Maximizing the operational range for training parameters while selecting training vectors for a machine-learning model

1. A method for training an inferential model based on selected training vectors, comprising:

receiving training data comprising observations for a set of time-series signals gathered from sensors in a monitored system during normal fault-free operation;

dividing the observations into N subgroups comprising non-overlapping time windows of observations;

selecting observations with a local minimum value and a local maximum value for all signals from each subgroup to be training vectors for the inferential model by:

dividing each subgroup into a training set and a validation set by sequencing through consecutive even/odd pairs of observations in the subgroup and assigning one observation in each pair to the training set and another observation in each pair to the validation set;

swapping members of pairs of observations between the training set and the validation set as necessary to ensure that the local minimum value and the local maximum value for each subgroup fall into the training set; and

selecting a user-specified number of observations with the local minimum value and the local maximum value from the training set to be the training vectors for the inferential model; and

training the inferential model using the selected training vectors.

2. The method of claim 1 , wherein selecting observations with local minimum and maximum values to be training vectors maximizes an operational range for the training vectors, which reduces clipping in estimates subsequently produced by the inferential model and thereby reduces false alarms.

3. The method of claim 1 , wherein the method further comprises using the validation set to tune parameters for the inferential model by:

evaluating an error function while running the inferential model on observations from the validation set; and

keeping parameters of the inferential model that have the smallest errors with respect to the validation set.

4. The method of claim 3 , wherein after tuning the inferential model based on the validation set, the method further comprises performing a final evaluation of the inferential model by running the inferential model on a testing dataset comprising observations for the set of time-series signals that are independent of the training data.

5. The method of claim 1 , wherein during a surveillance mode, the method further comprises:

using the inferential model to generate estimated values based on subsequently received time-series signals from the monitored system;

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

analyzing the residuals to detect the incipient anomalies in the monitored system.

6. The method of claim 5 , wherein analyzing the residuals involves:

performing a sequential probability ratio test (SPRT) on the residuals to produce SPRT alarms; and

detecting the incipient anomalies based on the SPRT alarms.

7. The method of claim 5 , wherein detecting the incipient anomalies in the monitored system comprises detecting one or more of the following:

an impending failure of the monitored system; and

a malicious-intrusion event in the monitored system.

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

9. A non-transitory computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for training an inferential model based on selected training vectors, the method comprising:

receiving training data comprising observations for a set of time-series signals gathered from sensors in a monitored system during normal fault-free operation;

dividing the observations into N subgroups comprising non-overlapping time windows of observations;

selecting observations with a local minimum value and a local maximum value for all signals from each subgroup to be training vectors for the inferential model by:

dividing each subgroup into a training set and a validation set by sequencing through consecutive even/odd pairs of observations in the subgroup and assigning one observation in each pair to the training set and another observation in each pair to the validation set;

swapping members of pairs of observations between the training set and the validation set as necessary to ensure that the local minimum value and the local maximum value for each subgroup fall into the training set; and

selecting a user-specified number of observations with the local minimum value and the local maximum value from the training set to be the training vectors for the inferential model; and

training the inferential model using the selected training vectors.

10. The non-transitory computer-readable storage medium of claim 9 , wherein selecting the observations with local minimum and maximum values to be training vectors maximizes an operational range for the training vectors, which reduces clipping in estimates subsequently produced by the inferential model and thereby reduces false alarms.

11. The non-transitory computer-readable storage medium of claim 9 , wherein the method further comprises using the validation set to tune parameters for the inferential model by:

evaluating an error function while running the inferential model on observations from the validation set; and

keeping parameters of the inferential model that have the smallest errors with respect to the validation set.

12. The non-transitory computer-readable storage medium of claim 11 , wherein after tuning the inferential model based on the validation set, the method further comprises performing a final evaluation of the inferential model by running the inferential model on a testing dataset comprising observations for the set of time-series signals that are independent of the training data.

13. The non-transitory computer-readable storage medium of claim 11 , wherein during a surveillance mode, the method further comprises:

using the inferential model to generate estimated values based on subsequently received time-series signals from the monitored system;

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

analyzing the residuals to detect the incipient anomalies in the monitored system.

14. The non-transitory computer-readable storage medium of claim 13 , wherein analyzing the residuals involves:

performing a sequential probability ratio test (SPRT) on the residuals to produce SPRT alarms; and

detecting the incipient anomalies based on the SPRT alarms.

15. The non-transitory computer-readable storage medium of claim 13 , wherein detecting the incipient anomalies in the monitored system comprises detecting one or more of the following:

an impending failure of the monitored system; and

a malicious-intrusion event in the monitored system.

16. A system that trains an inferential model based on selected training vectors, comprising:

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

a training mechanism that executes on the at least one processor, wherein during operation, the training mechanism trains an inferential model based on selected training vectors, wherein during the training process, the training mechanism:

receives training data comprising observations for a set of time-series signals gathered from sensors in a monitored system during normal fault-free operation;

divides the observations into N subgroups comprising non-overlapping time windows of observations;

selects observations with a local minimum value and a local maximum value for all signals from each subgroup to be training vectors for the inferential model by:

dividing each subgroup into a training set and a validation set by sequencing through consecutive even/odd pairs of observations in the subgroup and assigning one observation in each pair to the training set and another observation in each pair to the validation set;

swapping members of pairs of observations between the training set and the validation set as necessary to ensure that the local minimum value and the local maximum value for each subgroup fall into the training set; and

selecting a user-specified number of observations with the local minimum value and the local maximum value from the training set to be the training vectors for the inferential model; and

trains the inferential model using the selected training vectors.

17. The system of claim 16 , wherein selecting observations with local minimum and maximum values to be training vectors maximizes an operational range for the training vectors, which reduces clipping in estimates subsequently produced by the inferential model and thereby reduces false alarms.