Monitoring and fault detection in dynamic systems

• US 7,421,351 B2
• Filed: 12/21/2006
• Issued: 09/02/2008
• Est. Priority Date: 12/21/2006
• Status: Active Grant

• Current Assignee: Honeywell International Inc.
• Original Assignee: Honeywell International Inc.
• Inventors: Navratil, Roman
• Primary Examiner(s): Wachsman; Hal D
• Application Number:
  US11/644,726
• Publication Number:
  US 20080154544A1
• Time in Patent Office: 621 Days
• Field of Search: 702/58, 702/179, 702/185, 702/188, 702/196
• US Class Current: 702/58
• 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

Abstract

A system and method for monitoring and fault detection in dynamic systems. A “cross-covariance” matrix is used to construct and implement a principle component analysis (PCA) model and/or partial least squares (PLS) model. This system is further utilized for monitoring and detecting faults in a dynamic system. Time series information is synchronized, with respect to a set of training data. Based on historical data, consistency of correlations between variables can be checked with respect to a given time stamp.

Claims

1. A computer implemented method for fault detection and monitoring of a dynamic system, comprising:

obtaining a set of training data indicative of a normal process behavior of said dynamic system;

constructing a matrix associated with a cross-correlation chart utilizing said set of training data;

calculating a plurality of lass for a plurality of pair of tag variables by locating a maximum of an absolute value of a cross-correlation function in said cross-correlation chart;

constructing a matrix of said plurality of lass that tracks data between each pair of tag variables among said plurality of pair of tag variables;

developing a cross-covariance matrix utilizing said matrix of said plurality of lags comprising data indicative of a behavior of said dynamic system; and

analyzing said cross-covariance matrix to monitor and detect faults in said dynamic system.

2. The computer implemented method of claim 1 further comprising:

utilizing said cross-covariance matrix in a PCA (Principal Component Analysis) model.

3. The method of claim 2 further comprising:

comparing actual data generated by said dynamic system with said PCA model using said plurality of lags in the context of a T-PCA (Temporal-PCA) model input.

4. The computer implemented method of claim 3 further comprising processing said PCA model in parallel with said T-PCA model.

5. The computer implemented method of claim 1 further comprising:

monitoring a consistency of time dependent changes associated with said dynamic system in order to monitor and detect faults in said dynamic system.

6. The computer implemented method of claim 1 further comprising:

transforming said plurality of lags into a plurality of vectors of lags, wherein each of said plurality of lags possesses a specific lag defined with respect to a reference time.

7. The computer implemented method of claim 1 further comprising:

calculating said cross-covariance matrix according to an equation as follows;

$\mathrm{\text{'}"\text{'}"\text{'}\text{'}"\text{'}"\text{'}}<br><br>\mathrm{Cross}<br><br>\text{-}<br><br>\mathrm{covariance}<br><br>\mathrm{\text{'}"\text{'}"\text{'}\text{'}"\text{'}"\text{'}}<br><br>\text{;<br><br>}<br><br><br><br>\frac{\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br><br><br>\left(x_i-\stackrel{\_}{x}\right)<br><br>\left(y_{i-\mathrm{lag}<br><br>\left(y\right)}-\stackrel{\_}{y}\right)}{n-1}$

8. A computer implemented method for fault detection and monitoring of a dynamic system, comprising:

obtaining a set of training data indicative of a normal process behavior of said dynamic system;

constructing a matrix associated with a cross-correlation chart utilizing said set of training data;

calculating a plurality of lass for a plurality of pair of tag variables by locating a maximum of an absolute value of a cross-correlation function in said cross-correlation chart;

constructing a matrix of said plurality of lass that tracks data between each pair of tag variables among said plurality of pair of tag variables;

developing a cross-covariance matrix utilizing said matrix of said plurality of lags comprising data indicative of a behavior of said dynamic system;

utilizing said cross-covariance matrix in a PCA model; and

analyzing said cross-covariance matrix in said PCA model to monitor and detect faults in said dynamic system.

9. The computer implemented method of claim 8 further comprising:

comparing actual data generated by said dynamic system with said PCA model using said plurality of lags in the context of a T-PCA (Temporal-PCA) model input.

10. The computer implemented method of claim 8 further comprising:

monitoring a consistency of time dependent changes associated with said dynamic system in order to monitor and detect faults in said dynamic system.

11. The computer implemented method of claim 8 further comprising:

transforming said plurality of lags into a plurality of vectors of lags, wherein each of said plurality of lags possesses a specific lag defined with respect to a reference time.

12. The computer implemented method of claim 8 further comprising:

calculating said cross-covariance matrix according to an equation as follows;

$\mathrm{\text{'}"\text{'}"\text{'}\text{'}"\text{'}"\text{'}}<br><br>\mathrm{Cross}<br><br>\text{-}<br><br>\mathrm{covariance}<br><br>\mathrm{\text{'}"\text{'}"\text{'}\text{'}"\text{'}"\text{'}}<br><br>\text{;<br><br>}<br><br><br><br>\frac{\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br><br><br>\left(x_i-\stackrel{\_}{x}\right)<br><br>\left(y_{i-\mathrm{lag}<br><br>\left(y\right)}-\stackrel{\_}{y}\right)}{n-1}$

13. A system for fault detection and monitoring of a dynamic system, comprising:

a data-processing apparatus;

a module executed by said data-processing apparatus, said module and said data-processing apparatus being operable in combination with one another to;

obtain a set of training data indicative of a normal process behavior of said dynamic system;

construct a matrix associated with a cross-correlation chart utilizing said set of training set;

calculate a plurality of lass for a plurality of pair of tag variables by locating a maximum of an absolute value of a cross-correlation function in said cross-correlation chart;

construct a matrix of said plurality of lass that tracks data between each pair of tag variables among said plurality of pair of tag variables;

develop a cross-covariance matrix utilizing said matrix of said plurality of lass comprising data indicative of a behavior of said dynamic system; and

analyze said cross-covariance matrix to monitor and detect faults in said dynamic system.

14. The system of claim 13 wherein said data-processing apparatus and said module are further operable in combination with one another to utilize said cross-covariance matrix in a PCA (Principal Component Analysis) model.

15. The system of claim 14 wherein said data-processing apparatus and said module are further operable in combination with one another to compare actual data generated by said dynamic system with said PCA model using said plurality of lags in the context of a T-PCA (Temporal-PCA) model input.

16. The system of claim 15 further comprising wherein said data-processing apparatus and said module are further operable in combination with one another to process said PCA model in parallel with said T-PCA model.

17. The system of claim 13 wherein said data-processing apparatus and said module are further operable in combination with one another to monitor a consistency of time dependent changes associated with said dynamic system in order to monitor and detect faults in said dynamic system.

18. The system of claim 13 wherein said data-processing apparatus and said module are further operable in combination with one another to transform said plurality of lags into a plurality of vectors of lags, wherein each of said plurality of lags possesses a specific lag defined with respect to a reference time.

19. The system of claim 13 wherein said module and said data-processing apparatus being further operable in combination with one another to:

calculate said cross-covariance matrix according to an equation as follows;

$\mathrm{\text{'}"\text{'}"\text{'}\text{'}"\text{'}"\text{'}}<br><br>\mathrm{Cross}<br><br>\text{-}<br><br>\mathrm{covariance}<br><br>\mathrm{\text{'}"\text{'}"\text{'}\text{'}"\text{'}"\text{'}}<br><br>\text{;<br><br>}<br><br><br><br>\frac{\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br><br><br>\left(x_i-\stackrel{\_}{x}\right)<br><br>\left(y_{i-\mathrm{lag}<br><br>\left(y\right)}-\stackrel{\_}{y}\right)}{n-1}$