Robust sensor correlation analysis for machine condition monitoring

• US 7,769,561 B2
• Filed: 11/27/2006
• Issued: 08/03/2010
• Est. Priority Date: 12/01/2005
• Status: Expired due to Fees

• Current Assignee: Siemens Corp. (Siemens AG)
• Original Assignee: Siemens Corp. (Siemens AG)
• Inventors: Balderer, Christian, Huang, Tzu-Kuo, Neubauer, Claus, Yuan, Chao
• Primary Examiner(s): Tsai; Carol S
• Assistant Examiner(s): Ngon; Ricky
• Application Number:
  US11/563,396
• Publication Number:
  US 20070162241A1
• Time in Patent Office: 1,345 Days
• Field of Search: 702/179, 702/81, 702/82, 702/83, 702/84
• US Class Current: 702/179
• CPC Class Codes: G05B 19/4065 Monitoring tool breakage, life or condition
• CPC Class Codes: G05B 2219/37508 Cross correlation
• CPC Class Codes: G05B 23/024 Quantitative history assessment, e.g. mathematical relationships between available data; Functions therefor; Principal component analysis [PCA]; Partial least square [PLS]; Statistical classifiers, e.g. Bayesian networks, linear regression or correlation analysis; Neural networks

Abstract

A method for monitoring machine conditions is based on machine learning through the use of a statistical model. A correlation coefficient is calculated using weights assigned to each sample that indicate the likelihood that that sample is an outlier. The resulting correlation coefficient is more robust against outliers. The calculation of the weight is based on the Mahalanobis distance from the sample to the sample mean. Additionally, hierarchical clustering is applied to intuitively reveal group information among sensors. By specifying a similarity threshold, the user can easily obtain desired clustering results.

Claims

1. A method for machine condition monitoring, comprising the steps of:

in a machine condition monitoring system processor, determining a robust correlation coefficient ρ

_xy between pairs of sensors using data from a group of samples (x_i, y_i) from the pairs of sensors, the robust correlation coefficient ρ

_xy being determined by;

initializing a weight w_i for each sample (x_i, y_i), wherein 0≦

w_i≦

1 and Σ

w_i=1, each weight w_i being proportional to an inverse of a distance between the sample (x_i, y_i) and a sample mean;

estimating a mean μ and

covariance matrix Ω

of the sample as

μ

=Σ

w_iz_i and Ω

=Σ

w_i(z_i−

μ

)(z_i−

μ

)^T,

wherein z_i=[x_iy_i]^T;

updating the weight w_i for each observation (x_i,y_i) as

2. The method of claim 1, further comprising the step of:

clustering the sensors based on the robust correlation coefficient.

3. The method of claim 2, wherein the clustering is a hierarchical clustering.

4. The method of claim 2, wherein the step of clustering the sensors further comprises:

initializing a cluster list by placing each sensor in its own cluster C_i;

determining distances between pairs of clusters

5. A method for machine condition monitoring, comprising the steps of:

receiving a group of readings from a plurality of sensors;

in a machine condition monitoring system processor, for at least one pair of sensors (x, y) of the plurality of sensors, determining a robust correlation coefficient ρ

_xy, using a plurality of samples (x_i, y_i) from the group of readings, and using a weight w_i for each sample (x_i, y_i) based on how closely the sample obeys a joint distribution of the readings of the pair of sensors (x, y), the robust correlation coefficient being calculated as

6. The method of claim 5, wherein the weights w_i are determined by:

initializing the weight w_i for each sample (x_i, y_i), wherein 0≦

w_i≦

1 and Σ

w_i=1, each w_i being proportional to an inverse of a distance between the sample (x_i, y_i) and a sample mean;

estimating a mean μ and

covariance matrix Ω

of the sample as

μ

=Σ

w_iz_i and Ω

=Σ

w_i(z_i−

μ

)(z_i−

μ

)^T,

wherein z_i=[x_iy_i]^T;

updating the weight w_i for each sample (x_i,y_i) as

7. The method of claim 5, wherein the step of clustering the sensors further comprises:

initializing a cluster list by placing each sensor in its own cluster C_i;

determining distances between pairs of clusters

8. The method of claim 7, further comprising the step of:

adjusting the threshold to adjust a dissimilarity of sensors in each cluster.

9. The method of claim 5, wherein the weight w_i for each sample (x_i, y_i) is further based on a Mahalanobis distance from the sample to a sample mean.

10. A non-transitory computer-usable medium having computer readable instructions stored thereon for execution by a processor to perform a method comprising:

receiving a group of readings from a plurality of sensors;

for at least one pair of sensors (x, y) of the plurality of sensors, determining a robust correlation coefficient ρ

_xy, using a plurality of samples (x_i, y_i) from the group of readings, and using a weight w_i for each sample (x_i, y_i) based on how closely the sample obeys a joint distribution of the readings of the pair of sensors (x, y), the robust correlation coefficient being calculated as

11. The non-transitory computer-usable medium of claim 10, wherein the weights w_i are determined by:

initializing the weight w_i for each sample (x_i, y_i), wherein 0≦

w_i≦

1 and Σ

w_i=1, each w_i being proportional to an inverse of a distance between the sample (x_i, y_i) and a sample mean;

estimating a mean μ and

covariance matrix Ω

of the sample as

μ

=Σ

w_iz_i and Ω

=Σ

w_i(z_i−

μ

)(z_i−

μ

)^T,

wherein z_i=[x_iy_i]^T;

updating the weight w_i for each sample (x_i,y_i) as

12. The non-transitory computer-usable medium of claim 10, wherein the step of clustering the sensors further comprises:

initializing a cluster list by placing each sensor in its own cluster C_i;

determining distances between pairs of clusters