ON-MACHINE SHEET MATERIAL PROPERTY ANALYSIS

ANALYSE DES PROPRIETES D'UN MATERIEL EN FEUILLES, SUR MACHINE

English Abstract

ABSTRACT OF DISCLOSURE
ON-MACHINE SHEET MATERIAL PROPERTY ANALYSIS
A method and apparatus for determining on-machine,
components of variances over an entire frequency range, of a
property of a substantially continuous moving sheet
material. At least two property-sensing detectors measure
and each provide a signal Y(t) proportional to a sheet
material property at a different location in the cross
machine direction of a moving sheet material. Preferably a
spectrum analyzer, determines the power spectral density
function G(f) for each detector's signal, and the coherence
function COH(f) between the two detectors' signals. On the
basis of these results, the total variance, the machine
direction variance, the residual variance and the
contributions of the machine-directional cyclic and
non-cyclic variances of the property of interest are
determined, preferably by a computer. These contributions
are generally indicative of process and/or machine upsets.

Claims

The embodiments for which an exclusive property or
privilege is claimed are as follows:
1. A method for automatically determining on-machine,
components of the variance over an entire frequency range (f),
of a property of a substantially continuous sheet material
comprising:a)allowing said substantially continuous sheet
material to travel in a machine direction (MD), b)scanning
said sheet material along at least two longitudinally exten-
ding locations in a zone across said sheet material and
automatically generating an output signal proportional to said
property of said sheet material at each of said location,
c)transforming at least two of said output signals into their
corresponding power spectral density functions, d)from a pair
of said power spectral density functions,determining a
coherence function,e)from said coherence function, computing
a square root function of said coherence function, f)multip-
lying said square root function by a first power spectral
density function of said pair in step d),thereby obtaining a
machine direction output power,MDPO(f),g)from said machine
direction output power,MDPO(f),determining and generating data
for the displaying of a machine direction variance over said
entire frequency range, VMD ,by <IMG> (fj) where
MDOP(fj) is the machine direction output power at a frequency
fj, and n is the the number of frequencies in said entire
frequency range, with the proviso that said machine direction
variance is substantially pure and thereby does not include
a residual variance.
2. The method as defined in claim 1,including
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h) determining a residual variance over said entire
frequency range, VRES.
3. The method as defined in claim 1 including determining
a total variance over said entire frequency range, VTOT,
by
VTOT = <IMG>
where GFF(fi) is said first power spectral density
function at a frequency fi, and n is said number of
frequencies in said entire frequency range.
4. The method as defined in claim 2 wherein said residual
variance over said entire frequency range, VREs, is
determined by
VRES = <IMG>
where GFF(fi) is said first power spectral density
function at a frequency fi, MDOP(fi) is said machine
direction output power at a frequency fi, and n is said
number of frequencies in said entire frequency range.
5. The method as defined in claim 3 including determining
a residual variance over said entire frequency range,
VREs, by:
VREs = VTOT - VMD
6. The method as defined in claim 1 including determining
a cyclic machine direction variance over said entire
frequency range, VCMD, and a non-cyclic machine direction
variance over said entire frequency range, VNCMD.
7. The method as defined in claim 6 wherein said cyclic
machine direction variance over said entire frequency range,
VCMD, and said non-cyclic machine direction variance over
said entire frequency range, VNCMD, are determined by:
computing a threshold value, T, as T = m + (R.s), where

m is the mean value of said square root function, R is a
factor in the range of 1 to 3.29,and s is the standard
deviation of said square root function,
at each frequency fj in said entire frequency range,for
n number of frequencies, comparing said machine direction
output power at said frequency fj, MDOP (fj) to said threshold
value T, thereby obtaining contributions to said cyclic and
non-cyclic machine direction variances over said entire
frequency range,VCMD and VNCMD respectively.
8. The method as defined in claim 2, wherein steps b to h are
repeated at least once, whereby said sheet material is scanned
in at least one different zone across said sheet material,
thereby obtaining said residual variance over said entire
frequency range,VRES, at a plurality of zones across said sheet
material.
9. The method as defined in claim 2 wherein steps b to h are
substantially simultaneously duplicated in at least one other
zone across said sheet material, thereby substantially
simultaneously obtaining said residual variance over said
entire frequency range,VRES,at a plurality of zones across said
sheet material.
10. The method as defined in claim 1 wherein said property
is chosen from the group comprising basis weight, density,
temperature and moisture.
11. An apparatus for automatically determining on-machine,
components of the variance over an entire frequency range f, of
a property of a substantially continuous sheet material,
moving in a machine direction (MD), comprising: a) at least
21

two detectors, each for scanning said sheet material in said
machine direction and at a different longitudinally extending
location in a zone across said moving sheet material,b)at
least two of said detectors each generating a detector output
signal proportional to said property of said sheet material
at said location,c)means operatively connected to said
detectors for receiving at least two of said detector output
signals, converting them and generating converted signals
corresponding to their coherence function and at least a first
power spectral density function,d)means,operatively connected
to said means for receiving,converting and generating,for
receiving and processing said converted signals and generating
a processed signal indicative of machine direction variance
over said entire frequency range, VMD , of the property,
e)means, operatively connected to said means for receiving,
processing and generating,for receiving and displaying said
processed signal indicative of machine direction variance,with
the proviso that said machine direction variance is substan-
tially pure and thereby does not include a residual variance.
12. The apparatus as defined in 11,wherein said means for
receiving,processing and generating further computes a
residual variance over said entire frequency range,VRES.
13. The apparatus as defined in claim 11 wherein said means
for receiving,processing and generating further computes a
total variance over said entire frequency range, VTOT,whereby
VTOT = <IMG> (fj ),where GFF (fj)is said first power spectral
density function at a frequency fj ,and n is is said number of
frequencies in said entire frequency range.
22

14. The apparatus as defined in claim 13 wherein said means
for receiving,processing and generating, further computes a
residual variance over said entire frequency range,VRES,
whereby VRES =VTOT -VMD .
The apparatus as defined in claim 11 wherein said means
for receiving,processing and generating further computes a
cyclic machine direction variance over said entire frequency
range, VCMD , and a non-cyclic machine direction variance over
said entire frequency range, VNCMD .
16. The apparatus as defined in claim 11 wherein said
detectors are chosen to detect a property of the group
comprising basis weight and moisture,and wherein said sheet
material is chosen from the group comprising paper and roofing
felt.
17. The apparatus as defined in claim 11 wherein said means
for receiving,converting and generating is a spectrum analy-
zer.
23

Description

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FIELD OF THE INVENTION
This invention relates to a method and an apparatus for
determining on-machine, components of variances over an
entire frequency range, of a property of a substantially
continuous moving sheet material and more particularly to a
method and apparatus for determining on-machine, total,
machine direction, machine-directional cyclic,
machine-directional non-cylic, and residual variances of a
property of a moving sheet material.
BaCRGROUND OF THE INVENTION
Various materials are manufactured in the form of a sub-
stantially continuous sheet material. For example, a web of
sheet paper is manufactured by continuously depositing an
aqueous suspension of fibers onto a traveling wire. Much
water is drained from the wet sheet through the wire. The
wet sheet is further dewatered by a press section, dried by
driers and finished and smoothed by calenders. The sheet of
paper produced is substantially continuous and relatively
wide, generally 10 to 20 feet.
It is generally desirable to maintain certain proper-
ties of the sheet material substantially constant in the
direction of the traveling sheet (machine direction or MD)
and perpendicular thereto (cross machine direction or CD).
However, during the manufacture of sheet material, numerous
possible process and/or machine upsets may occur and it is
most difficult to determine their sources. When pure
machine direction variance over an entire frequency range is
detected for a property of interest and decomposed into its
cyclic and non-cyclic components, the sources of these
components are more easily determined and corrected. How-
~k

iZ930SS
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ever, a random variance is superposed on the pure machine
direction variance, therefore the latter can not be clearly
distinguished by a single detector.
Methods have been described wherein a property is
obtained at a plurality of points by one or two sensors
moving perpendicularly across the sheet material. Such
method is taught in U.S.P. 3,610,899 as invented by E.
Dahlin and issued on October 5, 1971. The data is recorded
and manipulated to obtain MD and CD profiles or varian-es in
their time domain of the property of interest and then
control for example, the slice adjustment of the paper
machine, accordingly. However, since the sheet material is
moving in the machine direction while the sensors move
across the sheet, the plurality of points are diagonally
taken on the sheet. Thus, points taken on a same
machine-directional line are far apart, i.e. 60 feet, and
cannot detect fluctuations shorter than 120 feet (as per
Nyquist Theorem). The profiles and variances are obtained
after exponential weighing or filtering of the data in the
time domain, which is non-indicative of the frequency
composition of these variances. Also, filtering results in
the loss of the contributions at higher frequencies.
Furthermore, Dahlin does not distinguish between cyclic and
non-cyclic MD variances.
It is an object of the present invention to provide a
method and apparatus for determining on-machine, components
of variances over an entire frequency range, of a property
of a substantially continuous moving sheet material.
It is also an object of this invention to determine
on-machine, total, machine direction, machine-directional

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cyclic and non-cyclic, and residual variances of a property
of a moving sheet material.
It is a further object of this invention to determine
residual variances at a plurality of zones across a moving
sheet material.
BRIEF DESCRIPTION OF THE INVENTION
Broadly stated, the invention is directed to a method
for automatically determining on-machine, components of
variances over an entire frequency range (f), of a property
of a substantially continuous sheet material comprising:
a) allowing said substantially continuous sheet material
to travel in a machine direction (MD),
b) scanning said property from at least two locations in a
zone across said sheet material and automatically providing
an output signal proportional to said property at each of
said locations,
c) transforming at least two of said output signals into
their corresponding power spectral density functions,
d) from a pair of said power spectral density functions,
determining a coherence function,
e) from said coherence function, computing a square root
function of said coherence function,
f) multiplying said square root function by a first power
spectral density function of said pair in step d), thereby
obtaining a machine direction output power, MDOPtf),
g) from said machine direction output power, MDOP(f),
determining a machine direction variance over said entire
frequency range, VMD, by
VMD = ~ MDOP(fi)

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where MDOP(fi) is the machine direction output power at a
frequency fi~ and n is the number of frequencies in said
entire freguency range.
The invention is also directed to an apparatus for
automatically determining on-machine, components of
variances over an entire frequency range f, of a property of
a substantially continuous sheet material moving in a
machine direction (MD), comprising:
a) at least two detectors, each for scanning said property
in said machine direction and at a different location in a
zone across said moving sheet material,
b) at least two of said detectors each providing a
detector output signal proportional to said property,
c) means for detecting and transforming at least two of
said detector output signals into their corresponding power
spectral density functions,
d) responsive to said means for detecting and trans-
forming, a means for determining a coherence function
corresponding to a pair of said power spectral density
functions,
e) responsive to said means for determining a coherence
function, a means for determining a square root function of
said coherence function,
f) responsive to said means for determining a square root
function, a means for multiplying said square root function
by a first power spectral density function of said pair,
thereby obtaining a machine direction output power, MDOP~f),
g) responsive to said means for multiplying, a means for
determining a machine direction variance over said entire
frequency range, VMD, by

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VMD = MDOP(fi)
~1
where MDOP(fi) is the machine direction output power at a
frequency fi, and n is the number of fre~uencies in said
entire frequency range.
BRIEF DESCRIPTION OF ~1~ DRAWINGS
Referring now to the drawings which illustrate the
invention.
Figure 1 is a plan view of a typical sheet material
manufacture.
Figure 2 is a diagram showing the relation between in-
put, output and noise signals.
Figure 3 is a diagram of a paper machine including a
preferred embodiment of the present invention.
Figure 4 is a graph showing a time history record of
basis weight, Yl, versus time t.
Figure 5 is a graph showing a time history record of
basis weight, Y2, versus time t.
Figure 6 is a graph showing power spectral density
function Gll versus inverse wavelength l/w.
Figure 7 is a graph showing power spectral density
function G22 (which is equivalent to total output power
TOTOP) versus inverse wavelength l/w.
Figure 8 is a graph showing coherence function COH12
versus inverse wavelength l/w.
Figure 9 is a graph showing machine direction output
power MDOP versus inverse wavelength l/w.
Figure 10 is a graph showing the square root of
coherence function,~ COHli versus inverse wavelength l/w,
and also showing threshold value T.

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Referring now to Figure 1, there is shown an overhead
view of a typical means for producing substantially con-
tinuous sheet material 10. Fluid for producing sheet
material flows through conduit 12, into flow spreader 14 and
usually onto a moviny wire (not shown). The fluid spread on-
to the wire forms sheet material 10 which is traveling in
the MD or machine direction. Perpendicular to the MD
direction and in the plane of sheet material 10 is the CD or
cross-machine direction.
Assuming, for example and nok as a limitation, that the
fluid flow in conduit 12 is unsteady. The fluctuations in
the flow will first cause fluctuations in the properties of
the sheet material at MDLl (machine direction line 1), then
at MDL2 and finally at MDL3. Two or more property-sensing
detectors A, B and C for example, are mounted above and/or
below the machine direction lines MDLl, MDL2 and MDL3
respectively and measure a sheet material property of
interest with respect to time (time history record). The
detectors are preferably mounted side by side in a
cross-machine direction either on a stationary frame or a
removable frame, not shown. However, the detectors may not
be mounted side by side, as long as none are aligned in the
machine direction. Ideally, the detectors A, B and C will
each provide a detector output signal proportional to the
property of interest, each output signal having the same
fluctuations in that property. However, the detector output
signals will contain residual fluctuations (noise), and will
be out of phase from each other, thereby hiding the --
similarities between the detector output signals.
There is shown in Figure 2, a diagram demonstrating how

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the above described fluctuations and signals can be inter-
preted. For way of example only, the following will con-
sider only two detector output signals. X(t), considered as
the input signal, is the time history record of the property
fluctuations common at all machine direction lines on a
travelling sheet material. To this common X(t) signal is
added, at each machine direction line, MDLl and MDL2,
extraneous noise nl(t) and n2(t) respectively (for example,
due to turbulence in the jet exiting the headbox or in the
forming area of a paper machine), the results being detected
at each machine direction line, by detectors A and B as
detector output signals Yl(t) and Y2(t). There is a linear
relationship between the signals Yl and Y2 which can be
extracted through spectral density functions, thereby
transforming the time history records into their frequency
domains.
The time histories Yl(t) and Y2(t) are transformed into
their power spectral density functions Gll(f) and G22(f)
respectively, frequency f always representing all frequen-
cies fl, f2, f3 -- fn- Their power cross-spectrum
G12(f) is also computed. The mathematical techniques of
obtaining power spectral density functions by Fourier
transforms or analog filtering, appear in various texts,
such as "Random Data: Analysis and Measurement Procedures"
by J.S. ~endat and A.G. Piersol, Wiley - Interscience, 1971.
Power spectral density function G22(f) is equivalent
to total output power at frequency f, at position 2,
TOTOP2(f). "Position 2" represents that this result is
based upon detector output signal Y2(t). Accordingly, power
spectral density function Gll(f) is equivalent to total

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_ 9 _
output power at frequency f, at position l, TOTOPl(f), as
this result is based upon detector output signal Yl(t). For
sake of consistency, "position 2" will be used throughout
the following discussion. Total output power at frequency
f, TOTOP2(f), summed over frequencies fl~ f2 .. fn
is equivalent to total variance at position 2, VTOT 2 (and
similarly for VToT~l) where:
VTOT 2 = TOTOP2(fi)
The degree to which signal Y2 depends on signal Yl is
expressed by the coherence function COHl2(f) where:
¦G12(f ) ¦
G11(f) G22(f)
When COHl2(f) = O at a particular frequencyl Yl(t)
and Y2(t) are incoherent or uncorrelated at that frequency.
If COHl2(f) = l for all frequencies, Yl(t) and Y2(t) are
said to be fully coherent.
In Figure 2, the detector output signals Yl(t) and
Y2(t) are out of phase and contain similar extraneous noise
nl(t) and n2(t) respectively, which are uncorrelated and
incoherent with each other and with noiseless signal X(t).
The extraneous noise nl(t) and n2(t), being similar, are
considered substantially equal. Their power spectral
density functiOnS Gnlnl(f) and Gn2n2(f) resp Y
are also substantially equal- Gn2n2(f) and Gnlnl(f)'
are equivalent to residual output power at frequency f, at
position 2, RESOP2(f), and residual output power at
frequency f, at position l, RESOPl(f), respectively.

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Residual output power at frequency f, RESOP2(f), summed
over frequencies fl~ f2 ... fn is e~uated to residual
variance at position 2, V~Es 2 (and similarly for
VREs,l) where:
n
VREs 2 = ~ RESP2(fi)
GXx(f), the power spectral density function of X(t)
is equivalent to the pure machine direction output power at
frequency f, at position 2, MDOP2(f) and is obtained by
GXX(f) = MDP2(f) = ~ COH12(f~ 2(
= ~ CHl2(f) G22(f)
CHl2(f) and G22(f), (or TOTOP2(f)), bei g
(having previously been computed), GXX(f), equivalent to
MDOP2(f), is determined. Machine direction output power
at frequency f, MDOP2(f) summed over frequencies fl,
f2 .... fn i8 equated to machine direction variance at
position 2, VMD 2 where:
r~
VMD 2 = MDop2(fi)
Thus, VREs 2 is equal to the difference between the total
variance and the pure machine direction variance. If the
RESOP2(f) is desired, it is obtained by RESOP2(f) =
TOTOP2(f) - MDOP2(f).
When a graph is made of the square root of the
coherence function,~ COHl2(f), (or of the coherence
function itself, versus frequency, it is often noticed
that ~ COHl2(f), (or COHl2(f)), peaks at certain
frequencies. These are considered to be frequencies at

lZ93~5S
which the common fluctuations in the detector output signals
are cyclic machine-directional. Thus, it is considered that
the amount of MDOP2(f) corresponding with each of these
peak frequencies, contributes to a cyclic machine-direction
output power at frequency f, at position 2, CMDOP2(f).
The sum of CMDOP2(f) over all frequencies fl~ f2
fn is equal to cyclic machine direction variance, at
position 2, VcMD 2. The individual peak frequencies fp,
are usually indicative of and can be useful in determining
the sources of cyclic fluctuations particularly due to
machine and/or process upsets. The above mentioned peaks
can be visually detected from the graph, however a more
practical criterium for peak detection is the following. A
threshold value T is computed as
T = m + 1.96s
where m is the mean value of the function ~COHl2(f)
over all the frequencies analyzed and s is its standard
deviation. The factor 1.96 is arbitrary but was chosen from
experience and it corresponds to a 97.5% confidence level
for a one-sided significance test on a Gaussian Distribu-
tion. The factor 1.96 may be altered to preferably remain
in the range of 1 to 3.29 corresponding to a range of 84% to
99.95% confidence level respectively.
At each frequency, the value ~ COHl2(f) is compared
to T and when ~ COHl2(f) is greater than or equal to T,
the value of MDOP2(f) corresponding with that frequency
contributes to CMDOP2(f). This comparison is repeated at
each frequency to obtain the entire CMDOP2(f), the latter
summed at frequenCies fl, f2 -- fn to obtain
VCMD,2- Then VCMD,2 is subtracted from VMD 2 thereby

`" lZ93~SS
obtaining the non-cyclic machine direction variance at
position 2, VNCMD 2. If desired, CMDOP2(f) may be
subtracted from MDOP2(f) to obtain the non-cyclic machine
direction output power at frequency f, at position 2,
NCMDOP2(f). The sum of NCMDOP2(f) at frequencies fl,
f2 ... fn would also be equal to VNCMD,2 In order
demonstrate which variances can be considered more
important, and thereby assessed first in order to correct
process and/or machine upsets which contributed to them, the
following percentages are preferably computed.
l. The percentage of machine direction to total variances
MD/TOT ~ = VMD,2/VTOT,2 x 100
2. The percentage of residual to total variances
RES/TOT % = VRES,2/VTOT,2 x 100
3. The percentage of cyclic machine direction to total
variances
CMD/TOT ~ = VCMD,2/VTOT,2 x 100
4. The percentage of non-cyclic machine direction to total
variances
NcMD/ToT % = VNCMD,2/VTOT x 100
5. The percentage of cyclic machine direction to machine
direction variances
CMD/MD % = VCMD,2/VMD,2 x 100
6. The percentage of non-cyclic machine direction to
machine direction variances
D/MD % VNCMD,2/VMD,2 x 100 = 100 - CMD/MD %
Throughout the previous analysis, it was assumed that
the residual variance is substantially equal at every
location in the cross machine direction, whereby the two
detectors may be located at any location in the cross

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machine direction. However, the property analysis may be
done for multiple zones of the moving sheet material and the
residual variance for each zone compared with each other.
In order to enable multiple zone property analysis, two
detectors may be movably mounted with the location of the
detectors changed after the property analysis of each zone.
or, more than one detector can be used, their signals
analyzed in pairs across the sheet material. This multiple
zone comparison may detect significant changes in residual
variance across the sheet material caused for example, by
local turbulence, particularly near the edges of the sheet
material.
Furthermore, the previous analysis is based on the
dependency of time history Y2(t) on time history Yl(t). How-
ever, substantially identical variances (TOT, MD, RES, CMD,
NCMD) will be obtained when the analysis is based on the
dependency of time history Yl(t) on time history Y2(t),
and/or "position 1"~
The methods described above apply for numerous types of
sheets or webs and numerous scalar properties of the sheet
or web. For example, these methods are applicable to basis
weight, moisture and temperature of paper moving on a paper
machine; basis weight and moisture of roofing felts; density
of roofing shingles; and density of extruded polymer films
such as polyethylene.
EXAMPLE
The above described methods have been applied to a
paper machine, analyzing its basis weight (weight per unit
surface).
Referring now to Figure 3, in paper machine 110, an

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aqueous suspension of fibers continuously flows from headbox
112 onto web 114, forming sheet of paper 116. Sheet 116
travels through press section 118, is dried by drier SeGtiOn
120 and is finished and smoothed by calenders 122. The
finished sheet 116 is wound on roll 124. The above des-
cribes only the general appearance of a paper machine as
well known by one skilled in the art.
Two basis weight detectors 126 and 128 are mounted
preferably side by side above sheet 116 between drier
section 120 and calenders 122.
The detectors 126 and 128 are preferably sensitive and
fast such as recent germanium detectors equipped with a
cryostat. Other well known basis weight detectors such as
light probes may be used, mounting them as necessary with
respect to the wet end or dry end of paper machine 110
according to the manner the detectors must operate.
The detectors 126 and 128 scan sheet 116 to detect the
basis weight of the moving sheet of paper for example at
about every 3.91 milliseconds for a period of 20 minutes.
Simultaneously, the detectors 126 and 128 develop an analog
signal Yl(t) and Y2(t) respectively, which represents the
paper's basis weight as it is scanned. Optionally, the
analog signals Yl(t) and Y2(t) are converted by a plotter
into plots of Yl(t) and Y2(t) with respect to time, as shown
in Figures 4 and 5 respectively for a shortened period of 1
second.
A spectrum analyzer 130 using Fast Fourier Transforms,
such as SD-375 by Spectral Dynamics Inc., receives the
analog signals Yl(t) and Y2(t) and, at four second inter-
vals, converts them into their power spectral density

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functions Gll(f) and G22(f) and also computes their
coherence function COH12(f) over a discrete frequency
range. At every four seconds for a period of 20 minutes,
new spectra of Gll(f), G22(f) and, C0H12(f) are
computed. The newly computed Gll(f), G22(f) and
COH12(f) are added to their corresponding averaging
memories. After the 20 minute period, ensemble averages are
obtained over the 300 spectra. With these averaged spectra,
the digital computer 132 computes ~COH12(f), the threshold
value T, and MDOP(f). Then computer 132 computes VTOT,
VRES~ VMD~ VCMD~ VNcMD and the percentages of VcMD
and VNCMD to VMD and VTOT. (The "position 2" has been
omitted for simplicity).
The computer optionally transfers the averaged
Gll(f)~ G22(f)~ CH12(f), MDOP(f) and ~COH12(f) and
T to plotter 134 which plots these values versus frequency
or versus inverse wavelength l/w as shown in Figures 6 to 10
respectively. The relationship between frequency and
wavelength will be described later. Printer 136 prints the
frequencies fp at which there are contributions to the
cyclic MD variance (which computer 132 inherently computed)
and the various variances and their percentages. With these
results, one skilled in the art can determine which type of
variances are most prevalent and how to correct them.
The above mentioned preferred averaging of Gll(f),
G22(f) and COH12(f) may be done according to different
methods as one skilled in the art may choose. One method is
to compute a linear average as outlined above. Another
preferred method is to compute a sliding average of
Gll(f)~ G22(f), and COH12(f), whereby with the use of

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commonly known time weighing or exponential weighing,
updated averaged values are available at about every four
seconds. Thus, if something upsets the analysis within the
20 minute period, such as a break in the paper web, all the
variances may still be computed, using the last available
averaged values, to help determine the cause of the upset.
From experience, it has been found that when RES/TOT%
is much greater than MD/TOT%, fluctuations originate in the
forming zone and headbox of the paper machine. When MD/TOT%
is much greater than RES/TOT% fluctuations originate up-
stream of the headbox, in the approach system. When CMD/MD%
is high, the fluctuations originate in pumps, screens, vibra-
tions, etc.
The spectrum analyzer 130, digital computer 132, plot-
ter 134 and printer 136 are preferably portable wherein they
can be easily moved, along with the removably mounted detec-
tors 126, 128, from one paper machine to another. Thereby,
the complete variance analysis is entirely done on-machine.
The graphs shown in Figures 4 to 10 are optional,
either being drawn by plotters or displayed on screens, and
they were presented here for illustrative purposes.
However, the results that one would usually desire are given
in Table 1, as printer 136 would supply (and/or an optional
screen could display) at 20 minute intervals. In this case,
computer 132 performed the additional calculation of
transforming the minimum frequency and the maximum frequency
of the discrete range of frequencies, including the peak
frequencies fp into their equivalent wavelengths w
according to (in the imperial system):

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w = (speed of paper~
5 x f
where wavelength w is in inches, speed of paper in feet per
minute, and frequency f in Hertz. In the case of metric
measurements,
w = ~speed of paper)
where w is in metres, speed of paper in metres per second,
and frequency f in Hertz.
TABLE 1
T = 0.261
VTOT = 0.856 (g/m2)
VREs = 0.644 (g/m2) RES/TOT % = 75.2
VMD = 0.212 (g/m2)2 MD/TOT % = 24.8
VcMD = 0.081 (g/m ) CMD/MD % = 38.2
VNCMD= 0.131 (g/m2)2 NCMD/MD % = 61.8
w(inches) CH12
17.22 0.28~
15.11 0.558
14.95 0.487
12.36 0.277
6.90 0.271
6.80 0.310
5.74 0.821
5.71 0.773
wMIN = 3.40 inches
wMAx = 1360.0 inches
The above example demonstrated a preferred embodiment
of the invention wherein the analysis was performed with a

`` lZ93~55
- 18 -
Fast Fourier Transform Spectrum Analyzer, digital computer
and a printer. However, one skilled in the art may perform
the analysis by a less preferred analog system. Also, one
may prefer to obtain the square root of the variances,
wherein the results would be in a more common unit, g/m2
instead of (g/m2)2.
Furthermore, the above analysis may be repeated,
whereby fluctuations in the residual variance may be
detected over time, such as may be caused by fluctuations in
stock consistency or fluctuations in the amount of retention
aid added to the pulp.
Having described the invention, modifications will be
evident to those skilled in the art without departing from
the spirit of the invention, as defined in the appended
claims.

Representative Drawing