Method and apparatus for the real time quantification of subtle variations in a planar material and identification of a corresponding source of the identified subtle variation

A method for diagnosing a source of subtle variations in a property of a planar material, the method comprising:

• (a) moving the planar material in a machine direction along a manufacturing line having a plurality of machine components, at least a subset of the plurality of machine components having a known corresponding periodic frequency, or period, the planar material having a longitudinal direction extending along the machine direction and a transverse direction perpendicular to the longitudinal direction;
• (b) obtaining from a sensor a dataset, the dataset comprising values of the property in an array of points extending along the machine direction and the transverse direction of the planar material, wherein the points taken along the transverse direction are at a series of longitudinal locations on the planar material, and wherein a distance between subsequent longitudinal locations is less than one half a travel distance of the planar material in one cycle of a machine component of the subset of the plurality of machine components having a highest periodic frequency;
• (c) measuring variations in the dataset and statistically decomposing the measured variations into a linear sum of components attributable to at least one of a predetermined mechanical cause and a predetermined fluid mechanical cause that are categorized into at least one of a plurality of groups:
• wherein a first group of the plurality of groups comprise a standing transverse direction variation, which include variations having no change in the machine direction that are estimated by taking an average of a multitude of transverse arrays along the machine direction, wherein the standing transverse direction variation is decomposed into one of (i) a periodic variation in the transverse direction and (ii) a non-periodic variation in the transverse direction,
• wherein the non-periodic variation in the transverse direction is attributed to an imperfection in a machine component and the periodic variation in the transverse direction is attributed to at least one of a fluid mechanical, a solid mechanical, a plastic, or a viscoelastic instability in the planar material;
• wherein a second group of the plurality of groups comprise oscillatory variations in the machine direction, which are decomposed into one of (i) periodic variations corresponding to a known frequency of a machine component, (ii) periodic variations independent of known frequencies of machine components, (iii) oscillatory but not truly periodic variations and (iv) variations associated with a feed stock,
• wherein the periodic variations at a known frequency are attributed to machine components associated with that frequency and the periodic variations independent of known frequencies are decomposed into one of (i) variations corresponding to a measured process variation, (ii) variations in the feedstock, (iii) non-periodic oscillatory variations attributed to non-periodic limit cycles in processing conditions and (iv) variations attributed to the fluid mechanical, the solid mechanical, the plastic, or the viscoelastic instability in the planar material;
• wherein a third group of the plurality of groups comprise non-oscillatory variations in the machine direction, which are attributed to a long term aperiodic variation in one of a feed material and a processing condition on the manufacturing line;
• (d) determining that the subset of the plurality of machine components exhibit oscillatory variations in the machine direction having periodic variations corresponding to the known frequencies of the subset, and determining a nature of a mechanical defect for the exhibited oscillatory variations by identifying a periodic length on the planar material corresponding to a period of each machine component in the subset and estimating, for each machine component in the subset, an average variation at each point in the transverse direction along a series of longitudinal locations occurring during movement of the planar material in the machine direction during one cycle, or period, of the machine component to create a two dimensional array of the variation at the machine component known frequency of the machine component, and diagnosing imperfections in the machine component corresponding to the known frequency of the machine component, wherein the exhibited oscillatory variations repeating at a known component frequency are decomposed into one of (i) variations manifesting as straight lines perpendicular to the machine direction and are attributed to machine components that exhibit a frequency of the variation;
• (ii) subtle variations manifesting as straight lines at an angle to the transverse direction and are attributed to machine components that exhibit variations at that frequency combined with asymmetry of the line;
• and (iii) subtle variations manifesting as curved lines and are attributed to a machine component that exhibits that frequency combined with at least one of the fluid mechanical, the solid mechanical, the plastic, or the viscoelastic effects in the planar material;
• (e) obtaining a residual variation based on the estimated average variation for at least one machine component in the subset;
• and
• (f) when the residual variation exceeds an acceptable level, perform a corrective action in the manufacturing line given the nature of the mechanical defect.