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TITLE OF THE INVENTION
SYSTEM AND METHOD FOR FURNACE MONITORING AND CONTROL
FIELD OF THE INVENTION
The present invention relates to a system and method for the monitoring and
control of a furnace. In particular, the present invention relates to a system
and
method for the monitoring and predictive control of a furnace containing
molten
metal based on a multivariate statistical control model for predicting changes
in
furnace integrity.
BACKGROUND OF THE INVENTION
The safe and efficient operation of a furnace holding molten material must
include a suitable control system to detect and act on any changes in the
integrity of the furnace. These furnaces have a refractory lining that can be
breached by the molten material they contain, causing a run-cut of molten
material which can damage equipment, injure workers and cause loss of
production.
Typical instrumentation for monitoring such a furnace includes measuring the
temperature at various locations in the furnace walls, hearth and roof and at
various depths within the lining. Additionally, temperature measurements can
be embedded in the refractory lining or lining cooling elements. In general,
temperatures are measured using thermocouples which sense temperature as
a result of a voltage generated between the joined end of two dissimilar metal
wires and the open end when the temperature at the joined end, the "hot"
junction, is different from the temperature at the open end, the "cold"
junction.
The voltage is proportional to the difference in temperature. Voltage from a
plurality of thermocouples can be readily sampled and provided to an online
control system for further processing.
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Existing technology for integrity and condition monitoring of these furnaces
entails triggering alarms based on high limits on temperature measurements
within the furnace lining. The usefuiness of this approach is limited by the
need
to set the sensitivity of the alarms high enough to detect true threats to the
integrity of the furnace lining and the need to reduce the sensitivity of the
alarms to avoid numerous false alarms. In an industrial application, alarm
points must be set high enough to allow for normal fluctuations in furnace
operating temperatures. Batch mode furnaces have lining temperatures
fluctuating significantly from the start to the end of a heat which
necessitates
insensitive alarms of the standard type. In a continuous process mode furnace,
lining temperature changes rapidly on re-start following a period of proionged
idleness or if the throughput or processing intensity of the furnace is
increased
which also necessitates insensitive standard type alarms. The need to set
alarm points high enough to avoid triggering false alarms from normal
operating
fluctuations can frequently result in non-detection of true high risk
conditions.
Therefore there is a need to provide a furnace temperature control system
which is insensitive enough to avoid triggering false alarms while at the same
sensitive enough to detect all true high risk conditions.
Current methods of fault detection and diagnosis in processes are typically
grouped into one of three main classes: methods based on a mechanistic
model, methods based on knowledge of the process and methods based on
data analysis. Since obtaining empirical data from sensors positioned
throughout the process is relatively easy there is an increasing interest in
methods of the third class, i.e. those based on data analysis. However, as
most
modern processes are data abundant, control of the process via the flow of
empirical data in its raw format is exceedingly difficult given the
overwhelming
size of the databases and because of the generally ill conditioned nature of
the
data being collected. On the other hand, all these variables are not
independent of one another. in fact, in a large industrial process typically
only a
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few underlying events are driving a process at any time, and all these
measurements are simply different reflections of these same underlying events.
Therefore, examining them one variable at a time as though they were
independent, makes interpretation and diagnosis extremely difficult. Such
methods only look at the magnitude of the deviation in each variable
independently of all others.
There is therefore a need for an online furnace monitoring and diagnosis
system which examines a large number of temperature readings
simultaneously in order to extract information on the directionality of the
process variations, that is on how all the temperature variables are behaving
relative to one another. Furthermore, as important events occur in the furnace
which are difficult to detect because the signal to noise ratio in each
variable is
very low, there is also needed a furnace control system which can detect
variations in the furnace in the presence of a high signal to noise ratio
and/or
reduce the noise levels. Finally, due to sensor failure and the like there is
also
often significant amounts of missing data and therefore there is a need for a
furnace control system which can continue to operate in the absence of at
least
a portion of data related to the current status of the furnace.
SUMMARY OF THE INVENTION
There is disclosed a method for monitoring the integrity of a furnace
containing
molten metal. The method comprises the steps of deriving a model of normal
operation of the furnace from a plurality of furnace variables, periodically
measuring current values of the plurality of furnace variables, analysing the
current values, the analysing step resulting in a representation of current
operation, comparing the representation of current operation with the model of
normal operation, and generating an alarm when the representation of current
operation deviates from the model of normal operation by a predetermined
amount.
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There is also disclosed a system for monitoring the integrity of a furnace,
the
furnace comprising a refractory lining and containing molten metal. The system
comprises a plurality of thermocouples for periodically measuring a current
temperature of the refractory lining, a model of normal operation of the
furnace,
a means for analysing the current temperatures, the analysing means
generating a model of current operation, and a means for comparing the model
of current operation with the model of normal operation. The comparing means
generates an alarm when the model of current operation deviates from the
model of normal operation by a predetermined amount.
Other objects, advantages and features of the present invention will become
more apparent upon reading of the following non-restrictive descripton of
specific embodiments thereof, given by way of example only with reference to
the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
In the appended drawings:
Figure 1 is a perspective view of a Mitsubishi continuous copper converting
furnace according to an illustrative embodiment of the present invention;
Figure 2a is cut-away side view of a converting furnace hearth according to an
illustrative embodiment of the present invention;
Figure 2b is a detailed view of the hearth in Figure 2a;
Figure 3a is a top view of a cooling block according to an illustrative
embodiment of the present invention;
Figure 3b is a side view of a cooling block according to an illustrative
embodiment of the present invention;
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Figure 3c is a cut-away view along 3c-3c in Figure 3b;
Figure 3d is a cut-away view along 3d-3d in Figure 3a of a cooling block
according to an illustrative embodiment of the present invention;
Figure 4 is a top view of a converting furnace hearth according to an
illustrative
embodiment of the present invention;
Figure 5 is a schematic diagram of a cooling system for cooling a converting
furnace according to an illustrative embodiment of the present invention; and
Figure 6 is a schematic diagram of a data acquisition and monitoring system,
system for a converting furnace according to an illustrative embodiment of the
present invention.
DETAILED DESCRIPTION OF THE ILLUSTRATIVE EMBODIMENTS
The present invention is a method for indicating an abnormal operation of a
high temperature furnace containing molten material and a system for
predicting changes in the integrity of a high temperature furnace containing
molten material. Predicted changes can include potential breach of the
furnace's refractory lining, changes in the condition of the furnace wall,
build up
and/or process equipment failure.
The interpretation of the furnace measurements, including but not limited to
furnace lining temperatures, using multivariate analysis greatly increases the
sensitivity in detecting upset conditions without triggering alarms due to
normal
process variations. Additional measurements can be added to improve
performance such as feed rates, including gas flow rates and solid addition
rates, temperatures in the freeboard and molten phases of the furnace, product
withdrawal rates, including waste gases and molten products and compositions
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of all feed and product materials. Additional variables relevant to monitoring
can be calculated from these measurements and added to the analysis such as
heat fluxes and estimated thickness of the lining.
Multivariate monitoring uses a model to produce a small number of variables
that summarise the state of the process. The state of the process is contained
in a larger set of variables that are input to the model. The model is
calibrated
on a training set of historical data taken from a time when the process
operation is deemed normal. The model is then applied to new data and
variables are produced that are monitored to indicate whether the state of the
process has changed. The advantages of multivariate monitoring over
monitoring all of the individual variables in the input to the model include a
reduction in the number of variables monitored, increased sensitivity to
faults
that are indicated by changes in the relationships between variables and a
reduction in false alarms.
When the number of measured variables is large, it is often found that the
variables are highly correlated with one another and with a covariance matrix
which is nearly singular. Approaches to reducing the dimensionality of the
variable space in such cases include Principal Components Analysis (PCA)
and Partial Least Squares (PLS). PCA is used throughout the present
illustrative embodiment as a basis for developing the models, although it
should
be understood that PLS is also applicable.
PCA is concerned with explaining the variance-covariance structure of a set of
variables through a few linear combinations of these variables. Its general
objectives are data reduction and interpretation. Additionally, an analysis of
principal components often reveals relationships that were not previously
suspected and thereby allows interpretation that would not ordinarily result.
PCA can reduce the dimensionality of large numbers of highly correlated
process measurements by projecting the information of original measurement
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spaces into low dimensional spaces defined by a handful of latent variables.
Given a sample of measurements with n observations on k variables y, The
first principal component of y is defined as that linear combination r1 = py
that
has maximum variance subject to Ipil= 1. The second principal component is
that linear combination defined by /2 = p2Ty which has next greatest variance
subject to 1p21= 1, and subject to the condition that it be uncorrelated with
(orthogonal to) the first principal component (t1). Additional principal
components up to k are similarly defined. In effect, PCA decomposes the
observation matrix Y as:
Y = TP T = tpf (1)
with the property that titi = 0,(i # j) and pr pi = 0,(i # j).
PCA is scale dependent, and so the Y matrix must be scaled in some
meaningful way. In practice, it is rarely needed to compute all the k
principal
components, since most of the variability in the data is typically captured in
the
first few principle components. Stated differently, although k components are
required to reproduce the total system variability, often much of this
variability
can be accounted for by a small number m of the principal components. If so,
there is almost as much information in the m components as there is in the
original k variables. The m principal components can then replace the k
variables, and the original data set, consisting of n measurements of k
variables, is reduced to a data set consisting of n measurements on m
principal
components. By abandoning the components which have little influence, the
data matrix Y can be rewritten as the sum of an estimation value if and
residual
E:
)TT + E , where)i..> =Et iplj. (2)
J=1
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The number m of principal components that are required to provide an
adequate description of the data can be assessed using a variety of methods.
A first group of methods are very much ad hoc rules of thumb, the use of which
are justified mainly on the grounds that they are intuitively plausible and
that
they work in practice. Others select a cumulative percentage point of the
total
variation that the selected principal components contribute, say 80% or 90%.
The required number of principal components is then the smallest value of m
for which the chosen percentage threshold is reached. Finally others, such as
the Predicted Residual Sums of Squares (PRESS) statistic, are computationally
intensive and use cross-validation. it is this final set of methods which are
exploited in the present illustrative embodiment to determine the number of
principle components necessary to adequately describe the data.
Generally, the PRESS statistic m of the number of principal components is
determined for a data matrix Y by increasing the number of principal
components successively until overall prediction of the yiith element is not
significantly improved. The yiith element is predicted based on a submatrix of
Y
that does not include the yiith element.
PCA models are created by "training" the model over a historical set of data.
By
establishing a PCA model based on historical data collected when only
common cause variation is present, future behaviour can be referenced against
this model (generally referred to as an "in control" model). Therefore, the
PCA
model is built based on historical databases of data collected from periods of
operation when performance vvas good. Any periods containing variations
arising from special events that are wished to be detected in the future are
omitted at this stage. The choice of the reference set is critical to the
successful
application of the procedure. When the data are serially autocorrelated the X
and Y matrices can be augmented with time-lagged values, in order to account
for the dynamics of the process and the disturbances. Dead times between
variables are accounted for by time shifting.
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Development of a Model
The development of a model of the present illustrative embodiment is primarily
an exercise in data mining, i.e. the analysis of a large observational data
set to
determine relationships between variables and to summarise the data in ways
which are meaningful to the user. The relationships and summaries derived
through the data mining exercise are typically referred to in the art as
models.
The process of seeking relationships within a data set, Le. of seeking
accurate,
convenient, and useful summary representations of some aspect of the data,
involves a number of steps:
= determining the nature and structure of the representation to be used;
* deciding how to quantify and compare how well different representations fit
the data (i.e. choosing an evaluation function);
= choosing an algorithmic process to optimise the evaluation function; and
= deciding what principles of data management are required to implement the
algorithms efficiently.
In this manner a control system can analyse a large amount of data by
simplifying the way it is used. In this manner not all variables are modelled
individually but rather they are combined through the use of the model and the
model's output monitored.
=
Traditionally, large fundamental models have been built and then these models
optimised for use in process monitoring and fault detection. However, building
such models or customising existing general models to a specific plant require
time and effort. Additionally, the theoretical equations only provide a
structure
of a model and many of the parameters must be fixed using expert knowledge
or estimated using past plant data. Also, both physical and chemical
mechanisms may be unknown and online measurements may be unavailable
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of inaccurate.
One approach to modelling a process with the objective of predicting abnormal
process behaviour is to first develop a model of the normal process behaviour.
5 In complex processes the model of normal behaviour ts typically derived
from
historical data collected over time during normal process operation. The
historical data is collected by means of a large number of sensors distributed
throughout the process. It will be apparent to one of ordinary skill in the
art that
the amount of historical data collected in a complex system can be quite large
10 and therefore, the step of deriving a model of normal behaviour is
invariably
supported by a computerised data processing system.
Multiple Models
At least two models are implemented. One model uses input variables whose
means have not been adjusted for drift over time (Long Range Model) and at
least one model has some input variables whose means are adjusted to
compensate for drift (Short Range Model). Compensation for drift may be
accomplished by calculating an average of the input samples over a period of
time that is short enough that no serious drift has occurred. Different
periods
may be used for different models or different input variables in the same
model.
A high pass filter may also be used to remove changes in the data that occur
over a long time scale and focus the model on short time scale variation.
Application of the Invention to a Mitsubishi Continuous Copper Converting
Furnace
Referring now to Figure 1, the invention will be applied to a Mitsubishi
continuous copper converting furnace in order to illustrate its use.
The Mitsubishi process is a continuous copper smelting and converting
technology which uses three furnaces: a circular smelting furnace 10, an
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elliptical slag cleaning furnace 12 and a circular converting furnace 14. The
three furnaces are linked with covered launders as in 16, through which all
the
molten materials (not shown) are continuously transferred by gravity force.
Typically, blister copper from the converting furnace 14 is continuously
delivered by gravity force to a blister holding furnace 18 (or alternatively a
pair
of anode furnaces, not shown).
Copper concentrate (Cu: 30%, S: 30%, Fe: 25%, Gangue minerals 15%) is fed
through lance pipes with oxygen enriched air into the smelting furnace then
oxidised and melted by exothermic reaction to form molten mixture of matte
(Cu: 68%) and slag. The matte is separated from slag by difference of specific
gravity in the slag cleaning furnace. The matte is further oxidised to form
blister
copper (Cu: 98 to 99%) in the converting furnace within which the sulphur
content has been controlled to about 0.8%.
The blister copper is purified in anode furnaces (not shown) by oxidation and
reduction to produce anode copper (Cu: 99.4%), and a strip produced by a
caster is cut into copper anodes (all not shown).
The mixture of matte and slag formed in the smelting furnace 10 flows
continuously to the slag cleaning furnace 12, where the denser copper matte
separates from the discard slag. The matte is then siphoned to the converting
furnace 14, to be continuously converted to blister copper and slag. The
latter
is water granulated, dried, and recycled to the smelting furnace 10, while
blister
copper is siphoned continuously from the converting furnace 14 to the blister
holding furnace 18 from where it is transported by crane to a pair of anode
furnaces (all not shown) for casting into anodes. Anode casting can be by
"wheel" or by twin-belt Hazelett caster.
Each furnace in the three-furnace system can be regarded as a "steady state"
reactor. The bath line within each furnace is constant (no tapping), allowing
for
a simplified refractory design and brick cooling. Control of the smelting
process
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maintains the matte grade at steady values and ensures optimum operating
conditions right through to continuous blister delivery to the blister holding
furnace.
Referring now to Figures 2a and 2b, a cross section of the lower portion of a
converting furnace 14 is disclosed. The converting furnace 14 is comprised of
a
bowl-like dish fabricated from structural steel plate 22 and lined with a
composite structure comprised of a first layer 24 of, for example, high
alumina
ram mix/plastic and a second layer 26 of, for example, fused cast refractory
bricks manufactured from magnesia chrome. As is known in the art, the high
alumina mix can be rammed to a high density and has expansile properties at
high temperature which reduces the possibility of cracking and ensures a
tightening of the lining at high temperatures.
Molten copper 28 is held in the converting furnace 14 within the refractory
lining
26 and, due to the continuous nature of the Mitsubishi refining process, a
constant bathline 30 is maintained between the molten copper blister 32 and
the layer of slag 34 which rests on top of the blister 32. Typically, a drain
36 is
also provided for in the bottom of the converting furnace 14 to allow for
molten
copper to be drained off when carrying out maintenance, or repairs on the
refractory lining 26, etc..
Referring now to Figures 3a through 3d in addition to Figures 2a and 2b, a
cooling system, comprised of a series of water cooled cooling blocks as in 38,
rings the refractory lining 26 at a point straddling the bath line 30 of the
molten
copper 28. The cooling blocks 38, which are manufactured from, for example, a
block of a conductive material such as copper, are cast around formed hollow
tubing such as Schedule 40 Mond 400 pipe, thus forming a series of hollow
passages 40 to allow the circulation of a coolant such as water therein. The
cooling liquid is pumped into the cooling block 38 via an inlet 42, circulates
through the passages 40 and exits the cooling block 38 via an outlet 44. The
curved hotface 46 of the cooling block 38 is comprised of a series of
horizontal
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and vertical grooves as in 48 and is in contact with the rearward side of the
refractory lining 26 which shield the cooling blocks 38 from the molten copper
28. Additionaliy, thermowells as in 50 fabricated from, for example, Schedule
80 AISI 304L pipe, are cast into the cooling blocks 38 at various points into
which thermocouples (not shown) are inserted for measuring temperature.
Referring now to Figure 4 in addition to Figures 2a and 2b, the cooling blocks
as in 38 are arranged side by side such that they form a ring around the
converting furnace 14 at the bath line 30. Molten copper matte is introduced
into the converting furnace 14 from the slag cleaning furnace (12 on Figure 1)
via a matte inlet 52. A blister siphon 54 is provided at the bath line 30 for
allowing molten copper blister 32 to flow by gravity via covered launders into
the blister holding furnace (18 on Figure 1). Additionally, a slag outlet 56
is
provided for removing slag 34 from the surface of the molten copper blister
32.
Referring now to Figure 5, as discussed hereinabove, cooling liquid, such as
water, is circulated through the cooling blocks 38 via a series of inlets 42
and
outlets 44 thereby providing cooling to the rearward side of the refractory
lining
26 at the level of the bathline. In the disclosed illustrative embodiment
thirty two
(32) circuits are provided at the bathline through each of which 200 litres
per
minute of water circulates. The thirty two (32) circuits are arranged in
parallel
such that 6400 litres per minute is used to cool the cooling blocks 38.
Although
not shown, cooling water is also circulated through the roof of the converting
furnace 14 to provide cooling therein.
Still referring to Figure 5, cooling water is circulated by means of a series
of
controllable pumps 58, such as 150 HP BJ VT pumps running at 1800 RPM,
which draw the cooling water from a hot well 60 and pump the water through a
network of pipes as in 62. The flow of water through the network of pipes 62
is
controlled by the speed of the pumps and a series of controllable valves as in
64 which interconnect various sections of the network of pipes 62. One way
valves as in 66 may also be provided for to prevent super heated water or
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steam from entering the network of pipes 62. A straining system 68 may also
be provided for in order to remove particulate matter from the cooling water.
In
order to provide for failure of one or more of the pumps 58, supplementary
cooling liquid may be provided from an auxiliary water tower 70.
Illustratively,
the water tower 70 is connected to the network of pipes 62 via a one way valve
72 and a controllable valve 74 which is actuated by a pressure sensor 76.
Heated water is returned from the cooling blocks 38 to the hot well 60 by a
return pipe 78. Water in the hot well 60 is cooled by transferring it by means
of
a pump 80 and piping 82 to a c:ooling tower 84. Cooled water is then returned
from the cooling tower 84 to a cooling tower basin 86. Water held in the
cooling
tower basin 86 is pumped to other parts of the system (indicated generally by
the numeral 88), for example to the slag cleaning furnace (12 on Figure 1) by
pumps as in 90. These pumps are, for example, 300HP pumps operating at
1800 RPM. This cooling water is then returned to the hot well 60 from the
other
parts of the system 88 via a second return pipe 92. Provision is also made in
the cooling system to make up for water lost due to evaporation, etc..
Referring back to Figures 3a through 3d, provision of multiple thermowells 50
is
made in each of the cooling blocks 38 for insertion of a thermocouple (not
shown), thereby allowing remote measurement and recording of the
temperature of the cooling blocks 38 at a given point in time. Referring now
to
Figure 4, in the present illustrative embodiment eighty-four (84) K-type
thermocouples as in 94, three (3) to each of the twenty-eight (28) cooling
blocks 38, were distributed around the bathline of the converting furnace 14.
As
is well known to persons of ordinary skill in the art, K-Type thermocouples
have
an operating range of between 0 F and 2500 F, nominally between 750 F and
2000 F. Two (2) thermocouples as in 94 where placed within two of the
thermowells 50 cast in the cooling blocks 38 while the third thermocouple was
attached using a water thermowell (not shown) to the outlets 44 of each of the
cooling blocks 38. Note that in the present illustrative embodiment no
thermocouples were used to take measurements in those cooling blocks
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immediately adjacent to the blister siphon 54 or the slag outlet 56, although
in a
given embodiment such thermocouples and their related temperature readings
could be provided for.
Referring now to Figure 6, temperature readings from the thermocouples 94
were sampled by a control module as in 96 and the vaue relayed via a
communications system 98, for example a local area network (LAN), to the
furnace temperature control monitoring subsystem 100. Additionally, the flow
of
oxygen 102 into the converting furnace was continually sampled by read
monitored by a control module as in 96 and relayed to the monitoring
subsystem 100, oxygen flowing into the furnace providing an indication that
the
furnace was indeed in operation. Values sampled from the eighty-four (84)
thermocouples 94 provided a correlated set of data measurements. The
thermocouples 94 are correlated in that the measurements tend to move
together with the temperature of the furnace. A pending breach of the
refractory
lining, changes in the condition of the furnace wall or build up and /or
process
equipment failure is typically indicated by one or more proximate
thermocouples deviating from an overall pattern of normal operation.
During furnace operation, sampled data was stored in a data store 104 for
later
retrieval and processing by the analysis subsystem 106.
The primary task of the analysis subsystem 106 comprises at a first step of
generating the models of normal system operation 108 and at a second step
processing data received to determine a representation of current system
operation 110 for comparison to the model of normal system operation 108.
Both the models of normal system operation 108 and the representation of
current system operation 110 are made available to the monitoring subsystem
100 which compares the representation of current system operation 110 with
the models of normal system operation 108 in order to determine if the furnace
is operating abnormally.
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in the present illustrative embodiment abnormal furnace operation is an
indication that the refractory lining of the furnace is in danger of being
pierced
by the molten copper held within the furnace. The monitoring subsystem 100
also displays, via a visual display 112, such as a CRT, both raw and analysed
data in ways which are meaningful to the operator. In particular, the data
processing subsystem generates alarm messages 114, for display, for
example, on the visual display 112 or, provided the requisite data transfer
network is present, for transfer to the operator via e-mail, etc.. On
detection of
abnormal operation the monitoring subsystem 100 may also take appropriate
actions to restore normal system operation and protect furnace integrity, for
example by shutting down the furnace. These steps include, for example,
shutting off the air oxygen flow into the converting furnace, conducting field
checks and shutting down the smelting furnace.
As stated above, in order to generate the models of normal system operation,
the analysis subsystem 106 analysed data related to temperature of the
refractory lining and water used to cool the lining collected over an extended
period of operation and stored in the data store 104. In this regard, once the
converting furnace 14 was filled with molten copper and in operation, each of
the eighty-four (84) thermocouples 94 was sampled regularly with a sampling
rate of a couple of seconds although it will be understood to a person of
ordinary skill in the art that a different sampling rate could also be used.
Indeed,
as will be understood by a person of ordinary skill in the art, the selection
of
sampling rate is a trade-off between the data generated and the level of
accuracy required.
Although as stated above the input variables for the models were temperatures
measured via the eighty-four (84) bath line thermocouples 94 only (as it was
found that the majority of problems vis-6-vis the integrity of the refractory
lining
occurred at the bath line, which suggested that the bath line thermocouples
would provide the strongest indications of a change in the bath line), other
temperature measurements, as well as other process parameters such as the
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oxygen lance flows and feed rates 'were available but not used. However, in a
given embodiment data with regard to these parameters could also serve as
input to the model and used subsequently for controlling the copper conversion
process.
In order to train the PCA model, a training data set comprisEng data collected
over the previous three months of operation was used. Certain periods of time
(such as shutdowns) were masked from the data set, so that the data set
represented normal operation is represented as closely as possible.
Although data was collected over an extended period of time, the duration of
time over which the data is collected must only be sufficient to provide a
good
representation of furnace operation. In this regard, data from several
successive periods of operation may be combined to provide the basis for the
model. The collected data was analysed offline using the analysis software
package monitorMVTm by Perceptive Engineering Ltd. (although many
commercial analysis software packages would suffice, for example SIMCA-PTm
from UMETRICS or UNSCRAME3LERTm from CAMO).
The first step in the analysis was the generation of a Long Range Model (LRM)
data matrix and a Short Range Model (SRM) data matrix. In this regard, the
data in the SRM data matrix was pre-processed using a sliding window which
subtracted the previous four (4) day average from the raw data prior to
placing
it in the data matrix in order to take into account any long term drift in the
temperature values sampled in the furnace. Pre-processing the data in this
manner provides a method by which measurement drift can be compensated
for. The difference in the response of the resultant LRM and the SRM provides
an indication of the rate of drift of the furnace. Drift compensation is
generally
necessary given subtle changes in the furnace and other factors, such as an
increase or decrease in the ambient seasonal temperatures. However, changes
which the drift compensated SRM might miss were shown by the
uncompensated LTM.
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The LRM data matrix and the SRM data matrix are then decomposed to
provide the coefficients used in the PCA model. A number of different
algorithms may be used to calculate the Principal Components of a set of data,
for example the NIPALS Algorithm or Decomposition of Covariance. The
NIPALS Algorithm gives more numerically accurate results when compared
with the Decomposition of Covariance method, but is slower to calculate. It is
believed that these algorithms are known to a person of ordinary skill in the
art
and will not be dealt with in more detail here.
The result of the decomposition of the LRM data matrix and the SRM data
matrix are the Principal Components. The nth Principal Component of p random
variables is represented by the coefficients of a linear function of the form:
anix anixl + an2x2 + + anpxp =Iaõxi (3)
Once the nth Principal Component has been determined, the linear function
cen.fix is sought which is uncorrelated to a'nx and has maximum variance. As a
result, although up to p Principal Components can be found, the bulk of the
variation in x will be accounted for by m Principal Components, where m <<p.
As stated above, in order to select the requisite number of Principal
Components (m) in the developed models, the PRESS statistic was used.
Using the method as proposed in "Cross-Validatory Estimation of the Number
of Components in Factor and Principal Components Models", S. Wold, 1978,
Technometrics, vol. 20, pages 397-405, the PRESS statistic of m Principal
Component can be determined using the following equation:
n p
PRESS(m)= E E(õ, _ x1 )2 (4)
To decide whether or not to include the Mth Principal Component, the following
ratio R is examined:
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PRESS(m)
R = (5)
n p
-xy)2
.õ.
If R < 1 then the implication is that a better prediction is achieved using m
rather than m-1 Principal Components, so that the rnth Principal Component
should be included. Note that the above describes only one method for
determining the number of Principal Components to be included, and others,
for example those developed in "Cross-Validatory Choice of the Number of
Components From a Principal Component Analysis", H. Eastment and W.
Krzanowski, 1982, Technometrics, vol. 24, pages 73-77, might also be applied
without removing from the spirit of the present invention.
Applying the above methodology to the training data set, it was first found
that
two Principal Components would give good results. However, during operation
it was found that two Principal Components led to too many false alarms and
therefore a single Principal Component was used. Using a single Principal
Component it was found that for the LRM 96.4% of the original training data
variance was recovered and for the SRM 94.1% of the original training data
variance was recovered.
As will now be apparent to a person of ordinary skill in the art, the PCA
models
reduce the large number of input data variables down to a few Principle
Components which can be used to create an estimate of the raw value of each
variable. When this is done, not all of the original signal is recovered, even
over
the training data set used to create the model. This is in fact a benefit as
during
normal operation the part of the raw signal that the model projection misses
may be regarded as random signal noise. Under abnormal operation, the
difference between the raw signal and the model projection is used to
determine which thermocouple (or thermocouples) are responsible for the
deviation from normal operation.
In application, the PCA Model is used to generate Principal Component scores
ti from which a Hotelling T2 chart is generated, as well as a SPE), (Squared
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Prediction Error) chart. Hotelling T2 and SPEx charts are used to recognise
trends in the measured values of the variables (in the case at hand, the
temperature of the refractory lining as measured by the thermocouples).
Typically, both the Hotelling T2 and SPEx charts are periodically regenerated
and graphed versus time with earlier values for display on the display device.
Illustratively, the Hotelling T2 and SPEx charts are determined as follows:
the
scores ti can be determined as follows:
if = a;xj, j =1,2,..., m (6)
where m is the number of principal components in the model. The Hotelling T2
chart can be derived from the PCA Model scores according to the following
formula:
e12
= E - (7)
;,, j=1st,
where sti is the estimated variance of the corresponding latent variable t.
The
estimated variance of the latent variable is determined from the scores from
the
modelling data set according to the following equation:
E
2 i=1
s, = (8)
N ¨1
where N is the number of observations.
The Hotelling T2 chart can be used to check whether a new observation of
measurements on k process variables projects on the hyperplane within the
limits determined by the training data set. The Hotelling T2 chart gives an
indication of how far in the hyperplane the new observation lies from the
centre
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point of the data used to train the models. As such, it provides an indication
of
how far the new observations, i.e. the current state of the process, have
strayed from the model of normal behaviour.
The SPE, chart can be calculated according to the following formula:
SPE), ¨1(xnewõ j)2 (9)
J=1
where .i is computed from the ?CA model. The SPE, is the sum of the
squares of the normalised residuals. The SPE, detects the occurrence of any
new events that cause process to move away from the hyperplane defined by
the training data set. As such, the SPEõ provides a measure of how much the
measured values are in agreement with the PCA modeL In the case at hand, a
low SPE value indicates that the furnace is behaving similarly to the furnace
which was used to train the PCA model (normal operation). A high SPE value is
an indication to the contrary (abnormal operation).
Another feature of a PCA Model is that it does not predict sampled values
ahead in time. Instead, all of the values associated with a PCA Model are
typically from the same sampling instant (although samples from different
times
can be used, although this was not done in the development of the present
illustrative embodiment). It is more accurate, therefore, to refer to model
'Projections' rather than model 'Predictions', although the term Prediction is
retained in the interests of continuity.
The training data set was passed through the PCA Models a number of times
which allowed the identification and removal from the training data set of
portions of the data which did not appear to represent normal operation. After
removal of data from the training data set the model was regenerated. The
final
result of this iterative process was a stable model representative of normal
furnace operation.
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The above developed Short Range and Long Range RCA Models were
implemented within the furnace temperature control monitoring system. The
initial response of the control system was to raise an alarm \Arlen the
monitored
system was found to be operating outside the modelled normal operating
ranges. Typically, during operation the following series of steps would be
repeated until an alarm condition is determined, Note that although data was
sampled from each thermocouple typically every couple of seconds, data was
fed into the monitorMV program for analysis once a minute.
= Retrieve current operation: measurements are read or sampled from the
thermocouples;
* Pre-process measurements for short range model: a four (4) day moving
average was subtracted from each of the 84 measurements for the short
range model;
O Analyse current operation: generate scores, NoteIlingT2 and SPE;
* Raise alarm: (1) check SPE against limit, raise alarm and continue of
over
(2) check individual residuals against limit, raise alarm and continue of over
(checks can include multiple residuals in one area being over the limit), (3)
shut off air and oxygen, and (4) investigate source of alarm; and
* Resolve alarm: identify the five (5) thermocouples having the largest
contributions.
Various levels of alarms are raised depending on how far the data was
determined to be from the hyperplane. In general the setting of the alert and
alarm limits is done in two steps. The alarm levels are initially determined
offline using past process data. An iterative process is then used to derive
suitable levels for the detection limits, i.e. in order to determine limits
that only
very rarely result in alarms during normal operation but always result in
alarms
in cases of abnormal operation. Once the monitoring system is in operation,
the
levels of the monitored variables and any instances of false or missed alarms
are used to adjust the alarm limits. The alarms levels on the SPE are 200 for
an
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advisory alert, 300 for a critical alert and 600 for a super-critical alert
that would
trigger the logic for shutting down the furnace automatically.
A similar iterative approach would also be used if introducing additional
thermocouples once the monitoring system was in actual operation. The limits
are adjusted based on the frequency of alarms and any instances of false or
missed alarms during actual operation of the furnace.
In addition to raising alarms, E-mail notifications are sent by a mechanism in
the monitoring system when the SPE goes above a certain level, illustratively
when the SPE is greater than 300. Additionally, the five (5) thermocouples
with
the largest contributions are identified and provided to the operator to help
diagnose the cause of any alarms.
Measurements from particular thermocouples can be temporarily removed from
the monitoring system by 'masking' them out (in which case missing data
methods are used, for example based on the NIPALS algorithm as known in
the art) or may be permanently removed if they are the source of many false
alarms. Differential temperatures across the coolers were initially included
but
found to be unsuitable for monitoring. They were therefore removed from the
monitoring system.
The models also need to be periodically re-built with new data when the
furnace has changed significantly or thermocouples have been added. This
was done after the furnace was re-built when enough data had been gathered
to have a representative sample from the new furnace.
