Title:
Method and system for characterizing streak defects in web structures
Kind Code:
A1


Abstract:
Streak defects in web structures are characterized by electronically obtaining a plurality of results of a plurality of tests of a web structure, electronically determining a location of and/or a quantification of one or more streak defects based on the plurality of results, and electronically characterizing the streak defect(s) as being static or stochastic based on the plurality of results.



Inventors:
Keller, Steven D. (Manlius, NY, US)
Kellomaki, Markku (Haapaniemi, FI)
Application Number:
10/245058
Publication Date:
03/20/2003
Filing Date:
09/16/2002
Assignee:
The Research Foundation of State University of New York (Albany, NY, US)
Primary Class:
Other Classes:
162/263, 700/129
International Classes:
D21G9/00; (IPC1-7): D21F11/00
View Patent Images:



Primary Examiner:
FORTUNA, JOSE A
Attorney, Agent or Firm:
HESLIN ROTHENBERG FARLEY & MESITI PC (ALBANY, NY, US)
Claims:
1. A method for characterizing a streak defect of a web structure, the method comprising: electronically obtaining a plurality of results of a plurality of tests of a portion of the web structure; electronically determining the streak defect of the portion of the web structure based on the plurality of results; and electronically characterizing the streak defect based on the plurality of results.

2. The method of claim 1 wherein the electronically characterizing comprises characterizing the streak defect to comprise a static non-uniformity.

3. The method of claim 1 wherein the electronically characterizing comprises characterizing the streak defect to comprise a random non-uniformity.

4. The method of claim 1 wherein the web structure comprises paper making components and the electronically obtaining comprises electronically obtaining the plurality of results during a papermaking process.

5. The method of claim 1 wherein the plurality of results comprises a plurality of results in a cross paper machine direction of a paper machine at a plurality of locations in a machine direction of the paper machine.

6. The method of claim 1 wherein the electronically determining the streak defect comprises at least one of locating and quantifying the streak defect.

7. The method of claim 1 wherein the streak defect comprises a static component and a stochastic component and the electronically characterizing comprises separating the static component and the stochastic component from each other.

8. The method of claim 1 further comprising electronically comparing the streak defect to a threshold criteria and providing an indication of the streak defect to a user, in response to the streak defect exceeding the threshold criteria.

9. The method of claim 1 further comprising providing an indication to a user of a potential cause of the streak defect based on the determining and the characterizing.

10. The method of claim 9 wherein the providing the indication comprises providing an indication of a portion of a paper machine potentially causing the streak defect.

11. The method of claim 1 wherein the streak defect comprises a non-uniformity of the web structure in at least one of gloss, moisture, thickness, formation, roughness, grammage and mass.

12. The method of claim 1 wherein the determining comprises creating a plurality of local energy maps from the plurality of results.

13. The method of claim 12 wherein the creating comprises applying a continuous wavelet transform to the plurality of results.

14. The method of claim 12 further comprising creating a composite local energy map from the plurality of local energy maps.

15. The method of claim 14 wherein the characterizing comprises decomposing the composite local energy map into a static mean profile local energy map and a composite stochastic normalized local energy map.

16. A system for characterizing a streak defect of a web structure comprising a testing mechanism for performing a plurality of tests on a portion of the web structure; a computing unit couplable to said testing mechanism; and wherein the computing unit is adapted to obtain a plurality of results of the plurality of tests, adapted to electronically determine the streak defect of the web structure based on the plurality of results, and adapted to electronically characterize the streak defect based on the plurality of results.

17. The system of claim 16 wherein the electronically characterizing comprises characterizing the streak defect to comprise at least one of a static non-uniformity and a random non-uniformity.

18. The system of claim 16 wherein the web structure comprises paper making components and said testing mechanism is adapted to perform the plurality of tests on the paper making components during a papermaking process.

19. The system of claim 16 wherein said testing mechanism is adapted to perform the plurality of tests in a cross paper machine direction of a paper machine at a plurality of locations in a machine direction of the paper machine.

20. The system of claim 16 wherein the electronically determining the streak defect comprises at least one of locating and quantifying the streak defect.

21. The system of claim 16 wherein the streak defect comprises a static component and a stochastic component and the electronically characterizing comprises separating the static component and the stochastic component from each other.

22. The system of claim 16 wherein the electronically characterizing comprises electronically comparing the streak defect to a threshold criteria and providing an indication of the streak defect to a user, in response to the streak defect exceeding the threshold criteria.

23. The system of claim 16 wherein the computing unit is adapted to provide an indication to a user of a potential cause of the streak defect based on the determining and the characterizing.

24. The system of claim 23 wherein the providing the indication comprises providing an indication of a portion of a paper machine potentially causing the streak defect.

25. The system of claim 16 wherein the streak defect comprises a non-uniformity of the web structure in at least one of gloss, moisture, thickness, formation, roughness, grammage and mass.

26. The system of claim 16 wherein the determining comprises creating a plurality of local energy maps from the plurality of results.

27. The system of claim 26 wherein the creating comprises applying a continuous wavelet transform to the plurality of results.

28. The system of claim 26 wherein said computing unit is adapted to create a composite local energy map from the plurality of local energy maps.

29. The system of claim 28 wherein the characterizing comprises decomposing the composite local energy map into a static mean profile local energy map and a composite stochastic normalized local energy map.

30. At least one program storage device readable by a machine, tangibly embodying at least one program of instructions executable by the machine to perform a method for characterizing at least one streak defect of a web structure, the method comprising: electronically obtaining a plurality of results of a plurality of tests of a portion of the web structure; electronically determining the streak defect of the portion of the web structure based on the plurality of results; and electronically characterizing the streak defect based on the plurality of results.

31. The at least one program storage device of claim 30 wherein the electronically characterizing comprises characterizing the streak defect to comprise at least one of a static non-uniformity and a random non-uniformity.

32. The at least one program storage device of claim 30 wherein the web structure comprises paper making components and the electronically obtaining comprises electronically obtaining the plurality of results during a papermaking process.

33. The at least one program storage device of claim 30 wherein the plurality of results comprises a plurality of results in a cross paper machine direction of a paper machine at a plurality of locations in a machine direction of the paper machine.

34. The at least one program storage device of claim 30 wherein the electronically determining the streak defect comprises at least one of locating and quantifying the streak defect.

35. The at least one program storage device of claim 30 wherein the streak defect comprises a static component and a stochastic component and the electronically characterizing comprises separating the static component and the stochastic component from each other.

36. The at least one program storage device of claim 30 wherein the method further comprises comparing the streak defect to a threshold criteria and providing an indication of the streak defect to a user, in response to the streak defect exceeding the threshold criteria.

37. The at least one program storage device of claim 30 wherein the method further comprises providing an indication to a user of a potential cause of the streak defect based on the determining and the characterizing.

38. The at least one program storage device of claim 37 wherein the providing the indication comprises providing an indication of a portion of a paper machine potentially causing the streak defect.

39. The at least one program storage device of claim 30 wherein the streak defect comprises a non-uniformity of the web structure in at least one of gloss, moisture, thickness, formation, roughness, grammage and mass.

40. The at least one program storage device of claim 30 wherein the determining comprises creating a plurality of local energy maps from the plurality of results.

41. The at least one program storage device of claim 40 wherein the creating comprises applying a continuous wavelet transform to the plurality of results.

42. The at least one program storage device of claim 40 further comprising creating a composite local energy map from the plurality of local energy maps.

43. The at least one program storage device of claim 42 wherein the characterizing comprises decomposing the composite local energy map into a static mean profile local energy map and a composite stochastic normalized local energy map.

Description:

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority from provisional U.S. application No. 60/322,226 filed on Sep. 14, 2001, the entire disclosure of which is incorporated by reference herein.

TECHNICAL FIELD

[0002] This invention relates generally to web structures and more particularly to methods and apparatus for characterizing streak defects in web structures.

BACKGROUND OF THE INVENTION

[0003] Production of web structures, for example, paper, may result in variation of certain properties throughout such web structures. The quality of paper depends heavily on the uniformity of material distribution, within the plane of the sheet and also through its thickness. For example, the heterogeneous porestructure substantially influences the absorption of inks and fountain solutions in printing. Also, small-scale variations in grammage, for example, from about 0.1 mm to 100 mm, referred to as mass formation, can have a significant impact on the print quality, coating uniformity, optical and mechanical properties. The stochastic (i.e., random) nature of the fiber distribution within the sheet is well recognized. Paper fibers may exhibit an increased tendency to cluster together and increased flocculation as compared to that found in a random distribution of fibers depending on fiber dimensions, forming conditions and wet end chemistry. Numerous investigators have developed methods to measure, analyze, and model the manner in which fibers are distributed in the final sheet. The uniformity of the fibrous structure may be further degraded by variability in the papermaking process. For example, deterministic variability in a machine direction (MD) grammage may result from paper machine vibration or non-uniform stock supply. Non-uniformity in a cross machine direction (CD) may occur at large scales, as, for example, edge effects due to pressure imbalances in the headbox or shrinkage in the dryer section, or at small scales such as uneven slice opening or the turbulent flows in the headbox and forming zone. Thus, the formation of paper is dependent on a variety of factors that determine the size distribution and intensity of features over a broad range of scale, in regular or random spatial distributions. To examine the statistically nonstationary nature of machine made papers, methods are necessary to identify characteristic scales for these factors.

[0004] Cross machine non-uniformities with relatively high persistency in the machine direction are referred to as “streaks” or “streak defects”. The occurrence of streaks is a serious concern for product quality from lightweight papers to board grades. Streaks may be regularly or randomly distributed across the cross machine direction. Their position may be essentially fixed, or they may be unstable and vary in cross machine position as the sheet is examined at different locations in the machine direction. Streaks are not limited to variations in grammage, but may also appear as variations in floc size distribution (formation), mean fiber orientation, filler or moisture content, thickness, surface roughness or even Z-directional tensile strength.

[0005] Analytical methods used to assess paper variability, such as grammage, thickness, roughness, moisture, etc., typically involve statistical or spectral analysis of the measured data arrays. It is most common to determine results for large areas, which provides an indication of the quality of the web in general, but information of the non-uniformity of paper variability data is usually lost. The presence of streaks or other localized non-uniformities are neither detected nor characterized using such methods. More rigorous methods are needed in order to obtain a thorough decomposition of the contributions from the various sources that contribute to the overall structure.

[0006] Thus, there is a need for systems and methods for determining the stochastic or deterministic nature of streak defects in the formation of web structures, specifically in the formation of paper and paper based products.

SUMMARY OF THE INVENTION

[0007] The present invention provides, in a first aspect, a method for characterizing a streak defect of a web structure. The method includes electronically obtaining a plurality of results of a plurality of tests of a portion of the web structure, electronically determining a location of and/or quantification of the streak defect based on the plurality of results, and electronically characterizing the streak defect as being static or stochastic based on the plurality of results.

[0008] The determining an existence of the streak defect may include creating a plurality of local energy maps from the plurality of results and creating a composite local energy map from the plurality of local energy maps. Creating the plurality of local energy maps may comprise applying a continuous wavelet transform to the plurality of results. The characterizing of the streak defect may include decomposing the composite local energy map into a static mean profile local energy map and a composite stochastic normalized local energy map.

[0009] The present invention provides, in a second aspect, a system for characterizing a streak defect of a web structure which includes a testing mechanism for testing a portion of the web structure which is couplable to a computing unit. The computing unit is adapted to obtain, from the testing mechanism, a plurality of results of a plurality of tests on the portion of the web structure, to electronically determine an existence and/or location of the streak defect of the portion of the web structure, and to electronically characterize the streak defect as being static or stochastic based on the plurality of results.

[0010] The computing unit may determine the location of the streak defect and/or its quantity by creating a plurality of local energy maps from the plurality of results and creating a composite local energy map from the plurality of local energy maps. Creating the plurality of local energy maps may comprise applying a continuous wavelet transform to the plurality of results. The characterizing of the streak defect may include decomposing the composite local energy map into a static mean profile local energy map and a composite stochastic normalized local energy map.

[0011] Further, the present invention provides, in a third aspect, at least one program storage device readable by a machine, tangibly embodying at least one program instruction executable by the machine to perform a method for characterizing a streak defect of a web structure. The method includes electronically obtaining a plurality of results of a plurality of tests of a portion of the web structure, electronically determining a location of and/or a quantification of the streak defect based on the plurality of results, and electronically characterizing the streak defect as being static or stochastic based on the plurality of results.

[0012] The determining of the location of the streak defect and/or its quantity may include creating a plurality of local energy maps from the plurality of results and creating a composite local energy map from the plurality of local energy maps. Creating the plurality of local energy maps may comprise applying a continuous wavelet transform to the plurality of results. The characterizing of the streak defect may include decomposing the composite local energy map into a static mean profile local energy map and a composite stochastic normalized local energy map.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0014] The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features, and advantages of the invention will be readily understood from the following detailed description of preferred embodiments taken in conjunction with the accompanying drawings in which:

[0015] FIG. 1 is a block diagram of an apparatus for characterizing streak defects in accordance with the present invention;

[0016] FIG. 2 is a side view of a portion of FIG. 1 depicting a paper machine;

[0017] FIG. 3 is a top view of a portion of FIGS. 1-2;

[0018] FIG. 4 is a flow diagram of a method for characterizing streak defects in paper stocks in accordance with the present invention;

[0019] FIG. 5 is an illustration of a creation of composite local energy maps from local energy maps in accordance with the present invention;

[0020] FIG. 6 is another embodiment of a method for characterizing streak defects in accordance with the present invention;

[0021] FIG. 7 is an illustration of the decomposition of a composite local energy map into static and stochastic components in accordance with the present invention;

[0022] FIG. 8 is an example of a characterization of stochastic and static defects of grammage and apparent density in accordance with the present invention; and

[0023] FIG. 9 is an illustration of a depiction of streak defects of a thickness of paper in accordance with the present invention.

DETAILED DESCRIPTION

[0024] In accordance with the principles of the present invention, a method for characterizing streak defects in web structures and a system for performing the method are provided.

[0025] In an exemplary embodiment depicted in FIG. 1, a system 5 for characterizing streak defects in paper includes a computing unit 10 coupled to a testing mechanism 20 for performing tests at various points in a papermaking process on a papermaking machine 40 or portions thereof.

[0026] Computing unit 10 may be a processor or computing unit, for example, an IBM mainframe or server, a Hewlett Packard system running HP-UX, a Unix derivative Operating System, or a personal computer, such as a personal computer with Microsoft WINDOWS as the operating system, and based on the Intel PC architecture. Computing unit 10 includes, for example, one or more central processing units, memory, one or more storage devices and one or more input/output devices, as is well known in the art. For example, computing unit 10 may have a display 11 to enable visual output for viewing by a user.

[0027] Computing unit 10 may be coupled to testing mechanism 20 via a standard connection 22, such as any type of wire connection, token ring or network connection, to name just a few examples. One example of a communications protocol used by one or more of these connections is TCP/IP which allows connection to a computer network, such as, for example, a local area network or a global computer network (e.g., the INTERNET).

[0028] Paper making machine 40 may be, for example, a Fourdrinier type paper machine, as is known by those skilled in the art. Papermaking machine 40 includes a wet end 45 which receives pulp or papermaking stock and a dry end 50 from which completed paper may be discharged, as depicted in FIGS. 1-2. The pulp passes through a headbox 50 which distributes the pulp on a wire 55 for forming paper. The pulp may pass through one or more presses 57 and then through a dryer section 60 which may include a plurality of steam heated cylinders 62 for drying the pulp. As noted above, throughout the papermaking process, non-uniformities or streaks may result in the pulp and/or final paper which is discharged from papermaking machine 40.

[0029] Testing mechanism 20 (FIG. 1) may include one or more devices for measuring properties of paper on paper forming machine 40 at particular points in the papermaking process. These measurements may be taken continuously or at specified instances of time as directly controlled by an operator or controlled by an operator through programming of computing unit 10 coupled to testing mechanism 20.

[0030] Further, the streaks or non-uniformities determined by apparatus 5 may be stochastic (i.e., random) or deterministic (i.e., static). The non-uniformities may exist in several properties of the paper making material (i.e, pulp), including gloss, moisture, thickness, floc size distribution or formation, roughness, grammage or mass in a given location, and fiber orientation, among others, as is known by those skilled in the art. These non-uniformities may be created due to the effects of the headbox, slice width of the headbox, the wire, or the effect of the dryer section, among others, as is known by those skilled in the art.

[0031] Measurements of the non-uniformities may be taken in the machine direction, that is, from the wet side to the dry side, or in the cross machine direction which is perpendicular to the machine direction, as described above. In one example, a profile or a plurality of measurements is taken in the cross machine direction at one or more particular points along the machine direction. Many such profiles of measurements in the cross machine direction may be taken at particular points in the machine direction at a certain point in time or continuously. FIG. 3 illustrates a portion of paper making machine 40 depicted in FIGS. 1-2 and further indicates a plurality of profiles 200, 210, 220, and 230 in the cross machine direction. For example, discrete measurement points in profile 200 include a measuring point 201 and a measuring point 202 in the cross machine direction. Exemplary measurement devices are described hereinafter.

[0032] Computing unit 10 may control testing mechanism 20 to conduct one or more tests on paper forming components (i.e., pulp), at various points as the components pass through paper machine 40. Computing unit 10 electronically and desirably automatically obtains a result of the test, e.g., from testing mechanism 20. Computing unit 10 may then automatically determine one or more streak defects in the pulp or finished paper based on a comparison among the measurements to determine if any of the measurements are non-uniform relative to one another in the cross machine direction. One or more results of non-uniformities in the cross machine direction are compared to one another to determine if such non-uniformities continue in the machine direction.

[0033] In a more specific example, a determination of streak defect locations in the cross machine direction and machine direction and the quantification thereof may be determined by computing unit 10 by a discrete implementation of a continuous wavelet transform to the data collected by testing mechanism 20. An application of this technique is described in “Wavelet Analysis of Simulated Paper Formation” by Keller et al., Paper and Timber, Volume 81, No. 719/99, and “Analysis of Paper Variability Using the Continuous Wavelet Transform”, by Keller et al., Paper and Timber, Vol. 81, No. 6/1999. Further, the use of the wavelet technique to determine stochastic and deterministic non-uniformities in the formation of paper is further described in “Characterization of Non-Stationary Structural Non-Uniformities in Paper”, 2001, by Keller et al., which was included in provisional U.S. patent application No. 60/322,226 from which the present application claims priority.

[0034] The wavelet transform is a method which provides spatial and spectral information in one and two dimensional data arrays. Unlike other methods used to characterize paper formation, such as first order statistics, texture analysis or power spectral analysis, this method assumes that the data set is statistically non-stationary in at least one direction, e.g., the machine cross direction. Specifically, a one dimensional wavelet transform is applied using a second order Gaussian function selective to the extreme of the data set. In order to achieve efficiency of processing continuous data signals, the wavelet transform is applied in the Fourier domain. In this way, several magnitudes of wavelength axis can be covered by selecting only a small subset of the most important individual wavelengths. Moreover, the discrete continuous wavelet transform is able to handle a continuous flux of data. This differs from most algorithms that make use of orthonormal basis wavelets applied in the spatial domain.

[0035] The continuous wavelet transform is analogous to a Fourier transform and converts a continuous input signal or function into continuous spatial and scale parameters. A discrete wavelet transform refers to a specific implementation of the wavelet transform where the spatial and scale parameters are discretely varied according to a set algorithm.

[0036] In order to analyze non-uniformities such as streaks, a non-uniformity is assumed to be persistent in one direction, i.e., the machine direction, for a given length interval, so that statistical stationarity can be assumed. In order to distinguish between streaks that result from generally increased or decreased grammage, for example, or those that result from variation in the structure, which causes a difference in the local formation, different averaging schemes may be applied to sequential sets of wavelet coefficients. For example, a data set of grammage variation (i.e., mass formation) may be obtained from a transmission radiographic image from an off line instrument, or from an online fixed beam detector, as is known by those skilled in the art. The wavelet coefficients are determined from this data set using the continuous wavelet transform via the Fourier domain. By averaging and normalization the static and stochastic components can be separated, for the finite data set, or in a continuous manner. Thus, the contributions of different types of streaks can be separated from the measured spectral energy map.

[0037] Computing unit 10 may perform such an algorithm (i.e., a continuous wavelet transform) on both finite and continuous data arrays. Thus, data may be continuously collected and processed as a paper making process proceeds. A clean bifurcation of the contributions of static and stochastic contributions to the paper variability data are thus provided. While examples have been used for paper formation, the method has applicability to variability of other properties such as thickness, density, roughness, moisture, or ash for paper, among others. It also has applicability for other web processes where variability of selected properties is of concern.

[0038] Thus, data may be collected from one or more points in the papermaking process by testing mechanism 20 and may be obtained by computing unit 10. Streak defects or non-uniformities in the paper at particular locations may be determined by computing unit 10 based on this data. The streak defects may be located in both the machine direction and cross machine direction and they may be characterized to determine if they are random (i.e., stochastic) defects or static (i.e., deterministic) defects. Static defects are often continually created due to settings of particular components of the papermaking machine or particularities of the papermaking process.

[0039] FIG. 4 depicts a flow chart which outlines one exemplary embodiment of a process for qualifying non-uniformities (i.e., streak defects) in paper of the present invention. At step 300, profiles of data in a cross machine direction are collected continuously in increments of 1 mm in a machine direction of paper machine 40. At step 310, a continuous wavelet transform is applied to the data and local energy maps are derived for each profile at step 320. Composite local energy maps are created at step 330 based on the profiles created at step 320. FIG. 5 depicts a creation of a composite local energy map from a plurality of local energy maps for a plurality of grammage profiles, for example, taken at 1 mm intervals in the machine direction. The composite local energy map is created by averaging the local energy maps. Returning to FIG. 4, decomposition into static and stochastic components is performed for composite local energy maps at step 340. Thus, this data may be analyzed relative to the location and quantification of static and stochastic non-uniformities in the paper stock. It will be understood by those skilled in the art that the local energy maps and composite local energy maps may be created for other web non-uniformities.

[0040] A more specific example of the flow chart in FIG. 4 is presented in FIG. 6. An electronic signal is received regarding paper variability profiles by computing unit 10 from testing mechanism 20 at step 510. The wavelet transfer is directly applied to these profiles at step 520 as they are received as indicated by an arrow 512. This is more particularly described below for steps 530-550. At step 515 an average of multiple cross machine profiles is taken. This average is continuously updated as the signal is fed from testing mechanism 20 to computing unit 10. A wavelet transform is applied to this average at step 520 as the individual profiles simultaneously have a wavelet transform applied to them.

[0041] Specifically, step 530 includes a Fourier transform being taken of the profiles and the average of the multiple profiles. Calculations are performed by applying a basis wavelet in the Fourier domain to the individual profile and the average of the multiple profiles at step 540. The basis wavelet is described in the following equation:

ΨG2(x)=(x2−1)e−x2/2 (equation 1)

[0042] This wavelet is known as the Mexican Hat or Marr wavelet as described in the Keller et al., articles referenced above. At step 550, an inverse Fourier transform of wavelet coefficients found in step 540 is performed. The inverse Fourier transform is described in the following equation:

{tilde over (f)}(a,b)=a1/2F−1({circumflex over (f)}(k){circumflex over (Ψ)} *(ka)(b) (equation 2)

[0043] F−1 denotes inverse Fourier transform, {circumflex over (f)}(k) is the Fourier transform of the function, and {circumflex over (Ψ)}(k) is Fourier transform of the mother wavelet wherein a is the scale of the wavelet (spatial width) and b is the position (center) of the wavelet. The performance of the inverse Fourier transform brings the data back into the spatial domain to facilitate representation and analysis thereof. At step 560, local energy densities ρ(a,b) are calculated from the results of the wavelet transform of the individual profiles as described in the following equation: 1ρ(a,b)da ab=CΨ-1f~(a,b)2 da dba2(equation  3)embedded image

[0044] CΨ is known as the admissibility constant as described in the Keller articles referenced above.

[0045] Particularly, wavelet coefficients are squared to convert amplitude to energy thus enhancing prominent features of the individual profiles and the average profiles. The local energy densities may be graphically represented in a two-dimensional spectral plot where wavelength is plotted as a function of the position in the data set, and the color or gray level intensity represents the spectral density or energy. Thus, the local energy densities are plotted as a function of wavelength at a given position within a sample set. These are referred to as local energy maps, as described above for FIGS. 4-5. For example, a color red may depict a highest energy and a color blue may depict a lowest energy, as depicted in a color scale 990 (FIG. 9). Further, the energy represents a population or quantity of flocs per unit area, for example.

[0046] At step 570 the local energy densities may be averaged to calculate the composite local energy density or mean energy map <ρ(a, b)>, as described above, illustrated in the following equation, and depicted in FIG. 5: 2ρ(a,b)da db=CΨ-1a21N(i=1Nfi~(a,b)2)da db=d Cab=CΨ-1a2fi~(a,b)2da db(equation  4)embedded image

[0047] N is the number of rows of the matrix. Thus, composite local energy maps may be plotted, as described above for FIGS. 4-5 and below for FIGS. 7-9.

[0048] Also, at step 560 a local energy density is obtained for the average profiles by squaring the result of step 520 to result in the static mean profile at step 575. Thus, at step 580 the static mean profile local energy may be subtracted from the composite local energy to result in a composite stochastic local energy density. Specifically, the following equation illustrates that the composite local energy density decomposes into static mean profile local energy (SMP-LE) (ρh(a,b)da db) and the stochastic local variation: 3ρ(a,b)=CΨ-1a2(fi~(a,b)2)+CΨ-1a2(gi~(a,b)2)=:ρh(a,b)+ρg(a,b)(equation  5)embedded image

[0049] {tilde over (g)}i(x) refers to the stochastic signal. When interested in local variation, it is preferred to analyze the composite stochastic local energy density (SLE) <ρg(a,b)> rather than <ρ(a,b)>. The composite normalized stochastic local energy density (CNSLE) (<ρgN(a,b)>da db) may then be obtained through the following equation: 4ρgN(a,b)=ρg(a,b)fi(b)=1fi(b)CΨ-1a2(f~i(a,b)2-f~i(a,b)2)(equation  6)embedded image

[0050] Thus, the stochastic component 585 and the static component 590 may then be indicated to a user through plotting of the static mean profile local energy map and the composite normalized stochastic local energy map.

[0051] Further, such information regarding a particular point in the paper making process, the quantification, and the random or static nature of a streak defect may be provided to the user through an output device, for example printer 30 or a display screen 11. The relative characterizations and/or location may be indicated in a composite local energy map which displays a distribution of energy among wavelets of different scales and at different positions, as described above. These non-uniformities may be displayed using different colors to indicate the degree of non-uniformities. These local energy maps may also be decomposed into two different maps which contain the energy related to the static and stochastic components, for example the static mean grammage profile and the local stochastic variability.

[0052] An example of a graphical analysis resulting from the method described above is depicted in FIG. 7. Specifically, FIG. 7 shows the results obtained from the analysis of paper made on a pilot paper machine, where streaks were present. As can be seen in a grammage map 610, the streaks are well formed and relatively stable (within the sampling region). The machine direction is oriented vertically as indicated by an arrow 611. A mean grammage profile 620 and a composite local energy map (C-LE) 630 directly below, show a pattern which suggests two principal wavelengths of flocs. Three streaks with wavelengths of about 50 mm are visible, and represent a static. In mean grammage profile 620, a variance about the streak sawtooth pattern is also apparent. Composite local energy map 630 quantifies the mean size of these two patterns, which can be seen as a row of circular peaks, and the ridge of elongated peaks centered at about 2-3 mm. While individual features are apparent, their size does not dominate the image. Thus, the general structural differences are more clearly visible in the spectral plots (i.e., by the differences in color).

[0053] The two lower spectral plots show the isolated static component, a static mean profile local energy (SMP-LE) power map 640, and a stochastic component, a composite normalized stochastic local energy (CNS-LE) power map 650. A clean separation of the two components is depicted. SMP-LE map 640 shows the energy related to the wavy character of the grammage variation. A subtle decrease in wavelength and intensity of the streaks, from image left to right, may be seen. CNS-LE map 650 has also a very rich structure of its own where the floc structure (i.e., formation) of the paper can be seen as the right of spectral peaks with λ intercept of about 2-3 mm. It also shows, for example, that at positions 50-75 mm the mean floc size is decreased independent of the local grammage profile, while floc intensity increases toward the right side of the image.

[0054] A different pilot machine sample was analyzed by applying the wavelet theory and comparing a grammage measurement analysis 700 and an apparent density measurement analysis 750, as depicted in FIG. 8. The sampling region is smaller (50 mm) than what was shown in FIG. 7 (200 mm). For a grammage map 705, a mean grammage profile map 710, a static component map 715 and a stochastic component map 720, the results are much the same as discussed above. Large-scale streak artifacts are isolated in the SMP-LE map 715, and the underlying formation structure is illustrated in CNS-LE map 720.

[0055] FIG. 9 shows a thickness map 910 and mean thickness values, as determined using a twin laser system. For example, a thickness might be mapped using an instrument based on two sided, laser profilometry, as described in Keller et al., “Characterization of Non-Stationary Structural Non-Uniformities in Paper” (at page 11). Thickness map 910 was used to determine apparent density map 755 shown in apparent density analysis 750 (FIG. 8). FIG. 9 also provides a representation 920 of the out of plane deformation that was determined for this sample. For example, a ridge that exists at the 40 mm position was visible to the unaided eye.

[0056] Returning to FIG. 8, apparent density map 755 suggests a relatively uniform apparent density. Since the paper depicted in the maps was uncalendered, this would be expected by those skilled in the art. Several large-scale features are visible in SMP-LE map 765. Again, the limited sample set (i.e., 50 mm) may make this data more subject to influence by individual features. The subtle differences between the peak locations cannot be attributed to actual differences in the structure. However, the stochastic component depicted in CNS-LE map 770 shows spatial variation in apparent density. Two large clusters, centered at 27 mm and 47 mm are apparent. Since there does not appear to be a correlation with the grammage map results, the differences must be due to differences in the internal structure.

[0057] In another embodiment of the present invention, as data is obtained by computing unit 20 from one or more testing units coupled to the paper making machine, local energy maps may be derived for each profile in a cross machine direction. The composite local energy map may be created from these local energy maps. Streaks may be determined based on this composite local energy map and this result may be compared to a threshold criteria previously set by an operator. A result of this comparison may be output to an output device, such as display screen 11 or printer 30 for the operator to view. This result may include the location and/or quantification of the streak defect which exceed the threshold criteria. This result also could include a message indicating to the operator a possible portion of paper machine 40 which could be adjusted to correct a defect discovered. The continuous collection during the paper making process might also result in such a comparison allowing a user to receive a message which indicates a particular cause of a non-uniformity or streak in the production of the paper. The composite local energy map may be further analyzed to decompose it into static (i.e., static mean profile local energy map) and stochastic (i.e., composite normalized stochastic local energy map) components which might be output to an output device, e.g., display 11, for viewing by an operator.

[0058] The testing of the paper or materials used to make the paper, obtaining the results of the tests, and displaying of results or messages might be performed concurrently or in real time, for example. In another example, a static mean profile local energy map and a composite stochastic normalized local energy map may be continuously created and output to a display screen during a paper making process. Alternatively, only streaks which exceed a preset threshold criteria may have a composite local energy map, a static mean profile local energy map, and/or a composite normalized stochastic local energy map displayed on the display device. Computing unit 20 might be located in the same location as paper making machine 40 or remotely coupled to one or more testing machines via a communications network, for example, the Internet.

[0059] It will be understood by those skilled in the art that the above described systems and methods might be utilized for webs other than paper, for example the creation of TYVEX type materials or other materials which are created using a paper forming type machine.

[0060] The above-described computing environment regarding the computing unit and the apparatus for characterizing streak defects in paper are only offered as examples. The present invention can be incorporated and used with many types of computing units, computers, processors, nodes, systems, work stations, paper analyzing systems and/or environments without departing from the spirit of the present invention.

[0061] The embodiments described herein are just examples. There may be many variations to the methods and/or devices described herein without departing from the spirit of the invention. For instance, the operational steps may be performed in a different order, or steps may be added, deleted, or modified. All of these variations are considered a part of the claimed invention.

[0062] Although preferred embodiments have been depicted and described in detail herein, it will be apparent to those skilled in the relevant art that various modifications, additions, substitutions and the like can be made without departing from the spirit of the invention and these are therefore considered to be within the scope of the invention.