Compensating for out-of-phase seasonality modes in time-series signals to facilitate prognostic-surveillance operations

1. A method for performing seasonality-compensated prognostic-surveillance operations for an asset, comprising:

obtaining time-series sensor signals (S 1 ) gathered from sensors in the asset during operation of the asset;

identifying two or more seasonality modes in the time-series sensor signals by:

determining serial correlations for the time-series sensor signals;

decomposing the serial correlations into an envelope of overlapping sinusoids; and

using the envelope of overlapping sinusoids to construct a corresponding Fourier composite (S 2 );

determining frequencies and corresponding lead/lag times for the identified two or more seasonality modes;

using the determined frequencies and corresponding lead/lag times to filter out the identified two or more seasonality modes from the time-series sensor signals to produce seasonality-compensated time-series sensor signals, wherein determining both frequencies and corresponding lead/lag times for the identified seasonality modes improves accuracy in filtering out multiple seasonality modes from the time-series sensor signals;

applying an inferential model to the seasonality-compensated time-series sensor signals to detect incipient anomalies that arise during operation of the asset; and

when an incipient anomaly is detected, generating a notification regarding the anomaly.

2. The method of claim 1 , wherein applying the inferential model to the seasonality-compensated time-series sensor signals involves:

using the inferential model to generate estimated values for the seasonality-compensated time-series sensor signals;

performing a pairwise differencing operation between actual values and the estimated values for the seasonality-compensated time-series sensor signals to produce residuals; and

performing a sequential probability ratio test on the residuals to detect the incipient anomalies that arise during operation of the asset.

3. The method of claim 1 , wherein prior to obtaining time-series sensor signals, the method further comprises training the inferential model by:

obtaining optimal time-series sensor signals gathered from sensors in the asset during optimal, error-free operation of the asset;

identifying seasonality modes in the optimal time-series sensor signals;

determining associated frequencies and corresponding lead/lag times for the identified seasonality modes;

using the determined frequencies and corresponding lead/lag times to filter out the seasonality modes from the optimal time-series sensor signals to produce seasonality-compensated optimal time-series sensor signals; and

training the inferential model using the seasonality-compensated optimal time-series sensor signals.

4. The method of claim 1 , wherein identifying the two or more seasonality modes in the time-series sensor signals further involves:

determining a magnitude-squared coherence between S 1 and S 2 ; and

applying a Heaviside step function to the magnitude-squared coherence to produce N steps, wherein each step is associated with a seasonality mode in the two or more seasonality modes.

5. The method of claim 4 , wherein determining the associated frequencies and corresponding lead/lag times for the identified two or more seasonality modes comprises:

computing a cross power spectral density (CPSD) of S 1 and S 2 ; and

for each step i of the N steps produced by the Heaviside step function, performing the following operations,

retrieving a maximum magnitude-squared coherence for step i,

determining a frequency associated with the maximum magnitude- squared coherence, and

using the computed CPSD to determine a phase lead/lag associated with the determined frequency.

6. The method of claim 5 , wherein while using the determined frequencies and corresponding lead/lag times to filter out the seasonality modes, the method further comprises converting each determined phase lead/lag into a corresponding lead/lag time by dividing each determined phase lead/lag by an associated frequency.

7. The method of claim 1 , wherein the inferential model comprises a Multivariate State Estimation Technique (MSET) model.

8. The method of claim 1 , wherein the incipient anomalies comprise indicators of an impending failure of the asset.

9. A non-transitory, computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for performing seasonality-compensated prognostic-surveillance operations for an asset, the method comprising:

obtaining time-series sensor signals (S 1 ) gathered from sensors in the asset during operation of the asset;

identifying two or more seasonality modes in the time-series sensor signals by:

determining serial correlations for the time-series sensor signals;

decomposing the serial correlations into an envelope of overlapping sinusoids; and

using the envelope of overlapping sinusoids to construct a corresponding Fourier composite (S 2 );

determining frequencies and corresponding lead/lag times for the identified two or more seasonality modes;

using the determined frequencies and corresponding lead/lag times to filter out the identified two or more seasonality modes from the time-series sensor signals to produce seasonality-compensated time-series sensor signals, wherein determining both frequencies and corresponding lead/lag times for the identified seasonality modes improves accuracy in filtering out multiple seasonality modes from the time-series sensor signals;

applying an inferential model to the seasonality-compensated time-series sensor signals to detect incipient anomalies that arise during operation of the asset; and

when an incipient anomaly is detected, generating a notification regarding the anomaly.

10. The non-transitory, computer-readable storage medium of claim 9 , wherein applying the inferential model to the seasonality-compensated time-series sensor signals involves:

using the inferential model to generate estimated values for the seasonality-compensated time-series sensor signals;

performing a pairwise differencing operation between actual values and the estimated values for the seasonality-compensated time-series sensor signals to produce residuals; and

performing a sequential probability ratio test on the residuals to detect the incipient anomalies that arise during operation of the asset.

11. The non-transitory, computer-readable storage medium of claim 9 , wherein prior to obtaining time-series sensor signals, the method further comprises training the inferential model by:

obtaining optimal time-series sensor signals gathered from sensors in the asset during optimal, error-free operation of the asset;

identifying seasonality modes in the optimal time-series sensor signals;

determining associated frequencies and corresponding lead/lag times for the identified seasonality modes;

using the determined frequencies and corresponding lead/lag times to filter out the seasonality modes from the optimal time-series sensor signals to produce seasonality-compensated optimal time-series sensor signals; and

training the inferential model using the seasonality-compensated optimal time-series sensor signals.

12. The non-transitory, computer-readable storage medium of claim 9 , wherein identifying the two or more seasonality modes in the time-series sensor signals further involves:

determining a magnitude-squared coherence between S 1 and S 2 ; and

applying a Heaviside step function to the magnitude-squared coherence to produce N steps, wherein each step is associated with a seasonality mode in the two or more seasonality modes.

13. The non-transitory, computer-readable storage medium of claim 12 , wherein determining the associated frequencies and corresponding lead/lag times for the identified two or more seasonality modes comprises:

computing a CPSD of S 1 and S 2 ; and

for each step i of the N steps produced by the Heaviside step function, performing the following operations,

retrieving a maximum magnitude-squared coherence for step i,

determining a frequency associated with the maximum magnitude-squared coherence, and

using the computed CPSD to determine a phase lead/lag associated with the determined frequency.

14. The non-transitory, computer-readable storage medium of claim 9 , wherein while using the determined frequencies and corresponding lead/lag times to filter out the seasonality modes, the method further comprises converting each determined phase lead/lag into a corresponding lead/lag time by dividing each determined phase lead/lag by an associated frequency.

15. The non-transitory, computer-readable storage medium of claim 9 , wherein the inferential model comprises an MSET model.

16. The non-transitory, computer-readable storage medium of claim 9 , wherein the incipient anomalies comprise indicators of an impending failure of the asset.

17. A system that performs seasonality-compensated prognostic-surveillance operations for an asset, comprising:

at least one processor and at least one associated memory; and

a prognostic-surveillance mechanism that executes on the at least one processor, wherein during operation, the prognostic-surveillance mechanism:

obtains time-series sensor signals (S 1 ) gathered from sensors in the asset during operation of the asset;

identifies two or more seasonality modes in the time-series sensor signals by:

determining serial correlations for the time-series sensor signals;

decomposing the serial correlations into an envelope of overlapping sinusoids; and

using the envelope of overlapping sinusoids to construct a corresponding Fourier composite (S 2 );

determines frequencies and corresponding lead/lag times for the identified two or more seasonality modes;

uses the determined frequencies and corresponding lead/lag times to filter out the identified two or more seasonality modes from the time-series sensor signals to produce seasonality-compensated time-series sensor signals, wherein determining both frequencies and corresponding lead/lag times for the identified seasonality modes improves accuracy in filtering out multiple seasonality modes from the time-series sensor signals;

applies an inferential model to the seasonality-compensated time-series sensor signals to detect incipient anomalies that arise during operation of the asset; and

when an incipient anomaly is detected, generates a notification regarding the anomaly.

18. The system of claim 17 , wherein while applying the inferential model to the seasonality-compensated time-series sensor signals, the system:

uses the inferential model to generate estimated values for the seasonality-compensated time-series sensor signals;

performs a pairwise differencing operation between actual values and the estimated values for the seasonality-compensated time-series sensor signals to produce residuals; and

performs a sequential probability ratio test on the residuals to detect the incipient anomalies that arise during operation of the asset.

19. The system of claim 17 , wherein while identifying the two or more seasonality modes in the time-series sensor signals, the system:

determines serial correlations for the time-series sensor signals;

decomposes the serial correlations into an envelope of overlapping sinusoids;

uses the envelope of overlapping sinusoids to construct a corresponding Fourier composite (S 2 );

determines a magnitude-squared coherence between S 1 and S 2 ; and

applies a Heaviside step function to the magnitude-squared coherence to produce N steps, wherein each step is associated with a seasonality mode in the two or more seasonality modes.

20. The system of claim 19 , wherein while determining the associated frequencies and corresponding lead/lag times for the identified two or more seasonality modes, the system:

computes a CPSD of S 1 and S 2 ; and

for each step i of the N steps produced by the Heaviside step function, performs the following operations,

retrieves a maximum magnitude-squared coherence for step i,

determines a frequency associated with the maximum magnitude-squared coherence, and

uses the computed CPSD to determine a phase lead/lag associated with the determined frequency.