Transferring failure samples using conditional models for machine condition monitoring

• US 10,108,513 B2
• Filed: 04/16/2014
• Issued: 10/23/2018
• Est. Priority Date: 04/16/2014
• Status: Active Grant

• Current Assignee: Siemens AG
• Original Assignee: Siemens AG
• Inventors: Yuan, Chao, Chakraborty, Amit, Hackstein, Holger, Weber, Hans
• Primary Examiner(s): LE, DIEU MINH T
• Application Number:
  US15/303,243
• Publication Number:
  US 20170031792A1
• Time in Patent Office: 1,651 Days
• Field of Search: 714 473, 714 471, 714 472, 714 26, 714 1
• CPC Class Codes: G05B 23/0224 Process history based detection method, e.g. whereby history implies the availability of large amounts of data
• CPC Class Codes: G06F 11/2257 using expert systems
• CPC Class Codes: G06N 20/00 Machine learning
• CPC Class Codes: G06N 20/10 using kernel methods, e.g. support vector machines [SVM]

Abstract

A method for predicting failure modes in a machine includes learning (31) a multivariate Gaussian distribution for each of a source machine and a target machine from data samples from one or more independent sensors of the source machine and the target machine, learning (32) a multivariate Gaussian conditional distribution for each of the source machine and the target machine from data samples from one or more dependent sensors of the source machine and the target machine using the multivariate Gaussian distribution for the independent sensors, transforming (33) data samples for the independent sensors from the source machine to the target machine using the multivariate Gaussian distributions for the source machine and the target machine, and transforming (34) data samples for the dependent sensors from the source machine to the target machine using the transformed independent sensor data samples and the conditional Gaussian distributions for the source machine and the target machine.

Claims

1. A computer-implemented method for predicting failure modes in a machine, the method implemented by the computer comprising:

learning a multivariate Gaussian distribution for each of a source machine and a target machine from data samples from one or more independent sensors of the source machine and the target machine, wherein said data samples are acquired under normal operating conditions for each machine;

learning a multivariate Gaussian conditional distribution for each of the source machine and the target machine from data samples from one or more dependent sensors of said source machine and said target machine using the multivariate Gaussian distribution for the independent sensors, wherein said data samples are acquired under normal operating conditions for each machine;

transforming data samples for the independent sensors from the source machine to the target machine using the multivariate Gaussian distributions for the source machine and the target machine;

transforming data samples for the dependent sensors from the source machine to the target machine using the transformed independent sensor data samples and the conditional Gaussian distributions for the source machine and the target machine,

acquiring data samples from the independent sensors of the source machine associated with a failure;

transforming said failure data samples for the independent sensors from the source machine to the target machine using the multivariate Gaussian distributions for the source machine and the target machine; and

transforming said failure data samples for the dependent sensors from the source machine to the target machine using the transformed independent sensor data samples and the conditional Gaussian distributions for the source machine and the target machine.

2. The method of claim 1, wherein the multivariate Gaussian conditional distribution is expressed as y_i|x_i˜

N(f_i(x_i), C_yi(x_i)), where y_i represents a dependent sensor, x_i represents an independent sensor, f_i(x₁) represents a mean of the multivariate Gaussian conditional distribution of independent sensor x_i, and C_yi(x_i) represents a conditional covariance of dependent sensor y_i given independent sensor x_i.

3. The method of claim 2, wherein the conditional covariance C_yi(x_i) is a diagonal matrix.

4. The method of claim 3, wherein the conditional covariance C_yi(x_i) is a constant.

5. The method of claim 2, wherein the transformation of independent sensor data samples from the source machine to the target machine is expressed by

x₁₂=C_x2^1/2C_x1⁻

1/2(x₁−

m_x1)+m_x2,

wherein x₁ represents independent sensor data for the source machine, m_x1 is a mean of the multivariate Gaussian distribution of an independent sensor of the source machine, m_x2 is a mean of the multivariate Gaussian distribution of an independent sensor of the target machine, C_x1 is a covariance of the multivariate Gaussian distribution of an independent sensor of the source machine, and C_x2 is a covariance of the multivariate Gaussian distribution of an independent sensor of the target machine.

6. The method of claim 5, wherein the transformation of dependent sensor data samples from the source machine to the target machine is expressed by

y₁₂=C_y2^1/2(x₁₂)C_y1⁻

1/2(x₁)(y₁−

f₁(x₁))+f₂(x₁₂), wherein

y₁ represents dependent sensor data for the source machine, y₂ represents dependent sensor data for the target machine, f₁(x₁) is the mean of the multivariate conditional distribution of an independent sensor of the source machine, f₂(x₁₂) is the mean of the multivariate conditional distribution of the transformed independent sensor for the target machine, C_y1(x₁) is a covariance of the multivariate Gaussian distribution of a dependent sensor y₁ given independent sensor x₁ for the source machine, and C_y2(x₁₂) is a covariance of the multivariate Gaussian distribution of a dependent sensor y₂ of the target machine given the transformed independent sensor x₁₂.

7. The method of claim 6, wherein the mean of the multivariate conditional distribution for a given machine is a regression function that maps independent sensor data for the given machine to dependent sensor data for the given machine, wherein the given machine is one of the source machine and the target machine.

8. The method of claim 1, further comprising receiving sensor data samples for each of a source machine and a target machine, and partitioning sensor data samples for each machine into data from independent sensors, and data from dependent sensors that depend on data values of the independent sensors.

9. The method of claim 1, further comprising:

learning the multivariate Gaussian distributions for the source machine and the target machine from the data samples from the independent sensors of the source machine and the target machine; and

learning the multivariate Gaussian conditional distributions for the source machine and the target machine from the data samples from the dependent sensors of said source machine and said target machine using the multivariate Gaussian distribution for the independent sensors.

10. A computer-implemented method for predicting failure modes in a machine, the method implemented by the computer comprising:

receiving sensor data samples for each of a source machine and a target machine, and partitioning sensor data samples for each machine into data from one or more independent sensors, and data from one or more dependent sensors whose sensor values depend on data values of the independent sensors, wherein said data samples are acquired under normal operating conditions for each machine;

transforming data samples for the independent sensors from the source machine to the target machine using a multivariate Gaussian distribution for the source machine and a multivariate Gaussian distribution for the target machine;

transforming data samples for the dependent sensors from the source machine to the target machine using the transformed independent sensor data samples and a conditional Gaussian distribution for the source machine and a conditional Gaussian distribution for the target machine;

acquiring data samples from the independent sensors of the source machine associated with a failure;

transforming said failure data samples for the independent sensors from the source machine to the target machine using the multivariate Gaussian distributions for the source machine and the target machine; and

transforming said failure data samples for the dependent sensors from the source machine to the target machine using the transformed independent sensor data samples and the conditional Gaussian distributions for the source machine and the target machine.

11. A non-transitory program storage device readable by a computer, tangibly embodying a program of instructions executed by the computer to perform the method steps for predicting failure modes in a machine, the method comprising:

learning a multivariate Gaussian distribution for each of a source machine and a target machine from data samples from one or more independent sensors of the source machine and the target machine, wherein said data samples are acquired under normal operating conditions for each machine;

learning a multivariate Gaussian conditional distribution for each of the source machine and the target machine from data samples from one or more dependent sensors of said source machine and said target machine using the multivariate Gaussian distribution for the independent sensors, wherein said data samples are acquired under normal operating conditions for each machine;

transforming data samples for the independent sensors from the source machine to the target machine using the multivariate Gaussian distributions for the source machine and the target machine;

transforming data samples for the dependent sensors from the source machine to the target machine using the transformed independent sensor data samples and the conditional Gaussian distributions for the source machine and the target machine,

acquiring data samples from the independent sensors of the source machine associated with a failure;

transforming said failure data samples for the independent sensors from the source machine to the target machine using the multivariate Gaussian distributions for the source machine and the target machine; and

transforming said failure data samples for the dependent sensors from the source machine to the target machine using the transformed independent sensor data samples and the conditional Gaussian distributions for the source machine and the target machine.

12. The computer readable program storage device of claim 11, wherein the multivariate Gaussian conditional distribution is expressed as y_i|x_i˜

N(f_i(x_i), C_yi(x_i)), where y_i represents a dependent sensor, x_i represents an independent sensor, f_i(x₁) represents a mean of the multivariate Gaussian conditional distribution of independent sensor x_i, and C_yi(x_i) represents a conditional covariance of dependent sensor y_i given independent sensor x_i.

13. The computer readable program storage device of claim 12, wherein the conditional covariance C_yi(x_i) is a diagonal matrix.

14. The computer readable program storage device of claim 13, wherein the conditional covariance C_yi(x_i) is a constant.

15. The computer readable program storage device of claim 12, wherein the transformation of independent sensor data samples from the source machine to the target machine is expressed by

x₁₂=C_x2^1/2C_x1⁻

1/2(x₁−

m_x1)+m_x2,

wherein x₁ represents independent sensor data for the source machine, m_x1 is a mean of the multivariate Gaussian distribution of an independent sensor of the source machine, m_x2 is a mean of the multivariate Gaussian distribution of an independent sensor of the target machine, C_x1 is a covariance of the multivariate Gaussian distribution of an independent sensor of the source machine, and C_x2 is a covariance of the multivariate Gaussian distribution of an independent sensor of the target machine.

16. The computer readable program storage device of claim 15, wherein the transformation of dependent sensor data samples from the source machine to the target machine is expressed by

y₁₂=C_y2^1/2(x₁₂)C_y1⁻

1/2(x₁)(y₁−

f₁(x₁))+f₂(x₁₂), wherein

y₁ represents dependent sensor data for the source machine, y₂ represents dependent sensor data for the target machine, f₁(x₁) is the mean of the multivariate conditional distribution of an independent sensor of the source machine, f₂(x₁₂) is the mean of the multivariate conditional distribution of the transformed independent sensor for the target machine, C_y1(x₁) is a covariance of the multivariate Gaussian distribution of a dependent sensor y₁ given independent sensor x₁ for the source machine, and C_y2(x₁₂) is a covariance of the multivariate Gaussian distribution of a dependent sensor y₂ of the target machine given the transformed independent sensor x₁₂.

17. The computer readable program storage device of claim 16, wherein the mean of the multivariate conditional distribution for a given machine is a regression function that maps independent sensor data for the given machine to dependent sensor data for the given machine, wherein the given machine is one of the source machine and the target machine.

18. The computer readable program storage device of claim 11, the method further comprising receiving sensor data samples for each of a source machine and a target machine, and partitioning sensor data samples for each machine into data from independent sensors, and data from dependent sensors that depend on data values of the independent sensors.