SYSTEM AND METHOD TO ASSESS SIGNAL SIMILARITY WITH APPLICATIONS TO DIAGNOSTICS AND PROGNOSTICS

• US 20100253512A1
• Filed: 07/17/2008
• Published: 10/07/2010
• Est. Priority Date: 07/17/2007
• Status: Active Grant

• Current Assignee: Clemson University
• Original Assignee: Clemson University
• Inventors: Lund, Robert B., Wagner, John R., Bassily, Hany F.
• Granted Patent: US 8,378,816 B2
• Time in Patent Office: Days
• US Class Current: 340/540
• CPC Class Codes: G05B 23/0229 knowledge based, e.g. expert systems; genetic algorithms

Abstract

Signal processing technology for assessing dynamic system similarity for fault detection and other applications is based on time- and frequency-domain time series analysis techniques and compares the entire autocorrelation structure of a test and reference signal series. The test and reference signals are first subjected to similar pre-processing to help guarantee signal stationarity. Pre-processing may include formation of multivariate signal clusters, filtering and sampling. Multivariate periodograms or autocovariance functions are then calculated for each signal series. Test statistics are computed and assessed to determine the equality of the test and reference signals. When the difference between sample autocovariance functions or periodograms of such signals exceeds a preselected threshold value, fault detection signals and/or related diagnostic information are provided as output to a user.

Claims

1. A method for assessing dynamic system similarity, said method comprising the following steps:

providing at least one multivariate test signal associated with an operational system;

providing at least one multivariate reference signal associated with an operational system;

comparing the signal similarity of the second-order moment of the at least one multivariate test signal with the second-order moment of the at least one multivariate reference signal;

establishing a selected threshold level defining a maximum allowable deviation for signal similarity of the at least one multivariate test and reference signals;

determining when the signal similarity of the second-order moments of the multivariate test and reference signals fails to remain within the selected threshold level; and

providing output to a user indicating instances when the selected threshold level is exceeded.

2. The method of claim 1, wherein said multivariate test and reference signals are Gaussian signals, and wherein the second-order moment of the multivariate test and reference signals comprises the autocorrelation structure of the test and reference signals.

3. The method of claim 1, wherein said step of comparing signal similarity is performed

using time-domain processing techniques and includes a step of calculating the auto-covariance matrix functions for the at least one respective multivariate test and reference signals.

4. The method of claim 1, wherein said step of comparing signal similarity is performed

using frequency-domain processing techniques and includes a step of calculating for a plurality of frequencies respective spectral vectors for the respective multivariate test and reference signals;

5. The method of claim 1, wherein said step of comparing signal similarity is performed

using time-domain processing techniques and more particularly comprises the steps of:

calculating the auto-covariance matrix functions for the at least one respective multivariate test and reference signals;

calculating the covariance of the auto-covariance of the multivariate reference signal;

generating a test statistic using in part the calculated auto-covariance matrix functions for the multivariate test and reference signals and the covariance of the auto-covariance of the multivariate reference signal;

determining when the test statistic crosses the selected threshold level.

6. The method of claim 5, wherein elements of each auto-covariance matrix function are

calculated for different time lags from time 0, 1,2, . . . , L, for a predetermined value L.

7. The method of claim 1, wherein said step of comparing signal equality is performed

using frequency-domain processing techniques and more particularly comprises the steps of:

calculating for a plurality of frequencies respective spectral vectors for the respective multivariate test and reference signals;

forming block matrices of the calculated spectral vectors to generate a test statistic; and

determining when the test statistic crosses the selected threshold level.

8. The method of claim 1, further comprising a step implemented before said comparing

step of pre-processing the multivariate test and reference signals, wherein the same pre-processing techniques are applied to both of the at least one multivariate test and reference signals, and wherein the pre-processing techniques are configured to increase signal stationarity.

9. The method of claim 8, wherein said step of pre-processing comprises one or more of

filtering and sampling the at least one multivariate test and reference signals.

10. The method of claim 1, wherein said step of providing output to a user comprises providing a probability calculation for each instance when the selected threshold is exceeded to indicate to a user the probability that the detection of signal dissimilarity is accurate.

11. The method of claim 1, wherein said comparing and determining steps are performed for a series of time-shifted samples of the at least one respective test and reference signals.

12. The method of claim 11, further comprising a step of providing output to a user indicating the likelihood that the selected threshold level will be violated by the operational system at a future time based on the comparing and determining steps performed for selected time-shifted samples of the at least one respective test and reference signals

13. A system for assessing dynamic system similarity, comprising:

a signal processor adapted to;

(i) receive at least one multivariate test signal and at least one multivariate reference signal associated with an operational system;

(ii) compare the signal similarity of the second-order moment of the at least one multivariate test signal with the second-order moment of the at least one multivariate reference signal; and

(iii) determine when the signal similarity of the second-order moments of the at least one multivariate test and reference signals fails to remain within a preselected threshold of signal similarity; and

an output device coupled to said signal processor, said output device configured to

provide visual or audio output to a user indicating instances when the selected threshold level of signal similarity is not met.

14. The system of claim 13, further comprising an input device adapted for providing user selection of the threshold used to determine signal similarity.

15. The system of claim 13, further comprising a data storage element coupled to said

signal processor for storing executable instructions, selected ones of the at least one multivariate test and reference signals, and selected outputs calculated by said signal processor.

16. The system of claim 13, wherein said signal processor is further adapted to determine the signal similarity of the autocorrelation structures of the at least one multivariate test and reference signals when the at least one multivariate test and reference signals have statistical properties consistent with Gaussian random variables.

17. The system of claim 13, wherein said signal processor is further adapted to calculate

the auto-covariance matrix functions for the at least one respective multivariate test and reference signals.

18. The system of claim 13, wherein said signal processor is further adapted to calculate

spectral vectors for the respective multivariate test and reference signals for a plurality of frequencies.

19. The system of claim 13, wherein said signal processor is further adapted to:

calculate the auto-covariance matrix functions for the at least one respective multivariate test and reference signals;

calculate the covariance of the auto-covariance of the multivariate reference signal;

generate a test statistic using in part the calculated auto-covariance matrix functions for the multivariate test and reference signals and the covariance of the auto-covariance of the multivariate reference signal; and

determine when the test statistic fails to remain within the preselected threshold of signal similarity.

20. The system of claim 19, wherein said signal processor is adapted to calculate elements of each auto-covariance matrix function for different time lags from time 0, 1, 2, . . . , L, for a predetermined value L.

21. The system of claim 13, wherein said signal processor is further adapted to:

calculate respective spectral vectors for the respective multivariate test and reference signals for a plurality of frequencies;

form block matrices of the calculated spectral vectors to generate a test statistic; and

determine when the test statistic fails to exceed the preselected threshold of signal similarity.

22. The system of claim 13, wherein said signal processor is further adapted to implemented similar pre-processing techniques to the at least one multivariate test and reference signals to increase signal stationarity.

23. The system of claim 22, wherein the pre-processing techniques implemented by said

signal processor comprise one or more of filtering and sampling the at least one multivariate test and reference signals.

24. The system of claim 13, wherein said signal processor is further adapted to compare

the signal similarity of the second-order moment of the at least one multivariate test signal with the at least one multivariate reference signal for a series of time-shifted samples of the at least one respective test and reference signals.

25. The system of claim 24, wherein said output device is further configured to provide

output to a user indicating the likelihood that the selected threshold level of signal similarity will be met at a future time based on the sequence of comparisons made for the selected time-shifted samples of the at least one respective test and reference signals