| 主权项 |
1. A method for at least one of a production and a processing of a web-shaped material, comprising:
activating at least one measuring system to record m measurement values yik (i=1, . . . , n; k=1, . . . , m) per measurement position over at least a portion of a width s of web-shaped material at n different measurement positions xi (i=1, . . . , n) within a fixed time interval Δt; determining a rational quality number Q, wherein a value of the rational quality number corresponds to a quality of the web-shaped material considered acceptable and lies within an acceptance range that is to be empirically determined for the production process, wherein the acceptance range has a lower limit U and an upper limit O, wherein U and O are in each case rational numbers subject to the condition according to:
U≦Q≦O, Formula 1:where the value of the quality number Q is calculated as a function of moments Mi according to formula 2, where:
Q=f(Mi), Formula 2:and where the moments Mi are calculated from a function value of a cubic spline function S(x) for the n different measurement positions according to formula 3, where:
S(x)=αi+βi·(x−xi)+γi·(x−xi)2+δi·(x−xi)3, Formula 3:where:
x is a control variable in direction of the width s of the web-shaped material in interval [xi, xi+1] xi (i=1, . . . , n) are the measurement positions corresponding to knots of the cubic spline function, for moments Mi,and wherein, based on the measurement values yik and using the formula 3 as a representation of the function value of the cubic spline function S(x), formula 4 applies to the moments Mi, where
Mi=2·γi (i=1, . . . , n-1), Mn=2·γn-1+δn-1·(xn−xn-1)[A2], Formula 4: wherein continued production and/or processing of the web-shaped material is controlled based at least in part upon the calculated quality number Q. |
