Method, computer program, and system for intrinsic timescale decomposition, filtering, and automated analysis of signals of arbitrary origin or timescale

• US 20040078160A1
• Filed: 10/10/2003
• Published: 04/22/2004
• Est. Priority Date: 10/11/2002
• Status: Active Grant

• Current Assignee: Flint Hills Scientific, LLC
• Original Assignee: Flint Hills Scientific, LLC
• Inventors: Frei, Mark G., Osorio, Ivan
• Granted Patent: US 7,054,792 B2
• Time in Patent Office: Days
• US Class Current: 702/79
• CPC Class Codes: G05B 23/0221 Preprocessing measurements, e.g. data collection rate adjustment; Standardization of measurements; Time series or signal analysis, e.g. frequency analysis or wavelets; Trustworthiness of measurements; Indexes therefor; Measurements using easily measured parameters to estimate parameters difficult to measure; Virtual sensor creation; De-noising; Sensor fusion; Unconventional preprocessing inherently present in specific fault detection methods like PCA-based methods
• CPC Class Codes: G06F 17/14 Fourier, Walsh or analogous domain transformations , e.g. Laplace, Hilbert, Karhunen-Loeve, transforms for correlation function computation G06F17/156; spectrum analysers G01R23/16
• CPC Class Codes: G06F 2218/02 Preprocessing
• CPC Class Codes: G06F 2218/08 Feature extraction

Abstract

A method, computer program, and system for intrinsic timescale decomposition, filtering, and automated analysis of signals of arbitrary origin or timescale including receiving an input signal into a processor, determining a baseline segment and a monotonic residual segment with strictly negative minimum and strictly positive maximum wherein said segments defined on a time interval comprising the interval between two successive extrema of the input signal and wherein the input signal on that interval is the sum of the baseline and residual segments, and producing a baseline output signal and a residual output signal wherein the baseline signal is obtained from the baseline segment and the residual signal is obtained from the residual segment such that the sum of the baseline and residual signals is equal to the input signal thereby forming a decomposition of the input signal. The method and system also includes determining at least one instantaneous frequency estimate from a proper rotation signal by inputing a proper rotation signal to a processor, determining a zero-crossing and a local extremum of the proper rotation signal, and applying linear interpolation to the proper rotation signal between the zero-crossing and the local extremum to determine an instantaneous frequency estimate of the proper rotation signal. The method and system further includes determining at least one instantaneous frequency estimate from a proper rotation signal by inputing a proper rotation signal to a processor, extracting an amplitude-normalized half wave from the proper rotation signal and applying an arcsine function to the amplitude-normalized half wave to determine an instantaneous frequency estimate of the proper rotation signal.

Claims

1. A method for decomposing an input signal into a baseline signal and a residual signal, comprising the steps of:

(a) receiving an input signal into a processor;

(b) determining a monotonic residual segment with strictly negative minimum and strictly positive maximum and a baseline segment wherein said segments defined on a time interval comprising the interval between two successive extrema of the input signal and wherein the input signal on that interval is the sum of the baseline and residual segments; and

(c) producing a baseline output signal and a residual output signal wherein the baseline signal is obtained from the baseline segment and the residual signal is obtained from the residual segment as determined in step (b), such that the sum of the baseline and residual signals is equal to the input signal thereby forming a decomposition of the input signal.

2. The method as described in claim 1, wherein the residual output signal produced in step (c) is a proper rotation.

3. The method as described in claim 1, wherein:

(a) the residual segment is monotonic with strictly negative minimum and strictly positive maximum; and

(b) the baseline and residual segments are;

(1) determined on a time interval comprising the interval between two successive extrema of the input signal, and

(2) the baseline segment comprises a transformation of the input signal on the time interval.

4. The method as described in claim 3, wherein the transformation is a linear transformation.

5. The method as described in claim 1, including the additional steps of of iteratively reapplying steps (a) through (c) to further decompose each produced baseline signal by treating each successive baseline signal as an input signal.

6. The method as described in claim 5, including the step of continuing the iterative decomposition until a pre-determined number of iterations have been completed.

7. The method as described in claim 5, including the step of continuing the iterative decomposition until a monotonic trend baseline signal is obtained.

8. The method as described in claim 5, wherein the iterative decomposition produces a resultant relatively low frequency baseline trend signal and a set of proper rotation residual signals, one for each iteration and each having a successfully lower relative frequency.

9. The method as described in claim 1, including the step of determining at least one instantaneous frequency estimate from the proper rotation residual signal using a Hilbert transform.

10. The method as described in claim 1, including the step of determining at least one instantaneous amplitude estimate from the proper rotation residual signal using a Hilbert transform.

11. The method as described in claim 1, wherein the input signal includes a sequence of data.

12. The method as described in claim 1, wherein the input signal is continuously received and the decomposition of the input signal in the interval between two successive extrema is performed upon receipt of the latter of the two successive extrema by the processor.

13. The method as described in claim 1, further including the steps of;

(a) quantifying at least one feature of a sequence of waveforms derived from at least one proper rotation signal;

(b) analyzing the resulting sequence of quantified feature values to determine which values satisfy a pre-determined set of constraints; and

(c) constructing at least one filtered signal from the waveforms corresponding to those values that satisfy the pre-determined set of constraints.

14. The method as described in claim 1, wherein the input signal consists of samples evenly spaced in time.

15. The method as described in claim 1, wherein the input signal consists of samples unevenly spaced in time.

16. The method as described in claim 1, wherein the input, baseline and residual signals are multi-dimensional.

17. The method as described in claim 1, including the step of preprocessing or applying a transformation to the input signal prior to step (b).

18. The method as described in claim 1, including the additional step of estimating the information content or complexity of the input signal by counting produced proper rotation signals in a time window.

19. A method for decomposing an input signal into a baseline signal and a residual signal wherein said residual signal will always be a proper rotation.

20. The method as described in claim 19, wherein the input signal is a pre-recorded signal from storage media.

21. A method of determining at least one instantaneous frequency estimate from a proper rotation signal, including the steps of:

(a) inputing a proper rotation signal to a processor;

(b) determining a zero-crossing and a local extremum of the proper rotation signal; and

(c) applying linear interpolation to the proper rotation signal between the zero-crossing and the local extremum to determine an instantaneous frequency estimate of the proper rotation signal.

22. A method of determining at least one instantaneous frequency estimate from a proper rotation signal, including the steps of:

(a) inputing a proper rotation signal to a processor;

(b) extracting an amplitude-normalized half wave from the proper rotation signal; and

(c) applying an arcsine function to the amplitude-normalized half wave to determine an instantaneous frequency estimate of the proper rotation signal.