# US 2019/0378022 A1 · Missing value imputation technique to facilitate prognostic analysis of time-series sensor data

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- Number: US 2019/0378022 A1
- Document ID: US20190378022A1
- Status: Published application
- Kind: A1
- Application number: 16/005,495
- Filed: 2018-06-11
- Published: 2019-12-12
- Earliest claimed: 2018-06-11
- Assignees: Oracle International Corporation
- Applicants: Oracle International Corporation
- Inventors: Guang C. Wang; Kenny C. Gross; Dieter Gawlick
- Web page: https://patentgrep.com/patent/US20190378022A1

## CPC

- G06N 20/10: using kernel methods, e.g. support vector machines [SVM]
- G06F 17/17: Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method ({G06F17/18 takes precedence } ; interpolation for numerical control G05B19/18)
- G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- G06F 18/214: Generating training patterns; Bootstrap methods, e.g. bagging or boosting
- G06N 5/04: Inference or reasoning models
- G06N 20/00: Machine learning
- G06N 3/08: Learning methods
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

First, the system obtains time-series sensor data. Next, the system identifies missing values in the time-series sensor data, and fills in the missing values through interpolation. The system then divides the time-series sensor data into a training set and an estimation set. Next, the system trains an inferential model on the training set, and uses the inferential model to replace interpolated values in the estimation set with inferential estimates. If there exist interpolated values in the training set, the system switches the training and estimation sets. The system trains a new inferential model on the new training set, and uses the new inferential model to replace interpolated values in the new estimation set with inferential estimates. The system then switches back the training and estimation sets. Finally, the system combines the training and estimation sets to produce preprocessed time-series sensor data, wherein missing values are filled in with imputed values.

## Claims

### Claim 1

A method for preprocessing time-series sensor data by filling in missing values with corresponding imputed values, comprising:
obtaining the time-series sensor data, which was gathered from sensors in a monitored system during operation of the monitored system;
identifying missing values in the time-series sensor data;
filling in the missing values in the time-series sensor data through interpolation;
dividing the time-series sensor data into a training set and an estimation set;
training an inferential model on the training set;
using the trained inferential model to replace interpolated values in the estimation set with corresponding inferential estimates;
when there exist interpolated values in the training set,
switching the training and estimation sets to produce a new training set and a new estimation set,
training a new inferential model on the new training set,
using the new inferential model to replace interpolated values in the new estimation set with corresponding inferential estimates, and
switching back the training and estimation sets; and
combining the training and estimation sets to produce preprocessed time-series sensor data, wherein missing values are filled in with imputed values.

### Claim 2 (depends on 1)

The method of claim 1,
wherein the inferential model is a multivariate state estimation technique (MSET) model; and
wherein using the inferential model to replace interpolated values in the estimation set with corresponding inferential estimates comprises:
using the MSET model to produce MSET estimates for the estimation set, and
replacing the interpolated values in the estimation set with corresponding MSET estimates.

### Claim 3 (depends on 1)

The method of claim 1, wherein identifying the missing values comprises:
converting timestamps in the time-series sensor data into corresponding time indices to produce a time array;
subtracting each value in the time array from a preceding value to produce a difference array; and
identifying the missing values by looking for jumps in the difference array.

### Claim 4 (depends on 1)

The method of claim 1, wherein dividing the time-series sensor data into the training set and the estimation set comprises:
selecting a first half of the time-series sensor data to be the training set; and
selecting a second half of the time-series sensor data to be the estimation set.

### Claim 5 (depends on 1)

The method of claim 1, wherein dividing the time-series sensor data into the training set and the estimation set comprises:
partitioning the time-series sensor data into a set of windows;
selecting a subset of alternating windows in the set of windows to be the training set; and
selecting a remaining subset of unselected alternating windows in the set of windows to be the estimation set.

### Claim 6 (depends on 1)

The method of claim 1, wherein the method further comprises:
training a prognostic inferential model for a prognostic pattern-recognition system based on the preprocessed time-series sensor data; and
during a surveillance mode for the prognostic pattern-recognition system,
receiving subsequently generated time-series sensor data from the monitored system,
using the prognostic inferential model to generate estimated values for the subsequently generated time-series sensor data,
performing a pairwise differencing operation between actual values and the estimated values for the subsequently generated time-series sensor data to produce residuals, and
performing a sequential probability ratio test (SPRT) on the residuals to detect incipient anomalies that arise during operation of the monitored system.

### Claim 7 (depends on 6)

The method of claim 6, wherein receiving the subsequently generated time-series sensor data involves preprocessing the subsequently generated time-series sensor data to fill in missing values with corresponding imputed values prior to using the prognostic inferential model to generate the estimated values for the subsequently generated time-series sensor data.

### Claim 8 (depends on 6)

The method of claim 6, wherein detecting the incipient anomalies comprises detecting one or more of the following:
an impending failure of the monitored system; and
a malicious-intrusion event in the monitored system.

### Claim 9 (depends on 1)

The method of claim 1, wherein obtaining the time-series sensor data comprises:
initially receiving the time-series sensor data during operation of the monitored system;
storing the time-series sensor data in a time-series database; and
subsequently retrieving the time-series sensor data from the time-series database.

### Claim 10

A non-transitory, computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for preprocessing time-series sensor data by filling in missing values with corresponding imputed values, the method comprising:
obtaining the time-series sensor data, which was gathered from sensors in a monitored system during operation of the monitored system;
identifying missing values in the time-series sensor data;
filling in the missing values in the time-series sensor data through interpolation;
dividing the time-series sensor data into a training set and an estimation set;
training an inferential model on the training set;
using the trained inferential model to replace interpolated values in the estimation set with corresponding inferential estimates;
when there exist interpolated values in the training set,
switching the training and estimation sets to produce a new training set and a new estimation set,
training a new inferential model on the new training set,
using the new inferential model to replace interpolated values in the new estimation set with corresponding inferential estimates, and
switching back the training and estimation sets; and
combining the training and estimation sets to produce preprocessed time-series sensor data, wherein missing values are filled in with imputed values.

### Claim 11 (depends on 10)

The non-transitory, computer-readable storage medium of claim 10,
wherein the inferential model is a multivariate state estimation technique (MSET) model; and
wherein using the inferential model to replace interpolated values in the estimation set with corresponding inferential estimates comprises:
using the MSET model to produce MSET estimates for the estimation set, and
replacing the interpolated values in the estimation set with corresponding MSET estimates.

### Claim 12 (depends on 10)

The non-transitory, computer-readable storage medium of claim 10, wherein identifying the missing values comprises:
converting timestamps in the time-series sensor data into corresponding time indices to produce a time array;
subtracting each value in the time array from a preceding value to produce a difference array; and
identifying the missing values by looking for jumps in the difference array.

### Claim 13 (depends on 10)

The non-transitory, computer-readable storage medium of claim 10, wherein dividing the time-series sensor data into the training set and the estimation set comprises:
selecting a first half of the time-series sensor data to be the training set; and
selecting a second half of the time-series sensor data to be the estimation set.

### Claim 14 (depends on 10)

The non-transitory, computer-readable storage medium of claim 10, wherein dividing the time-series sensor data into the training set and the estimation set comprises:
partitioning the time-series sensor data into a set of windows;
selecting a subset of alternating windows in the set of windows to be the training set; and
selecting a remaining subset of unselected alternating windows in the set of windows to be the estimation set.

### Claim 15 (depends on 10)

The non-transitory, computer-readable storage medium of claim 10, wherein the method further comprises:
training a prognostic inferential model for a prognostic pattern-recognition system based on the preprocessed time-series sensor data; and
during a surveillance mode for the prognostic pattern-recognition system,
receiving subsequently generated time-series sensor data from the monitored system,
using the prognostic inferential model to generate estimated values for the subsequently generated time-series sensor data,
performing a pairwise differencing operation between actual values and the estimated values for the subsequently generated time-series sensor data to produce residuals, and
performing a sequential probability ratio test (SPRT) on the residuals to detect incipient anomalies that arise during operation of the monitored system.

### Claim 16 (depends on 15)

The non-transitory, computer-readable storage medium of claim 15, wherein receiving the subsequently generated time-series sensor data involves preprocessing the subsequently generated time-series sensor data to fill in missing values with corresponding imputed values prior to using the prognostic inferential model to generate the estimated values for the subsequently generated time-series sensor data.

### Claim 17 (depends on 15)

The non-transitory, computer-readable storage medium of claim 15, wherein detecting the incipient anomalies comprises detecting one or more of the following:
an impending failure of the monitored system; and
a malicious-intrusion event in the monitored system.

### Claim 18 (depends on 10)

The non-transitory, computer-readable storage medium of claim 10, wherein obtaining the time-series sensor data comprises:
initially receiving the time-series sensor data during operation of the monitored system;
storing the time-series sensor data in a time-series database; and
subsequently retrieving the time-series sensor data from the time-series database.

### Claim 19

A system that preprocesses time-series sensor data by filling in missing values with corresponding imputed values, comprising:
at least one processor and at least one associated memory; and
a preprocessor that executes on the at least one processor, wherein during operation, the preprocessor:
obtains the time-series sensor data, which was gathered from sensors in a monitored system during operation of the monitored system;
identifies missing values in the time-series sensor data;
fills in the missing values in the time-series sensor data through interpolation;
divides the time-series sensor data into a training set and an estimation set;
trains an inferential model on the training set;
uses the trained inferential model to replace interpolated values in the estimation set with corresponding inferential estimates;
when there exist interpolated values in the training set,
switches the training and estimation sets to produce a new training set and a new estimation set,
trains a new inferential model on the new training set,
uses the new inferential model to replace interpolated values in the new estimation set with corresponding inferential estimates, and
switches back the training and estimation sets; and
combines the training and estimation sets to produce preprocessed time-series sensor data, wherein missing values are filled in with imputed values.

### Claim 20 (depends on 19)

The system of claim 19,
wherein the inferential model is a multivariate state estimation technique (MSET) model; and
wherein while using the inferential model to replace interpolated values in the estimation set with corresponding inferential estimates, the preprocessor:
uses the MSET model to produce MSET estimates for the estimation set, and
replaces the interpolated values in the estimation set with corresponding MSET estimates.