초록 ▼

A reference matrix contains valid measurements characterizing operation of a multivariate process (220). Modeling parameters of the reference matrix are derived (222-232). The final model parameters, balanced with respect to measuring and modeling uncertainties (232), are applied to model (204) a ne

A reference matrix contains valid measurements characterizing operation of a multivariate process (220). Modeling parameters of the reference matrix are derived (222-232). The final model parameters, balanced with respect to measuring and modeling uncertainties (232), are applied to model (204) a new set of measurements (200). If the new set has no faults (206) then all modeled values and modeling uncertainties (208) can be used to control the process (218). If the new set has only one fault (210) ten the modeled value and modeling uncertainty of the faulted measurement plus the measured values and measuring uncertainties of the unfaulted measurements (212) can be used to control the process (218) while repair procedures are implemented for the identified fault (216). If the new set has more than one fault ( 214) then the process (218) should be shut down, and repair procedures should be implemented (216) for all identified faults.

대표청구항 ▼

What is claimed is: 1. A method of controlling an m variable multivariate system or process, characterized by: (a) obtaining (220) historical reference data comprising numerical measurements of said m variables, said measurements collectively encompassing a plurality of variations within one or mor

What is claimed is: 1. A method of controlling an m variable multivariate system or process, characterized by: (a) obtaining (220) historical reference data comprising numerical measurements of said m variables, said measurements collectively encompassing a plurality of variations within one or more operational states of said system or process; (b) modeling (222) said historical reference data to produce modeled values, modeling uncertainties and measuring uncertainties of said reference data set measurements; (c) deriving (224-230) a final model of said historical reference data by sequentially repeating said modeling until successively derived sums of all of said measurement uncertainties are approximately equal and successively derived sums of all of said modeling uncertainties are approximately equal; (d) deriving (232) a set of modeling parameters characteristic of said final model; and, (e) combining said measuring uncertainties with a new data set (200) comprising numerical measurements of said m variables, said new data set measurements collectively encompassing said plurality of variations within said one or more operational states of said system or process to control (218) continued operation of said multivariate system or process. 2. A method as defined in claim 1, further characterized by: (a) determining (232) whether said modeling uncertainties exceed said measurement uncertainties; (b) for said modeling uncertainties that do not exceed said measurement uncertainties: (i) determining (206) whether there are no faults in said new data set measurements; and, (ii) if there are no faults in maid new data set measurements, applying (208) all of said modeled values of said reference data set measurements and all of said modeled values of said new data set measurements to control (218) said multivariate system or process. 3. A method as defined in claim 1, further characterized by: (a) determining (232) whether maid modeling uncertainties exceed said measurement uncertainties; (b) for said modeling uncertainties tat do not exceed said measurement uncertainties; (i) determining (206) whether there are no faults in said new data set measurements; and, (ii) if there are no faults in said new data set measurements, applying (208) all of said modeling uncertainties of said reference data set measurements to control (218) said multivariate system or process. 4. A method as defined in claim 1, further characterized by: (a) determining (232) whether said modeling uncertainties exceed said measurement uncertainties; (b) for said modeling uncertainties that do not exceed said measurement uncertainties: (i) determining (210) whether there is a fault in only one said new data set measurements ; and, (ii) if there is a fault in only one of said new data set measurements, applying (212) said modeled value of said faulted one of said new data set measurements to control (218) said multivariate system or process. 5. A method as defined in claim 1, further characterized by: (a) determining (232) whether said modeling uncertainties exceed said measurement uncertainties; (b) for said modeling uncertainties that do not exceed said measurement uncertainties: (i) determining (210) whether there is a fault in only one of said new data set measurements; and, (ii) if there is a fault in only one of said new data set measurements, applying (212) said modeling uncertainty of said faulted one of said new data set measurements to control (218) said multivariate system or process. 6. A method as defined sidelined in claim 1, further characterized by: (a) determining (232) whether said modeling uncertainties exceed said measurement uncertainties; (b) for said modeling uncertainties that do not exceed said measurement uncertainties: (i) determining (210, 214) whether there is a fault in more than one of said new data set measurements; and, (ii) if there is a fault in more than one of side new data set measurements, determining the identity of each faulted one of said more than one of said new data set measurements; and, (iii) applying (214) said identity of said each faulted one of said more than one of said new data set measurements said modeling uncertainties of all of said new data set measurements to repair (216) said multivariate system or process. 7. A method as defined in claim 1, further characterized by: (a) determining (232) whether said modeling uncertainties exceed said measurement uncertainties; (b) for said modeling uncertainties that do not exceed said measurement uncertainties: (i) determining (210) whether there is a fault in only one of said new data set measurements; (ii) if there is a fault in only one of said new data set measurements: (1) determining the identity of said faulted one of said now data set measurements; and, (2) applying (212) said identity of said faulted one of said new data set measurements to control (218) said multivariate system or process. 8. A method as defined in claim 1, further characterized by: (a) determining (232) whether said modeling uncertainties exceed said measurement uncertainties; (b) for said modeling uncertainties that do not exceed said measurement uncertainties: (i) determining (210) whether there is a fault in only one of said new data set measurements; (ii) if there is a fault in only one of said new data set measurements: (1) determining the identity of said faulted one of said new data set measurements; and, (2) applying (212) said identity of said faulted one of said new data set measurements to repair (216) said multivariate system or process. 9. A method as defined in claim 1, wherein said multivariate system or process is any physical process. 10. A method as defined in claim 1, wherein said multivariate system or process is any informational process. 11. A method as defined in claim 1, wherein said multivariate system or process is any manufacturing, operational, or informational process. 12. A method as defined in claim 1, wherein said multivariate system or process is any one of an aircraft, aeronautics, biology, chemical, electric power, food product, genetic, metals, oil refining, pharmaceutical, plastic, pulp and paper, semiconductor, econometric, financial, investment, loan, or psychometric process. 13. A method as defined in claim 1, further characterized by before said modeling of said historical reference data to produce said modeled values of said reference data set measurements, comparing ( 32) said reference data set measurement to a corresponding set of predefined criteria to determine whether said reference data set measurements adequately characterize variations within said reference data set measurements. 14. A method as defined in claim 1, further characterized by, during said deriving of said final model, comparing (32) said sums of all of said measurement and modeling uncertainties to a corresponding set of predefined criteria to determine whether said reference data set measurements adequately characterize variations within said reference data set measurements. 15. A method as defined in claim 1, further characterized by, during said deriving of said final model, comparing (94, 96, 98) said sums of all of said measurement and modeling uncertainties to a corresponding set of predefined criteria to determine whether said sums of all of said measurement and modeling uncertainties are normally distributed. 16. A method as defined in claim 1, further characterized by, during said applying of said modeling parameters to said new data set, comparing (146, 148, 152) said new data set measurements to a corresponding set of predefined criteria to determine whether said new data set measurements adequately characterize variations within said new data set measurements. 17. A method as defined in claim 16, further characterized by, after determining that said new data set measurements adequately characterize said variations within said new data set measurements, associating all of said measurement uncertainties with all of said new data set measurements. 18. A method as defined in claim 17, further characterized by comparing (174, 180) said new data set measurements to said corresponding set of predefined criteria to determine whether said new data set measurements contain any faults. 19. A method as defined in claim 17, further characterized by comparing (174, 180) said new data set measurements to said corresponding set of predefined criteria to determine (192) whether said new data set measurements contains one and only one fault and to identify that one of said new data set measurements which is faulted. 20. A method as defined in claim 17, further characterized by comparing (174) said new data set measurements to said corresponding set of predefined criteria to determine (176) whether said new data set measurements contains more than one fault and to identify each one of said new data set measurements which is faulted. 21. A method as defined in claim 18, further characterized by, if said new data set measurements contain no faults, replacing said new data set measurements with said modeled values of said new data set measurements. 22. A method as defined in claim 18, further characterized by, if said new data set measurements contain no faults, replacing said measurement uncertainties with said modeling uncertainties. 23. A method defined in claim 19, further characterized by, if said new data set measurements contain one and only one fault replacing said faulted one of said new data set measurements with said modeled one of said new data set measurements corresponding to said faulted one of said new data set measurements. 24. A method defined in claim 19, further characterized by, if said new data set measurements contain one and only one fault replacing said measurement uncertainty of said faulted one of said new data set measurements with said modeling uncertainty of said faulted one of said new data set measurements. 25. A method of modeling m variable multivariate system or process, said method characterized by: (a) forming (10) an m row by n column matrix X having: (i) n column vectors Xj respectively comprising numerical measurements of said m variables, said measurements collectively encompassing a plurality of variations within one or more operational states of said system or process, each one of said column vectors having elements xij where i=1 to m and j=1 to n; (ii) m row vectors iX, each said row vector iX comprising elements xij having a range ranx i and an average avexi; and, (b) deriving (12) a similarity xij#x ik=max(0, 1,-|xij-xik|/wi) between a jth example of an ith one of said measurements and a kth example of said ith one of said measurements, where wi is a weighting factor having an initial value equal to ranxi. 26. A method as defined in claim 25, further characterized by: (a) selecting (20) an element xab common to both a row vector aX and a column vector Xb of said matrix X; (b) removing (22) said element xab from said column vector Xb to produce an m-1 element column vector X' b; (c) removing (24) said row vector aX from said matrix X to produce an m-1 row by n column matrix X'; (d) deriving (26), for all j=1 to n, similarities X'jT#X'b between said column vector X'b and a column vector X'j in said matrix X', wherein: description="In-line Formulae" end="lead"X' jT#X'b=(x1j#x 1b+x2j#x2b+ . . . +xa-1j#xa-1b+xa+1j#xa+1b + . . . +xmj#xmb)/(m-1)description="In-line Formulae" end="tail" (e) selecting (28) the largest n' of said n similarities, wherein 2<n'<m and wherein each one of said n' selected similarities is not equal to unity and not equal to zero; and, (f) determining (30, 32) that said matrix X inadequately characterizes said system or process in at least one of said operational states if said n' similarities do not exist. 27. A method as defined in claim 26, further characterized by: (a) transforming (38, 40) said matrix X' into an m-1 row by n' column matrix X" by removing from said matrix X' all of said column vectors X'j lacking said n' similarities; (b) deriving (42), for all j=1 to n' and all k=1 to n', similarities X"jT#X"k between said column vector X'j and said column vector X"k in said matrix X" wherein: description="In-line Formulae" end="lead"X" jT#X"k=(x1j#x 1k+x2j#x2k+ . . . +xa-1j#xa-1k+xa+1j#xa+1k + . . . +xmj#xmk)/(m-1)description="In-line Formulae" end="tail" (c) deriving (44), for all j=1 to n', similarities X"jT#X'b between said column vector X"j in said matrix X" and said column vector X'b, wherein: description="In-line Formulae" end="lead"X" jT#X'b=(x1j#x 1b+x2j#x2b+ . . . +xa-1j#xa-1b+xa+1j#xa+1b + . . . +xmj#xmb)/(m-1)description="In-line Formulae" end="tail" (d) deriving (46) an n' element column vector C=(X" T#X")-1(X"T#X'b), wherein: (i) X"T#X" is a square matrix of n'2 similarities X"jT#X"k; (ii) X"T#X'b is a column vector of n' similarities X"jT#X'b; (iii) said n' elements of said column vector C have a sum cab; (iv) n' squares of elements of said column vector C have a sum c2ab; (e) defining (48) a model yab of said element xab, wherein: description="In-line Formulae" end="lead"y ab=aXC+(1-cab)avex a;description="In-line Formulae" end="tail" (f) producing (50) pluralities yij, c ij, and c2ij for said models yab said sum cab, and said sum c2ab for all i=1 to m and for all j=1 to n; (g) assembling (52) said plurality yij of models into an m row by n column model matrix Y comprising: (i) n column vectors Yj each one of said column vectors Yj having elements yij; (ii) m row vectors iY, each said row vector iY comprising elements yij having an average ave yi; (h) deriving (54) similarities xij#yij between corresponding elements in said matrix X and said matrix Y, wherein: description="In-line Formulae" end="lead"x ij#yij=max(0, 1|xij-y ij|/wi);description="In-line Formulae" end="tail" (i) deriving (56) average similarities si between elements in corresponding rows of said matrix X and said matrix Y for each one of said rows, wherein: description="In-line Formulae" end="lead"s i=((xi1#yi1) +(xi2 #yi2)+ . . . +(xin#yin))/ n;description="In-line Formulae" end="tail" (j) deriving (64) root-mean-square deviations ti between elements in corresponding rows of said matrix X and said matrix Y for each one of said rows, wherein: description="In-line Formulae" end="lead"t i=(((xi1-yi1)2+(x i2-yi2)2+ . . . +(xin-yin)2)/n)1/2;description="In-line Formulae" end="tail" (k) defining (66) a quantity M; for each row of said matrix X wherein: description="In-line Formulae" end="lead"M i=ranxi/ti;description="In-line Formulae" end="tail" (l) selecting (70) an integer M which approximates the largest one of said Mi; and, (m) redefining (72) said weighting factor wi as wi=Mti. 28. A method as defined in claim 27, further characterized by: (a) sequentially repeating (78, 80, 84) said method with said redefined weighting factor and without reselecting said integer M, until successive values of 1-si differ by less than 10%; and, (b) determining (86) that said matrix X contains inaccurate measurements if said successive values of 1-si do not differ by less than 10% after a selected number of sequential repetitions of said method. 29. A method as defined in claim 28, further characterized by: (a) concluding (92, 94, 98) that differences between said xij and said yij are approximately normally distributed with a mean of zero if said 1-si values lie within 10% of 1-exps, wherein: description="In-line Formulae" end="lead"exp s=1-(2/C)1/2/M;description="In-line Formulae" end="tail" (b) determining (100) a limit minci, below which 1% of said column vector sums cij lie; (c) deriving (102) averages avec2 i of c2ij; (d) locating (104) maxima maxc2i of c2ij; (e) initially assigning (106) measuring uncertainty upper limit values equal to ti; (f) initially assigning (108) modeling uncertainty upper limit values equal to ti; (g) determining (114, 120) that modeling uncertainty limit values are less than measuring uncertainty limit values if maxc2i<1; (h) assigning (122) measuring uncertainty lower limits and reassigning (124) said modeling uncertainty upper limits as ui if maxc2i<1, wherein ui =ti(1/2)1/2; and, (i) assigning (126) said modeling uncertainty lower limits as vi if maxc2i<1, wherein vi=ti(avec2i/2)1/2. 30. A method as defined in claim 29, further characterized by: (a) acquiring (132) a column vector X having m numerical elements xi; (b) selecting (134) an element xn common to said row vector aX and to said vector X; (c) removing (136) said selected element xa from said column vector X to produce an m-1 element column vector X'; (d) removing (142) said row vector aX from said matrix X to produce an m-1 row by n column matrix X'; (e) defining similarities xij#xi between the said xij and said elements xi wherein: description="In-line Formulae" end="lead"x ij#xi=max(0, 1-|xij-x i|/wi);description="In-line Formulae" end="tail" (f) deriving (138, 140), for all j=1 to n, similarities X'jT#X' between a column vector X'j in said matrix X' and said column vector X', wherein: description="In-line Formulae" end="lead"X' jT#X'=(x1j#x1+ x2j#x2+ . . . +xa-1j#x a-1+xa+1j#xa+1+ . . . +x mj#xm)/(m-1)description="In-line Formulae" end="tail" (g) selecting (144) the largest said n' of said n similarities wherein each one of said n' selected similarities is not equal to unity and not equal to zero; (h) determining (146, 148) that said vector X is an invalid description of the process characterized by said matrix X if n' of said similarities X'jT#X' not equal to zero and not equal to unity cannot be formed; (i) transforming (154, 156) said matrix X' into an m-1 row by n' column matrix X" by removing from said matrix X' all column vectors in said matrix X' lacking said n' selected similarities; (j) deriving (158), for all j=1 to n' and all k=1 to n', similarities X"jT#X"k between said column vector X"j and said column vector X"k in said matrix X" wherein: description="In-line Formulae" end="lead"X" jT#X"k=(x1j#x 1k+x2j#x2k+ . . . +xa-1j#xa-1k+xa+1j#xa+1k + . . . +xmj#xmk)/(m-1)description="In-line Formulae" end="tail" (k) deriving (164), for all j=1 to n', similarities X"jT#X' between said column vector X"j in said matrix X" and column vector X' wherein: description="In-line Formulae" end="lead"X" jT#X'=(x1j#x1+ x2j#x2+ . . . +xa-1j#x a-1+xa+1j#xa+1+ . . . +x mj#xm)/(m-1);description="In-line Formulae" end="tail" (l) deriving (166) a column vector C with n' elements, wherein: C=(X"T#X")-1(X"T#X') wherein: (i) X"T#X" is the square matrix of n'2 similarities X"jT#X"k; (ii) X"T#X' is the column vector of n' similarities X"jT#X'; (iii) n' elements of said column vector C have a sum c a; (m) producing (168) a model ya of element xa wherein: description="In-line Formulae" end="lead"y a=aXC+(1-ca)avex a;description="In-line Formulae" end="tail" (n) producing (170) pluralities yi and ci for said model ya and said sum ca for all i=1 to m; (o) collecting (172) said models y; into a column vector Y; (p) determining (174, 180, 182) that said vector X contains no faults if more than one of said sums ci are greater than minci; (q) associating all said yi, all said ti, all said ui, and all said vi with all said xi if said vector X contains no faults; (r) determining (174, 180, 192) that said vector X contains only one fault if only one of said sums ci is greater than minci; (s) associating (186) said yi, said ui and said vi with said xi for which said sum ci is greater than minci if said vector X contains only one fault; (t) associating (196) said ti and said ui with said xi for which said sums ci are not greater than minci if said vector X contains only one fault; and, (u) determining (174, 176) that said vector X contains more than one fault if none of said sums ci are > minci.