CN103406364A - Method for predicting thickness of hot-rolled strip steel on basis of improved partial robust M-regression algorithm - Google Patents

Abstract

The invention discloses a method for predicting the thickness of hot-rolled strip steel on the basis of an improved partial robust M-regression algorithm, and relates to a method for predicting the thickness of hot-rolled strip steel. By the aid of the method, the problem of incapability of acquiring an accurate analytical model or extremely high time consumption of a modeling procedure of an existing method for predicting the thickness of hot-rolled strip steel is solved. The method includes monitoring operational data of seven finishing mills to acquire observational variables (x<i>, y<i>), defining an input data matrix X and an output data matrix Y and computing initial values omega<i> of robust weighting factors; weighting the observational variables (x<i>, y<i>) to acquire predicted data, performing partial least-square analysis on the predicted data to acquire a partial least-square model of the predicted data and continuously computing to obtain a partial least-square regression model and regression coefficients B; judging whether estimation errors of a k<th> regression coefficient B and a (k-1)<th> regression coefficient B are smaller than a set threshold value or not, acquiring a certain regression coefficient B and determining a partial least-square regression model which is a prediction result for the thickness of the hot-rolled strip steel. The method can be widely applied to predicting the thickness of the hot-rolled strip steel.

Description

A kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm

Technical field

The present invention relates to a kind of hot-strip thickness prediction method.

Background technology

At many industrial circles, as Chemical Manufacture, papermaking and oil refining etc., for control and the monitoring that can survey regression relation analysis between data and quality of production variable and help production process.A kind of suitable regression model can be used as soft survey tool, assists process engineering teacher to predict the final production quality, and this control for production process, optimization and error diagnosis have great importance.

The main Key Performance Indicator (KPI) of hot strip mill is thickness, width and the shape with steel, and wherein, thickness is the decisive factor that strip quality and iron and steel are produced productive rate.Under the huge draught pressure of milling train, be can't be guaranteed by the method apart from obtaining the belt steel thickness of wanting simply arranged between work roll.At front several finishing mills, surpass rolling-mill housing under the draught pressure of 3000 tons and can form the outside stretching, extension of much half inch after the steel bar access arrangement.Therefore, most important according to the thickness that the pre-measuring tape steel of running status is final, can reach the purpose that accurate dimension is controlled.

The most reliable method of thickness prediction is to set up analytical model, yet on the one hand accurate analytical model be can't obtain or modeling process be extremely time consuming, nowadays the many producers in steel and iron industry have set up large-scale database be used to storing measurable procedural information on the other hand.

Summary of the invention

The present invention for the method that solves the pre existing Thickness Measurement by Microwave exist accurate analytical model be can't obtain or modeling process be extremely time consuming problem, thereby a kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm is provided.

A kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm, it comprises the steps:

Step 1: the operational data of 7 finishing mills of monitoring obtains observational variable (x _i, y _i), and according to observational variable (x _i, y _i) definition input data matrix X and output data matrix Y, calculate robust weighted factor initial value ω _i

The operational data of described finishing mill comprises the work roll average headway of every finishing mill, every finishing mill gross pressure, every finishing mill work roll crimp force;

Step 2: to observational variable (x _i, y _i) be weighted and process the acquisition prediction data

And to prediction data

Carry out partial least squares analysis, obtain the partial least square model of prediction data

And calculate Partial Least-Squares Regression Model for the first time

With regression coefficient B;

Step 3: according to the Partial Least-Squares Regression Model of step 2 acquisition

With regression coefficient B, calculate the robust weighted factor ω after upgrading _i

Step 4: according to the robust weighted factor ω after upgrading _iCalculate the Partial Least-Squares Regression Model of the k time

With the regression coefficient B of the k time, k>=2 wherein;

Step 5: whether the evaluated error that judges the regression coefficient B of the k time regression coefficient B and the k-1 time is less than setting threshold, enters step 6 if be less than, if be not less than, upgrades robust weighted factor ω _iAnd return to step 4;

Step 6: obtain regression coefficient B and determine Partial Least-Squares Regression Model Be hot-strip thickness prediction result.

Adopt the present invention to realize the hot-strip thickness prediction based on the inclined to one side robust M of modified regression algorithm.Regression coefficient obtains a regression model by the judgement of iterative computation and threshold value

, wherein Y is namely the thickness of the hot-strip of Key Performance Indicator KPI needs.This regression model has been realized according to input state variable prediction belt steel thickness, and the actual (real) thickness after not needing by the time out to adopt afterwards with steel; The benefit of prediction is to predict in advance the abnormal conditions that may occur, thereby obtains by suitable control the accurate dimension that we need.

The accompanying drawing explanation

Fig. 1 is the flow chart of a kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm of the present invention.

The specific embodiment

The specific embodiment one, in conjunction with Fig. 1, this specific embodiment is described.A kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm, it comprises the steps:

Step 1: the operational data of 7 finishing mills of monitoring obtains observational variable (x _i, y _i), and according to observational variable (x _i, y _i) definition input data matrix X and output data matrix Y, calculate robust weighted factor initial value ω _i

The operational data of described finishing mill comprises the work roll average headway of every finishing mill, every finishing mill gross pressure, every finishing mill work roll crimp force;

Step 2: to observational variable (x _i, y _i) be weighted and process the acquisition prediction data And to prediction data Carry out partial least squares analysis, obtain the partial least square model of prediction data

And calculate Partial Least-Squares Regression Model for the first time With regression coefficient B;

Step 3: according to the Partial Least-Squares Regression Model of step 2 acquisition With regression coefficient B, calculate the robust weighted factor ω after upgrading _i

Step 4: according to the robust weighted factor ω after upgrading _iCalculate the Partial Least-Squares Regression Model of the k time

With the regression coefficient B of the k time, k>=2 wherein;

Step 5: whether the evaluated error that judges the regression coefficient B of the k time regression coefficient B and the k-1 time is less than setting threshold, enters step 6 if be less than, if be not less than, upgrades robust weighted factor ω _iAnd return to step 4;

Step 6: obtain regression coefficient B and determine Partial Least-Squares Regression Model

Be hot-strip thickness prediction result.

What the specific embodiment two, this specific embodiment one were different is described step 1: the operational data of 7 finishing mills of monitoring obtains observational variable (x _i, y _i), and according to observational variable (x _i, y _i) definition input data matrix X and output data matrix Y, calculate robust weighted factor initial value ω _iProcess be:

The operational data of 7 finishing mills obtains observational variable (x _i, y _i), wherein:

X _iFor i the row vector of input data X, x _I1..., x _I7Be respectively the work roll average headway of every finishing mill, x _I8..., x _I14Be respectively every finishing mill gross pressure, x _I15..., x _I21Be respectively every finishing mill work roll crimp force; y _iFor final outlet hot-strip thickness;

According to input data X and output data Y, total Squared Error Loss center of calculating respectively input data X

Total Squared Error Loss center with the output data Y

$\stackrel{\&OverBar;}{e}\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_{\mathrm{inputi}}{x}_i$

$\stackrel{\&OverBar;}{e}\left(Y\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_{\mathrm{outputi}}{y}_i$

Wherein, n is sample total:

$k_{\mathrm{inputi}}=\frac{1}{\sqrt{1+{{4x}_i}^2}}/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{\sqrt{1+{{4x}_j}^2}}$

$k_{\mathrm{outputi}}=\frac{1}{\sqrt{1+{{4y}_i}^2}}/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{\sqrt{1+{{4y}_j}^2}}$

According to input observed quantity x _iTotal Squared Error Loss center with input data X Calculate respectively each input observed quantity x _iTotal Squared Error Loss center with the input data

Total Squared Error Loss distance:

$d_i=\frac{{[x_i-\stackrel{\&OverBar;}{e}\left(X\right)]}^2}{\sqrt{1+4{\left[\stackrel{\&OverBar;}{e}\left(X\right)\right]}^2}}$

According to output data y _iTotal Squared Error Loss center with the output data Y

Calculate respectively each output observed quantity y _iWith the output total Squared Error Loss of data center Difference residual error r _i:

$r_i=y_i-\stackrel{\&OverBar;}{e}\left(Y\right)$

Calculate residual error r _iTotal Squared Error Loss center

$\stackrel{\&OverBar;}{e}\left(r\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_{\mathrm{ri}}{r}_i$

Wherein:

$k_{\mathrm{ri}}=\frac{1}{\sqrt{1+{{4r}_i}^2}}/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{\sqrt{1+{{4r}_j}^2}}$

Calculate respectively robust leverage points weighted factor initial value

With the remaining point of robust weighted factor initial value

${\mathrm{\&omega;}}_i^x=f(\frac{d_i}{{\stackrel{\&OverBar;}{e}}_i\left(d_i\right)},c)$

${\mathrm{\&omega;}}_i^r=f(\frac{r_i-\stackrel{\&OverBar;}{e}\left(r\right)}{{\stackrel{\&OverBar;}{e}}_i\left(\right|r_i-\stackrel{\&OverBar;}{e}\left(r\right)\left|\right)},c)$

Wherein the formula right side is Fair function f (z, c), and expression formula is:

$f(z,c)=\frac{1}{1+{\left|\frac{z}{c}\right|}^2}$

Wherein c, for adjusting constant, gets c=4;

According to the remaining point of robust weighted factor initial value

With robust leverage points weighted factor initial value

Calculate robust weighted factor initial value ω _i:

${\mathrm{\&omega;}}_i={\mathrm{\&omega;}}_i^r{\mathrm{\&omega;}}_i^x.$

What the specific embodiment three, this specific embodiment were different from the specific embodiment one or two is described step 2: to observational variable (x _i, y _i) be weighted and process the acquisition prediction data

And to prediction data

Carry out partial least squares analysis, obtain the partial least square model of prediction data

Partial Least-Squares Regression Model With the process of regression coefficient B, be:

With every delegation of input data matrix X and output data matrix Y, be not multiplied by

Obtain the weighted observation data $(\sqrt{{\mathrm{\&omega;}}_i}{x}_i,\sqrt{{\mathrm{\&omega;}}_i}{y}_i);$

The weighted observation data are carried out to partial least squares analysis, obtain weighting least square model afterwards:

$X={\mathrm{TP}}^T+\tilde{X}$

$Y=\mathrm{TQ}+\tilde{Y}$

Wherein, T is score matrix; P is load matrix;

For the residual error of X, Q is the regression coefficient of score matrix T Residual error for Y;

Least square model after weighting is carried out to classical partial least-squares regressive analysis, obtain

$Y=\mathrm{XB}+\tilde{Y}$

Wherein B is regression coefficient;

The every delegation of score matrix T calculated all divided by

Reduce.

What the specific embodiment four, this specific embodiment were different from the specific embodiment three is described according to Partial Least-Squares Regression Model

With regression coefficient B, calculate the robust weighted factor ω after upgrading _iProcess be:

According to partial least square model

Vectorial t counts the score _iTotal Squared Error Loss distance:

$\stackrel{\&OverBar;}{e}\left(T\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_{\mathrm{ti}}{t}_i$

Wherein

$k_{\mathrm{ti}}=\frac{1}{\sqrt{1+{{4t}_i}^2}}/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{\sqrt{1+{{4t}_j}^2}}$

According to the Fair function, calculate respectively the remaining weighted factor of new robust With robust lever weighted factor

${\mathrm{\&omega;}}_i^r=f(\frac{r_i-\stackrel{\&OverBar;}{e}\left(r\right)}{{\stackrel{\&OverBar;}{e}}_i\left(\right|r_i-\stackrel{\&OverBar;}{e}\left(r\right)\left|\right)},c)$

${\mathrm{\&omega;}}_i^x=f(\frac{d_i}{{\stackrel{\&OverBar;}{e}}_i\left(d_i\right)},c)$

Wherein

r _i=y _i-t _iq

$d_i=\frac{{[t_i-\stackrel{\&OverBar;}{e}\left(T\right)]}^2}{\sqrt{1+4{\left[\stackrel{\&OverBar;}{e}\left(T\right)\right]}^2}}$

According to the remaining point of robust weighted factor

With robust leverage points weighted factor

Calculate new robust weighted factor value

${\mathrm{\&omega;}}_i={\mathrm{\&omega;}}_i^r{\mathrm{\&omega;}}_i^x.$

What the specific embodiment five, this specific embodiment were different from the specific embodiment one is that the described setting threshold of step 5 is 10 ^-2.

Specific embodiment: this specific embodiment is estimated the simulation comparison of PLS, inclined to one side robust M homing method PRM for contrasting the inclined to one side robust M of modified regression algorithm mPRM and offset minimum binary.

At first by the data sample (x of N=1000 group without abnormity point _0i, y _0i) being divided into two parts: a part is sample (x _i, y _i) quantity is n, be used to estimating regression coefficient B, wherein will add abnormity point; Another part is sample (x _Vi, y _Vi) quantity is N _rep=N-n, be used to verifying prediction accuracy.

Suppose score matrix (T ₀) _{N * h}And matrix (P ₀) _{P * h}Meet T ₀, P ₀～N (3,1).Data matrix (X ₀) _{N * p}By X ₀=T ₀P ₀ ^TCalculate X ₀Variable between will have good linear relationship.Corresponding output matrix Y ₀Meet

Y ₀=X ₀B ₀=T ₀P ₀ ^TB ₀

Β wherein ₀Be regression coefficient, might as well set Β ₀～N (3,1).In order to calculate the accuracy of estimating output, we adopt mean square deviation (MSE) concept, and mean square deviation is less, illustrate that the accuracy of forecast model output is higher.

Table 1

Table 1 is depicted as three kinds of method offset minimum binaries and estimates PLS, inclined to one side robust M homing method PRM, and the inclined to one side robust M of modified regression algorithm mPRM is in the performance existed in the abnormity point situation.The emulation mode proposed at " Partial robust M-regression " literary composition according to S.Serneel etc., respectively for three groups of different (n, p, h) repeat six kinds of different errors distribution (standardized normal distributions, pull-type distribution, t5 distributes, and t2 distributes, and Cauchy distributes and oblique line distributes) carry out emulation.

As can be seen from Table 1, offset minimum binary estimates PLS in the situation that noise is obeyed standardized normal distribution, and mean square deviation is minimum all the time, but when noise is obeyed asymmetric distribution, offset minimum binary estimates that the advantage of PLS has not just had, and its mean square deviation can become very large on the contrary.Robust M homing method PRM and the inclined to one side robust M of modified regression algorithm mPRM are all the time very little for the mean square deviation of Asymmetrical distributed noise partially, for front four kinds of errors, robust M homing method PRM is slightly better partially, but in the situation of latter two distribution, the inclined to one side robust M of modified regression algorithm mPRM is good than inclined to one side robust M homing method PRM.

In order further to compare the performance of the inclined to one side robust M of modified regression algorithm mPRM and inclined to one side robust M homing method PRM, set (n, p, h) be (100,5,2), noise is obeyed standardized normal distribution, by 5%, 10% in observation data, 15%, 20% and 25% normal point replaces with abnormity point, abnormity point is obeyed N (35,0.2), thereby a certain proportion of lever abnormity point just has been added in observation data.Table 2 has shown simulation result.

Table 2

As can be seen from Table 2, offset minimum binary estimates that PLS does not possess good robustness for the lever abnormity point of arbitrary proportion; Robust M homing method PRM keeps good robustness in the abnormity point situation below 15% partially, and still along with the increase of abnormity point ratio, the robustness of robust M homing method PRM can decline to a great extent partially; The inclined to one side robust M of modified regression algorithm mPRM, under the ratio condition of all considerations, all keeps fabulous robustness.

Claims (5)

1. the hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm, is characterized in that it comprises the steps:

Step 1: the operational data of 7 finishing mills of monitoring obtains observational variable (x _i, y _i), and according to observational variable (x _i, y _i) definition input data matrix X and output data matrix Y, calculate robust weighted factor initial value ω _i

The operational data of described finishing mill comprises the work roll average headway of every finishing mill, every finishing mill gross pressure, every finishing mill work roll crimp force;

Step 2: to observational variable (x _i, y _i) be weighted and process the acquisition prediction data

And to prediction data

Carry out partial least squares analysis, obtain the partial least square model of prediction data

And calculate Partial Least-Squares Regression Model for the first time

With regression coefficient B;

Step 3: according to the Partial Least-Squares Regression Model of step 2 acquisition

With regression coefficient B, calculate the robust weighted factor ω after upgrading _i

Step 4: according to the robust weighted factor ω after upgrading _iCalculate the Partial Least-Squares Regression Model of the k time

With the regression coefficient B of the k time, k>=2 wherein;

Step 5: whether the evaluated error that judges the regression coefficient B of the k time regression coefficient B and the k-1 time is less than setting threshold, enters step 6 if be less than, if be not less than, upgrades robust weighted factor ω _iAnd return to step 4;

Step 6: obtain regression coefficient B and determine Partial Least-Squares Regression Model

Be hot-strip thickness prediction result.

2. a kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm according to claim 1, is characterized in that described step 1: the operational data acquisition observational variable (x of 7 finishing mills of monitoring _i, y _i), and according to observational variable (x _i, y _i) definition input data matrix X and output data matrix Y, calculate robust weighted factor initial value ω _iProcess be:

The operational data of 7 finishing mills obtains observational variable (x _i, y _i), wherein:

X _iFor i the row vector of input data X, x _I1..., x _I7Be respectively the work roll average headway of every finishing mill, x _I8..., x _I14Be respectively every finishing mill gross pressure, x _I15..., x _I21Be respectively every finishing mill work roll crimp force; y _iFor final outlet hot-strip thickness;

According to input data X and output data Y, total Squared Error Loss center of calculating respectively input data X

Total Squared Error Loss center with the output data Y

$\stackrel{\&OverBar;}{e}\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_{\mathrm{inputi}}{x}_i$

$\stackrel{\&OverBar;}{e}\left(Y\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_{\mathrm{outputi}}{y}_i$

Wherein, n is sample total:

$k_{\mathrm{inputi}}=\frac{1}{\sqrt{1+{{4x}_i}^2}}/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{\sqrt{1+{{4x}_j}^2}}$

$k_{\mathrm{outputi}}=\frac{1}{\sqrt{1+{{4y}_i}^2}}/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{\sqrt{1+{{4y}_j}^2}}$

According to input observed quantity x _iTotal Squared Error Loss center with input data X Calculate respectively each input observed quantity x _iTotal Squared Error Loss center with the input data

Total Squared Error Loss distance:

$d_i=\frac{{[x_i-\stackrel{\&OverBar;}{e}\left(X\right)]}^2}{\sqrt{1+4{\left[\stackrel{\&OverBar;}{e}\left(X\right)\right]}^2}}$

According to output data y _iTotal Squared Error Loss center with the output data Y Calculate respectively each output observed quantity y _iWith the output total Squared Error Loss of data center

Difference residual error r _i:

$r_i=y_i-\stackrel{\&OverBar;}{e}\left(Y\right)$

Calculate residual error r _iTotal Squared Error Loss center

$\stackrel{\&OverBar;}{e}\left(r\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_{\mathrm{ri}}{r}_i$

Wherein:

$k_{\mathrm{ri}}=\frac{1}{\sqrt{1+{{4r}_i}^2}}/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{\sqrt{1+{{4r}_j}^2}}$

Calculate respectively robust leverage points weighted factor initial value

With the remaining point of robust weighted factor initial value

${\mathrm{\&omega;}}_i^x=f(\frac{d_i}{{\stackrel{\&OverBar;}{e}}_i\left(d_i\right)},c)$

${\mathrm{\&omega;}}_i^r=f(\frac{r_i-\stackrel{\&OverBar;}{e}\left(r\right)}{{\stackrel{\&OverBar;}{e}}_i\left(\right|r_i-\stackrel{\&OverBar;}{e}\left(r\right)\left|\right)},c)$

Wherein the formula right side is Fair function f (z, c), and expression formula is:

$f(z,c)=\frac{1}{1+{\left|\frac{z}{c}\right|}^2}$

Wherein c, for adjusting constant, gets c=4;

According to the remaining point of robust weighted factor initial value

With robust leverage points weighted factor initial value Calculate robust weighted factor initial value ω _i:

${\mathrm{\&omega;}}_i={\mathrm{\&omega;}}_i^r{\mathrm{\&omega;}}_i^x.$

3. a kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm according to claim 1 and 2, is characterized in that described step 2: to observational variable (x _i, y _i) be weighted and process the acquisition prediction data

And to prediction data

Carry out partial least squares analysis, obtain the partial least square model of prediction data

Partial Least-Squares Regression Model

With the process of regression coefficient B, be:

With every delegation of input data matrix X and output data matrix Y, be multiplied by respectively

Obtain the weighted observation data $(\sqrt{{\mathrm{\&omega;}}_i}{x}_i,\sqrt{{\mathrm{\&omega;}}_i}{y}_i);$

The weighted observation data are carried out to partial least squares analysis, obtain weighting least square model afterwards:

$X={\mathrm{TP}}^T+\tilde{X}$

$Y=\mathrm{TQ}+\tilde{Y}$

Wherein, T is score matrix; P is load matrix;

For the residual error of X, Q is the regression coefficient of score matrix T

Residual error for Y;

Least square model after weighting is carried out to classical partial least-squares regressive analysis, obtain

$Y=\mathrm{XB}+\tilde{Y}$

Wherein B is regression coefficient;

The every delegation of score matrix T calculated all divided by

Reduce.

4. a kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm according to claim 3, is characterized in that described according to Partial Least-Squares Regression Model With regression coefficient B, calculate the robust weighted factor ω after upgrading _iProcess be:

According to partial least square model Vectorial t counts the score _iTotal Squared Error Loss distance:

$\stackrel{\&OverBar;}{e}\left(T\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_{\mathrm{ti}}{t}_i$

Wherein

$k_{\mathrm{ti}}=\frac{1}{\sqrt{1+{{4t}_i}^2}}/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{\sqrt{1+{{4t}_j}^2}}$

According to the Fair function, calculate respectively the remaining weighted factor of new robust With robust lever weighted factor

${\mathrm{\&omega;}}_i^r=f(\frac{r_i-\stackrel{\&OverBar;}{e}\left(r\right)}{{\stackrel{\&OverBar;}{e}}_i\left(\right|r_i-\stackrel{\&OverBar;}{e}\left(r\right)\left|\right)},c)$

${\mathrm{\&omega;}}_i^x=f(\frac{d_i}{{\stackrel{\&OverBar;}{e}}_i\left(d_i\right)},c)$

Wherein

r _i=y _i-t _iq

$d_i=\frac{{[t_i-\stackrel{\&OverBar;}{e}\left(T\right)]}^2}{\sqrt{1+4{\left[\stackrel{\&OverBar;}{e}\left(T\right)\right]}^2}}$

According to the remaining point of robust weighted factor

With robust leverage points weighted factor

Calculate new robust weighted factor value

${\mathrm{\&omega;}}_i={\mathrm{\&omega;}}_i^r{\mathrm{\&omega;}}_i^x.$

5. a kind of hot-strip thickness prediction method based on the inclined to one side robust M of modified regression algorithm according to claim 1, is characterized in that the described setting threshold of step 5 is 10 ^-2.

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