Residual signal alert generation for condition monitoring using approximated SPRT distribution

• US 6,975,962 B2
• Filed: 06/07/2002
• Issued: 12/13/2005
• Est. Priority Date: 06/11/2001
• Status: Expired due to Fees

• Current Assignee: SmartSignal Corporation (Emerson Electric Company)
• Original Assignee: SmartSignal Corporation (Emerson Electric Company)
• Inventors: Wegerich, Stephan W., Pipke, Robert Matthew
• Primary Examiner(s): Hoff, Marc S.
• Assistant Examiner(s): Barbee, Manuel L.
• Application Number:
  US10/165,119
• Publication Number:
  US 20030055607A1
• Time in Patent Office: 1,285 Days
• Field of Search: 702 33- 36, 702 38- 40, 702 57- 59, 702179-185, 700 29- 31, 700/47, 700/51, 700/174, 703/7, 340/511, 340/3.1, 340/3.43
• US Class Current: 702/182
• CPC Class Codes: G06F 11/3447 Performance evaluation by modeling
• CPC Class Codes: G06F 11/3452 Performance evaluation by statistical analysis
• CPC Class Codes: G07C 3/00 Registering or indicating the condition or the working of machines or other apparatus, other than vehicles

Abstract

A system and method for monitoring a condition of a monitored system. Estimates of monitored parameters from a model of the system provide residual values that can be analyzed using a sequential probability ratio test (“SPRT”). The invention employs empirically derived distributions in the SPRT to provide more accurate and sensitive alerts of impending faults, breakdowns and process deviations. The distributions can be generated from piecewise continuous approximation or spline functions based on the actual distribution of residual data to provide improved computational performance. The distributions can be provided before monitoring, or can be updated and determined during monitoring in an adaptive fashion.

Claims

1. An apparatus for monitoring operation of a system instrumented with sensors, comprising:

a data acquisition front-end for receiving actual sensor signal values descriptive of the operation of the monitored system;

an information processor for executing a computational model for generating sensor signal estimates in response to the actual sensor signal values from said data acquisition front-end;

said information processor subtracting the sensor signal estimates generated with the computational model from the actual sensor signal values to provide residual values for the sensors on the monitored system;

a memory for storing an empirically determined distribution of residual values determined from residuals corresponding to estimates from said computational model for normal operation of the system as a plurality of piecewise continuous functions; and

said information processor further operable to perform a sequential probability ratio test on the residual values using the functions in said memory to indicate whether a sequence of observations represents residual values within the empirically determined distribution for normal operation.

2. An apparatus as recited wherein claim 1 wherein said memory stores piecewise continuous functions defining a histogram.

3. An apparatus as recited wherein claim 1 wherein said memory stores piecewise continuous functions defining a curve that is smooth in the first derivative.

4. An apparatus as recited wherein claim 3 wherein said memory stores piecewise continuous functions defining a curve that is smooth in the second derivative.

5. An apparatus as recited wherein claim 4 wherein said piecewise continuous functions comprise a cubic spline.

6. An apparatus as recited wherein claim 1 wherein said computational model uses a nonparametric regression to generate estimates.

7. An apparatus as recited in claim 6 wherein said computation model uses a kernel regression to generate estimates.

8. An apparatus as recited in claim 6 wherein said computation model uses a similarity operation to generate estimates.

9. A computer program product for detecting faults in a monitored system instrumented with sensors and having a plurality of operational modes, comprising:

a modeling module for generating sensor estimates in response to successive observations of actual sensor values, and for generating residual values as the difference between actual sensor values and corresponding sensor estimates;

a statistical testing module disposed to indicate a detected fault in the monitored system if a sequence of residual values for a sensor differs from an expected distribution of residual values for that sensor determined from residuals corresponding to estimates from said modeling module, associated with desired operation of said system;

a mode selection module for selecting an expected residual distribution for a sensor corresponding to a current operational mode of said system for use by said statistical testing module, from among a stored set of distributions.

10. A computer program product according to claim 9 wherein said mode selection module selects an expected residual distribution corresponding to a current operational mode of the system determined from the value of at least one of said actual sensor values.

11. A computer program product according to claim 9 further comprising a distribution determination module for generating and storing an expected residual distribution empirically from a sequence of residuals for a sensor for a given mode of operation of said system.

12. A computer program product according to claim 11 wherein said distribution determination module generates an expected residual distribution by generating a histogram of residuals for a sensor for a given mode of operation of said system.

13. A computer program product according to claim 11 wherein said distribution determination module generates an expected residual distribution by fitting a curve to a histogram of residuals.

14. A computer program product according to claim 13 wherein said distribution determination module fits a plurality of piecewise continuous curves to a histogram of residuals.

15. A computer program product according to claim 14 wherein said distribution determination module fits a histogram of residuals with a cubic spline.

16. A computer program product according to claim 9 wherein said modeling module employs a nonparametric regression to generate sensor estimates.

17. A computer program product according to claim 16 wherein said modeling module employs a kernel regression to generate sensor estimates.

18. A computer program product according to claim 16 wherein said modeling module employs a similarity operation to generate sensor estimates.

19. A method for monitoring a system instrumented with sensors, comprising the steps of:

generating sensor estimates in response to successive observations of actual sensor values;

generating residual values as the difference between actual sensor values and corresponding sensor estimates;

statistically testing a sequence of residual values for a sensor to determine if they are representative of an expected distribution of residual values for that sensor associated with desired operation of said system; and

updating the expected distribution according to a moving window of past observations of residual values for that sensor.

20. A method according to claim 19 further comprising the step of generating an alert if the step of statistically testing indicates the sequence of residual values is not representative of the expected distribution.

21. A method according to claim 20 wherein said updating step is performed only if the window of past observations has an occurrence of alerts less than a threshold.

22. A method according to claim 21 wherein the threshold is 5% of observations in the window.

23. A method according to claim 19 wherein said step of statistically testing comprises performing a sequential probability ratio test using the expected distribution.

24. A method according to claim 19 wherein said step of generating estimates comprises employing a nonparametric regression to estimate a sensor value.

25. A method according to claim 24 wherein said step of generating estimates comprises employing a kernel regression to estimate a sensor value.

26. A method according to claim 24 wherein said step of generating estimates comprises employing a similarity operation to estimate a sensor value.

27. A method according to claim 19 wherein said updating step comprises generating a histogram of residual values comprising residual values selected from the window of past observations.

28. A method according to claim 27 wherein said updating step further comprises fitting a curve to the histogram.

29. A method according to claim 28 wherein said updating step further comprises fitting a piecewise continuous set of functions to the histogram.

30. A method according to claim 29 wherein the fitted piecewise continuous set of functions is continuous in the first derivative.

31. A method according to claim 29 wherein the fitted piecewise continuous set of functions is continuous in the second derivative.

32. A method according to claim 29 wherein the fitted piecewise continuous set of functions is a cubic spline.

33. A method for monitoring operation of a system instrumented with sensors comprising:

receiving actual sensor signal values descriptive of the operation of the monitored system;

generating sensor signal estimates with a computational model in response to the actual sensor signal values from the receiving step;

subtracting the sensor signal estimates generated with the computational model from the actual sensor signal values to provide residual values for the sensors on the monitored system;

storing an empirically determined distribution of residual values determined from residuals corresponding to estimates from said computational model, for normal operation of the system as a plurality of piecewise continuous functions;

statistically testing the residual signals with values using the functions in said memory to indicate whether a sequence of observations in time represent residual values within an expected distribution for normal operation; and

selecting an empirically determined distribution of residual values from a plurality of modes in relation to a sensor corresponding to a current operational mode of the system for use by the statistically testing step from among a stored set of distributions.

34. A method as recited in claim 33 wherein the storing step comprises values of the piecewise continuous functions organized as a histogram normalized to provide an approximate distribution shape.

35. A method as recited in claim 33 wherein the storing step comprises values from the piecewise continuous functions defining a curve approximated for fitting an empirical distribution.

36. A method as recited in claim 35 wherein the piecewise continuous functions comprise fitting the defined curve with splining techniques.

37. A method as recited in claim 33 comprising updating the empirically determined distribution according to a moving window of past observations of residual values for respective sensors.