CN103406364B

CN103406364B - Method for predicting thickness of hot-rolled strip steel on basis of improved partial robust M-regression algorithm

Info

Publication number: CN103406364B
Application number: CN201310326469.XA
Authority: CN
Inventors: 尹珅; 潘瑞; 王光; 卫作龙; 高会军
Original assignee: Bohai University
Current assignee: Bohai University
Priority date: 2013-07-31
Filing date: 2013-07-31
Publication date: 2015-04-22
Anticipated expiration: 2033-07-31
Also published as: CN103406364A

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, y), defining an input data matrix X and an output data matrix Y and computing initial values omega of robust weighting factors; weighting the observational variables (x, y) 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 Thickness Prediction Method of Hot-rolled Strip Based on Improved Partially Robust M-Regression Algorithm

技术领域technical field

本发明涉及一种热轧带钢厚度预测方法。The invention relates to a method for predicting the thickness of hot-rolled strip steel.

背景技术Background technique

在许多工业领域，如化工生产、造纸和炼油等，对于可测数据和生产质量变量之间的回归关系分析有助于生产过程的控制和监测。一种合适的回归模型可以作为软测量工具，协助过程工程师预测最终生产质量，这对于生产过程的控制、优化和错误诊断具有重要的意义。In many industrial fields, such as chemical production, papermaking and oil refining, etc., the analysis of the regression relationship between measurable data and production quality variables is helpful for the control and monitoring of the production process. A suitable regression model can be used as a soft-sensing tool to assist process engineers to predict the final production quality, which is of great significance for the control, optimization and error diagnosis of the production process.

带钢热轧机的主要关键性能指标(KPI)是带钢的厚度、宽度和形状，其中，厚度是带钢质量和钢铁生产产率的决定因素。在轧机的巨大轧制压力下，通过简单设置工作轧辊之间的距离来获取想要的带钢厚度的方法是无法得到保证的。在前几个精轧机超过3000吨的轧制压力下轧机机架在钢条进入设备后会形成多大半英寸的向外伸展。因此，根据运行状态预测带钢最终的厚度至关重要，可以达到精确尺寸控制的目的。The main key performance indicators (KPIs) for hot strip mills are strip thickness, width and shape, where thickness is the determining factor for strip quality and steel production yield. Achieving the desired strip thickness by simply setting the distance between the work rolls cannot be guaranteed under the enormous rolling pressure of the rolling mill. With rolling pressures in excess of 3,000 tons in the first few finishing mills, the mill stands would develop as much as half an inch of outreach after the bar enters the facility. Therefore, it is very important to predict the final thickness of the strip according to the operating state, so as to achieve the purpose of precise dimensional control.

预测厚度最可靠的方法是建立分析模型，然而一方面精确的分析模型是无法获得的或建模过程是极其消耗时间的，另一方面如今钢铁工业中的许多生产者建立了大型的数据库用于存储可测量的过程信息。The most reliable way to predict the thickness is to build an analytical model. However, on the one hand, accurate analytical models are not available or the modeling process is extremely time-consuming. On the other hand, many producers in the steel industry today have established large databases for Store measurable process information.

发明内容Contents of the invention

本发明为了解决现有预测厚度的方法存在精确的分析模型是无法获得的或建模过程是极其消耗时间的的问题，从而提供一种基于改进型偏鲁棒M回归算法的热轧带钢厚度预测方法。In order to solve the problem that the accurate analytical model cannot be obtained or the modeling process is extremely time-consuming in the existing methods for predicting the thickness, the present invention provides a hot-rolled strip thickness based on the improved partial robust M regression algorithm method of prediction.

一种基于改进型偏鲁棒M回归算法的热轧带钢厚度预测方法，它包括如下步骤：A method for predicting the thickness of hot-rolled strip steel based on the improved partial robust M regression algorithm, which includes the following steps:

步骤一：监测7台精轧机的工作数据获得观测变量(x_i,y_i)，并根据观测变量(x_i,y_i)定义输入数据矩阵X和输出数据矩阵Y，计算鲁棒加权因子初值ω_i；Step 1: Monitor the working data of the 7 finishing mills to obtain the observed variables (xi _, y _i ), and define the input data matrix X and output data matrix Y according to the observed variables ( _xi , y _i ), and calculate the initial robust weighting factor value ω _i ;

所述精轧机的工作数据包括每台精轧机的工作轧辊平均间距，每台精轧机总压力，每台精轧机工作轧辊卷曲力；The working data of the finishing mill includes the average spacing of the working rolls of each finishing mill, the total pressure of each finishing mill, and the crimping force of the working rolls of each finishing mill;

步骤二：对观测变量(x_i,y_i)进行加权处理获得预测数据并对预测数据进行偏最小二乘分析，获得预测数据的偏最小二乘模型并计算第一次偏最小二乘回归模型和回归系数B；Step 2: Weighting the observed variables ( _xi , _y ) to obtain forecast data and predict data Perform partial least squares analysis to obtain a partial least squares model for the forecast data and calculate the first partial least squares regression model and regression coefficient B;

其中，T为得分矩阵；P为负载矩阵；为X的残差，Q为得分矩阵T的回归系数，为Y的残差；Among them, T is the score matrix; P is the load matrix; is the residual of X, Q is the regression coefficient of the scoring matrix T, is the residual of Y;

步骤三：根据步骤二获得的偏最小二乘回归模型和回归系数B，计算更新后的鲁棒加权因子ω_i；Step 3: Partial least squares regression model obtained from step 2 and regression coefficient B, calculate the updated robust weighting factor ω _i ;

步骤四：根据更新后的鲁棒加权因子ω_i计算第k次的偏最小二乘回归模型和第k次的回归系数B，其中k≥2；Step 4: Calculate the k-th partial least squares regression model according to the updated robust weighting factor ω _i And the regression coefficient B of the kth time, where k≥2;

步骤五：判断第k次回归系数B和第k-1次的回归系数B的估计误差是否小于设定阈值，若小于则进入步骤六，若不小于则更新鲁棒加权因子ω_i并返回步骤四；Step 5: Determine whether the estimation error of the regression coefficient B of the kth time and the regression coefficient B of the k-1th time is less than the set threshold, if less than, enter step 6, if not, update the robust weighting factor ω _i and return to step Four;

步骤六：获取回归系数B并确定偏最小二乘回归模型即为热轧带钢厚度预测结果。Step 6: Obtain the regression coefficient B and determine the partial least squares regression model That is, the prediction result of hot-rolled strip thickness.

采用本发明实现了基于改进型偏鲁棒M回归算法的热轧带钢厚度预测。回归系数通过迭代计算与阈值的判断获得一个回归模型其中Y即是关键性能指标KPI需要的热轧带钢的厚度。这个回归模型实现了根据输入状态变量预测带钢厚度，而不需要等到带钢出来之后采后的实际厚度；预测的好处在于可以提前预知可能出现的异常情况，通过适当的控制从而获得我们需要的精确尺寸。The invention realizes the prediction of the thickness of the hot-rolled strip steel based on the improved partially robust M regression algorithm. The regression coefficient obtains a regression model through iterative calculation and threshold judgment Among them, Y is the thickness of the hot-rolled strip required by the key performance indicator KPI. This regression model realizes the prediction of the thickness of the strip steel based on the input state variables, without waiting for the actual thickness after the strip steel comes out; the advantage of the prediction is that it can predict possible abnormal situations in advance, and obtain what we need through appropriate control Exact size.

附图说明Description of drawings

图1为本发明一种基于改进型偏鲁棒M回归算法的热轧带钢厚度预测方法的流程图。Fig. 1 is a flow chart of a method for predicting the thickness of hot-rolled strip steel based on the improved partially robust M regression algorithm of the present invention.

具体实施方式Detailed ways

具体实施方式一、结合图1说明本具体实施方式。一种基于改进型偏鲁棒M回归算法的热轧带钢厚度预测方法，它包括如下步骤：DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 1. This specific implementation will be described with reference to FIG. 1 . A method for predicting the thickness of hot-rolled strip steel based on the improved partial robust M regression algorithm, which includes the following steps:

具体实施方式二、本具体实施方式一不同的是所述步骤一：监测7台精轧机的工作数据获得观测变量(x_i,y_i)，并根据观测变量(x_i,y_i)定义输入数据矩阵X和输出数据矩阵Y，计算鲁棒加权因子初值ω_i的过程为：Specific embodiment 2. The difference of this specific embodiment 1 is the step 1: monitor the working data of 7 finishing mills to obtain the observed variables ( _xi , y _i ), and define the input according to the observed variables ( _xi , y _i ) Data matrix X and output data matrix Y, the process of calculating the initial value ω _i of the robust weighting factor is:

7台精轧机的工作数据获得观测变量(x_i,y_i)，其中：Observation variables (x _i , y _i ) are obtained from the working data of 7 finishing mills, where:

x_i为输入数据X的第i个行向量，x_i1,…,x_i7分别为每台精轧机的工作轧辊平均间距，x_i8,…,x_i14分别为每台精轧机总压力，x_i15,…,x_i21分别为每台精轧机工作轧辊卷曲力；y_i为最终出口热轧带钢厚度；x _i is the i-th row vector of the input data X, x _i1 ,..., x _i7 are the average spacing of the work rolls of each finishing mill respectively, x _i8 ,..., x _i14 are the total pressure of each finishing mill respectively, x _i15 ,…, x _i21 are the crimping force of the working rolls of each finishing mill; y _i is the thickness of the final export hot-rolled strip;

根据输入数据X与输出数据Y，分别计算输入数据X的总平方损失中心和输出数据Y的总平方损失中心 According to the input data X and the output data Y, calculate the total square loss center of the input data X respectively and the total squared loss centered on the output data Y

$\overset{&OverBar; &OverBar;}{e e} ((X x)) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{inputi input} {x x}_{i i}$

$\overset{&OverBar; &OverBar;}{e e} ((Y Y)) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{outputi output} {y the y}_{i i}$

其中，n为样本总量：Among them, n is the total sample size:

${k k}_{inputi input} = = \frac{11}{\sqrt{11 + + 44 {x x}_{i i}^{22}}} / / {Σ Σ}_{j j = = 11}^{n no} \frac{11}{\sqrt{11 + + 44 {x x}_{j j}^{22}}}$

${k k}_{outputi output} = = \frac{11}{\sqrt{11 + + 44 {y the y}_{i i}^{22}}} / / {Σ Σ}_{j j = = 11}^{n no} \frac{11}{\sqrt{11 + + 44 {y the y}_{j j}^{22}}}$

根据输入观测量x_i和输入数据X的总平方损失中心分别计算每个输入观测量x_i与输入数据的总平方损失中心的总平方损失距离：The total squared loss centered on input observations _xi and input data X Compute the total squared loss centered for each input observation _xi with the input data separately The total squared loss distance of :

${d d}_{i i} = = \frac{{[[{x x}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((x x))]]}^{22}}{\sqrt{11 + + 44 {[[\overset{&OverBar; &OverBar;}{e e} ((X x))]]}^{22}}}$

根据输出数据y_i和输出数据Y的总平方损失中心分别计算每个输出观测量y_i与输出数据总平方损失中心的差值残差r_i：The total squared loss centered on output data y _i and output data Y Compute each output observation y _i separately from the total squared loss center of the output data The difference residual r _i :

${r r}_{i i} = = {y the y}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((Y Y))$

计算残差r_i的总平方损失中心 Compute the total squared loss centered on the residual r _i

$\overset{&OverBar; &OverBar;}{e e} ((r r)) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{ri the ri} {r r}_{i i}$

其中：in:

${k k}_{ri the ri} = = \frac{11}{\sqrt{11 + + {44 r r}_{i i}^{22}}} / / {Σ Σ}_{j j = = 11}^{n no} \frac{11}{\sqrt{11 + + {44 r r}_{j j}^{22}}}$

分别计算鲁棒杠杆点加权因子初值和鲁棒残余点加权因子初值 Calculate the initial value of the weighting factor of the robust leverage point separately and the initial value of the robust residual point weighting factor

${ω ω}_{i i}^{x x} = = f f ((\frac{{d d}_{i i}}{{\overset{&OverBar; &OverBar;}{e e}}_{i i} (({d d}_{i i}))},, c c))$

${ω ω}_{i i}^{r r} = = f f ((\frac{{r r}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((r r))}{{\overset{&OverBar; &OverBar;}{e e}}_{i i} ((| | {r r}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((r r)) | |))},, c c))$

其中公式右侧为Fair函数f(z,c)，表达式为：The right side of the formula is the Fair function f(z,c), and the expression is:

$f f ((z z,, c c)) = = \frac{11}{11 + + {| | \frac{z z}{c c} | |}^{22}}$

其中c为调整常数，取c＝4；Where c is the adjustment constant, take c=4;

根据鲁棒残余点加权因子初值和鲁棒杠杆点加权因子初值计算鲁棒加权因子初值ω_i：According to the initial value of the weighting factor of the robust residual point and the initial value of the robust leverage point weighting factor Calculate the initial value ω _i of the robust weighting factor:

${ω ω}_{i i} = = {ω ω}_{i i}^{r r} {ω ω}_{i i}^{x x} . .$

具体实施方式三、本具体实施方式与具体实施方式一或二不同的是所述步骤二：对观测变量(x_i,y_i)进行加权处理获得预测数据并对预测数据进行偏最小二乘分析，获得预测数据的偏最小二乘模型偏最小二乘回归模型和回归系数B的过程为：Specific embodiment 3. The difference between this specific embodiment and specific embodiment 1 or 2 is the step 2: weighting the observed variables (xi _, y _i ) to obtain forecast data and predict data Perform partial least squares analysis to obtain a partial least squares model for the forecast data Partial Least Squares Regression Model And the process of regression coefficient B is:

分别用输入数据矩阵X和输出数据矩阵Y的每一行乘以得到加权观测数据 $(\sqrt{ω_{i}} x_{i}, \sqrt{ω_{i}} y_{i});$ Multiply each row of the input data matrix X and output data matrix Y by Get weighted observation data $(\sqrt{ω_{i}} x_{i}, \sqrt{ω_{i}} {the y}_{i});$

对加权观测数据进行偏最小二乘分析，得到加权之后的最小二乘模型：Partial least squares analysis is performed on the weighted observation data, and the weighted least squares model is obtained:

$X x = = {TP TP}^{T T} + + \overset{~ ~}{X x}$

$Y Y = = TQ T Q + + \overset{~ ~}{Y Y}$

其中，T为得分矩阵；P为负载矩阵；为X的残差，Q为得分矩阵T的回归系数为Y的残差；Among them, T is the score matrix; P is the load matrix; is the residual of X, and Q is the regression coefficient of the scoring matrix T is the residual of Y;

对加权之后的最小二乘模型进行经典偏最小二乘回归分析，得到The classical partial least squares regression analysis is performed on the weighted least squares model, and it is obtained

$Y Y = = XB XB + + \overset{~ ~}{Y Y}$

其中B为回归系数；where B is the regression coefficient;

计算得到的得分矩阵T每一行均除以进行还原。Each row of the calculated score matrix T is divided by to restore.

具体实施方式四、本具体实施方式与具体实施方式三不同的是所述根据偏最小二乘回归模型和回归系数B，计算更新后的鲁棒加权因子ω_i的过程为：Embodiment 4. The difference between this embodiment and Embodiment 3 is that according to the partial least squares regression model and regression coefficient B, the process of calculating the updated robust weighting factor ω _i is:

根据偏最小二乘模型计算得分向量t_i的总平方损失距离：According to the partial least squares model Compute the total squared loss distance for the score vector t _i :

$\overset{&OverBar; &OverBar;}{e e} ((T T)) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{ti ti} {t t}_{i i}$

其中in

${k k}_{ti ti} = = \frac{11}{\sqrt{11 + + {44 t t}_{i i}^{22}}} / / {Σ Σ}_{j j = = 11}^{n no} \frac{11}{\sqrt{11 + + 44 {t t}_{j j}^{22}}}$

根据Fair函数，分别计算新的鲁棒残余加权因子和鲁棒杠杆加权因子 According to the Fair function, calculate the new robust residual weighting factor respectively and the robust leverage weighting factor

其中in

r_i＝y_i-t_iqr _i =y _i -t _i q

${d d}_{i i} = = \frac{{[[{t t}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((T T))]]}^{22}}{\sqrt{11 + + 44 {[[\overset{&OverBar; &OverBar;}{e e} ((T T))]]}^{22}}}$

根据鲁棒残余点加权因子和鲁棒杠杆点加权因子计算新的鲁棒加权因子值According to the robust residual point weighting factor and the robust leverage point weighting factor Compute new robust weighting factor values

${ω ω}_{i i} = = {ω ω}_{i i}^{r r} {ω ω}_{i i}^{x x} . .$

具体实施方式五、本具体实施方式与具体实施方式一不同的是步骤五所述设定阈值为10^-2。Embodiment 5. This embodiment is different from Embodiment 1 in that the threshold value set in step 5 is 10 ⁻² .

具体实施例：本具体实施例用于对比改进型偏鲁棒M回归算法mPRM与偏最小二乘估计PLS、偏鲁棒M回归方法PRM的仿真对比。Specific embodiments: This specific embodiment is used to compare the simulation comparison of the improved partial robust M regression algorithm mPRM with the partial least squares estimation PLS and the partial robust M regression method PRM.

首先将N＝1000组无异常点的数据样本(x_0i,y_0i)分成两部分：一部分为样本(x_i,y_i)数量为n，用于估计回归系数B，其中将加入异常点；另一部分为样本(x_vi,y_vi)数量为N_rep＝N-n，用于验证预测准确度。First, divide N=1000 groups of data samples (x _0i , y _0i ) without abnormal points into two parts: one part is samples ( _xi , y _i ) with a number of n, which is used to estimate the regression coefficient B, which will add abnormal points; The other part is that the number of samples (x _vi , y _vi ) is N _rep =Nn, which is used to verify the prediction accuracy.

假设得分矩阵(T₀)_N×h和矩阵(P₀)_p×h满足T₀,P₀～N(3,1)。数据矩阵(X₀)_N×p由X₀＝T₀P₀ ^T计算得到，X₀的变量之间将会有很好的线性关系。相应的输出矩阵Y₀满足It is assumed that the scoring matrix (T ₀ ) _N×h and the matrix (P ₀ ) _p×h satisfy T ₀ , P ₀ ˜N(3,1). The data matrix (X ₀ ) _N×p is calculated by X ₀ =T ₀ P ₀ ^T , and there will be a good linear relationship between the variables of X ₀ . The corresponding output matrix Y ₀ satisfies

Y₀＝X₀B₀＝T₀P₀ ^TB₀ Y ₀ ＝X ₀ B ₀ ＝T ₀ P ₀ ^T B ₀

其中Β₀是回归系数，不妨设定Β₀～N(3,1)。为了计算预计输出的精确性，我们采用均方差(MSE)概念，均方差值越小，则说明预测模型输出的准确性越高。Among them, Β ₀ is the regression coefficient, it is advisable to set Β ₀ ~ N (3,1). In order to calculate the accuracy of the predicted output, we use the concept of mean square error (MSE), the smaller the value of the mean square error, the higher the accuracy of the predicted model output.

表1Table 1

表1所示为三种方法偏最小二乘估计PLS，偏鲁棒M回归方法PRM，改进型偏鲁棒M回归算法mPRM在存在异常点情况下的性能。根据S.Serneel等在“Partial robustM-regression”一文所提出的仿真方法，分别对于三组不同的(n,p,h)重复六种不同的误差分布(标准正态分布，拉式分布，t5分布，t2分布，柯西分布以及斜线分布)进行仿真。Table 1 shows the performance of the three methods of partial least squares estimation PLS, partial robust M regression method PRM, and improved partial robust M regression algorithm mPRM in the presence of outliers. According to the simulation method proposed by S. Serneel et al. in the article "Partial robustM-regression", six different error distributions (standard normal distribution, pull distribution, t5 distribution, t2 distribution, Cauchy distribution, and slash distribution) for simulation.

从表1中可以看出，偏最小二乘估计PLS在噪声服从标准正态分布的情况下，均方差始终是最小的，但是当噪声服从非对称分布的时候，偏最小二乘估计PLS的优势就没有了，反而其均方差会变得非常大。偏鲁棒M回归方法PRM和改进型偏鲁棒M回归算法mPRM对于非对称分布噪声的均方差则始终很小，对于前四种误差，偏鲁棒M回归方法PRM略胜一筹，但是最后两个分布的情况下，改进型偏鲁棒M回归算法mPRM则比偏鲁棒M回归方法PRM好。It can be seen from Table 1 that the partial least squares estimation PLS has the smallest mean square error when the noise obeys the standard normal distribution, but when the noise obeys an asymmetric distribution, the partial least squares estimation PLS has the advantage There will be no more, but its mean square error will become very large. The partial robust M regression method PRM and the improved partial robust M regression algorithm mPRM are always small for the mean square error of asymmetrically distributed noise. For the first four errors, the partial robust M regression method PRM is slightly better, but the last two In the case of two distributions, the improved partial robust M regression algorithm mPRM is better than the partial robust M regression method PRM.

为了进一步比较改进型偏鲁棒M回归算法mPRM和偏鲁棒M回归方法PRM的性能，设定(n,p,h)为(100,5,2)，噪声服从标准正态分布，将观测数据中的5％，10％，15％，20％和25％的正常点替换为异常点，异常点服从N(35,0.2)，从而一定比例的杠杆异常点就被加入到了观测数据中。表2显示了仿真结果。In order to further compare the performance of the improved partial robust M regression algorithm mPRM and the partial robust M regression method PRM, set (n, p, h) as (100, 5, 2), the noise obeys the standard normal distribution, and the observation 5%, 10%, 15%, 20% and 25% of the normal points in the data are replaced by abnormal points, and the abnormal points obey N(35,0.2), so that a certain proportion of leverage abnormal points are added to the observation data. Table 2 shows the simulation results.

表2Table 2

从表2中可以看出，偏最小二乘估计PLS对于任意比例的杠杆异常点都不具备良好的鲁棒性；偏鲁棒M回归方法PRM在15％以下的异常点情况下保持良好的鲁棒性，但是随着异常点比例的增加，偏鲁棒M回归方法PRM的鲁棒性会大幅下降；改进型偏鲁棒M回归算法mPRM在所有考虑的比例条件下，均保持极好的鲁棒性。It can be seen from Table 2 that the partial least squares estimation PLS does not have good robustness for any proportion of leverage outliers; the partial robust M regression method PRM maintains good robustness under the condition of outliers below 15%. However, as the proportion of outliers increases, the robustness of the partial robust M regression method PRM will drop significantly; the improved partial robust M regression algorithm mPRM maintains excellent robustness under all proportion conditions considered. Stickiness.

Claims

1. a method for predicting the thickness of hot-rolled strip steel based on the improved partial robust M regression algorithm, is characterized in that it comprises the steps:

Step 1: Monitor the working data of the 7 finishing mills to obtain the observed variables (xi _, y _i ), and define the input data matrix X and output data matrix Y according to the observed variables ( _xi , y _i ), and calculate the initial robust weighting factor value ω _i ;

The working data of the finishing mill includes the average spacing of the working rolls of each finishing mill, the total pressure of each finishing mill, and the crimping force of the working rolls of each finishing mill;

Step 2: Weighting the observed variables ( _xi , _y ) to obtain forecast data and predict data Perform partial least squares analysis to obtain a partial least squares model for the forecast data and calculate the first partial least squares regression model and regression coefficient B;

Among them, T is the score matrix; P is the load matrix; is the residual of X, Q is the regression coefficient of the scoring matrix T, is the residual of Y;

Step 3: Partial least squares regression model obtained from step 2 and regression coefficient B, calculate the updated robust weighting factor ω _i ;

Step 4: Calculate the k-th partial least squares regression model according to the updated robust weighting factor ω _i And the regression coefficient B of the kth time, where k≥2;

Step 5: Determine whether the estimation error of the regression coefficient B of the kth time and the regression coefficient B of the k-1th time is less than the set threshold, if less than, enter step 6, if not, update the robust weighting factor ω _i and return to step Four;

Step 6: Obtain the regression coefficient B and determine the partial least squares regression model That is, the prediction result of hot-rolled strip thickness.

2. a kind of hot-rolled steel strip thickness prediction method based on improved partial robust M regression algorithm according to claim 1, is characterized in that described step one: monitor the work data of 7 finishing mills and obtain observed variable (x _i , y _i ), and define the input data matrix X and output data matrix Y according to the observed variables ( _xi , y _i ), the process of calculating the initial value ω _i of the robust weighting factor is:

Observation variables (x _i , y _i ) are obtained from the working data of 7 finishing mills, where:

x _i is the i-th row vector of the input data X, x _i1 ,..., x _i7 are the average spacing of the work rolls of each finishing mill respectively, x _i8 ,..., x _i14 are the total pressure of each finishing mill respectively, x _i15 ,…, x _i21 are the crimping force of the working rolls of each finishing mill; y _i is the thickness of the final export hot-rolled strip;

According to the input data X and the output data Y, calculate the total square loss center of the input data X respectively and the total squared loss centered on the output data Y

\overset{&OverBar; &OverBar;}{e e} ((X x)) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{inputi input} {x x}_{i i}

\overset{&OverBar; &OverBar;}{e e} ((Y Y)) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{outputi output} {y the y}_{i i}

Among them, n is the total sample size:

{k k}_{inputi input} = = \frac{11}{\sqrt{11 + + {44 x x}_{i i}^{22}}} / / {Σ Σ}_{j j = = 11}^{n no} \frac{11}{\sqrt{11 + + {44 x x}_{j j}^{22}}}

{k k}_{outputi output} = = \frac{11}{\sqrt{11 + + {44 y the y}_{i i}^{22}}} / / {Σ Σ}_{j j = = 11}^{n no} \frac{11}{\sqrt{11 + + {44 y the y}_{j j}^{22}}}

The total squared loss centered on input observations _xi and input data X Compute the total squared loss centered for each input observation _xi with the input data separately The total squared loss distance of :

{d d}_{i i} = = \frac{{[[{x x}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((X x))]]}^{22}}{\sqrt{11 + + 44 {[[\overset{&OverBar; &OverBar;}{e e} ((X x))]]}^{22}}}

The total squared loss centered on output data y _i and output data Y Compute each output observation y _i separately from the total squared loss center of the output data The difference residual r _i :

{r r}_{i i} = = {y the y}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((Y Y))

Compute the total squared loss centered on the residual r _i

\overset{&OverBar; &OverBar;}{e e} ((r r)) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{ri the ri} {r r}_{i i}

in:

{k k}_{ri the ri} = = \frac{11}{\sqrt{11 + + {44 r r}_{i i}^{22}}} / / {Σ Σ}_{j j = = 11}^{n no} \frac{11}{\sqrt{11 + + {44 r r}_{j j}^{22}}}

Calculate the initial value of the weighting factor of the robust leverage point separately and the initial value of the robust residual point weighting factor

{ω ω}_{i i}^{x x} = = f f ((\frac{{d d}_{i i}}{{\overset{&OverBar; &OverBar;}{e e}}_{i i} (({d d}_{i i}))},, c c))

{ω ω}_{i i}^{r r} = = f f ((\frac{{r r}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((r r))}{{\overset{&OverBar; &OverBar;}{e e}}_{i i} ((| | {r r}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((r r)) | |))},, c c))

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

f f ((z z,, c c)) = = \frac{11}{11 + + {| | \frac{z z}{c c} | |}^{22}}

Where c is the adjustment constant, take c=4;

According to the initial value of the weighting factor of the robust residual point and the initial value of the robust leverage point weighting factor Calculate the initial value ω _i of the robust weighting factor:

{ω ω}_{i i} = = {ω ω}_{i i}^{r r} {ω ω}_{i i}^{x x} . .

3. A kind of method for predicting the thickness of hot-rolled steel strip based on the improved partial robust M regression algorithm according to claim 1 or 2, characterized in that said step ₂ : _performing Weighted processing to obtain forecast data and predict data Perform partial least squares analysis to obtain a partial least squares model for the forecast data Partial Least Squares Regression Model And the process of regression coefficient B is:

Multiply each row of the input data matrix X and output data matrix Y by Get weighted observation data

(\sqrt{ω_{i}} x_{i}, \sqrt{ω_{i}} {the y}_{i});

Partial least squares analysis is performed on the weighted observation data, and the weighted least squares model is obtained:

X x = = {TP TP}^{T T} + + \overset{~ ~}{X x}

Y Y = = TQ T Q + + \overset{~ ~}{Y Y}

Among them, T is the score matrix; P is the load matrix; is the residual of X, and Q is the regression coefficient of the scoring matrix T is the residual of Y;

The classical partial least squares regression analysis is performed on the weighted least squares model, and it is obtained

Y Y = = XB XB + + \overset{~ ~}{Y Y}

where B is the regression coefficient;

Each row of the calculated score matrix T is divided by to restore.

4. a kind of hot-rolled steel strip thickness prediction method based on improved partial robust M regression algorithm according to claim 3, is characterized in that described according to partial least squares regression model and regression coefficient B, the process of calculating the updated robust weighting factor ω _i is:

According to the partial least squares model Compute the total squared loss distance for the score vector t _i :

\overset{&OverBar; &OverBar;}{e e} ((T T)) = = {Σ Σ}_{i i = = 11}^{n no} {k k}_{ti ti} {t t}_{i i}

in

{k k}_{ti ti} = = \frac{11}{\sqrt{11 + + {44 t t}_{i i}^{22}}} / / {Σ Σ}_{j j = = 11}^{n no} \frac{11}{\sqrt{11 + + {44 t t}_{j j}^{22}}}

According to the Fair function, calculate the new robust residual weighting factor respectively and the robust leverage weighting factor

{ω ω}_{i i}^{r r} = = f f ((\frac{{r r}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((r r))}{{\overset{&OverBar; &OverBar;}{e e}}_{i i} ((| | {r r}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((r r)) | |))},, c c))

{ω ω}_{i i}^{x x} = = f f ((\frac{{d d}_{i i}}{{\overset{&OverBar; &OverBar;}{e e}}_{i i} (({d d}_{i i}))},, c c))

in

r _i =y _i -t _i q

{d d}_{i i} = = \frac{{[[{t t}_{i i} - - \overset{&OverBar; &OverBar;}{e e} ((T T))]]}^{22}}{\sqrt{11 + + 44 {[[\overset{&OverBar; &OverBar;}{e e} ((T T))]]}^{22}}}

According to the robust residual point weighting factor and the robust leverage point weighting factor Compute new robust weighting factor values

{ω ω}_{i i} = = {ω ω}_{i i}^{r r} {ω ω}_{i i}^{x x} . .

5 . The method for predicting the thickness of hot-rolled strip steel based on the improved partially robust M regression algorithm according to claim 1 , wherein the threshold value set in step five is 10 ^-2 .