engineering reality based on the wearing and tearing forecast model of influence factor.And in fact, the rate of wear of water screen tube (wear extent or wall thickness reduction amount) but is tangible, can accurately measure.So, just can bypass complicated influence factor, start with, predict the wearing and tearing in the follow-up moment from the wear data of actual measurement.And the wear problem of the Circulating Fluidized Bed Boiler in the actual production is exactly a typical gray system, after obtaining surveying wear data, just can set up grey forecasting model follow-up wear extent is predicted, thereby can make assessment life of furnace according to measured data.

In fact, the wall thickness reduction of water screen tube is also not exclusively caused by wearing and tearing in the burner hearth, the factors such as caustic corrosion that also comprise the high-temperature oxydation and the inwall of outer wall, so the wall thickness reduction amount that raw data and prediction draw also not exclusively is a wear extent, but make the amount of wall thickness reduction in the pipe operational process owing to a variety of causes.Therefore, the residual life evaluation that this predicted value is used for pipe is fully passable.But do not occur as yet at present adopting this kind method to carry out the method for boiler tube life appraisal.

Summary of the invention

Purpose of the present invention is exactly to be difficult for assessment in order to solve the present boiler tube life-span, thereby the problems such as normal operation that influence is produced, provide that a kind of to have method simple, needn't consider complicated wearing and tearing even comprise that corrosion waits other to make the factor of wall thickness reduction, the raw data that needs is few, convenience of calculation, the precision height can be used for the lifetime estimation method based on the CFB boiler tube of gray prediction theory of advantages such as engineering reality.

For achieving the above object, the present invention adopts following technical scheme:

A kind of lifetime estimation method of the CFB boiler tube based on gray prediction theory, its step is:

1) one group of wear data of actual measurement;

2) utilize measured data, adopt raw data add up and tire out in the process of subtracting to the time set up not even time interval grey GM (1, the 1) forecast model that the CFB boiler tube based on the wear extent measured data weares and teares apart from carrying out method that weight handles;

3) utilizing the forecast model of setting up is that the wall thickness reduction amount is calculated to wear extent;

4) result of calculation and measured result are compared,,, then change next step over to if accuracy test is qualified so that model is carried out accuracy test; Otherwise just model is optimized;

5) draw the concrete forecast model of the boiler tube wall thickness reduction amount of this boiler;

6) utilize the concrete forecast model of setting up that follow-up wear extent is predicted, calculate life of furnace.

One group of wear data of described step 1) is minimum to be 3 data, and many persons do not limit.Must be that the data that the same position of same pipe records just can be included one group in.For example, the initial wall thickness of supposing pipe is 7mm, and after operation a period of time, recording wall thickness for the first time is 6.5mm, measured again three times at same measuring point later on, wall thickness is respectively 6.3mm, 6.0mm and 5.8mm, and can obtain one group of actual measurement wear data so is (0.5,0.7,1.0,1.2).Actual measurement be the wall thickness of pipe, the pipe initial wall thickness deducts wall-thickness measurement and is wear extent, i.e. wall thickness reduction amount, here the wall thickness reduction amount as wear data.In the same position of pipe, to measure at set intervals and once just obtain a wall thickness reduction amount, continuous coverage just obtains one group of wall thickness reduction amount several times, is exactly one group of wear data.

Described step 2) in, even time interval grey GM (1,1) forecast model is not:

Measured data is formed the raw data row:

x ⁽⁰⁾={ x ⁽⁰⁾(i) } i=1 wherein, 2,3 ..., n (1)

And x ⁽⁰⁾(i) and x ⁽⁰⁾(i-1) the time distance between is T (i)-T (i-1)), then the one-accumulate formula of raw data is:

$\left\{\begin{array}{cc}{x}^{\left(1\right)}\left(i\right)=x^{\left(0\right)}\left(i\right)& i=1\\ x^{\left(1\right)}\left(i\right)=x^{\left(1\right)}(i-1)+(T\left(i\right)-T(i-1))\·x^{\left(0\right)}\left(i\right)& i=\mathrm{2,3},\·\·\·,n\end{array}\right.---\left(2\right)$

T (i) wherein, i=1,2 ..., n, for x ⁽⁰⁾(i) corresponding and x ⁽⁰⁾(1) T.T. between at interval.

The formation sequence that obtains increasing progressively:

x ⁽¹⁾＝{x ⁽¹⁾(i)} i＝1，2，3，…，n (3)

If (3) formula satisfies the single argument ordinary differential equation:

$\frac{{\mathrm{dx}}^{\left(1\right)}\left(t\right)}{\mathrm{dt}}+{\mathrm{ax}}^{\left(1\right)}=u---\left(4\right)$

Following formula is the albefaction differential equation of GM (1,1) model, and wherein a, u are parameter to be identified, claims a to be the development coefficient, and u is the grey action; A, u can be according to the sequence x after generating through one-accumulate ⁽¹⁾Estimate its value by least square method; So, the discrete form separated of equation (4) is exactly a response function:

$\widehat{x^{\left(1\right)}}\left(i\right)=[x^{\left(0\right)}\left(1\right)-\frac{u}{a}]e^{-a(i-1)}+\frac{u}{a}$ i＝1，2，3，… (5)

(5) formula is carried out once tired subtracting to be generated reduction and obtains original series x ⁽⁰⁾(i) predicted value:

$\left\{\begin{array}{cc}\widehat{x^{\left(0\right)}}\left(i\right)=\widehat{x^{\left(1\right)}}\left(i\right)& i=1\\ \widehat{x^{\left(0\right)}}\left(i\right)=(\widehat{x^{\left(1\right)}\left(i\right)}-\widehat{x^{\left(1\right)}}(i-1))/(T\left(i\right)-T(i-1))& \\ =[x^{\left(0\right)}\left(1\right)-\frac{u}{a}](1-e^a)e^{-a(i-1)}/(T\left(i\right)-T(i-1))& i=\mathrm{2,3},\·\·\·n\end{array}\right.---\left(6\right).$

Utilizing the forecast model of setting up in the described step 3) is that the wall thickness reduction amount is calculated to wear extent, promptly writes computer program according to model and calculates.

The method that in the described step 4) result of calculation and measured result is compared check is:

At first utilize the average relative error check, the relative error of model predication value and raw data is:

$e\left(i\right)=\frac{|x^{\left(0\right)}\left(i\right)-\widehat{x^{\left(0\right)}}\left(i\right)|}{x^{\left(0\right)}\left(i\right)}$ i＝1，2，3，…，n (7)

Average relative error is:

$\stackrel{\‾}{\mathrm{\Δ}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}e\left(i\right)$

For given a, when Δ＜a sets up, claim that model is the qualified model of residual error;

Secondly, carry out degree of association check,

Order $\left|S\right|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\Σ}}}(x^0\left(i\right)-x^0\left(1\right)+\frac{1}{2}(x^0\left(n\right)-x^0\left(1\right))\right|$ X in the formula ⁽⁰⁾(i) be initial value, i.e. measured data

$\left|\hat{S}\right|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\Σ}}}(\widehat{x^0}\left(i\right)-\widehat{x^0}\left(1\right)+\frac{1}{2}(\widehat{x^0}\left(n\right)-\widehat{x^0}\left(1\right))\right|$ In the formula

Be predicted value

$|\hat{S}-S|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\Σ}}}\right[(x^0\left(i\right)-x^0\left(1\right))-(\widehat{x^0}\left(i\right)-\widehat{x^0}\left(1\right))]+\frac{1}{2}[(x^0\left(n\right)-x^0\left(1\right))-(\widehat{x^0}\left(n\right)-\widehat{x^0}\left(1\right))\left]\right|$

X then ⁰(i) with The absolute degree of association be:

$\mathrm{\ϵ}=\frac{1+\left|S\right|+\left|\hat{S}\right|}{1+\left|S\right|+\left|\hat{S}\right|+|\hat{S}-S|}$

For given ε ₀＞0, if ε＞ε ₀, claim that then model is the qualified model of the absolute degree of association; ε ₀For the index critical value, see Table 1; Once more, carry out the check of posteriority difference

If ${\mathrm{\ϵ}}^0\left(i\right)=x^0\left(i\right)-\widehat{x^0}\left(i\right)$ (i=1,2,3 ..., be i residual error constantly n), then the residual error average is:

$\stackrel{\‾}{\mathrm{\ϵ}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ϵ}}^0\left(i\right)$

The residual mean square (RMS) difference is:

$S_2^2=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{({\mathrm{\ϵ}}^0\left(i\right)-\stackrel{\‾}{\mathrm{\ϵ}})}^2$ S ₂Root for the residual mean square (RMS) difference;

The raw data average is:

$\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}^0\left(i\right)$

The raw data mean square deviation is:

$S_1^2=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x^0\left(i\right)-\stackrel{\‾}{x})}^2$ S ₁Root for the raw data mean square deviation;

The first posteriority difference index (being the mean square deviation ratio) is:

$C=\frac{S_2}{S_1}$

The second posteriority difference index (being the little probability of error) is:

$p=P\left\{\right|\mathrm{\&epsiv;}\left(i\right)-\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}|<0.6745S_1\}$

The precision of model is described jointly by C and p, for given C ₀＞0, if C＜C ₀, claim that model is that mean square deviation is than qualified model; For given p ₀＞0, if p＞p ₀, claim that model is the qualified model of the little probability of error.

Generally model accuracy is divided into 4 grades, model accuracy classification standard commonly used is as shown in table 1.

Table 1 precision of forecasting model inspection level standard reference table

In the described step 4), the method that model is optimized is: carry out the data sequence translation, each data of original data sequence are added a constant a ₀, utilize the method for inspection, find out the comprehensive optimum a of model accuracy by analog computation ₀Value is got the best a of precision of prediction at last ₀Above-mentioned sequence is carried out setting up GM (1,1) model again after the translation predicts that detailed process is:

If y ⁽⁰⁾(i)=x ⁽⁰⁾(i)+a ₀, this formulate adds a constant a with each data of original data sequence ₀, being about to the original data sequence translation, y is the new data sequence that obtains, and then can get the forecast model calculating formula:

$\widehat{x^{\left(0\right)}}\left(i\right)=(y^{\left(0\right)}\left(1\right)-\frac{u^{\&prime;}}{a^{\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i-1)}-a_0---\left(8\right)$

A ', u ' are parameter to be identified in the formula, claim a ' to be the development coefficient, and u ' is the grey action, and must keep new sequence after the sequence translation is the plus or minus sequence;

Perhaps, carry out residual error corrections

Use residual error to set up GM (1,1) model, the fundamental forecasting model is proofreaied and correct.Note generates residual error

${\mathrm{\&epsiv;}}^{\left(0\right)}\left(i\right)=x^1\left(i\right)-\widehat{x^1}\left(i\right),$

Set up GM (1,1) model to generating residual sequence, establishing selected translation constant is a ₁:

$\widehat{{\mathrm{\&epsiv;}}^0}\left(i\right)=({\mathrm{\&epsiv;}}^0\left(1\right)-\frac{u^{\&prime;\&prime;}}{a^{\&prime;\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i-1)}-a_1---\left(9\right)$

In conjunction with (7), (8) formula, get data correction generation model:

$\widehat{x^{\left(0\right)}}\left(i\right)=(y^{\left(0\right)}\left(1\right)-\frac{u^{\&prime;}}{a^{\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i^{\&prime;}-1)}-a_0+\mathrm{\&delta;}(i-\mathrm{\&tau;})[({\mathrm{\&epsiv;}}^0\left(1\right)-\frac{u^{\&prime;\&prime;}}{a^{\&prime;\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i-\mathrm{\&tau;}-1)}-a_1]---\left(10\right)$

τ represents not to be used to set up the residual error number of residual error model in the formula,

$\mathrm{\&delta;}(i-\mathrm{\&tau;})=\left\{\begin{array}{cc}1& i>\mathrm{\&tau;}\\ 0& i\&le;\mathrm{\&tau;}\end{array}\right.$

The breath model GM (1,1) of reforming such as perhaps draw.General GM (1,1) is that GM (1,1) model is the continuous function of time by all data modeling before the reality moment t=n, and in theory, this model can extend to following any one moment from initial value always.But for the intrinsic gray system, As time goes on, factors such as some following disturbances and interference will constantly enter system and impact.Therefore the data of GM (1,1) model prediction meaning maximum are exactly t=n several data before, and it is more little that the time pushes away prediction significance more forward.For these factors in future are taken into account, GM (1,1) model will the data that each is new be sent in the original series, rebulids GM (1,1) and predicts again, be i.e. innovation model.And As time goes on, the information meaning of old data will progressively reduce, and therefore, whenever replenishes a fresh information, just removes data the oldest, to keep the number of data sequence, obviously is rational.The sequence of Jian Liing such as is called at the breath sequence of reforming like this, and corresponding model is called that waiting reforms ceases model, also is Metabolic GM (1,1) model.

When the model accuracy disqualified upon inspection, can further set up GM (1, the 1) model of predicted value residual sequence, promptly to residual sequence ${\mathrm{\&epsiv;}}^0\left(i\right)=x^0\left(i\right)-\widehat{x^0}\left(i\right)$ (i=1,2,3 ..., n) add up to generate and set up GM (1,1) model, and then tiredly subtract the predicted value that reduction obtains residual error, and then the residual prediction value is added on the original predicted value, to improve precision;

As residual sequence ε ⁰When having negative value (i), select a positive number a ', compare ε ⁰(i) absolute value of a minimum negative value gets final product slightly greatly in, is added to ε ⁰(i) in, make ε ⁰(i) become non-bearing can satisfy gray prediction to the non-negative condition of original data sequence requirement, then with ε ⁰(i) add up and generate non-negative ascending series and set up model, find the solution reduction; Notice that tired subtracting when reducing deducts a ' with predicted value, promptly get the residual prediction value, be added to then on the original predicted value, promptly get the modified value of last predicted value;

Residual sequence be on the occasion of the time, be normal condition; When having negative value, select a positive number a ', compare ε ⁰(i) absolute value of a minimum negative value gets final product slightly greatly in, is added to ε ⁰(i) in, make ε ⁰(i) become non-bearing can satisfy gray prediction to the non-negative condition of original data sequence requirement, then with ε ⁰(i) add up and generate non-negative ascending series and set up model, find the solution reduction; Notice that tired subtracting when reducing deducts a ' with predicted value, promptly get the residual prediction value, be added to then on the original predicted value, promptly get the modified value of last predicted value;

Do one time one step residual error corrections and do accuracy test again after trying to achieve modified value, can be again when defective once revised predicted value and raw data subtract each other and obtain two and go on foot residual sequences, use the same steps as correction again, carry out three times and can meet the demands generally at most.

In the described step 6), calculate the life of furnace method and be, prepare a computer program, find the solution wear extent and be 70%8 moment T by the forecast model after optimizing _e, T _eDeduct current time T _nBe residual life R _i(h), i.e. R _i(h)=T _e-T _n, wherein, δ is the pipe initial wall thickness.

The invention has the beneficial effects as follows: needn't consider complicated wearing and tearing even comprise that corrosion waits other factors that makes wall thickness reduction, the raw data that needs is few, convenience of calculation, and the precision height can be used for engineering reality.

Embodiment

The invention will be further described below in conjunction with embodiment.

Set up not even time interval grey GM (1,1) forecast model:

Measured data is formed the raw data row:

x ⁽⁰⁾＝{x ⁽⁰⁾(i)} (i＝1，2，3，…，n) (1)

And x ⁽⁰⁾(i) and x ⁽⁰⁾(i-1) the time distance between is (T (i)-T (i-1)), and then the one-accumulate formula of raw data is:

$\left\{\begin{array}{cc}{x}^{\left(1\right)}\left(i\right)=x^{\left(0\right)}\left(i\right)& (i=1)\\ x^{\left(1\right)}\left(i\right)=x^{\left(1\right)}(i-1)+(T\left(i\right)-T(i-1))\&CenterDot;x^{\left(0\right)}\left(i\right)& (i=\mathrm{2,3},\&CenterDot;\&CenterDot;\&CenterDot;,n)\end{array}\right.---\left(2\right)$

T (i) wherein, (i=1,2 ..., n), for x ⁽⁰⁾(i) corresponding and x ⁽⁰⁾(1) T.T. between at interval.

The formation sequence that obtains increasing progressively:

x ⁽¹⁾＝{x ⁽¹⁾(i)} (i＝1，2，3，…，n) (3)

If (3) formula satisfies the single argument ordinary differential equation:

$\frac{{\mathrm{dx}}^{\left(1\right)}\left(t\right)}{\mathrm{dt}}+{\mathrm{ax}}^{\left(1\right)}=u---\left(4\right)$

Following formula is the albefaction differential equation of GM (1,1) model, and wherein a, u are parameter to be identified, claims a to be the development coefficient, and u is the grey action.A, u can be according to the sequence x after generating through one-accumulate ⁽¹⁾Estimate its value by least square method.So, the discrete form separated of equation (4) is exactly a response function:

$\widehat{x^{\left(1\right)}}\left(i\right)=[x^{\left(0\right)}\left(1\right)-\frac{u}{a}]e^{-a(i-1)}+\frac{u}{a}$ (i＝1，2，3，…) (5)

(5) formula is carried out once tired subtracting to be generated reduction and obtains original series x ⁽⁰⁾(i) predicted value:

$\left\{\begin{array}{cc}\widehat{x^{\left(0\right)}}\left(i\right)=\widehat{x^{\left(1\right)}}\left(i\right)& (i=1)\\ \widehat{x^{\left(0\right)}}\left(i\right)=(\widehat{x^{\left(1\right)}}\left(i\right)-\widehat{x^{\left(1\right)}}(i-1))/(T\left(i\right)-T(i-1))& \\ =[x^{\left(0\right)}\left(1\right)-\frac{u}{a}](1-e^a)e^{-a(i-1)}/(T\left(i\right)-T(i-1))& (i=\mathrm{2,3},\&CenterDot;\&CenterDot;\&CenterDot;)\end{array}\right.---\left(6\right)$

At first result of calculation and measured result are compared, model is carried out accuracy test,, then directly utilize model that follow-up wear extent is predicted if accuracy test is qualified; Otherwise just model is optimized.

1. accuracy test

The precision of forecast model adopts methods such as average relative error check, degree of association check, posteriority poor (the mean square deviation ratio and the little probability of error) check to test.

(1) average relative error check

The relative error of model predication value and raw data is:

$e\left(i\right)=\frac{|x^{\left(0\right)}\left(i\right)-\widehat{x^{\left(0\right)}}\left(i\right)|}{x^{\left(0\right)}\left(i\right)}$ (i＝1，2，3，…，n) (7)

Average relative error is:

$\stackrel{\&OverBar;}{\mathrm{\&Delta;}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}e\left(i\right)$

For given a, when Δ＜a sets up, claim that model is the qualified model of residual error.

(2) degree of association check

Order $\left|S\right|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\&Sigma;}}}(x^0\left(i\right)-x^0\left(1\right)+\frac{1}{2}(x^0\left(n\right)-x^0\left(1\right))\right|$

$\left|\hat{S}\right|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\&Sigma;}}}(\widehat{x^0}\left(i\right)-\widehat{x^0}\left(1\right)+\frac{1}{2}(\widehat{x^0}\left(n\right)-\widehat{x^0}\left(1\right))\right|$

$|\hat{S}-S|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\&Sigma;}}}\right[(x^0\left(i\right)-x^0\left(1\right))-(\widehat{x^0}\left(i\right)-\widehat{x^0}\left(1\right))]+\frac{1}{2}[(x^0\left(n\right)-x^0\left(1\right))-(\widehat{x^0}\left(n\right)-\widehat{x^0}\left(1\right))\left]\right|$

X then ⁰(i) with

The absolute degree of association be:

$\mathrm{\&epsiv;}=\frac{1+\left|S\right|+\left|\hat{S}\right|}{1+\left|S\right|+\left|\hat{S}\right|+|\hat{S}-S|}$

For given ε ₀＞0, if ε＞ε ₀, claim that then model is the qualified model of the absolute degree of association.

(3) posteriority difference check

If ${\mathrm{\&epsiv;}}^0\left(i\right)=x^0\left(i\right)-\widehat{x^0}\left(i\right)$ (i=1,2,3 ..., be i residual error constantly n), then the residual error average is:

$\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}^0\left(i\right)$

The residual mean square (RMS) difference is:

$S_2^2=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{({\mathrm{\&epsiv;}}^0\left(i\right)-\stackrel{\&OverBar;}{\mathrm{\&epsiv;}})}^2$

The raw data average is:

$\stackrel{\&OverBar;}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}^0\left(i\right)$

The raw data mean square deviation is:

$S_1^2=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x^0\left(i\right)-\stackrel{\&OverBar;}{x})}^2$

The first posteriority difference index (being the mean square deviation ratio) is:

$C=\frac{S_2}{S_1}$

The second posteriority difference index (being the little probability of error) is:

p＝P{|ε(i)-ε|＜0.6745S ₁}

The precision of model is described jointly by C and p.For given C ₀＞0, if C＜C ₀, claim that model is that mean square deviation is than qualified model; For given p ₀＞0, if p＞p ₀, claim that model is the qualified model of the little probability of error.

Generally model accuracy is divided into 4 grades, model accuracy classification standard commonly used is as shown in table 1.

Table 1 precision of forecasting model inspection level standard reference table

2. model optimization

In order to improve the precision of model, adopt following method that model is optimized.

(1) data sequence translation

Each data of original data sequence are added a constant a ₀, utilize methods such as the check of posteriority difference, initial point error-tested, correlation analysis, find out the comprehensive optimum a of model accuracy by analog computation ₀Value is got the best a of precision of prediction at last ₀Above-mentioned sequence is carried out setting up GM (1,1) model again after the translation to be predicted.

If y ⁽⁰⁾(i)=x ⁽⁰⁾(i)+a ₀, then can get the forecast model calculating formula:

$\widehat{x^{\left(0\right)}}\left(i\right)=(y^{\left(0\right)}\left(1\right)-\frac{u^{\&prime;}}{a^{\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i-1)}-a_0---\left(8\right)$

It should be noted that with keeping new sequence after the sequence translation be the plus or minus sequence.

(2) residual error corrections

Use residual error to set up GM (1,1) model, the fundamental forecasting model is proofreaied and correct.Note generates residual error

${\mathrm{\&epsiv;}}^{\left(0\right)}\left(i\right)=x^1\left(i\right)-\widehat{x^1}\left(i\right),$

The generation residual sequence is set up GM (1,1) model, and (establishing selected translation constant is a ₁):

$\widehat{{\mathrm{\&epsiv;}}^0}\left(i\right)=({\mathrm{\&epsiv;}}^0\left(1\right)-\frac{u^{\&prime;\&prime;}}{a^{\&prime;\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i-1)}-a_1---\left(9\right)$

In conjunction with (7), (8) formula, get data correction generation model:

$\widehat{x^{\left(0\right)}}\left(i\right)=(y^{\left(0\right)}\left(1\right)-\frac{u^{\&prime;}}{a^{\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i^{\&prime;}-1)}-a_0+\mathrm{\&delta;}(i-\mathrm{\&tau;})[({\mathrm{\&epsiv;}}^0\left(1\right)-\frac{u^{\&prime;\&prime;}}{a^{\&prime;\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i-\mathrm{\&tau;}-1)}-a_1]---\left(10\right)$

τ represents not to be used to set up the residual error number of residual error model in the formula,

$\mathrm{\&delta;}(i-\mathrm{\&tau;})=\left\{\begin{array}{cc}1& i>\mathrm{\&tau;}\\ 0& i\&le;\mathrm{\&tau;}\end{array}\right.$

(3) etc. the breath model GM (1,1) of reforming

General GM (1,1) is that GM (1,1) model is the continuous function of time by all data modeling before the reality moment t=n, and in theory, this model can extend to following any one moment from initial value always.But for the intrinsic gray system, As time goes on, factors such as some following disturbances and interference will constantly enter system and impact.Therefore the data of GM (1,1) model prediction meaning maximum are exactly t=n several data before, and it is more little that the time pushes away prediction significance more forward.For these factors in future are taken into account, GM (1,1) model will the data that each is new be sent in the original series, rebulids GM (1,1) and predicts again, be i.e. innovation model.And As time goes on, the information meaning of old data will progressively reduce, and therefore, whenever replenishes a fresh information, just removes data the oldest, to keep the number of data sequence, obviously is rational.The sequence of Jian Liing such as is called at the breath sequence of reforming like this, and corresponding model is called that waiting reforms ceases model, also is Metabolic GM (1,1) model.

When the model accuracy disqualified upon inspection, can further set up GM (1, the 1) model of predicted value residual sequence, promptly to residual sequence ${\mathrm{\&epsiv;}}^0\left(i\right)=x^0\left(i\right)-\widehat{x^0}\left(i\right)$ (i=1,2,3 ..., n) add up to generate and set up GM (1,1) model, and then tiredly subtract the predicted value that reduction obtains residual error, and then the residual prediction value is added on the original predicted value, to improve precision.

As residual sequence ε ⁰When having negative value (i), select a positive number a ', compare ε ⁰(i) absolute value of a minimum negative value gets final product slightly greatly in, is added to ε ⁰(i) in, make ε ⁰(i) become non-bearing can satisfy gray prediction to the non-negative condition of original data sequence requirement, then with ε ⁰(i) add up and generate non-negative ascending series and set up model, find the solution reduction.Notice that tired subtracting when reducing deducts a ' with predicted value, promptly get the residual prediction value, be added to then on the original predicted value, promptly get the modified value of last predicted value.

Do one time one step residual error corrections and do accuracy test again after trying to achieve modified value, can be again when defective once revised predicted value and raw data subtract each other and obtain two and go on foot residual sequences, use the same steps as correction again, carry out three times and can meet the demands generally at most.

Embodiment 1:

1, wear measurement

On a 465t/h circulating fluidized bed boiler water-cooling wall (φ 63 * 6.5), the representational measuring point in 1 place is set, in accumulative total in working time of 11256 hours, utilize booster and other accident furnace outage times, with the NDT711 supersonic thickness meter each measuring point is carried out wall thickness measuring, it ought time wall-thickness measurement be the wear extent that records when inferior that initial wall thickness deducts.Test data is as shown in table 1.

Table 1.CFB boiler water wall abrasion amount measuring value

Number of times	1	2	3	4	5	6	7	8	9	10	11
												Accumulated running time t (h)	7776	8136	8496	9168	9432	9960	10296	10584	10944	11136	11256
Wear extent (mm)	0.3	0.7	0.7	0.9	1.0	1.2	1.2	1.3	1.3	1.4	1.5

2, wearing and tearing prediction

6 secondary data were as raw data in the past, and structure raw data row are set up model, and it is as shown in table 2 to try to achieve predicted value.

Table 2 original value predicts the outcome

According to predicting the outcome, the precision of model is tested, the result is as shown in table 3.

Table 3 precision of forecasting model assay

For further improving model accuracy, model is carried out the follow-up moment being predicted after the step residual error corrections again master mould and correction back model prediction the results are shown in table 4.Can calculate, through after the residual error corrections, the average relative error of predicted value is 5.104%.

Table 4 wear extent predicts the outcome

Employing is carried out two step residual error corrections with quadrat method, and obtaining average relative error is 4.937%, as seen, after a step residual error corrections, the precision of model raises significantly, can meet the engineering error after proofreading and correct through secondary less than 5% requirement, but the amplitude that precision improves reduces.If improve precision again, can carry out reform breath models such as residual error corrections or employing again to model this moment and all can.

3, residual Life Calculation

This boiler tube initial wall thickness is 6.5mm, principle according to " the wall thickness reduction amount of station boiler pressure-bearing carbon steel and low alloy steel steel pipe should be changed greater than 30% of initial wall thickness " among the DL647-2004 " station boiler pressure vessel inspection procedure ", should be replaced when the residual wall thickness of this boiler tube is 6.5 * 30%=1.95mm as can be known, the pairing moment of wall thickness reduction amount 6.5-1.95=4.55mm deducts present moment and is this life of furnace so.

According to forecast model, the moment when calculating wear extent and being 4.55mm is 60398h, and this life of furnace is 60398-11256=49142h so.

Claims (9)

1. lifetime estimation method based on the CFB boiler tube of gray prediction theory is characterized in that its step is:

1) one group of wear data of actual measurement;

2) utilize measured data, adopt raw data add up and tire out in the process of subtracting to the time set up not even time interval grey GM (1, the 1) forecast model that the CFB boiler tube based on the wear extent measured data weares and teares apart from carrying out method that weight handles;

3) utilizing the forecast model of setting up is that the wall thickness reduction amount is calculated to wear extent;

4) result of calculation and measured result are compared,,, then change next step over to if accuracy test is qualified so that model is carried out accuracy test; Otherwise just model is optimized;

5) draw the concrete forecast model of the boiler tube wall thickness reduction amount of this boiler;

6) utilize the concrete forecast model of setting up that follow-up wear extent is predicted, calculate life of furnace.

2. the lifetime estimation method of the CFB boiler tube based on gray prediction theory as claimed in claim 1, it is characterized in that, the method that described step 1) is surveyed one group of wear data is, same position at same pipe, measure the wall thickness reduction amount that once just obtains at set intervals, continuous coverage just obtains one group of wall thickness reduction amount several times, is exactly one group of wear data.

3. the lifetime estimation method of the CFB boiler tube based on gray prediction theory as claimed in claim 1 is characterized in that described step 2) in, even time interval grey GM (1,1) forecast model is not:

Measured data is formed the raw data row:

x ⁽⁰⁾={ x ⁽⁰⁾(i) } i=1 wherein, 2,3 ..., n (1)

And x ⁽⁰⁾(i) and x ⁽⁰⁾(i-1) the time distance between is T (i)-T (i-1)), then the one-accumulate formula of raw data is:

$\left\{\begin{array}{cc}{x}^{\left(1\right)}\left(i\right)=x^{\left(0\right)}\left(i\right)& i=1\\ x^{\left(1\right)}\left(i\right)=x^{\left(1\right)}(i-1)+(T\left(i\right)-T(i-1))\&CenterDot;x^{\left(0\right)}\left(i\right)& i=\mathrm{2,3}\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}\right.---\left(2\right)$

T (i) wherein, i=1,2 ..., n is x ⁽⁰⁾(i) the corresponding moment and x ⁽⁰⁾(1) T.T. between the corresponding moment at interval; The formation sequence that obtains increasing progressively:

x ⁽¹⁾＝{x ⁽¹⁾(i)} i＝1，2，3，…，n (3)

If (3) formula satisfies the single argument ordinary differential equation:

$\frac{{\mathrm{dx}}^{\left(1\right)}\left(t\right)}{\mathrm{dt}}+a{x}^{\left(1\right)}=u---\left(4\right)$

Following formula is the albefaction differential equation of GM (1,1) model, and wherein a, u are parameter to be identified, claims a to be the development coefficient, and u is the grey action; A, u can be according to the sequence x after generating through one-accumulate ⁽¹⁾Estimate its value by least square method; So, the discrete form separated of equation (4) is exactly a response function:

$\widehat{x^{\left(1\right)}}\left(i\right)=[x^{\left(0\right)}\left(1\right)-\frac{u}{a}]e^{-a(i-1)}+\frac{u}{a},i=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;---\left(5\right)$

(5) formula is carried out once tired subtracting to be generated reduction and obtains original series x ⁽⁰⁾(i) predicted value:

$\left\{\begin{array}{cc}\widehat{x^{\left(0\right)}}\left(i\right)=\widehat{x^{\left(1\right)}}\left(i\right)& i=1\\ \widehat{x^{\left(0\right)}}\left(i\right)=(\widehat{x^{\left(1\right)}}\left(i\right)-\widehat{x^{\left(1\right)}}(i-1))/(T\left(i\right)-T(i-1))& \\ =[x^{\left(0\right)}\left(1\right)-\frac{u}{a}](1-e^a)e^{-a(i-1)}/(T\left(i\right)-T(i-1))& i=\mathrm{2,3},\&CenterDot;\&CenterDot;\&CenterDot;n\end{array}\right.---\left(6\right).$

4. the lifetime estimation method of the CFB boiler tube based on gray prediction theory as claimed in claim 1, it is characterized in that, utilizing the forecast model of setting up in the described step 3) is that the wall thickness reduction amount is calculated to wear extent, promptly writes computer program according to model and calculates.

5. the lifetime estimation method of the CFB boiler tube based on gray prediction theory as claimed in claim 1 is characterized in that, the method that in the described step 4) result of calculation and measured result is compared check is:

At first utilize the average relative error check, the relative error of model predication value and raw data is:

$e\left(i\right)=\frac{|x^{\left(0\right)}\left(i\right)-\widehat{x^{\left(0\right)}}\left(i\right)|}{x^{\left(0\right)}\left(i\right)},i=\mathrm{1,2,3},\&CenterDot;\&CenterDot;\&CenterDot;,n---\left(7\right)$

Average relative error is:

$\stackrel{\&OverBar;}{\mathrm{\&Delta;}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}e\left(i\right),$

For given a, when Δ＜a sets up, claim that model is the qualified model of residual error;

Secondly, carry out degree of association check,

Order $\left|S\right|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\&Sigma;}}}(x^0\left(i\right)-x^0\left(1\right)+\frac{1}{2}(x^0\left(n\right)-x^0\left(1\right))\right|$ In the formula, x ⁽⁰⁾(i) be initial value, i.e. measured data

$\left|\hat{S}\right|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\&Sigma;}}}(\widehat{x^0}\left(i\right)-\widehat{x^0}\left(1\right)+\frac{1}{2}(\widehat{x^0}\left(n\right)-\widehat{x^0}\left(1\right))\right|$ In the formula, Be predicted value

$|\hat{S}-S|=\left|\underset{i=2}{\overset{n-1}{\mathrm{\&Sigma;}}}\right[(x^0\left(i\right)-x^0\left(1\right))-(\widehat{x^0}\left(i\right)-\widehat{x^0}\left(1\right))]+\frac{1}{2}[(x^0\left(n\right)-x^0\left(1\right))-(\widehat{x^0}\left(n\right)-\widehat{x^0}\left(1\right))\left]\right|$

X then ⁰(i) with

The absolute degree of association be:

$\mathrm{\&epsiv;}=\frac{1+\left|S\right|+\left|\hat{S}\right|}{1+\left|S\right|+\left|\hat{S}\right|+|\hat{S}-S|}$

For given ε ₀＞0, if ε＞ε ₀, claim that then model is the qualified model of the absolute degree of association; ε ₀Be the index critical value; Once more, carry out the check of posteriority difference

If ${\mathrm{\&epsiv;}}^0\left(i\right)=x^0\left(i\right)-\widehat{x^0}\left(i\right)$ (i=1,2,3 ..., be i residual error constantly n), then the residual error average is:

$\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}^0\left(i\right)$

For:

$S_2^2=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{({\mathrm{\&epsiv;}}^0\left(i\right)-\stackrel{\&OverBar;}{\mathrm{\&epsiv;}})}^2$ S ₂Root for the residual mean square (RMS) difference

The raw data average is:

$\stackrel{\&OverBar;}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}^0\left(i\right)$

The raw data mean square deviation is:

$S_1^2=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x^0\left(i\right)-\stackrel{\&OverBar;}{x})}^2$ S ₁Root for the raw data mean square deviation

The first posteriority difference index is that the mean square deviation ratio is:

$C=\frac{S_2}{S_1}$

The second posteriority difference index (being the little probability of error) is:

$p=\stackrel{\&CenterDot;}{P}\left\{\right|\mathrm{\&epsiv;}\left(i\right)-\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}|<0.6745S_1\}$

The precision of model is described jointly by C and p, for given C ₀＞0, if C＜C ₀, claim that model is that mean square deviation is than qualified model; For given p ₀＞0, if p＞p ₀, claim that model is the qualified model of the little probability of error.

6. the lifetime estimation method of the CFB boiler tube based on gray prediction theory as claimed in claim 1, it is characterized in that, in the described step 4), the method that model is optimized is: carry out the data sequence translation, each data of original data sequence are added a constant a ₀, utilize the method for inspection, find out the comprehensive optimum a of model accuracy by analog computation ₀Value is got the best a of precision of prediction at last ₀Above-mentioned sequence is carried out setting up GM (1,1) model again after the translation predicts that detailed process is:

If y ⁽⁰⁾(i)=x ⁽⁰⁾(i)+a ₀, this formulate adds a constant a with each data of original data sequence ₀, being about to the original data sequence translation, y is the new data sequence that obtains, and then can get the forecast model calculating formula:

$\widehat{x^{\left(0\right)}\left(i\right)=(y^{\left(0\right)}\left(1\right)-\frac{u^{\&prime;}}{a^{\&prime;}})(1-e^{a^{\&prime;}})}{e}^{-a^{\&prime;}(i-1)}-a_0---\left(8\right)$

A ', u ' are parameter to be identified in the formula, claim a ' to be the development coefficient, and u ' is the grey action, and must keep new sequence after the sequence translation is the plus or minus sequence.

7. the lifetime estimation method of the CFB boiler tube based on gray prediction theory as claimed in claim 1 is characterized in that, in the described step 4), the method that model is optimized is: carry out residual error corrections, use residual error to set up GM (1,1) model, the fundamental forecasting model is proofreaied and correct, and note generates residual error and is

${\mathrm{\&epsiv;}}^{\left(0\right)}\left(i\right)=x^1\left(i\right)-\widehat{x^1}\left(i\right),$

Set up GM (1,1) model to generating residual sequence, establishing selected translation constant is a ₁:

$\widehat{{\mathrm{\&epsiv;}}^0}\left(i\right)=({\mathrm{\&epsiv;}}^0\left(1\right)-\frac{u^{\&prime;\&prime;}}{a^{\&prime;\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i-1)}-a_1---\left(9\right)$

In conjunction with (7), (8) formula, get data correction generation model:

$\widehat{x^{\left(0\right)}}\left(i\right)=(y^{\left(0\right)}\left(1\right)-\frac{u^{\&prime;}}{a^{\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i^{\&prime;}-1)}-a_0+\mathrm{\&delta;}(i-\mathrm{\&tau;})[({\mathrm{\&epsiv;}}^0\left(1\right)-\frac{u^{\&prime;\&prime;}}{a^{\&prime;\&prime;}})(1-e^{a^{\&prime;}})e^{-a^{\&prime;}(i-\mathrm{\&tau;}-1)}-a_1]---\left(10\right)$

τ represents not to be used to set up the residual error number of residual error model in the formula,

$\mathrm{\&delta;}(i-\mathrm{\&tau;})=\left\{\begin{array}{cc}1& i>\mathrm{\&tau;}\\ 0& i\&le;\mathrm{\&tau;}\end{array}\right..$

8. the lifetime estimation method of the CFB boiler tube based on gray prediction theory as claimed in claim 1, it is characterized in that in the described step 4), the method that model is optimized is: utilize and wait the breath model GM (1 of reforming, 1), this model is whenever to replenish a fresh information, just removes data the oldest, to keep the number of data sequence, the sequence of Jian Liing such as is called at the breath sequence of reforming like this, reforms such as corresponding model is called cease model, also are Metabolic GM (1,1) model;

When the model accuracy disqualified upon inspection, can further set up GM (1, the 1) model of predicted value residual sequence, promptly to residual sequence ${\mathrm{\&epsiv;}}^0\left(i\right)=x^0\left(i\right)-\widehat{x^0}\left(i\right)$ (i=1,2,3 ..., n) add up to generate and set up GM (1,1) model, and then tiredly subtract the predicted value that reduction obtains residual error, and then the residual prediction value is added on the original predicted value, to improve precision;

As residual sequence ε ⁰(i) be on the occasion of the time, be normal condition; When having negative value, select a positive number a ', compare ε ⁰(i) absolute value of a minimum negative value gets final product slightly greatly in, is added to ε ⁰(i) in, make ε ⁰(i) become non-bearing can satisfy gray prediction to the non-negative condition of original data sequence requirement, then with ε ⁰(i) add up and generate non-negative ascending series and set up model, find the solution reduction; Notice that tired subtracting when reducing deducts a ' with predicted value, promptly get the residual prediction value, be added to then on the original predicted value, promptly get the modified value of last predicted value;

Do one time one step residual error corrections and do accuracy test again after trying to achieve modified value, can be again when defective once revised predicted value and raw data subtract each other and obtain two and go on foot residual sequences, use the same steps as correction again, carry out three times and can meet the demands generally at most.

9. the lifetime estimation method of the CFB boiler tube based on gray prediction theory as claimed in claim 1, it is characterized in that in the described step 6), calculating life of furnace method is, prepare a computer program by the forecast model after optimizing, finding the solution wear extent is the moment T of 70% δ _e, T _eDeduct current time T _nBe residual life R _i(h), i.e. R _i(h)=T _e-T _n, wherein, δ is the pipe initial wall thickness.