The geometric parameters describing the features of the cross-sectional profile of the hot-rolled strips do not give a complete picture of the flatness acquired by the cold-rolled strips rolled from these strips. An additional analysis showed that there are four characteristic classes of cross-sectional profiles of hot rolled strips that have a significant effect on the shape of the strips during cold rolling, three of which negatively affect the flatness of the cold rolled strips. The cross-sectional profiles of hot-rolled strips with a concave middle part and (or) marginal thickenings lead to the appearance of edge waviness, peak-like cross-sectional profiles cause central warping. Therefore, the actual task is to determine the factual shape of cross-sectional profile. Sixth order polynomials were used to digitalize and parameterize hot-rolled profile. As a result, we developed analytic function of the transverse profile, which keeps important information about its near-edge areas and features in the middle part. To assign a specific cross-sectional profile of a hot-rolled strip to one of four characteristic classes of cross-sections, mathematical software was developed, called a classifier, and implemented with the programming environment R. To classify the profiles of the hot-rolled cross-section according to characteristic classes, a linear discriminant method was used as a machine learning method analysis. The result is an adequate mathematical model for recognizing the shape of the cross-sectional profile.

描述热轧带材横截面轮廓特征的几何参数并不能完整描述由这些带材轧制而成的冷轧带材所获得的平整度。另一项分析表明，热轧带钢的横截面轮廓有四种特征类别，它们在冷轧过程中对带钢的形状有显着影响，其中三种对冷轧带钢的平直度有负面影响。中间部分凹入和（或）边缘加厚的热轧带钢横截面轮廓导致边缘出现波纹，峰状横截面轮廓导致中心翘曲。因此，实际的任务是确定横截面轮廓的实际形状。六阶多项式用于数字化和参数化热轧轮廓。因此，我们开发了横向轮廓的分析函数，该函数将有关其近边缘区域和特征的重要信息保留在中间部分。为了将热轧带钢的特定横截面轮廓分配给四种特征横截面类别之一，开发了称为分类器的数学软件，并在编程环境 R 中实现。对热轧带钢的轮廓进行分类根据特征类轧制横截面，采用线性判别法作为机器学习方法分析。结果是用于识别横截面轮廓形状的适当数学模型。它将有关其近边缘区域和特征的重要信息保留在中间部分。为了将热轧带钢的特定横截面轮廓分配给四种特征横截面类别之一，开发了称为分类器的数学软件，并在编程环境 R 中实现。对热轧带钢的轮廓进行分类根据特征类轧制横截面，采用线性判别法作为机器学习方法分析。结果是用于识别横截面轮廓形状的适当数学模型。它将有关其近边缘区域和特征的重要信息保留在中间部分。为了将热轧带钢的特定横截面轮廓分配给四种特征横截面类别之一，开发了称为分类器的数学软件，并在编程环境 R 中实现。对热轧带钢的轮廓进行分类根据特征类轧制横截面，采用线性判别法作为机器学习方法分析。结果是用于识别横截面轮廓形状的适当数学模型。并用编程环境R实现。为了根据特征类别对热轧横截面的轮廓进行分类，使用线性判别方法作为机器学习方法分析。结果是用于识别横截面轮廓形状的适当数学模型。并用编程环境R实现。为了根据特征类别对热轧横截面的轮廓进行分类，使用线性判别方法作为机器学习方法分析。结果是用于识别横截面轮廓形状的适当数学模型。