Simplex Enhanced Numerical Modeling of the Temperature Distribution in a Hydrogen Cooled Steel Coil Annealing Process

Soft-Sensing in Batch Annealing Based on Finite Differential Method and Support Vector Regression

“…Haouam et al [14] have proposed a numerical model of the temperature distribution of steel coils during annealing process on differential equations of heat conduction. The resolution is performed with the method of finite differences.…”

“…Thus, the linear regression in the high-dimensional feature space corresponds to the non-linear regression in the low dimensional input space R n . The prediction f(T) from the pattern T can be mathematically written as dot products in the low-dimensional input space as the following [27]: (14) where: l is the number of patterns (T 1 , T 2 , …, T l ), parameter b represents the limit value or the so-called threshold and parameters α i , α i * have an intuitive interpretation as the forces of pull or push of f(T i ) to y i measurement. If considering two points T i T j , then the function that returns the scalar product between their images in high-dimensional feature space is known as the kernel function.…”

“…If considering two points T i T j , then the function that returns the scalar product between their images in high-dimensional feature space is known as the kernel function. In equation (14), the kernel function k(T i , T j ) = (Ф(T i ) • Ф(T j )) is established. In this paper the Gaussian kernel, i.e., function k(T i , T j ) = e -γ‖Ti-Tj ‖ 2 (γ represents the sensitivity of the kernel function) and linear kernel, i.e., k(T i , T j ) = T i T T j were used.…”