CA2179719A1 - Method for monitoring multivariate processes - Google Patents

Abstract

A method for monitoring and control of an industrial or other technical process, in which the process is dependent on a multiple of variables (X) relevant to the process. The process comprises a description of the relevant variables as a multidimensional room, where each variable represents an independent component in the room, that the observations of the variable values at a certain time point represent a point in the multidimensional room, that observations from a number of time points form a point swarm in the room, that at least one first (pa) and one second (pb) principal direction of the point swarm are calculated, that the projections of the observations onto these first and second principal directions are determined, that the observations are illustrated graphically in the plane which is formed by the first and second principal directions in the point swarm, further that the principal directions (pa, pb) are continuously updated during the course of the process, the graphic information thus becoming dynamic, and, finally, that the process operator or the monitoring member, on the basis of the presented information, adapts members which influence variable quantities in the process such that the process is controlled to optimum operating conditions.

Description

WO 95118420 ~ 1 7 9 7 1 9 P~ L~1208 ~ethod Gor i tor;nr 1'`'71 tiv~riate ~rocecæes ~T~rTTNTrAT, FIELD
5 The present invention relates to method of monitoring an industrial process which is dependent on a large number of parameters, available through measured data, in a way which makes it possible to control the process to the desired conditions by allowing the relevant variables of the process 10 to be represented by the axes in a linear space with as many ,li~ cinnq as the number of variables, whereupon the pracess is proj ected onto a plane or a three-dimensional room, such that a calculated model of the process is ohtA; ne~1 on-line and by comparing the model of the process with a reference m~del 15 of the process such that a distance to the ref erence model is obtained, whereupon, when observing a drift of some parameter, the process can be restored to at least one norm range f or the process by acting upon a deviating variable.
20 RArT~rRnT~Nn ART
For obtaining, for instance, the desired quality of a manufac-tured produce in a manufacturing process with the best economy or otherwise monitoring an industrial process or industrial 25 application, it is necessary to control the processes as efficiently and optimally as possible. A manufacturing process includes many importanT variable quantities (here only referred to as variables), the values of which are affected by the variations of the variables during the course of the 3 0 process . The optimum result is achieved if the process-monitoring operator or the process-monitoring member is able to handle and control all the process-in~ Pnrin~ variables in one and the same operation.
35 A conventional method of optimizing a process is to consider one variable at a time only, one-~ n~l optimization. All the variables are fixed except one, whereupon the non-fixed variable is adjusted to an optimum result. ~hereafter, the Wo 95/18420 7 ~9 PCT/SE94101208 free varia~le is fixea and one of the other variables adjus-ted, and so on.
When the process variables have been set in this way one by 5 one, it is supposed that the best working point of the process has been obtained. ~owever, the fact is that this is not the whole truth. The process may still be far from its optimum working point, since the method does not take the mutual influence of the process variables into account. The diffi-lO culty of this method is to obtain a total overview of theprocess based on a number of mutually independent process variables as necPqci t~tP~ by such a view. It is only when the relationship between these variables can be interpreted correctly that the process operator gets a real overview and 15 understanding of the process.
An operator is limited by his or her human ability to under-stand and control only a limited number of variables per unit of time. A process monitoring system measures up to hundreds 20 of variables, of which perhaps some 20 more or less d~rectly control the process. Such a monitoring system requires a computer which can continuously reqister if and when slight variations occur in any of the variables.
25 A model of a process is realized substantially by two diffe-rent types of ,~Pl 1 i nq techniques, mechanistic and empirical modelling. Mpoh~niRtic models are used, for example, in physics. Data are used to discard or Yerify the mechanistic model. A qood ~ ~ -ni qtic model has the advantage of being 30 based on estAhl i qhPd t_eories and is usually very reliable over a wide range. However, the ~p~h~ni qtic del has its limitations and is only ~rrlic~hle for relatively small, simple systems, whereas it is insufficient, if even possible to use, for h~ i n!r an axiom around a complex industrial ~5 process. lY[any attempts have been made to model processes with the aid of -h~nictic models 'oased on differential equationS.
An important disadvantage of t_ese models, however, is that they are qreatly ~pl>pn~i~nt on the dependence of certain WO 9S/18420 2 1 7 9 7 ! 9 PCT/SE94/01208 pCL ' ers on each other. Such parameters with great depen-dence on each other must be det~rminF~rl for the model to function. In the majority of cases it is very difficult to cluantify them in a reliabLe manner. A consequence of this is 5 that it is very difficult to obtain -hi~ni qtiC models that work in practice.
In empirical ~ 1 ing the model is based on real data, which, of course, reguires good-o,uality data. Process data consist of lO many different measured values. In other words, process data are multivariate, which presupposes multivariate techniques for process data to be modelled and illustrated. rlifferent statistical methods exist for multivariate modelling.
Traditional multivariate ~l.ol 1 in~ technique, as for example 15 linear regression ~LR), assume independent and error-free data. For that reason, such techni~ue cannot handle process data, since they are highly interdependent and, in addition, influenced by noise.
20 A solution to the above problems is to use projection technique. This techniyue is capable of selecting the actual variation in data and expressing this information in so-called latent (underlying) variables. The technique is described in Ass Review 4/93, sert Skagerberg, Lasse Sundin. The projection 25 technic~,ue is most advantageous for obtaining a fast overview of a complex process. The two projection techniques, PCA and PLS, that is, Principal C ~-,t Analysis and Projection to Latent Structures, are tailor-made for solving problems such as process overview and irl,ontific~t;on of r-1~tionqhi 30 between different process variables.
~odels created with these two methods can be executed directly (on-line) in the process infnrr-ti~)n system and can be used for process monitoring. PlS is highly suitable for predicting 35 various ouality-related variables, which are normally diffi-cult to measure or ' i ~ even impossible to measure routinely since they occur late in the process.

Wo 95/18420 ~ PCrlSE94101208 ~i~9~9 Mn-l~l 1 ;n~ by means o~ projection technioues (PCA, PLS) is best explained by the use of simple ~eometry in the form of points, lines and planes. Process data are usually listed in the form of tables, wherein a row represents a set of observations, 5 that is, registration of variable values, in the process at a certain time. For practical reasons, and for the sake of clarity, the description will be restricted in the following to a data table with three variables, that is, three columns, which can be illustrated geometrically with the aid of a 0 three~ ci~n;~l coordinate system (FiS~. 1), where the variables in the process are represented by the axes in the coordinate system. However, the method functions for an arbitrary number of variables, K, where K > 3, e.s~. K = 50 or K = 497. An observation of the releva~t variables in the 15 process at a certain time may here be represented by a point in the coordinate system which is common to all variables, which means that the measured value of each variable corre-sponds to a coordinate for the respective axis. M;~th~ ti-cally, independently of the number of coordinates, a row in 20 the table still co~respon~s to a point. All n rows in the table then correspond to a swarm of points ~Fig . 2 ) . The r-th t i cal procedure for describing a process with K
relevant variables is handled in the same way by the observa-tions at each time beinSJ represented by a point in a multi-25 ~ ln;ll room wlth K coordinates.
The projection method works on the assumption that two pointsthat lie close together are also closely related in the process .
The data set may now be projected to latent variables in a series of simple ~reometrical operations as follows:
- ~he midpoint in the data set is ~ clll At~d. This r:3l rl~ t~d 35 point is called x. The mi~roint coordinates correspond to the mean value of all the vari~bles in the system (FisJ. 3 ), - Starting f~om the midpoint x, a first straight line, pl, is -Wo 95/18420 21 7 9 71 9 PCTISEg4101208 drawn, which is adapted to the data set such that the distance to the line for the individual points is as small as possible.
This line corresponds to the direction in the data set which explains the ~reatest variation in the process, that is, the 5 dominating direction in the data set and is referred to as the f irst principal direction . The direction coef f icient of this line is combined in the loading vector P1. Each point in the data set is then projected orthogonally to this line. The coordinates from the projection of all the points to the line 10 form a new vector t1. ~Each point gives a value, here called ~score", as a I ~ ^-lt in the vector tl- ) - The new vector (t1) is usually called score vector and describes the first latent variable. This latent variable 1~ expresses the most important direction in the data set and is a linear combination of all three variables (or in a multi- =~
dimensional system all K variables involved). Each variable has an influence on the latent variable which is proportional to the size of the direction coefficient in the loading vector 20 Pl-- Even if the line, the f irst principal direction, P1, given by the loading vector, ~1, according to the above is one that most closely agrees to the data set, it can still be seen from 25 Figure 4 that the deviations from the line are relatively large. A second line, p2, may be adapted to the point swarm which represents data in the process. This second line, p2, is orthogonal to the first line, pl, and describes the next most important direction in the point swarm (Figure 4) and is 30 referred to as the second principal direction. The score vector t2 and the direction coPffi ,-; Pnt ~2 are interpreted analogously to t 1 and ~1-Analogously, a third projection line can be constructed with 3 5 the direction ~3 and the score vector t3 . However, the valueof computing a third principal ,,, ^-,t in this three-dimensional example is limited, since the resulting three latent variables tl, t2 and t3 only represent a rotated W095/~8420 2~-~9~g PCr/SE94/01208 version of the three-dimensional coordinate system.
If, instead, a look is taken at the projection plane which iB
defined by the first two principal directions, Pl and P2, it 5 can be determined that this plane describes the point swarm well in two dimensions only. The advantage of this is that points projected onto a plane reproduce infrrr~ n which emanates from variables in three dimensions. This is one of the reasons for using PCA to analyze a complex data structure.
lO From a number of variables a small number of underlying latent variables may be ootained, these latent variables describing the main part of the systematic infnrr~t;~n about current process data. From experience, it has proved that more than 2-6 latent variables are not required. This can also be shown 15 theoretically. The latent variables provide an overview of the data set and can be presented in the form o~ different types of diagrams or graphic images. Part of the variation of the data set will remain af ter the latent variables have been extracted and are called residuals (deviations). These contain 20 no systematic information and may therefore be regarded as superfluous and are often referred to as noise.
According to one approach, the projection plane, defined by the lines Pl and P2, may be seen as a two-dimensional window 25 into the lt-ifli qinn~l (in the example the three-dimensional) world. The basic idea behind PCA is to construct such a projection window, providing the viewer with a picture of the mul~iAi- ~ion~l data set. Consequently, PCA ensures the best possible window, that which contains the optimum 30 picture of the data set. Further, the window can be saved and displayed graphically. The projection window v; q-l~,l i 7.~A on a computer screen provides an operator, for example, with an overview of a complex process.
35 ~ The projections described above are essentially a geometrical interpretation of the principal component analyses which have proved to be very suitable for obtaining an overview of process data. Normally, it is sufficient also among hundreds W095/18420 21 79 71 J PCr/SE94/01208 of variables to calculate about three r~in^iI~Al, nnAntq to describe the principal information in the data set. Ty,oical o the PCA method, when applied to process data, is that the system easily selects a strong first ~ A^t, a less impor-5 tant second, ^^~, and a third ~ describing littlebut systematic information.
The PCA method is suitable to use for analyzing blocks of process data. Questions which may be answered in an industrial lO process by means of PCA are:
- overview of a ~uantity of data - Classification (e.g. if the process continues normally or if it deviates) 15 - Real-time monitoring (e.g to track the process conditions and discover an incipient deviation as early as possible).
Another i ~ problem is to identify rA1;1ti~^~nqhirq between =~
process data, X, and more ouality-related data, Y This type 20 of rP1~tinnqhirs are ~iffi~ to analyze, if even possible using traditional aAl 1 inj techni~dues, since the relation-ships are often hidden in complex interactions and correlation patterns involving different process variables.
25 Projection to latent structures, PI~S, is a projection technioue which offers a method of ,1~11 ;nj complex relation-ships in a process. PLS ~ rAq two blocks of data, X and Y, into principal ~, ^^,tq as projections (Fig. 5). The two blocks are similar to the solution according to the 30 PCA method, but differ in that in PLS the projection is made to explain X and Y simultaneously for the purpose of nhtA~ini the best possible correlation between X and Y. Thus, the PLS
method serves to model the X block in such a way that a model iS nhtA~;nAri which in the best way predicts the Y block. A PLS
35 model can thus be very useful for predictiny (Iuality-related ~c~ ^rs, which are otherwise both expensive and difficult to measure. Instead of haviny to wait perhaps a week before a critical value from the ciuality control laboratory becomes available, this value can be; 1;A~_A1Y predicted in a model.

WO95118420 21~ 9719 PCr/SE94101208 ~
Figure 6 illustrates an example of how the study and monito-ring of an ;nA~lqtr;~l process can be v;q~ l;7eA by means of a computer screen on-line. The left half of the figure shows a score plot, that is, a representation of the observations of 5 the measured data of the process from two latent variables ta and tb reproduced with two principal directions Pa and Pb as axes in the coordinate system of the graph. The left half of the picture shows both a static and a movable picture. The static picture consists of points which describe the variation 10 in the reference da~ a which are used for building the model .
If these reference data are chosen in the best way, the picture consists of good working ranges for the process as well as ranges which should be avoided in the process. The picture may be compared to a map ~nnt~;n;n~ infnr~~t;nn as to lS which conditions the operator should strive to direct the process to, and which conditions should be avoided.
On-line F-~ t; nn of measured process data results in calcula-ted markings, that is, that observations made at a new time 20 are reproduced as a new point in the plane which is represen-ted by that plane which, in the form of the two selected principal directions Pa and Pb, constitute the coordinates of the graph on the screen. This means that each new point contains information about all the relevant measured data 25 because of the pro~ection to the latent variables according to the PLS method. Changes in the process may then be reproduced on-line on the screen in the form of a line in the left half of the VDU. The changes are reproduced with the aid of a movable figure in the form of a curve which connects the 30 observations at different times. The curve will thus move in time over the screen like a crawling "snake". To make the operator better understand the q;~n;f;nAn~f~ of the infnrr-t;nn provided by the crawling snake, the snake may be divided into a head and a tail, which are also illustrated in aifferent 35 colours and symbols. The head consists of present observa-tions, whereas the tail is built up of ~historical~ observa-tions. If an alarm is raised, that is, when the curve (the snake) detects "prohibited" areas, the snake may change Wo 95/18420 2 ~ P~ 01208 colour, for example to red.
The movable curve is an aid to the operator to continuously monitor the status of the process by viewing the process 5 through a ~window~ on the screen into the multivariate rooms of the process. The location of the snake's head is compared with the area where reference data of high sluality have been attained. The ambition of the operator or the monitoring member of the process should be to control the process to thls 10 area.
To the right in Figure 6 there is shown an example of other information which may be imparted to the operator via the screen with the aid of the PLS method. The right picture is a 15 reproduction of loading vectors, a loading plot. This is a map of how the score plot, that is, the curve in the left picture, is influenced by the individual variables in the process. The left and right picture halves also contain associated informa-tion . This means that the direction in the lef t picture has a 20 direct corrocpnn-l~n- e in the right picture. The operator may receive guidance from the right picture i~ he/she is to con-trol individual process variables for the purpose of moving the process (the ~snake~' ) to achieve better operating conditions for the process.
The use of the method described above means a powerful instru-ment in monitoring processes which are dependent on a large cluantity of process variables in a simple and clear way. As examples of t~onhnir~l fields, within which process monitoring 30 of industrial processes according to the described methods may advantageously be utilized, may be mentioned the pulp, paper, r-h~miri:l, food, ph~rr-re~ltical, cement and petrochemical industries as well as power generation, power and heat distri-bution, and a wide range of other ap~l in~innc . ~owever, the 35 PCA and PLS methods, respectively, used according to the prior art suffer from a weakness in that the projection plane which is built up of two principal directions, and to which plane the observations are projected, are fixed and do not c~ange WO 9~/18420 ~t ~ ~ 9 PCrlSE94/01208 during the course of the process. This means that changes in the swarm of points in the multi~i cinr~l space, which has constituted the base of the r~lr~ tinn of the principal directions Pa and Pb, are not taken into account. At the same 5 time new observation series are constantly added during the process, in which variable values may be changed, which means that the geometry of the point swarm in space may be changed and that the r~lr~ tP~ principal directions which are inten-ded to reflect the shape of the point swarm are no longer of 10 interest. This is not reflected by the graphically reproduced information about the course of the process according to the above .
SUM~IARY OF THE lN V ~ l(JN
The present invention relates to a method for monitoring and control of an industrial or other technical process, in which the course of the process is dependent on a multiple of varia-bles relevant to the process. The method involves a descrip-20 tion of the relevant variables as a mul~ c;nn;ll room,wherein each variable represents an independent, A nnPnt in the room, that the observations of the variable values at a certain time represent a point in the mul~ onal room, that the observations from a number of times form a point 25 swarm in the room, that at least one first and one second principal direction of the point swarm are calculated, that the projections of the observations on these first and second principal directions are determined, that the observations are illustrated rr~rh;r~l ly in the plane which is formed by the 30 first and second principal directions in the point swarm, further that the principal directions are continuously updated during the course of the process, whereby the graphic informa-tion becomes dynamic, and, finally, that the operator or the monitoring member of the process, based on the presented 35 information, adapts members which influence variable rluanti-ties in the process such that the process is controlled to optimum operating conditions.

-WO95/18420 79 71~ PCrlSE94/01208 .

According to the prior art, in~ormation about the course of the process is oht~inP~1 by projecting measured data onto a plane which i8 comprised in the variable space which describes the process. The novel feature according to the invention is 5 that the plane to which measured data are projected, according to the PCA and PLS methods, dynamically follows the flow of new series of measured process data, the projection plane being able to rotate in the multivariate room which describes the process. This provides a constant monitoring of the lO process in relation to the present stage and not, as previously, in relation to a ~process historical~ stage.

The illustration of the course of the process may take place according to previously known technique, on-line or off-line lS in the form of a snake which crawls on a screen according to the above, or i~ the form of ordinary historical trend curves.

When the process is vi qll~ ; 7P~ with the aid of a snake crawling over a plane, this means according to the invention 20 that the direction of crawling of the snake illustrates a direction of the process taking into consideration how variable quantities t~ ily influence the model of the process, in that variable values ~hich slide away in different directions in the process influence the above-mentioned point 25 swarm to assume new geometries When showing the course of the process as a graph on a screen, reference data for the process are also plotted on the screen in the form of regions to which the process should be control-30 led. Also process-;nfll1Pn~;n~ parameters are plotted on the screen to i~dicate which variables in the process have a strong inf luence on the process when the process slides in a certain direction ;nt~ t~d by the direction of - v~ - of the graph on the screen.

If the process is on its way into prohibited or non-optimum regions, which is ;n~ tP~ on the screen by the graph moving into regions which are marked on the screen as forbidden, the WO 95118420 ,~ PCT/S1~94101208 operator controls the process towards allowea regions by acti-vely infl11Pnr;nrJ at least one member in the process which inf luences the variable or variables which is or are denoted by the graph as being capable of being ;nfl~Pncpd by the 5 memoer or members which restore the process ta the norm or reference region plotted on the screen.
It i8 also possible, if desired, to automate the monitoring, by using known technique, by sensing which variable or l0 variables can restore the process to the above-mentioned desired regions with known electronic devices, which then control the variable-influencing members in the process such that the process is T--int~inPfl within given frames.
lS According to the invention, new current models of the process are r~1r-~l~tP~ dynamically. sy continuously comparing the last calculated model with a reference model fl~tprminp(i for the process, a real-time ri~l r~ tPfl value of the distance of the process from the reference model is nht~inPrl, When this dis-20 tance exceeds a value fixed for the process, lt is practicalto initiate an alarm. A variant of this alarm is arranged such that the most interesting part of the process, indicated as a graph in the form of a crawling snake on a screen, when this graph enters fnrhi flrlPn regions for the process, is coloured, 25 for example, red. Other devices for calling attention requiring action are also to raise an alarm, for example, by means of a signal, a light, a lamp, etc.
In another variant of the invention, a third principal direc-30 tion for the point swarm in the variable space is rAlr~
whereupon the observations are projected to the three-dimen-sional room which is defined and spanned by the three princi-pal directions, and that the three principal directions accor-ding to the invention are continuously updated during the 35 course of the process, and that the observations are illustra-ted gr~rhi~lly on-line as projections in the room spanned by the three principal directions, which also in this case may take place by a graph in the form of a snake crawling between WO95/18420 21 79 71~ PCr/SE94/01208 the coordinates in the room to which the current observations of the process are ~rojectea.
Applying the described method, process automation is given a 5 very powerful instrument for monitoring and controlling, in a well-arranged manner, also very compIex processes.
BRIEP DESCRIPTION OF THE DRAWINGS
l0 Figure l shows how collected data can be represented in a coordinate system with as many ~ qionQ as the number of variables. An observation of the process represented as a row in a matrix with variable values gives rise to a point in the coordinate system.
Figure 2 shows a swarm of points, each one representinEr an observation of the process, in the coordinate system.
Figure 3 shows how a first principal direction of the point 20 swarm is formed.
Figure 4 shows how a second principal direction of the point swarm is formed.
25 Figure 5 illustrates how the PLS method models and identifies dependencies between two data sets, for example measured process data and quality-related data, which makes possible an -'liAtF prediction of the occurrence of the process.
30 Figure 6 illustrates in the left picture a score plot, which shows the state of the current process with the aid of a so-called "snake~ which follows the course of the process, whereas the right picture shows a loading plot which, in turn, indicates how the process is influenced by process variables 35 ~TOT, FAR, PKR, etc. ) introduced into the coordinate system.
Figure 7 illustrates the weighting of the observations in the monitQred process in a long-term memory and a short-term WO 95/1~420 2 i~ PCT/SE94/01208 1~
memory, respectively, according to the method.
Figure 8 shows the llt i 1; 7~t i nn of control limits in the form of limits to the standard deviation from the mean value of the 5 process, which limlts may be used in a monitoring system to justify intervention into the process.
Figure 9 exPlains how the projection plane, onto which all the observations are proj ected according to the invention, under 10 certain circumstances may be subjected to an lln;nt~nt;-mAl rotation of the model.
Figure l0 denotes the F~x}rln~nt;~l weights v in the data block and the loading block in the EWM-PCA algorithm.
Figure ll shows a so-called "distance-to-model~ curve or DCL
(Distance-To-class~ curve, which has been obtained explicitly for presentation of multivariate processes. The DCL curve describes the distances to the limits of the reference model.
20 A multivariate alarm is defined ~ Pn~n~ on the level of the DCL ~ Dmo d ) .
Figure 12 shows a schematic flow chart of the calculation steps in the ~ lllAtiny units which carry out the calcula-25 tions to obtain the model o~ the process as well as the dis-tance to the reference model.
DESCRIPTION OF T~E PREFERRED EMBODIMENTS
30 Accordiny to the invention, 1~ '~11 in~ by means of PCA and PLS
is used oy dynamic updating of the process model by means of ~cpnnl~nt; Al ly weighted observations and ls described as multi-variate slener~l i7Ationc of the G~nPn~iAlly weighted moviny average, abbreviated EWMA (F-~on~ntiAlly Weighted Moving 3 5 Average ~ .
Principles and ~F~t~rrinAtion algorithms for l1tili7in~ EW~5A and realizing dynamic models, which according to the invention WO95/18420 ~1 79 71~9. P~

make it possible to obtain optimum monitorin;r of a process, are presented in the following. Further, predicted control charts based on these models are shown.
5 Standard PCA and PLS models assume an independence of process times, that is, that no process memory is llt i 1 i 7P~ . Since projected observations (scores) by means of PCA and PLS entail good "cross sections" of process data, a natural way to model ~memory effects~' would be to develop simple time-series models 10 in these scores. One of the simplest models is available via EW~5A, which provides both a good picture of the current status in a process and a ~one-step-ahead'~ forecast about the process. In this way, an EWMA model based on multivariate projected observation (scores) from PCA and PLS constitutes a 15 natural Pl.rtl~nq; rln of multivariate model standards for process applications .
A geners l i 7:~t i ~n of EWMA into EWM-PCA and EWM-PLS consists of two parts. The first part is related to the use of scores 20 instead of individual variables in control charts and predic-tions. The second part is the dynamic updating of the PCA and PLS models to allow the model to take into account the drift in the process.
25 The obvious field of application of EWMA-PCA/PLS is process monitoring and control. Multiple responses are common in all types of ;'lltl t i C process control today, both because it is simple and inPlcrPncive to measure many process-in~lllPn~in~
quantities and because complicated products/controls impose 3 0 many demands on criteria which must be monitored and controll -ed to ensure high quality of the product/control. As an example to illustrate EW~A-PCA in this disclosure, we use a (49x17) matrix with collected measured data of 17 variables from a paper machine over a period of time of 49 equal time 35 intervals. The 17 variables comprise values from measured quantities such as the weight of the paper pulp, the moisture content, the brea~cing stress of the paper, the velocity of the machine, etc. ~he method of utilizing EW~ offers, per se, WO95118420 21~ PCT/SE94101208 also entirely di~ferent rr~ihi 1 i ties within ~ields which attract increasing interest, such as pnllt1tinn of rivers, lakes, oceans, etc. when monitoring such prllutinn~ a plura-lity of variablefi are measured where the method according to 5 the invention would offer a clear and well-arranged way of presenting data. In the case of, for example, emission of substances/particles from an industry into a reception area, such monitoring would permit feedback of presented measured values and permit control of a change of ~ lll,S in the 0 ~.mi q~i r,nR .
In, for example, rhF~mir~1/trrhnirAl contexts, other sequences than changes are often studied over time. Natural polymers, such as cellulose, DNA and proteins are built up of ser,uences 15 of a set of monomers, wherein local monomeric E~MA- PCA
properties can be used to obtain information about such things as binding sites, etc . In such P~rr] i rAti nnq, it may be a natural thing to extend t~te expnnrntiA1 1y decreasing weighs in both directions from the centre of t~te model.
In the following description of the model, to achieve the method according to the invention, ~.~qi~nAtinnC according to the following table are used 25 X a matrix with process variables (entries to predict Y) Y a matrix witlt ~result " variables in PLS (responses output values, product properties) i, j index of observations, rows in X and Y; (i, j = l, 2, . ..
N) 30 N number of elentents, observations, samplings, or process times; (rows in X and Y) k variable ind~x in X and Y; (k = l, 2, ..., ~) K number of variables in X or Y; (columns in X or Y) * used for designating a memory matrix for old values 35 m index of response variables; (m = l, 2, ..., M~
M number of PLS Y variables; (columns in Y in PLS model) Vi weight of the observation i a component index; (a = l, 2, ..., A) WO 95/l8420 9 719 ~ PCI/SE94/01208 A number of, ~ntq in the model W matrix of PLS weights (~i - Rinn R x Wa columns in W, X weights of c ~ ^~t a P loading matrix, rii - Ai nn (K x A) 5 Q memory matrix of lnAflinss (or PLS weights) C matrix of PLS Y weights, ~lir^~qinn (M x A) Ca columns in C, Y weights of c~ t a T score matrix of X, ~lir ~inn (N x A) ta columns in matrix T, scores of c nn~nt a 10 U matrix of u-scores, ~ir -inn (N X A) Ua columns in matrix U, second scores of ~ , onf~nt a Ea X or Y residuals after ~ --nt a, ~li Ri nn (N x K) Fa PLS Y residuals after ~, ^nt a, dimension (N X M) 15 EWMA may be regarded as a model with two components. The first -`'It concerns the creation of a modelling variable y and predicting this variable y at a subsequent point in time. The second ( -'lt concerns the dLLallSI~ t of a control chart based on the model.
The basic idea behind EWMA is to model y as a weighted moving average, with the latest observations weighted heavier than earlier observations. F~nn,ontiAl weights vi = ~,(l_~,)t-l (1) are used for the i'th observation which precedes the current one (i=t), see Figure 7. This gives the predicted value at the time t+1 according to equations (2) and (3). These eguations 3 0 may at the same time be utilized to recursively update the EWMA model from time t to time t+1 according to:
~t+1 = ~Yt + (1-~)Yt (2) = Yt + ~(Yt ~ Yt) = Yt ~ ~et (3) Assuming that the residuals, e~, have a constant variance ~2, the variance of EWMA will be:

WO95/18420 ~971~ PCIIS1~94/01208 1~

Var(EWMA) = a2~/(2-~ (4) A corresponding standard deviation (SD~ may be used for creating control limits as, for example, three-sigma limits.
5 Thus, the EW~qA diagram can be used as a monitoring instrument for indicating if the process is significant at the side of the desired region to thereby justify an intervention. See Figure 8. Since, on the other hand, the model provides us with a prediction of y at the next observation time, EWMA may also lO be used as a base ~or modifyins the difference between the prediction and the score value, that is, an achieved dynamic process control For this purpose, a 'if;~d EWMA is rer rlPrl as follows:
EWMA = ~t+l = Yt + ~let + ~2 ~ et + ~3 ~et ~ et-l) (5) The values of the parameters 1.l to ~3 are estimated from the process history.
20 The principal ~ ~ t analYsis, PCA, is usually based on an analysis of an (N x K) data matrix, Y, which starts with a matrix, centred and scaled into uniform column variance. PCA
models this nnrr-1;7ed matrix as a product of an (N x A) score matrix ~, and an (A x R) loading matrix, P, as well as an (N
25 x K) residual matrix, E:. The number of product terms, the r, ^~tc A, define the ~1imPnc;nn~l;ty of the PC model. If the number of product terms, A, is equal to, or greater than, the rl; c;nn of X, N or K, the residuals E are i~Pnti~lly equal to zero. The number of significant . , nnPntC:, A, may be 30 estimated in a plurality of ways; here we advocate cross-VAl ifl~qtinn Y = ~;ata~Pa ' + E = T P ' + E ( 6 ) 35 The scores (the columns in T) are orthogonal and ln many waysprovide the best summary of data. This provides a good picture of the process if these scores are plotted into a diagram aæ
rlPrPn~lPnt on time.

~ WO 95118420 ~17 9 71~ PCT/SE9V01208 For an unweighted ~ ti~n of the principal component5, ta and Pa, division into singularity values ~SVD) is a method to prefer if all the components are desired (a = 1,2, ...
min (N,K) ) . If only a small number of first principal compo-5 nents are of interest, a method known under the name NIPALS
(see, e.g., H. Wold, Nrml in~r esti~-ti-m by Iterative I.east Squares Procedures, Research Papers in Statistics, Wiley, New York 1966) may be applied as this method is faster since only the first ^nt.c ' i~n~ri are ~tPrmin~d. The NIPAIIS
lO interpretation of the loading values (Pak) as partial regression coefficients makes the r~ tjnn of PC models uncomplicated, as is shown below.
Ea_l =~ {eik/a_l~ = X - ~ba 1 tb~Pb (7) eik~a_l = tia `r Pak + eik (8) Pak = ~iN ( eik I tia ) / ~iN (tia ~ tia) (9) The elements in pa are normally nr~rr-l i 7ed to the unit length 25 ( ¦¦P~¦¦ = 1) which gives tia = ~k Yikpak (lO) The standard deviation (SD) of the row i of the residuals, si, 3~ is a mea:,ul~ ' of the distance between the i'th observation vector and the PCA model. For this reason, this standard deviation, DMod, is often referred to as the distance to the model .
35 To develop an ~Yp~n~nti~l ly weighted moving principal com-ponent analysis (EWMI~), which is llt;li7~ri according to the invention, two steps are required. The first step, which com-prises updating and prediction (forecasting) o the process WO9S118420 2~ i9 PCr/SE94101208 values at the next point in time t + 1, is unc, 1 i oAtP~l if an existing PCA model +or the process is assumed. The second step, updating this PCA model for a proce;s which is driving, proves to be complex.

The forecasting part is achieved }~ means of K multivariate process responses Y = ~Yl, Y2, .-, Ym, --, YM}, and a PCA
model with A ~c which is ~ilotprm;n~d from these Y data.
A process time point has A scores, ti~, ~a=l, 2, ..,, A), 10 associated with it, which form a row in the score matrix T.
Now, assuming a certain auto-regressive auto-correlation structure and a stable cross-section correlation structure in the data set, and thus a stable PCA model, the EWMA values in 15 the scores ta will provide us with a base for multivariate and dynamic process control.
Here we assume that the process is driven by only A indepen-dent ~latent variables~, which indirectly are '~observed" by 20 the Y variables and ~t~ npd as scores ta ~a = 1, 2 , . . ..
A). This gives two alternatives for achieving control charts.
Either one control chart may be r~int~;npd for each PC compo-nent, a, which is justi~ied i~ the ~ n~C have a separate physical meaning. An additional control chart may be construc-25 ted from the residuals of the st~ndard deviation, the DModtable. A second ~ltF~n~;ve is obtained by nn~l~inin~ all the significant t and D~od into one single table, which, however, leads to a loss of information about the separate model (9i - ci nnR, The prediction about the score vector t (with A elements ) at the time t+l is analogous to the equations ~2) and (3) accor-ding to:
35 et+l = ~tt + (l-oet ~11) = t + ~tt ~ et)t (12) WO95/18420 2179 719 PC}/SE94/01208 The more elaborate ~orm analogous to equation ( 5 ) is obvious .
These thus predicted scores forecast the vector y of N
variables according to:
5 Yt+l = et+l P' (13) The variance of ~t+l,a is directly given by eguation (4) with ~a2 'l~PtPrminP~ 'oy means of scores from a long series of ~historical~ data in the process. secause of a non-full rank 10 of the matrix Y, nlAcRicAl variances of Yt+l cannot be determined without additional assumptions. If Upartial least-squares Aq ~' innq~ are made about some inAPrPnl1Pn~ regula-rity of each Yk, an acceptable variance of the forecasted vector Yk would be:5 var(yk~t+l = a Pka2 ~cL2 (14) In the model according to the invention, an updated dynami-cally P~nn~ntiAlly weighted PCA iS further reguired, a way of 20 l~ n(~l i n~ the risk of rotation in the model, which will be dis-cussed below, as well as closer definition of centering and scaling. These questions will be dealt with one at a time.
To achieve a weighed PCA, we are using exponentially decrea-25 sing observation weights, vi, according to equation (l), whereby, with the aid of the weighted least-sguares formulas and equation (9 ), the following is directly obtained:
Pak = iN (vi ~ eik ~ tia) / iN (vi ~ tia ~ tia) (15) Consequently, the NIPAIIS algorithm can be lS- i 1 i 7Prl directly with only minor modifications when r~ in~ EWM-PC
lni4~ingq by using the eXponPn~iAlly decreasing weights, vi, according to PqnA~inn (l). For a single, fixed Y, the other 35 NIPALS steps remain unchanged. The unweighted scores, ta, however, are no longer orthogonal, whereas the weighted tia~ are orthogonal.

WO 95118420 217 9 ~ 19 PCTISE94/01208 ~

Prior to a multivariate '~17 in~, data are usually centered by subtraction of the column mean values from the data matrix.
The mean vector may be interpreted as a first loading vector, po, with a ~:u~ J~ ;n~ score vector, to, which has each 5 element e~ual to l/N.
In the present Ar~ t; f~n, there are two natural ways to proceed for de~-~rmin;n~ a centering vector. In one case, a constant mean value vector is used, ~t~rm;n~l from a long 10 process history. In the second case, EWNA is used for each variable, (y3~), with a much smaller ~ than what is used in the E~MA-PCA weights (vl). To staoilize the estimation of this EWMAk, this is ~-Al rl~l At~ by using the residuals of the PC
model instead of ~nr~ l;ze~i) raw data. Thus, the observation 15 vector Yt+l is centered and scaled by using the pa- -~-DrS at time t. Then, the predicted values are subtracted (by means of equation (13) ), to give the residuals et+l, which are used to update EWNAk in accordance with the equations (l) and (2~.
20 After the centering, data are scaled by multiplying each column in the data set by a scalar weight ~P k. sy means of variance scaling ~aut~ Al;n~ k is ~Alr~lAt~q as l/~k~
where ~k is the standard deviation for columns. This again leads to two obvious choices; to calculate ~k from a long 25 process history or to use an updated computation of ~k based on weighted local data. A third option is based on a slowly updated "spanning~ database, which is .~ ;hf-d below.
Important variables may be scaled up by thereafter multiplying q' k by a value between l and 3 and inversely. other less 30 important variables may in a ~.~JLL~L~ ;n5~ way be scaled down.
The abovc ~ n~d rotation problem, which may arise when that point swarm of observations in space, which in the model is projected onto first and second principal directions, more 35 or less has a circular propagation. In such situations, each bilinear model, both PCA and PLS, is partially ~lntl~f;n~d with respect to rotation. See Figure 9. IrL dynAm~'Ally updated models, this leads to a potential instability; when a new ~lO 95118420 9 71~ pcrlsE94lol2o8 process observation i5 introduced in the model, this may lead to a rotation o the i ~ tPly preceding model, even if the new observation point lies very close to the model plane. This manifests itself as a jump in the score plot shown, which is S incorrectly interpreted as a change of the process itself. To avoid this ~ln;ntPnt;rnA1 rotation, loading vectors from the preceding model are saved in an auxiliary matrix, a "P-memory"
matrix, ( ~W-memory~ in PLS), here designated Q. Thereafter, when estimating the updated model, this P-memory matrix, 10 PxpnnPnti~lly weighted, is ;nrll-~1P~ according to the multi-block PCA/PLS algorithm ~lhl; AhP(l in "~ULDAST NEWS ~ eport from the ~LDAST symposium in Umea, 4-8 June, 1984, S. Wold et al. This can be seen as a sayesean est;r-t;n-n of the PC model, where information from previous events is stored in Q, the P-15 memory matrix, See Figure lO.
The consequence of ;nrl.-~;ns a memory matrix is that the updatea loading vectors Pa, ~or wa in PLS) are forced not to differ too much from the preceding loading vectors. The 20 balance between new and old values is checked by an adjustable parameter, c~. The full algorithm is given below.
A further difficulty to take into consideration is that, when losing the memory during an instability period, each recursive 25 model es~;r~t;nn has a tendency to lose the information about previous periods. This is due to the fact that if the process is stable sufficiently long, only data without appreciable variation are retained and earlier data are weighted down and will have irlsi~n;f;r~nt influence in the expr,nPntiAl ly 30 decreasing weights.
To force the model to " '- important events further back in its history, a second auxiliary matrix is also used, a reference data matrix, Y~, in the model ~t~rm;n;~t;nn~ This 35 matrix ,rr~nt~;nq those ob8ervations (points~ in the process which span all the space of previous observations and which are updated whenever a new process observation has a score (ta) which exceeds a certain fixed limit value. These limit WO9~/18420 21~ 9 7 i 9 PCrlSE94/01208 ~

values may be derived from historical~ da~a, that is, previously occurring extreme values, or be preset by the process operator. By analogy with this, an additional reference matrix for the loading vectors, Q~, is involved such 5 that the process memory regarding the loading vectors does not ,1; q~rpP~r during some period of instability.
As in the P-memory matrix ~Q~, the rows in the reference matrices (Y~ and Q~) are P~nnPnti~l ly weighted, but with a 10 slower decrease by the use of a smaller value y which is used instead of the greater ~ in equation ~1).
Many processes now and then generate ~ spikes , that is, devia-ting values which should not be included in the r~r~pll;ns~
15 work. The simplest way of handling these spikes is to cal-culate the distance in the Y-space between a new observation and the preceding one. ~bserYations with widely differing values, which create scores Ita) far beyond the ~norm ranges~
compared with the Yalues of reference data according to the 20 above, are discarded after a message to the operator, unless several consecutive process observations demonstrate a consistently deviating pattern.
Applying the method ~ncn~lin~ to the invention (EWM-PCA or 25 PLS ) to a set o~ historical data with a given set of parameter values ~1 to ~3 gives predicted errors of one-step-ahead forecasts for each score, ta, and for each y-variable. The sum of the s~uares of the differences between actual values and predicted values thus forms an estimation of predictive power 30 of the model in the same way as with cross-validation. This sum, P~ESS, has ~ c from each score, or y-variable, or both, weighted according to their perceived importance. To find the best combination of the values of ~1 to ~3, "Response Surface Mn~Pl l i n~ SM) is re~ In this approach, 15 35 models with different paL 7~Prs are evaluated in parallel.
The 15 parameter combinations (j=1,2,...,15) are selected according to a ~Central Composite Inscribed~ (CCI) design with low and high values being around, for example, 0.15 and 0.45.

217~7 This is then followed k~ a regression of y=log ~PRESSj ) against the extended design matrix X=A, which gives a predic-ted, ' niqt i rn of parameter values which provides a minimumof PRESS.

A step-by-step overview of the process model according to the invention will be presented in the following:
l. Select parameters ~l to ~3 in eguation ~5~ (or egs. ll, 12 ) in the simplest case. This is done based on experience or estimation of values which give the best predictions in a longer process history.

2. Select a starting matrix, Yo, in accordance with process data at the beginning of the time interval of interest.
If PLS modelling is used, the two starting matries Xo and Yo are needed. Erom these, column mean values and stan-dard deviation are calculated for centering and scaling of data.

3. Use weighted PCA (or PI.S) to derive an initial moael of :~
the process from nr~ i 7ed data according to step 2 .

4. Initiate the data memory matrix by in~ ;n~ the data rom Yo in PCA and Xo in PLS which correspond to the maximum and minimum score values of each del dimension, a.

5. Initiate the loading or weighting memory matrices, Qa, (Pmem or Wmem), one for each ~nF~nt, a, with ~a' or wa' as the first and single rows.

6. Initiate Q~, the long-term spanning Pa or Wa matrices, identical with those in step 5.
3~

7 . Make a one-step-ahead forecast of scores ta, t I l . Then calculate predicted y values from Ca, t~l and P ' (PCA) or C ( PLS ) .

Wo 95/18420 2 ~ Pcr/S~:94/01208

8. Fetch the observed valuec Yt+l ~and xt+l for PLS).
Investigate whether they contain spikes. Center and scale them by using normalization parameters from the previous step (time=t) and rAlrlllAtf~ the current scores ta,t+l and the 1, ininr residuals e ~ Yt+l - ta,t+lPt -

9. Update the centering pCl.L tprs by means of the residuals e.

10 10. Update the l~-PC or PLS model by iterating the algorithm to ~.:UllV~L y t:llce .

11 update the memory matrices Qa, (PIDen,a or Wme""a for PLS), and, if justified, also the data memory matrix Y
lS and the matrices P, W, Q~a and the memory matrix Y~.
The difference between EW~-PC}~ and E~WM-PLS may be described such that, in the "PLS" citllAtir~n~ the process data have been divided into two (or more) blocks; X referring to input data 20 and Y referring to ~output data~, that is, a performance and r,,uality assessment of the product It may here be desired to monitor and forecast the process (X), the result ~Y), or both.
I~he algorithm for llp~9Atin~ the model becomes somewhat more complicated by the inclusion of the ~ block. The data memory 25 will also have a Y block. Forecasts of Y are made directly from the forecasted X scores ~t), as shown in step 7 above, and X data in the same way as with EWM-PC~. The inclusion of the Y block stabilizes the model and reduces the constraints on P
One of the most ~iet~rmininr advantages of the process model according to the invention is that it ~ecomes possible to follow the course of the process dynamically with the aid of a display, wherein first scores (tl and t2) are plotted against 35 each other or separately versus time. Such a representation gives a good picture of how the process is developed. The distance to the model, Dwod, that is, the standard deviation of the Y residuals (X residuals for PLS) may be inrll~ d as a ~9719 Wo 95/18420 r~

separate repr flll~ti~n or be ;nr~ q in the score repr~flllr-ti as colour in dependence on the distance t; t~nP~ . See Figure 11 .
5 Tests with process monitoring according to the model have been carried out experimentally, inter alia on ore treatment, which has allowed the process to be monitored and clearly shown when the process does not lie within the normal framework.
lO Further, in summary, it can be said that the present model with EWM-PCA and EW~-PI,S provides us with multivariate windows on a dynamic process, wherein the dominating properties of the development in the process are shown as scores plus a measured value of how far process data (new observations) lie from the 15 model. If there is an auto-correlation structure in the scores, one-step-aheaa forecasts of process scores (ta) and process variables (y or x) may be used for diagnosing and controlling the process.
20 The algorithms for modelling the process are shown in the following step by step.
It is assumed that suitable values of the parameters ~l to ~3 are available, both as values of centering and scaling con-25 stants, EWM~k and ~k for the variables (Xk, Yk)-The EWM-PC algorithm l. Select suitable paL --.or values (~j,~).
2. Start with an initial matrix Yo, magnitude No X lC. Set Y=Yo. The memory matrices Y* and Q are initialized as empty .
3 5 3 . The weights vi and v~ * are calculated accordi~g to equation (l) with the parameters ~ and r. The weighted mean value of each variable (k) is .~ tP~i from Y:
EW2~k = ~;iVi *Yik / ~;ivi ~

-WO 95/18420 2,~rl 9~1 ~ PCT/SE94/01208 The scaling weights (q~k) are r~ tPc' from both Y and Y (note that Y* is centered):
sk2 = ~,~ivi(yik - EwMAk) ~ + (l-~)~;jvj Yjk 2]/[~ivi +

(l-,~)~jvj~]
~k = 1 ~ Sk l~ The constants are lef t as zeros with zero weight .
Important variables may be scaled up or down by multipli-cation of the scaling welghts above by a suitable adjus-ter between, for example 0.3 and 3 The parameter ~ which determines the relative ef iect on the current data and reference data may lie somewhere between D . l and 0 . 9 depending on the stability of the process.
4~ Center and scale Y with the centering parameters Ew~k and the scaling ~aL - ~Pr q~k.
Yik(nrmalized) = (yik(row) - EWMAk) *d~k 5. The central part of the EWM-PC alqorithm is initiated here: the ~ tPrmin~tinn of the weighted PC model. The additional steps caused by cross-v~ 1 i tl~t i nn are not explicitly shown; they substantially comprise elaboration of the al~orithm below several times with different parts of data deleted and afterwards predicting the deleted data from the model. ~he model ~ nn, A, with the smallest prediction error (PRESS) is selected, with preference for a smaller A, if PRESS is largely the same for different model .1; -;nnq (i) Set ,1~- cinn index a to one.
(ii) As starting vectors for ~a and qa (loading vector), the ones from the previous time points are used. At the very first time, the last row in Yo is used, ~ WO95118420 21 79719 PCT/SE:94101208 normalized to length l.
(iii) Calculate the scores tia. TO compensate for missing data, dummy variables ~d~ik) are used, which are zero if element Yik is mis&ing, otherwise equal to one.
tia = ~;k dikyikpka / ~;k dikPka2 If there is a reference matrix, Y*, the C~LLt~
ding scores, ti~*, for this matrix are calculated by using lljk and Yjk* instead of ~ik and Yik in the aoove equation.
~iv) Calculate the loading vectors, Pka, using the same dik for ~ q~tion of missing data.
Pka = ~i dikYiktia / ~i diktia2 Nnrr~1i7e Pa to length one; Pa = Pa / ¦IP II
If there is a reference matrix, Y*, the correspon-ding loading scores, Pka*, for this matrix are cal-culated by using ~Ijk and Y~k* and tia* instead of dik, Yik and tia in the above equation.
Form Pa as the weighted I ' in;~t;nn of two calcu-lated Pa values.
3 0 Pa = ¦~ Pa + ~ ) Pa Nnr~-~1;7e the new Pa to length one.
~v) Check the :u--v~Lycllce of IPa new--Pa old¦¦/¦¦Pa neW ¦¦ which must be smaller than 10-6 to ;n~ tP ~ llV~Lyt~lCe. If ~,1.v~:Ly~11ce exists, proceed with step (ix), otherwise step (vi).

Wo 95/18420 ~ PCTISE94/01208 (vi~ If the n~ tinn iS made at a first time, return to step (iii). Otherwise, continue to step (vii).
(vii) Calculate the scores ua and ua~ for the loading matrix P and the reference matrix P~, respectively.
uia = ~k Pmem, a, ik Pka / ~k Pka2 Uja* = ~k Pref, a, jk Pka / ~k Pka2 (Viii) S~lc~ tp the ~loadings" of the two loading and reference mat~ices according to:
~ka = ~i Pmem, a, ik uia ~ ~;i uia2 qka = ~;j Pref, a, jk Uja / j (uia ) 2 Form ~a as the weighted ~ in;~tinn of two calcula-2 û ted qa values .
qa = 1~ qa + (l-~)qa ~nrl--l i 7e this new qa value to length one Use the weighted, ~ in;~tinn (weight ~ of this vector and Pa ~weight l~ and return to step ~
~ix~ If convergence exists, the final ta and ta* for the two data blocks are calculated, and from these t~ Ola~y loading vectors which are used only to form the residuals to provide data in the next model ii qinn calculations. This is necessary to preserve orthogonality of the scores and is analogous to the orthognn~1i7~tinn step w ~ t ~ p in ordinary PI.S regression.
Af ter this, the residuals Y - tapa ' and Y*
- ta*pa* are formed. Add one to the model dimen-WO9~18420 ~179 719 PCr/SE94/01208 sion (a = a + l) and proceed with the next dimen-sion by using the residuals Y and Y* as the data matrices in th1s next dimension.
S (x) The algorithm is tPrminAt~od when the number of ~i - i nnc, a, of the model equals the desired number of "Ri~nif;cAnt~ r~ir ::innq (variables), A, in the model, which is determined by cross- -vA1i~iAtinn, or based on experience.
If instead an EWM-PLS algorithm is used, the difference ~~
between these is that the latter (PLS) includes both X
blocks and Y blocks for data and reference data, respec-tively. sy replacing Y by X and Y* by X*, loadings by PLS
lS weights and p by w in the algorlthm above, some sub-steps are added in step (iii) in the above algorithm. After calculating the scores ta and ta*, these are used for calculating Y weights, ca and ca*, respectively, which in turn leads to Y scores, here (lPc~nAted ra instead of Ua.
(iiia) Y and Y* weights cma = ~i dim Yim tia / ~i dim tia and analosouSly for Cma -(iiib) Scores t~, and ta ria = ~;m dim Yim Cma ~ ~m dim Cma2 and analogously for r;a -These scores, r and r;a*, are ther. used instead of t and t, respectively, to calculate the PLS weights in step (iv).
Finally, after c~,..Y~ ce, the residuals (Fa) of each Y block W0 95A8420 217 g 7 1 ~ PCT/SE94/01208 ~
are formed by subtractin~ the relevant t vector multiplied by the relevant c vector. These residuals are then used as Y and Y* in the next ~; ci r,n, 5 After ~ullv~Ly,:llce of the above algorithm, the resulting scores ~only t and u values) are compared with maximum and minimum values with ~,LL.~ ",rlinr scores for the reference data and the loading matrices . Thus, when the ref erence matrices are initially empty, the data vectors corr~crnn~inr to the 10 greatest and smallest t and u values for each model ,1;- -ir,n are saved in the ref erence data matrix Y* and P*, respec-tively. The extreme scores are saved for later compa~isons. In following updates, a score value which is below the minimum or above the maximum previous score with the same fii- cirn means 15 that the co~responding data vector is~lnr~ in the re~erence matrix and a new score value is saved. Two variants of Y* may be noted, one where old data are deleted from Y* and where no exponential weighting of Y~ is made, and another, re~ variant, where Y* is extended wlth the new data 20 vector by using a slowly decreasing exponential weighting of Y*. The ~ame principles are used for the reference matrices for loadings or PL$ weights.
The described als~orithm forms the basis of how a multivariate 25 process can be illustrated graphically, as mentioned above in the description of the invention. On the basis of observed facts, as, for example, because of the drift of some indi-vidual variable, the process may be restored to a nr,rr~l i 7ed position by the fact that the variable in the process may be 30 directly ;nflll~.nrP~, Physically, the process monitoring according to the invention is achieved by measuring the measured data of relevant quanti-ties by means of measuring devices for the respective physical 35 r~uantity in the monitored proress in a known manner. The measured values are passed via a process link to a computer, which is PLUYL ~ tl to create models of the process according to the invention. The model or models are presented graphi-Wo 95118420 217 9 719 PCr/SE94/01208 33cally on a screen, where according to the invention the process in its entirety is projected onto a plane or a hyper-plane and where the projection contains all relevant informa-tion about the process, which makes it possible for the opera-5 tor to take accurate action, based on facts, in the form ofintervention in the physical r~uantities of the process, for example by adjusting the pressure or temperature levels, contact forces for rolls in a machine, etc., all according to which is indicated according to the vi~Ali7Atinn of the lO process. This type of information and the possibility of physical intervention in the process have not existed accor-ding to the prior art, since a real-time on-line study of the effect of many quantities on one another in a process has not been possible.
The calr1-1Atinnq for the different steps to obtain the model of the process, referred to according to the invention, are implemented by rA1r711A~;n~ units, which are schematically reproduced in Figure 12 where a clear overview of the 20 calculation steps is given by means of a flow chart. If, in step 2 irl Figure 12, ta,i+l and/or ~odX end up outside the allowable control interval, different loading plots are used to identi~y which process variables (Xk~ have caused the process to leave its operative norm range, whereby the 25 variable or variables which have caused the drift in the process are adjusted to values which are predicted to restore che proc~ss to ~ norm ~ange a~ ~oon ~ po~ 1e.
.

Claims (12)

1. A method for monitoring and control of an industrial or other technical process, the course of which is dependent on a multiple of variables relevant to the process, comprising the steps of - registering the measured values of the variables as an observation at a certain time, - describing the variables as a multidimensional room, wherein each variable represents one dimension in the room, - representing each observation as a point in the multi-dimensional room, whereby a series of observations carried out at different times will be represented by a point swarm in space, - calculating at least one first (pa) and one second (pb) principal direction in space for the point swarm, - determining the projections of the observations onto the principal directions (pa, pb), - inserting the projection of the observations onto a point as a point on an electronic screen in a linear room which is spanned by the principal directions (pa, pb), characterized in that - the principal directions (pa,pb) of the point swarm in space are updated during the course of the process, which allows the process to be dynamically monitored, - the norm range of the process, as well as process-influencing variables, are indicated on the screen, - the process-influencing variable or variables which indicate drift in the process are adjusted by the process operator or the monitoring member, whereby the process is restored to the norm range.

2. A method according to claim 1, characterized in that the process is illustrated dynamically, on-line, as a picture on a screen, wherein a first (Pa) and a second (Pb) principal direction define the plane shown on the screen, wherein the projections of the observations are illustrated as points on the screen, and wherein the process is visualized in the form of a snake which crawls over the screen from one point to another point representing consecutive observations of the process in time.

3 . A method according to claim 1, characterized in that the process is illustrated dynamically, on-line, as a picture on a screen, wherein a first, a second and a third principal direc-tion (pa,pb) define a three-dimensional room which is shown on the screen, wherein the projections of the observations are illustrated as points on the screen, and wherein the process is visualized in the form of a snake which crawls over the screen from one point to another point representing consecu-tive observations of the process in time.

4. A method according to claim 2 or 3, characterized in that the process is illustrated dynamically, on-line, by deter-mining the deviations ( the residuals ) between the calculated model of the process and the reference model as a quantity (Dmod) and by indicating this distance of the process to the model (Dmod) by the snake changing colour in dependence on the distance to the model (Dmod).

5. A method according to claim 4, characterized in that all of or parts of the crawling snake representing the course of the process are coloured in various colours in dependence on the magnitude of Dmod, that is, a certain colour for the visualized parts of the process where the distance to the model is outside a certain norm range for Dmod and other colours for the visualized parts of the process where this is within the norm range of the process.

6. A method according to claim 2 or 3, characterized in that the snake initiates an alarm when the snake on the screen enters a range which lies outside a norm range for the process defined on the screen in advance

7. A method according to claim 2 or 3, characterized in that that part of the process which is of current interest is indicated as a more intensely or brightly represented snake.

8. A method for monitoring and control of an industrial or other technical process, the course of which is dependent on a multiple of variables relevant to the process, comprising the steps of - registering the measured values of the variables as an observation at a certain time, - describing the variables as a multidimensional room, wherein each variable represents one dimension in the room, - representing each observation as a point in the multi-dimensional room, whereby a series of observations carried out at different times will be represented by a point swarm in space, - calculating at least one first (pa) and one second (pb) principal direction in space for the point swarm, - determining the projections of the observations onto the principal directions (pa, pb), whereby a model of the process is obtained, - calculating the deviation (Dmod) between the calculated model and a reference model for the process.
characterized in that - the principal directions (pa,pb) of the point swarm in space are updated during the course of the process, whereby the calculated model of the process is dynami-cally adapted to the process in real time, - initiating an alarm when the distance of the process to the model exceeds a predetermined alarm limit .

9. A method according to claim a, characterized in that that the distance of the process to the model (Dmod) is shown on-line in a figure where said distance to the model (Dmod) is plotted as a function of the time of process observations made.

10. A method according to claim 8, characterized in that the distance of the process to the model (Dmod) consists of the standard deviation for the deviation of the respective obser-vation from a reference model of the process.

11. A method according to claim 2, characterized in that the relevant variables in the process are illustrated as a picture on a screen, a score reproduction, wherein a first (pa) and a second (pb) principal direction define the plane shown on the screen, wherein the positions of the individual variables are projected onto this plane, and the midpoint (x) of the point swarm in this plane is illustrated as points on the screen.

12. A method according to claim 11, characterized in that the process, indicated in the form of a snake as well as a score plot, is at the same time visualized on the basis of the same plot plane defined by the same first (pa) and second (pb) principal directions on separate or on the same screen image, whereby the movement of the snake over the screen can be immediately related to process-driving variables, in that the directions from the midpoint (x) of the point swarm in the two images correspond to each other, whereby the direction of crawling of the snake away from the midpoint (x) of the point swarm indicates an influence on the process by one or more variables which in the score plot lie in the same direction of travel as the movement of the snake, which means that the process operator or the monitoring member receives information about which variable/variables result in drift in the process, allowing the operator or the monitoring member to easily act on the disturbing variable.