System and method for extracting principal time series data

1. A method for extracting a set of principal time series data of dynamic latent variables comprising:

detecting, by a plurality of sensors, dynamic samples of data each corresponding to one of a plurality of original variables;

analyzing, using a controller, the dynamic samples of data to determine a plurality of latent variables that represent variation in the dynamic samples of data;

selecting, by the controller, at least one inner latent variable that corresponds to at least one of the plurality of original variables; and

estimating an estimated current value of the at least one inner latent variable based on previous values of the at least one inner latent variable,

wherein selecting the at least one inner latent variable includes selecting the at least one inner latent variable based on a desire for a relatively large correlation between the estimated current value of the at least one inner latent variable at a selected time and an actual current value of the at least one inner latent variable at the selected time.

2. The method of claim 1 wherein analyzing the dynamic samples of data is performed using at least one of dynamic-inner principal component analysis (DiPCA) or dynamic-inner canonical-correlation analysis (DiCCA).

3. The method of claim 1 wherein:

selecting the at least one inner latent variable of a first set of original variables includes selecting the at least one inner latent variable from the first set of original variables based on a desire for a relatively large correlation between the estimated current value of the at least one inner latent variable at a selected time and an actual current value of the at least one inner latent variable at the selected time; and

the estimated current value of the at least one inner latent variable at the selected time is estimated from at least one of past values of the at least one inner latent variable or past values of at least another inner latent variable of another set of original variables.

4. The method of claim 1 wherein the at least one inner latent variable corresponds to a dynamic relationship between at least some of the dynamic samples of data.

5. The method of claim 1 wherein the dynamic samples of data correspond to at least one of process data or equipment data used in a data-driven process.

6. The method of claim 1 wherein the dynamic samples of data contain oscillating dynamics.

7. The method of claim 1 wherein the method is utilized to perform Granger causality analysis.

8. The method of claim 1 wherein the dynamic samples of data are inner latent dynamic samples.

9. The method of claim 1 further comprising outputting, by an output device, output data corresponding to the estimated current value of the at least one inner latent variable.

10. A method for extracting a set of principal time series data of dynamic latent variables comprising:

receiving, by a controller, dynamic samples of data each corresponding to one of a plurality of original variables;

analyzing, using the controller, the dynamic samples of data to determine a plurality of latent variables that represent variation in the dynamic samples of data;

selecting, by the controller, at least one inner latent variable that corresponds to at least one of the plurality of original variables based on a desire for:

a relatively large correlation between the estimated current value of the at least one inner latent variable at the selected time and the actual current value of the at least one inner latent variable at the selected time; and

estimating, by the controller, the estimated current value of the at least one inner latent variable based on previous values of the at least one inner latent variable.

11. The method of claim 10 wherein analyzing the dynamic samples of data is performed using at least one of dynamic-inner principal component analysis (DiPCA) or dynamic-inner canonical-correlation analysis (DiCCA).

12. The method of claim 10 wherein:

selecting the at least one inner latent variable of a first set of original variables includes selecting the at least one inner latent variable from the first set of original variables based on a desire for a relatively large correlation between the estimated current value of the at least one inner latent variable at a selected time and an actual current value of the at least one inner latent variable at the selected time; and

the estimated current value of the at least one inner latent variable at the selected time is estimated from at least one of past values of the at least one inner latent variable or past values of at least another inner latent variable of another set of original variables.

13. The method of claim 10 wherein the estimated current value of the at least one inner latent variable at the selected time is estimated from at least one its past values of the at least one inner latent variable or past values of at least another inner latent variable of another set of original variables.

14. The method of claim 10 wherein the at least one inner latent variable corresponds to a dynamic relationship between at least some of the dynamic samples of data.

15. A system for extracting a set of principal time series data of dynamic latent variables comprising:

a plurality of sensors configured to detect dynamic samples of data each corresponding to one of a plurality of original variables;

an output device configured to output data; and

a controller coupled to the plurality of sensors and configured to:

analyze the dynamic samples of data to determine a plurality of latent variables that represent variation in the dynamic samples of data,

select at least one inner latent variable that corresponds to at least one of the plurality of original variables,

estimate an estimated current value of the at least one inner latent variable based on previous values of the at least one inner latent variable, and

control the output device to output data based on the estimated current value of the at least one inner latent variable,

wherein the controller is configured to select the at least one inner latent variable based on a desire for a relatively large correlation between the estimated current value of the at least one inner latent variable at a selected time and an actual current value of the at least one inner latent variable at the selected time.

16. The system of claim 15 wherein the controller is configured to analyze the dynamic samples of data using at least one of dynamic-inner principal component analysis (DiPCA) or dynamic-inner canonical-correlation analysis (DiCCA).

17. The system of claim 15 wherein the estimated current value of the at least one inner latent variable at the selected time is estimated from at least one of past values of the at least one inner latent variable or past values of at least another inner latent variable of another set of original variables.