Univariate method for monitoring and analysis of multivariate data

• US 7,917,240 B2
• Filed: 03/20/2007
• Issued: 03/29/2011
• Est. Priority Date: 09/29/2006
• Status: Active Grant

• Current Assignee: Fisher-Rosemount Systems Incorporated (Emerson Electric Company)
• Original Assignee: Fisher-Rosemount Systems Incorporated (Emerson Electric Company)
• Inventors: Samardzija, Nikola
• Primary Examiner(s): Kasenge; Charles R
• Application Number:
  US11/688,772
• Publication Number:
  US 20080082195A1
• Time in Patent Office: 1,470 Days
• Field of Search: 700/28, 700/29, 700/30, 700/31, 700/108, 700/109, 702/179, 702/182, 702/183, 702/185, 702/186, 703/2
• US Class Current: 700/109
• CPC Class Codes: G05B 23/021 adopting a different treatment of each operating region or a different mode of the monitored system, e.g. transient modes; different operating configurations of monitored system
• CPC Class Codes: G05B 23/024 Quantitative history assessment, e.g. mathematical relationships between available data; Functions therefor; Principal component analysis [PCA]; Partial least square [PLS]; Statistical classifiers, e.g. Bayesian networks, linear regression or correlation analysis; Neural networks
• CPC Class Codes: G05B 23/0245 based on a qualitative model, e.g. rule based; if-then decisions
• CPC Class Codes: Y10S 715/965 for process control and configuration

Abstract

A method and system of monitoring multivariate process data in a process plant, where the multivariate process data comprises a plurality of process variables each having a plurality of observations, includes defining each process variable as a process variable vector comprising a set of observation components, where the set of observation components comprises time dependent process data corresponding to the observations of the process variable, calculation, a multivariable transformation as a function of a plurality of process variable vector transformation each corresponding to one of the process variables, where each process variable vector transformation is a function of a univariate variable unifying the process variables, and representing the operation of the process based on the multivariable transformation, where the representation of the operation of the process designates a multivariate projection of the process data by the univariate variable for each of the process variables.

Claims

1. A method of monitoring multivariate process data in a process plant, wherein the multivariate process data comprises a plurality of process variables each having a plurality of observations, wherein at least one process variable comprises an unknown process variable control limit, the method comprising:

collecting a set of data for the at least one process variable, wherein the set of collected process variable data is representative of a normal operation of the process when the process is operating normally and comprises a plurality of observations of the at least one multivariate process variable;

determining the unknown process variable control limit under the normal operation of the process;

defining each process variable as a process variable vector comprising a set of observation components, wherein the set of observation components comprises time dependent process data corresponding to the observations of the process variable;

normalizing each of a plurality of process variable vector transformations to the same process variable control limit using a scaling parameter unique to each process variable to generate a common process variable control limit for the process variables, wherein each process variable vector transformation is a function of a univariate variable unifying the process variables;

calculating a multivariable transformation as a function of the plurality of process variable vector transformations each corresponding to one of the process variables; and

representing an operation of a process based on the multivariable transformation, wherein the representation of the operation of the process designates a multivariate projection of the process data by the univariate variable for each of the process variables, wherein representing the operation of the process based on the multivariable transformation comprises monitoring each process variable in relation to the determined process variable limit.

2. The method of claim 1, further comprising transposing the set of observations for each of the plurality of process variables, wherein defining each process variable as a process variable vector comprises defining each process variable as a process variable vector comprising the transposed set of observations.

3. The method of claim 1, further comprising calculating the transformation of each process variable vector as a function of the univariate variable unifying the process variables.

4. The method of claim 3, wherein calculating the transformation of each process variable vector comprises calculating the transformation of each process variable vector as a function of the univariate variable unifying the process variables and as a function of a position parameter unique to the process variable vector.

5. The method of claim 3, wherein calculating the transformation of each process variable vector comprises calculating the transformation of each process variable vector as a function of the univariate variable unifying the process variables and as a function of a scaling parameter applied to each observation component within the set of observation components.

6. The method of claim 1, wherein the calculating a multivariable transformation as a function of a plurality of process variable vector transformations comprises calculating the multivariable transformation as a product of the plurality of process variable vector transformations.

7. The method of claim 1, wherein representing the operation of the process based on the multivariable transformation comprises representing the operation of the process based on a scaling parameter applied to the multivariable transformation.

8. The method of claim 1, wherein each observation component within the set of observation components comprises a vector dimension.

9. The method of claim 8, further comprising:

collecting the process data from a process within the process plant over a period of time; and

determining each vector dimension as a function of a sampling rate of the observations and as a function of the period of time of data collection.

10. The method of claim 1, wherein the univariate variable comprises a variable designated to bundle the process variables.

11. The method of claim 1, wherein representing the operation of the process based on the multivariable transformation comprises generating a visualization of the multivariate transformation as a function of the univariate variable.

12. The method of claim 11, wherein generating a visualization of the multivariate transformation as a function of the univariate variable comprises generating a visualization displaying each process variable with a unique position relative to the univariate variable as determined by a position parameter unique to the process variable vector.

13. The method of claim 1, wherein each process variable comprises a known process variable control limit, the method further comprising normalizing each process variable vector transformation to the same process variable control limit using a scaling parameter unique to each process variable to generate a common process variable control limit for the process variables, wherein representing the operation of the process based on the multivariable transformation comprises monitoring each process variable in relation to the common process variable limit.

14. The method of claim 1, further comprising collecting the process data from a process within the process plant comprising a measure of a real-time operation of the process.

15. The method of claim 14, wherein collecting the process data from a process within the process plant comprises collecting monitored on-line process data from a process within the process plant comprising a measure of a real-time operation of the process when the process is on-line.

16. The method of claim 14, wherein representing the operation of the process based on the multivariable transformation comprises generating a visualization of the multivariate transformation as a real-time function of the univariate variable.

17. A computer readable medium having computer executable instructions stored in memory for monitoring a process in a process plant, wherein the process generates multivariate process data comprising a plurality of process variables each having a plurality of observations, wherein each process variable is defined as a process variable vector comprising a set of observation components having time dependent process data corresponding to the observations of the process variable, and wherein at least one process variable comprises an unknown process variable control limit, the computer executable instructions comprising:

a data collection tool adapted to collect a set of data for the at least one process variable, wherein the set of collected process variable data is representative of a normal operation of the process when the process is operating normally and comprises a plurality of observations of the at least one multivariate process variable;

an analysis tool adapted to determine the unknown process variable control limit under the normal operation of the process;

a normalization tool adapted to normalize each of a plurality of process variable vector transformations to the same process variable control limit using a scaling parameter unique to each process variable to generate a common process variable control limit for the process variables, wherein each process variable vector transformation is a function of a univariate variable unifying the process variables;

a process variable transformation tool adapted to calculate a multivariable transformation as a function of the plurality of process variable vector transformations each corresponding to one of the process variables; and

a monitoring tool adapted to represent an operation of the process based on the multivariable transformation, wherein the representation of the operation of the process designates a multivariate projection of the process data by the univariate variable for each of the process variables wherein the monitoring tool is adapted to monitor each process variable in relation to the common process variable limit.

18. The computer readable medium having computer executable instructions of claim 17, wherein each process variable is defined as a process variable vector comprising a transposed set of the observations for each of the plurality of process variables.

19. The computer readable medium having computer executable instructions of claim 17, wherein the process variable transformation tool is adapted to calculate the transformation of each process variable vector as a function of the univariate variable unifying the process variables.

20. The computer readable medium having computer executable instructions of claim 19, wherein the process variable transformation tool is adapted to calculate the transformation of each process variable vector as a function of the univariate variable unifying the process variables and as a function of a position parameter unique to the process variable vector.

21. The computer readable medium having computer executable instructions of claim 19, wherein the process variable transformation tool is adapted to calculate the transformation of each process variable vector as a function of the univariate variable unifying the process variables and as a function of a scaling parameter applied to each observation component within the set of observation components.

22. The computer readable medium having computer executable instructions of claim 17, wherein the process variable transformation tool is adapted to calculate the multivariable transformation as a product of the plurality of process variable vector transformations.

23. The computer readable medium having computer executable instructions of claim 17, wherein the monitoring tool is adapted to represent the operation of the process based on a scaling parameter applied to the multivariable transformation.

24. The computer readable medium having computer executable instructions of claim 17, wherein each observation component within the set of observation components comprises a vector dimension.

25. The computer readable medium having computer executable instructions of claim 24, further comprising a data collection tool adapted to collect the process data from a process within the process plant over a period of time, wherein each vector dimension is determined as a function of a sampling rate of the observations and as a function of the period of time of data collection.

26. The computer readable medium having computer executable instructions of claim 17, wherein the univariate variable comprises a variable designated to bundle the process variables.

27. The computer readable medium having computer executable instructions of claim 17, wherein the monitoring tool is adapted to generate a visualization of the multivariate transformation as a function of the univariate variable.

28. The computer readable medium having computer executable instructions of claim 27, wherein the monitoring tool is adapted to generate a visualization displaying each process variable with a unique position relative to the univariate variable as determined by a position parameter unique to the process variable vector.

29. The computer readable medium having computer executable instructions of claim 17, wherein each process variable comprises a known process variable control limit, the system further comprising a normalization tool adapted to normalize each process variable vector transformation to the same process variable control limit using a scaling parameter unique to each process variable to generate a common process variable control limit for the process variables, wherein the monitoring tool is adapted to monitor each process variable in relation to the common process variable limit.

30. The computer readable medium having computer executable instructions of claim 17, further comprising a data collection tool adapted to collect the process data from a process within the process plant comprising a measure of a real-time operation of the process.

31. The computer readable medium having computer executable instructions of claim 30, wherein the data collection tool is adapted to collect monitored on-line process data from a process within the process plant comprising a measure of a real-time operation of the process when the process is on-line.

32. The computer readable medium having computer executable instructions of claim 30, wherein the monitoring tool is adapted to generate a visualization of the multivariate transformation as areal-tine function of the univariate variable.

33. A computer readable medium having computer executable instructions stored in memory for monitoring a process in a process plant, the computer executable instructions comprising:

a first analysis tool adapted to collect a set of data for at least one multivariate process variable, wherein at least one of the multivariate process variables comprises an unknown process variable control limit, and wherein the set of collected multivariate process variable data is representative of a normal operation of the process when the process is operating normally and comprises a plurality of observations of the at least one multivariate process variable;

a second analysis tool adapted to determine the unknown process variable control limit under the normal operation of the process;

,

a third analysis tool adapted to generate a univariate statistical representation for each of the plurality of multivariate process variables each having a plurality of observations based on a univariate variable unifying the multivariate process variables;

a fourth analysis tool adapted to normalize each univariate statistical representation of a multivariate process variable to a common process variable control limit;

a fifth analysis tool adapted to generate a univariate statistical representation of an operation of the process based on the plurality of univariate statistical representations of the plurality of multivariate process variables; and

a sixth analysis tool adapted to monitor the operation of the process based on the univariate statistical representation of the operation of the process as a function of the univariate variable, and adapted to monitor each multivariate process variable as represented by the univariate statistical representation of the operation of the process in relation to the common process variable control limit.

34. The computer readable medium having computer executable instructions of claim 33, further comprising a seventh analysis tool adapted to define each process variable as a process variable vector comprising a set of observation components, wherein the set of observation components comprises time dependent process data corresponding to the observations of the multivariate process variable.

35. The computer readable medium having computer executable instructions of claim 33, further comprising a seventh analysis tool adapted to transform the plurality of multivariate process variables to a univariate representation of the plurality of multivariate process variables based on the combination of the plurality of univariate statistical representations of the plurality of multivariate process variables.

36. The computer readable medium having computer executable instructions of claim 35, wherein the fifth analysis tool is adapted to generate the univariate statistical representation of the operation of the process based on the univariate representation of the plurality of multivariate process variables.

37. The computer readable medium having computer executable instructions of claim 33, wherein the sixth analysis tool is adapted to monitor the real-time operation of the process based on the univariate statistical representation of the operation of the process as a function of the univariate variable.

38. The computer readable medium having computer executable instructions of claim 33, wherein the sixth analysis tool is adapted to generate a visualization of the univariate statistical representation of the operation of the process as a function of the univariate variable.

39. The computer readable medium having computer executable instructions of claim 38, wherein the sixth analysis tool is adapted to generate a visualization displaying each process variable with a unique position relative to the univariate variable.

40. The computer readable medium having computer executable instructions of claim 33, wherein each multivariate process variable comprises a known process variable control limit, the system further comprising a seventh analysis tool adapted to normalize each univariate statistical representation of a multivariate process variable to a common process variable control limit, wherein the sixth analysis tool is adapted to monitor each multivariate process variable as represented by the univariate statistical representation of the operation of the process in relation to the common process variable control limit.

41. The computer readable medium having computer executable instructions of claim 33, wherein the univariate statistical representation for each of a plurality of multivariate process variables is calculated by the third analysis tool as:

p_i=[(y−

α

_i)²+k_ix_ij²]

wherein;

y=the univariate variable,

α

_i=position parameter unique to a process variable vector of each multivariate process variable,

k_i=a scaling parameter,

x_ij=an observation component within a set of observation components of the process variable vector,

i=1, . . . , n where n corresponds to the number of multivariate process variables, and

j=1, . . . , m where m corresponds to a vector dimension for each observation component determined by a sampling rate in collecting the observations and the total time in collecting the observations.

42. The computer readable medium having computer executable instructions of claim 41, wherein the process variable vector of each multivariate process variable is calculated by a seventh analysis tool as:

X_i=[x_i,1, x_i,2, . . . , x_i,m]^T

wherein T comprises a transpose operation.

43. The computer readable medium having computer executable instructions of claim 33, wherein the univariate statistical representation of the operation of the process is calculated by the fifth analysis tool as:

M_v(y)=K_p/P(y)

wherein;

K_p=a scaling parameter

P(y)=p₁(y)* p₂(y)* . . . p_n(y)

y=the univariate variable,

p_n(y)=the univariate statistical representation for the n_th multivariate process variable, and

n=the number of multivariate process variables.