METHOD OF ESTIMATING UNKNOWN OR IMPRECISELY KNOWN VARIABLES IN A PAPER MAKING PROCESS

PROCEDE POUR FAIRE UNE ESTIMATION DE VARIABLES INCONNUES OU CONNUES DE FACON IMPRECISE DANS UN PROCESSUS DE FABRICATION DE PAPIER

English Abstract

Method of estimating unknown or imprecisely known variables in a paper making
process wherein a mathematical model of a process is formed, the model
including at least one target variable which is unknown or imprecisely known.
A plurality of process variables and at least one property of a manufactured
paper are measured. At least one of said measured variables or properties is
chosen as a reference variable. An initial value is chosen for the target
variable for solving the mathematical model and a difference between the
simulated reference variable and the measured reference variable is
determined. The difference constitutes a cost function which is optimized to
estimate the unknown or imprecisely known value of the target variable.

French Abstract

L'invention concerne un procédé pour faire une estimation de variables inconnues ou connues de façon imprécise dans un processus de fabrication de papier, selon lequel on établit un modèle mathématique du processus, le modèle comprenant au moins une variable cible inconnue ou connue de façon imprécise. On mesure plusieurs variables du processus et au moins une des propriétés du papier manufacturé. Au moins une de ces variables mesurées est choisie comme variable de référence. Une valeur initiale est choisie pour la variable cible afin de solutionner le modèle mathématique, et l'on détermine une différence entre la variable de référence simulée et la variable mesurée. La différence constitue une fonction de coût qui est optimisée pour estimer la valeur inconnue ou connue de façon imprécise de la variable cible.

Claims

6
CLAIMS
1. A method of estimating unknown or imprecisely known variables
in a paper making process, the method comprising the steps of
forming a mathematical model of a process, the model including at
least one target variable which is unknown or imprecisely known,
measuring a plurality of process variables and at least one property
of a manufactured paper web,
utilizing the measurements as initial and boundary values of the
model,
choosing at least one of said measured process variables or
measured web properties as a reference variable,
choosing an initial value for the target variable,
solving the mathematical model,
simulating a value of the reference variable utilizing the model,
determining a difference between the simulated reference variable
and the measured reference variable, the difference constituting a cost
function,
and optimizing the cost function to estimate the unknown or
imprecisely known value of the target variable.
2. A method according to claim 1, wherein the process is a flow
process in a headbox and the target variable is a variable of the headbox.
3. A method according to claim 2, wherein the target variable is a
slice opening profile of the headbox.
4. A method according to claim 3, wherein the reference variable is
a fiber orientation angle profile.
5. A method according to claim 3, wherein the reference variable is
a basis weight profile.
6. A method according to claim 3, wherein the reference variable is
a dry weight profile.
7. A method according to claim 2, wherein the measured process
variables comprise headbox pressure and headbox consistency.
8. A method according to claim 2, wherein the measured process
variables comprise a profile of dilution valve positions.

Description

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METHOD OF ESTIMATING UNKNOWN OR IMPRECISELY KNOWN
VARIABLES IN A PAPER MAKING PROCESS
The invention relates to a method of estimating unknown or
imprecisely known variables in a paper making process.
US patent 5 812 404 discloses a method for the continuous overall
regulation of a headbox of a paper machine. A physical fluid flow model of a
pulp suspension flow discharged from the headbox to be regulated is formed
and solved to obtain a simulated flow state based, e.g., on data on the
geometry of the headbox and initial and boundary conditions related to the
headbox. A target flow state based on the quality requirements of the paper
produced from the pulp suspension flow, the costs of operation and runnability
of the machine is obtained and a difference between the simulated flow state
obtained as the solution of the flow model and the target flow state is
~5 determined. This difference constitutes a cost function which is optimized
to
determine optimal regulation values and set values for instrumentation devices
and actuators of the headbox which affect the pulp suspension flow.
Provision of accurate initial and boundary conditions is
advantageous in a method disclosed in US 5812404 but the solution of US
20 5 821 404 relies on measurements alone to provide said conditions.
Measurements alone cannot provide all required initial values with adequate
accuracy. The values of variables are also too imprecise or unknown at
several other points of the paper making process, and thus it would be
necessary to obtain a more accurate estimate of the variable values.
25 An object of the present invention is to provide a method for
obtaining a more accurate estimate of unknown or imprecisely known
variables of a .paper making process.
The method of the invention is characterized by comprising the
steps of
3o forming a mathematical model of a process, the model including at
least one target variable which is unknown or imprecisely known,
measuring a plurality of process variables and at least one property
of a manufactured paper web,
utilizing the measurements as initial and boundary values of the
35 model,

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choosing at least one of said measured process variables or
measured web properties as a reference variable,
choosing an initial value for the target variable,
solving the mathematical model,
simulating a value of the reference variable utilizing the model,
determining a difference between the simulated reference variable
and the measured reference variable, the difference constituting a cost
function,
and optimizing the cost function to estimate the unknown or
~o imprecisely known value of the target variable.
The essential idea of the invention is that a mathematical model of
a process is formed, the model including at least one target variable which is
unknown or imprecisely known. Plural process variables are measured and at
least one property of the manufactured paper web is measured. At least one of
~5 said measured process variables or measured web properties is chosen as a
reference variable. Boundary conditions for the mathematical model are
obtained from the remaining measured process variables and measured web
properties. An initial value is chosen for the target variable for solving the
mathematical model, the reference variable is thereby simulated, and a
2o difference between the simulated reference variable and the measured
reference variable is determined. This difFerence constitutes a cost function
which is optimized to estimate the unknown or imprecisely known value of the
target variable. The idea of a preferred embodiment is that the process is a
flow process in a headbox and the target variable is a variable of the
headbox.
25 An advantage of the invention is that variables of the paper making
process can be estimated in a more accurate and diverse manner than earlier,
which allows ~to improve control of the paper making process. The method
applies particularly to estimation of unknown or imprecisely known variables
which are multivariate or vector quantities, such as the cross machine profile
3o of a process variable or web property, or the statistical distribution of a
variable
whose value changes with position or time.
In this disclosure the term "paper" also refers to paper board and
tissue.
The invention will be described in greater detail in the
3s accompanying drawings, in which
Figure 1 is a schematic side view of a paper making process,

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Figure 2 is a simplified block diagram of a method of the invention,
and
Figure 3 is a simplified flowchart for an optimizing controller in which
the method of the invention can be utilized.
Figure 1 schematically shows a paper machine. The paper machine
comprises a headbox 1, from which pulp is fed into a former 2, where a fiber
web 3 is formed of the pulp. The web 3 is conveyed to a press 4 and further to
a dryer unit 5. From the dryer unit 5 the web 3 is conveyed to a reel 6. A
paper
machine may also comprise, for example, a size press, coaters or a calender,
1o which are not illustrated in the Figure 1 for the sake of clarity.
Furthermore, the
function of the paper machine is known per se for those skilled in the art,
and
will therefore not be further explained in this context.
The paper machine also comprises at least one measuring device 7
for measuring properties of the paper web 3. The measuring device 7 is used
~5 for measuring e.g. the basis weight BW, dry weight profile DWP and the
fiber
orientation angle profile FO of the paper web 3. The paper machine also
comprises other measuring devices for measuring values and properties at
different parts of the paper machine. Headbox pressure P, headbox
consistency Cs, a profile of dilution valve positions DVP and headbox upper
lip
2o profile ULP are given as examples of such measurements in Figure 1.
Additional properties of the paper web or of process streams can be measured
from samples taken from the manufactured paper or process streams using
instruments located elsewhere.
The invention relates to a method for estimating unobserved
25 variables or imprecisely measured process variables in a paper machine
during operation, and especially for estimating an unknown or imprecisely
measured process variable in the headbox 1 of a paper machine or in the
sheet formed of the headbox discharge. A mathematical model of the process
is formed based for example on the geometry of the headbox 1 and physical
3o models of the flow phenomena occurring therein, and including at least one
target variable which is unknown or imprecisely known. Plural process
variables are measured, for example using instruments in or around the
headbox 1 and the various process streams leading to or from the headbox,
and ~at least one property of the manufactured paper web 3 is measured using
35 instruments elsewhere on the machine or in a laboratory. At least one of
said
measured process variables or measured web properties is chosen as a

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reference variable. Boundary conditions for the mathematical model are
obtained from the remaining measured process variables and measured web
properties. An initial value is chosen for the target variable for solving the
mathematical model, the reference variable is thereby simulated, and a
difference between the simulated reference variable and the measured
reference variable is determined. This difference constitutes a cost function
which is optimized to estimate the unknown or imprecisely known value of the
target variable. The initial value chosen can be, for example, an imprecise
measurement of the target variable, so that the optimization produces an
~o estimate which is of superior accuracy to the measurement.
A simplified flow chart for the estimation process is depicted in
Figure 2. The physical and geometric parameters are known a priori. The
measurements of known states are provided by measuring instruments or
operator input. The initial estimate of the unknown variable or state may be
~5 supplied from an approximate measurement, or may be provided by other
means of estimation, or by an operator.
For example, in the headbox 1 the slice opening profile is
approximately known. The profile of the upper lip ULP is measured at a
number of locations across the slice, but the shape of the lower lip is
generally
2o unknown. However, various profiles which depend on the slice opening
profile
are measured, such as the basis weight profile BW or dry weight profile DWP
and the fiber orientation angle profile FO.
The optimization uses the measured slice lip shape as an initial
estimate of the slice opening profile. One or more suitable measurements,
25 such as the fiber orientation angle profile FO or dry weight profile DWP or
basis weight profile BW are used as reference variables. Other
measurements, such as headbox pressure P, consistency Cs, temperatures,
flows, a profile of dilution valve positions DVP etc. are used as inputs to a
mathematical model of the flow process in the headbox 1 and jet. By solving
3o the mathematical model of the headbox 1, a simulation of the fiber
orientation
angle profile is obtained. A penalty to be optimized is calculated from the
difference between the measured fiber orientation angle profile and simulated
fiber orientation angle profile. This penalty is optimized by adjusting the
estimate of the slice opening profile, the optimum being reached when the
35 simulated fiber orientation angle profile most closely matches the measured
fiber orientation angle profile.

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This invention solves a mathematical model of the headbox to
estimate unknown or imprecisely known current operating parameters
consistent with measured properties of the current product.
The present invention is particularly well suited for estimation of the
5 initial conditions for a method of optimizing control such as that disclosed
in
US 5 812 404 which is incorporated herein by reference. The present invention
uses inverse modeling to provide such a controller with improved estimates of
its initial and boundary conditions. The present invention can utilize similar
mathematical and physical models to those used by such a controller, or can
use different ones.
A simplified flow chart for an optimizing controller is depicted in
Figure 3. One or more of the "measurements of known variables/states" in that
figure can be supplied by the estimation process of this invention.
The drawings and the description thereof are merely intended to
~5 illustrate the inventive idea. The details of the invention may vary within
the
scope of the claims. Thus the method of the invention can in principle be
applied at any point of the paper making process.

Representative Drawing