Abstract:
Control and output-quality variables of a process plant ( 1 ) are plotted against parallel axes in a display unit ( 7 ). Convex hulls between pairs of variables are calculated from sets of the variable-values accumulated historically in stores ( 7, 9 ) during successive runs of the process, and hulls (HH; TC, BC) between successive axis-pairs are displayed. New variable-values for process optimization are fixed for the variables taken in turn, each selection being made within displayed ranges (Rn—Rn) derived from the hulls effective between the respective variable and the variables already fixed. A display unit ( 13 ) provides on-line parallel-axis display of variable-values from the plant ( 1 ), showing alarm carets (DC, UC) where values violate limits (UL, LL) determined by the convex hulls, and allowing variation in the displayed-value for observing the resultant effect in avoiding alarm situation and towards optimization.

Description:
FIELD OF THE INVENTION 
   This invention relates to multi-variable processes. 
   BACKGROUND OF THE INVENTION 
   The invention is particularly concerned with methods and systems for displaying variables of multi-variable processes. 
   SUMMARY OF THE INVENTION 
   According to one aspect of the present invention a method for displaying variables of a multi-variable process, comprises deriving a multi-dimensional display representation in parallel coordinates of a feasible region of the process-variables, the representation being derived from sets of values for the process-variables accumulated respectively from multiple operations of the process, deriving a further set of values for said variables within said region and displaying them within said representation, and defining within the display representation available ranges for the variables according to the values of other variables within said further set. 
   According to another aspect of the present invention a system for displaying variables of a multi-variable process, comprises means for providing a multi-dimensional display representation in parallel coordinates of a feasible region of the process-variables, the representation being derived from sets of values for the process-variables accumulated respectively from multiple operations of the process, means for deriving a further set of values for said variables within said region and displaying them within said representation, and means for defining within the display representation available ranges for the variables according to the values of other variables within said further set. 
   The definition of available ranges of the process-variables in the method and system of the invention may be carried out by reference to convex hulls calculated for each pair of variables from the accumulated sets of values. A convex hull in orthogonal coordinates is a closed polygon that encloses all relevant data points of the two-dimensional space, whereas in parallel coordinates it is a pair of spaced linear curves that as between corresponding parallel axes, bound the region occupied by the lines that represent (in the parallel-coordinate space) those data points. A feature of convex hulls used in the present invention is that when the value of one variable is fixed a range of values from maximum to minimum of the other can be derived. 
   The invention may be applied to monitoring and optimisation of multi-variable processes. More especially, the invention is applicable to ensuring safe and efficient on-line operation of multi-variable processes, in particular by providing a display representation including warning alarm limits on some or all of the variables where these limits are continuously re-calculated in accordance with current operating conditions. Furthermore, the invention is applicable to assist selection of values for the variables of the process and to systems for providing display representations for use in such selection. 
   According to a feature of the present invention a method for selection of values for variables of a multi-variable process, comprises a first step of deriving a multidimensional display representation in parallel coordinates of a feasible region of the variables, the representation being derived from sets of values for the process-variables accumulated respectively from multiple operations of the process, a second step of selecting, so as to fix, a value within said region for one of said variables and defining available ranges for the other variables in accordance with the selection made, and a third step of selecting, so as to fix, a value within the available range defined for one of the remaining unfixed-value variables and re-defining the available ranges for the other unfixed-value variables in accordance with the selections so far made, this third step being repeated until values for all unfixed-value variables have been fixed by the selections made. 
   According to another feature of the invention a system for providing a display representation for use in selection of values for variables of a multi-variable process, comprises means storing sets of values for the process-variables accumulated respectively from multiple operations of the process, display means providing a multi-dimensional display representation in parallel coordinates, the representation including in accordance with the stored sets of values, display of a feasible region of the variables, and selection means that is operable successively to select, so as to fix, values within said region for all said variables in turn, said display means being operative upon each operation of the selection means to define available ranges for such of the other variables that remain of un-fixed value. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A method and system according to the present invention will now be described, by way of example, with reference to the accompanying drawings, in which: 
       FIG. 1  is a schematic representation of a system according to the invention in the context of collection and utilisation of data derived from operation of a multi-variable processing plant; 
       FIG. 2  is illustrative of a plot in multidimensional space defined by parallel coordinate axes, of operation of the multi-variable processing plant of  FIG. 1 ; 
       FIG. 3  shows in part a multiplicity of plots corresponding to that of  FIG. 2  resulting from variation of operation of the multi-variable process; 
       FIGS. 4  to  6  are illustrative of displays provided during successive stages of the method according to the invention, for assisting with selection of values for the variables of operation of the processing plant of  FIG. 1 ; 
       FIGS. 7  to  10  are illustrative of further displays provided according to the invention to assist further in selection of values for variables of operation of the processing plant of  FIG. 1 ; and 
       FIGS. 11  to  13  are illustrative of displays derived in varying circumstances during on-line monitoring of operation of the processing plant of FIG.  1 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The example of method and system to be described is related to the operation of a multi-variable process carried out by a simple, notional processing plant. Details of the plant and its purpose are not of consequence, and indeed the method and system of the invention are related more specifically to operation of the plant as an example of a multi-variable process rather than to the purpose of the process performed, being applicable in the generality to any situation involving a multi-variable process. In the context of description of the present specific example, however, there are fourteen variables involved in plant-operation, and of these, eleven are control variables to the extent that their values determine the outcome of the process. The remaining three variables are quality variables in the sense that their values define, or more especially are defined by, that outcome. 
   Referring to  FIG. 1 , the plant  1  has an input  2  and an output  3  between which there are a multiplicity of processing stages  4 . The processing within each stage  4  is carried out in accordance with one or more variables that, in this example, are regulated by eleven controllers  5 . The values of these variables for each operation or ‘run’ of the process are communicated to a data collection unit  6  to be accumulated in a store  7 . The term ‘run’ in this context may refer to a discrete operation of the process, but it may also refer to what applies at a discrete point in time within continuous operation. 
   The outcome at the output  3  of each run of the process, is submitted to a unit  8  for analysis in respect of its quality as determined according to three variables. The values of these three quality variables are accumulated in a store  9 , so that each run of the process and its outcome is defined by an accumulated set of fourteen values, eleven in the store  7  and three in the store  9 , for the fourteen variables respectively. 
   As the process is run again and again, a multiplicity of different sets of fourteen values are accumulated to provide a historical record in the stores  7  and  9  of the successive runs. This record is used in the method of the present invention to assist selection of the values of the various variables appropriate to achieving a particular outcome. More especially, the fourteen values of each individual set, eleven in the store  7  and three in the store  9 , are brought together in a merge unit  10  and each scaled to the range 0 to 1. The scaled values are then processed in a unit  11  according to a convex-hull model to plot them in an electronic display unit  12 . The scaled values of each set are plotted in fourteen-dimensional space using a system of parallel coordinates as illustrated in FIG.  2 . 
   Referring to  FIG. 2 , the fourteen values are plotted on fourteen equally-spaced, parallel axes X 01 -X 14  representing the fourteen variables respectively. The first three, axes, X 01 -X 03 , are used for the quality variables, and the plots are joined up to form a polygonal line L that is representative of the single fourteen-value operating point of the process. The other sets of process-values are each correspondingly plotted against the same axes X 01 -X 14  resulting in a multiplicity of polygonal lines corresponding to the line L; this is illustrated in part in FIG.  3 . Each polygonal line is representative of an individual operating point or run of the process from the historical record. 
   Referring further to  FIG. 3 , convex hulls H for all pairs of adjacent variables of the parallel-axis system, are calculated in the unit  11  and displayed. Between each pair of adjacent axes X 01 -X 14  there will be an upper and lower hull H defining upper and lower limiting boundaries between those two axes, of the operating-point lines. The upper and lower hulls H of the successive pairs of adjacent axes join together to define top and bottom boundaries or chains TC and BC respectively. Calculation of the convex hulls applicable to all the other pairings of variables is also made, but are not displayed in display unit  12 . 
   Once the calculation of all the convex hulls has been completed, a display as shown in  FIG. 4  is provided in which the upper and lower hulls H are restricted for simplicity to those parts lying within the range 0 and 1. In this way, the upper and lower hulls H are seen more clearly as joining up together as top and bottom chains TC and BC respectively, defining (for example, in colour red) the upper and lower boundaries of a region within which feasible operation of the process can take place. Clearly, the larger the number of historical sets of operational data used, with as wide as possible range of values for the individual variables, the more accurately will this region, be defined. 
   It is optional whether representation in the form of  FIG. 3  is provided by the display unit  12 , but representation in the form of  FIG. 4  is displayed and utilised for the selection of the process-variables to be used in optimum, or otherwise, operation of the process. The steps of selection begin with fixing the first variable, that is to say, the variable of axis X 01 . This is a quality variable and the selection made establishes the value, Q 1 , this variable is to have in the outcome of the prospective process-run. The selection may be made by moving a cursor up the axis X 01  in the display using a mouse (not shown), and clicking at the appropriate position. 
   The selection of the value Q 1  of the first variable, brings about display of a polygonal line L 1  (for example in colour blue) representing the operating point that would result in the event that the other thirteen variables were each fixed at the midpoints of their available ranges. In this regard, a calculation is made for each of these unfixed variables of the restricted range of values which is open for selection in respect of that variable as a consequence of the selection of value Q 1  for the first variable. The range is derived in each case by reference to the convex hull between the fixed first variable and the unfixed variable. These ranges are denoted in the display for each unfixed variable by the intersection with its respective axis X 02 -X 14  of two lines R 1  (for example in colour green) that diverge from the immediately preceding axis X 01 -X 13 ; the lines R 1  are tangential to the convex hull between the fixed first variable and the unfixed variable. The lines R 1  that intersect the axis X 02  of the second variable diverge from the selected value Q 1  on the axis X 01 , whereas in each other case (for the variables of axes X 03 -X 14 ) they diverge from the mid-point of the available range of the variable of the immediately preceding axis X 02 -X 13 . It is this mid-point that is assumed selected for each of the unfixed variables, in the plotting of the line L 1 . 
   The next step is the selection of the value Q 2  of the variable of the second axis X 02 . Selection is made by moving the cursor up the axis X 02  and clicking the mouse at the appropriate position, and has the effect of changing the display to that shown in  FIG. 5. A  new line L 2  is displayed joining the fixed points Q 1  and Q 2  between axes X 01  and X 02  and extending from point Q 2  through the mid-points of the available ranges of the other twelve, unfixed variables. These available ranges, which are denoted by divergent lines R 2  (for example in colour green), are each derived by reference to the overlap with the range previously calculated for the fixed value Q 1  and denoted by lines R 1 . The available range defined for each unfixed variable by the lines R 2  is restricted by virtue of the overlap to the range of values of that variable which is available for selection having regard to both selected values Q 1  and Q 2 . The lines R 1  and L 1  may, as indicated in  FIG. 5 , be retained in the display (but for example now in colour grey) for reference purposes to indicate the range available for each unfixed variable before selection of value Q 2 , and the previous course of the line L 1  from the axis X 02 . 
   The selection method now proceeds to the step of selecting in a similar way the value Q 3  of the third variable (axis X 03 ), and then on from there through successive steps until the values Q 4 -Q 14  of all the remaining variables have been selected to complete definition of the value-set for the desired operating point. The display changes as the selections are made, and for example appears as in  FIG. 6  when the values Q 1 -Q 5  of the first five variables have been selected. In this case, lines R 5  identify the available ranges for the remaining variables of axes X 06 -X 14 , and lines R 4  show the ranges available immediately before the value Q 5  was selected. The polygonal line L 5  interconnects the already-selected values Q 1 -Q 5  and the mid-point values of the available ranges of the remaining unfixed variables, whereas line L 4  shows its previous course from axis X 05 . 
   As each individual selection is made to fix the value Qn of the next unfixed variable (in the order of the axes X 01 -X 14 ); so the restricted range due to each already-fixed variable is calculated using the relevant convex hull between those fixed and unfixed variables. The available range is displayed for each unfixed variable using, lines Rn. The lines Rn define the available range of each unfixed variable as the portion of the relevant axis X which is common to (overlapped by) the restricted ranges derived for that variable and each of the fixed variables. The polygonal line Ln is established passing through all the values Q selected for the currently-fixed variables and also through the mid-points of the available ranges of the unfixed variables. 
   The polygonal line Ln connects the fixed values of the fixed variables and the working (or suggested) values of the unfixed variables. To ensure that the line Ln always represents a feasible operating point of the process, the working values of the unfixed variables apart from that to the immediate right of the last fixed variable, are calculated using a more restricted range than that displayed. In this regard, the range due to the fixed variables is overlapped with the ranges due to the working values of all the unfixed variables to the left of the one whose working value is being calculated to give the working range, and the mid-point of this range is taken as the working value. These working ranges may be optionally displayed in a different colour from the ranges due to the fixed variables. 
   Throughout the method of the invention as the display progresses step-by-step from that of  FIG. 4  to that of  FIGS. 5 and 6 , and so on until all selections have been made, the operator is presented with information that enables selection of feasible values of the variables consistent with desired objectives of economy, efficiency and outcome of the process. The information is derived without the need to fit a functional model to the historical data and the disadvantages associated with this, and is applicable to adjustment or re-setting of the controllers  5  of the plant  1  for optimisation of plant-operation. 
   The values of the variables that have been fixed in the display of unit  12  can be changed. This enables the operator to search for sets of values that give the ‘best’ ranges for the unfixed variables, and in this regard the ‘best’ range in any particular case may simply be a narrow range about a desired value. The limits within which each fixed variable can be moved while holding the other fixed variables constant, are calculated using the convex hulls between the fixed variables, and are included in the display. This display changes continuously as the fixed variable is changed. 
   These characteristics of the display may be used with particular advantage if the controllable variables are fixed and arranged to the left of all the quality variables. The controllable variables can then be moved until satisfactory values of the quality variables are obtained. 
   The latter functionality of the display is illustrated in the example of  FIGS. 7  to  10 . In this example, variables p 11 , p 12 , p 13  and p 14  are considered to be ‘process’ variables which can be manipulated, and variables q 7  and q 8  are considered to be ‘quality’ variables which depend on the process variables. 
   In  FIG. 7 , point Fp 11  is the value to which the variable p 11  has been set, and points Wp 12  to Wpl 4  and Wq 7  and Wq 8  are the working values of variables p 12  to p 14  and q 7  and q 8  respectively. These points are joined by a polygonal line L 1 , and line-pairs RF 1  to RF 5  display the ranges of the respective variables p 12  to p 14  and q 7  and q 8 , that are due to variable p 11  having the value Fp 11. The range in each case is shown by the intercept the line-pair makes with the axis of the relevant variable. 
   A line-pair RW 2  (the upper line of which is co-linear with the upper line of the line-pair RF 2 ) show by their intercepts on the axis p 13  the range of variable p 13  that is due to variable p 11  having the value Fp 11  and the variable p 12  having the value Wpl 2 . The value Wp 13  is the mid-point of this range. Similarly, a line-pair RW 3  displays the range of variable p 14  that is due to variables p 11 , p 12  and p 13  having the values Fp 11 , Wp 12  and Wp 13  respectively, and value Wp 14  is the mid-point of this range. Line-pairs RW 4  and RW 5  correspondingly display ranges, with mid-points Wq 7  and Wq 8 , of the variables q 7  and q 8  that are due respectively to the values set for the four variables p 11  to p 14 , and the five variables p 11  to p 14  and q 7 . 
     FIG. 8 , illustrates the display that results from now setting the variables p 11  to p 14  to the values Fp 11  to Fp 14  respectively. Carets at Up 11  and Lp 11  indicate the calculated limits (as referred to above) between which the value of variable p 11  may be moved while holding variables p 12 , p 13  and p 14  at values Wp 12 , Wp 13  and Wp 14  respectively. Similarly, carets at Up 12  and Lp 12  indicate the limits between which the variable p 12  may be moved while holding variable p 11  at value Fp 11 , variable p 13  at value Fp 13 , and variable p 14  at value Fp 14 . Carets Up  13  and Lp 14  and Up 14  and Lp 14  are correspondingly provided for the variables p 13  and p 14 , and the upper carets Up 11  to Up 14  are joined by polygonal line UC and the lower carets Lp 11  to Lp 14  by polygonal line LC. 
     FIG. 9  illustrates the effect of moving the point Fp 13  to the current lower limit represented by caret Lpl 3 . The limits represented by the other carets have in general changed, and so too have the ranges of variables q 7  and qB represented by the line-pairs RF 4  and RF 5 . In particular, the upper limit of variable p 14  represented by caret Upl 4 , has moved down to the current value Fp 14 , indicating that the convex hull between axes p 13  and p 14  is setting the most restrictive lower limit on variable p 13 . 
     FIG. 10  illustrates the situation when the user, by experimenting with the values of variables p 11  to p 14 , has discovered settings for these variables which keep the value of variable q 8  within a narrow range near the value 0.5, as evidenced by the intercepts of both lines RF 5  with the axis of variable q 8 , close to this value. 
   The display techniques described above may be used to determine appropriate warning alarm levels on plant variables during process operation, and to display those alarm levels and the current values of the corresponding variables to the processing operator. This is achieved as illustrated in  FIG. 1 , using a further electronic display unit  13 . The display unit  13  is driven from an alarm-algorithm unit  14  in accordance with data from the unit  11  and the values of the process variables in real time, supplied from the unit  6 . All the variables are treated as of fixed value. 
   Whenever a new set of values for the process variables is received from the unit  6 , the unit  14  identifies which variables have values lying in the ‘best-operating’ zone or region defined between the relevant top and bottom chains of convex hulls. Upper and lower limits for all variables are calculated from these values within the best-operating zone using the relevant convex hull as for the display of unit  12 . Furthermore, the unit  14  identifies which, if any, of the variables have values that lie outside these limits, and gives warning by indication in the display of unit  13  or otherwise, of the condition. As each new set of values is received, the display changes, and the limits on all the variables are recalculated and shown in the display of unit  13 , exactly as if the point had been moved by the program-user in offline operation. The quality variables are treated no differently from the control variables in determining the on-line alarm limits. 
   In this way the display unit  13  provides representation of warning alarm limits for all variables simultaneously. These limits are always calculated using the current values of all the other variables; no model-fitting or statistical assumptions are required. 
   Displays provided by the unit  13  in three different circumstances are illustrated in  FIGS. 11  to  13 , for ten variables plotted against axes Xa-Xj. 
   Referring to  FIG. 11 , the plotted values Qa to Qj are all within the current best-operating zone defined between top and bottom chains Tc and Bc respectively. Upper and lower current limits calculated for the individual variables and plotted on the respective axes Xa-Xj are joined up to provide polygonal lines UL and LL. The lines UL and LL define the zone within which the values of the variables are to be retained. In this example, all values Qa to Qj are within the zone, but this is not so in the circumstances of the displays illustrated in  FIGS. 12 and 13 . 
   In the circumstances of the display of  FIG. 12 , the value Qc for the variable plotted on the axis Xc is on the upper limit UL, and the values Qb, Qg, Qi and Qj for the variables plotted on axes Xb, Xg, Xi and Xj respectively, are on the lower limit LL. On the other hand, in the circumstances of the display of  FIG. 13 , the values Qc and Qd of the variables plotted on axes Xc and Xd, are the only ones within the best-operating zone between the limit lines UL and LL. In both cases, as illustrated in  FIGS. 12 and 13 , a caret (for example of colour red) is included in the display where a variable-value is on the boundary or outside the best-operating zone. More particularly, a downwardly-directed caret DC is displayed on the relevant axis of any variable where the value is on or above the line UL and an upwardly-directed caret UC is correspondingly displayed where the value is on or below the line LL. 
   The process operator can interact with the display unit  13  to adjust one or more of the fixed values Qa-Qj up or down their respective axes experimentally, to see the effect this has on the limits of the other variables. When an alarm condition exists, and several variables are on or beyond their limits, adjusting the value Q of even one of them may be found to move the limit lines UL and LL outwardly from one another sufficiently to relieve the alarm condition on the others. 
   Accordingly, by using the on-line display of unit  13 , the operator can not only monitor the current settings and results of the process, but can also be made aware of alarm situations and receive guidance in focussed investigation of the remedial action necessary.