Method and apparatus for selecting condition indicators in determining the health of a component
Disclosed are techniques used in connection with determining a health indicator (HI) of a component, such as that of an aircraft component. The HI is determined using condition indicators (CIs) which parameterize characteristics about a component minimizing possibility of a false alarm. Different algorithms are disclosed which may be used in determining one or more CIs. The HI may be determined using a normalized CI value. Techniques are also described in connection with selecting particular CIs that provide for maximizing separation between HI classifications. Given a particular HI at a point in time for a component, techniques are described for predicting a future state or health of the component using the Kalman filter. Techniques are described for estimating data values as an alternative to performing data acquisitions, as may be used when there is no pre-existing data.
1. A method for ranking condition indicators used in determining a health indicator for a component comprising:
receiving a first set of a plurality of said condition indicators and a whitening transformation matrix that whitens a covariance matrix of said first set of said plurality of condition indicators;
determining differences between expected values for a plurality of health classes used for a between health class scatter matrix;
determining a whitened transformation of said between health class scatter matrix using said whitening transformation matrix; and
selecting a portion of said plurality of condition indicators in accordance with those condition indicators which have a largest corresponding value in said whitened transformation of said between health class scatter matrix.
2. The method of claim 1 , wherein said whitened transformation of said between health class scatter matrix has diagonal values, each of said diagonal values corresponds to one of said condition indicators, and the method further comprising:
sorting said diagonals in descending order.
3. The method of claim 1 , wherein said first plurality of condition indicators correspond to an observed data acquisition.
4. A method for ranking condition indicators used in determining a health indicator for a component comprising:
determining a first set of a plurality of said condition indicators;
determining a covariance matrix corresponding to said plurality of condition indicators;
determining a whitening transformation matrix that whitens the covariance matrix;
using said whitening transformation matrix to determine differences between said first plurality of condition indicators and expected values for said condition indicators belonging to a health class, each health class having a corresponding health indicator;
selecting a portion of said plurality of condition indicators in accordance with those condition indicators which have the smallest of said differences; and
determining a measure of between class scatter, Sb, represented as:
S
b
=
∑
i
=
1
L
P
i
(
M
i
-
M
0
)
(
M
i
-
M
0
)
T
,
M
0
=
∑
i
=
1
L
P
i
M
i
,
where M0 is an expected value of all L classes, Mi represents an expected value of a particular class, and Pi is the probability of a class i.
5. The method of claim 4 , further comprising:
determining a whitening transformation of Sb as Sbw represented as:
S bw =A T S b A, for the whitening transformation matrix A.
6. The method of claim 5 , wherein said whitening transformation matrix A is:
Λ −1/2 Φ T with a corresponding eigenvalue matrix Λ and a corresponding eigenvector matrix Φ.
7. A computer program product for ranking condition indicators used in determining a health indicator for a component comprising machine executable code for:
receiving a first set of a plurality of said condition indicators and a whitening transformation matrix that whitens a covariance matrix of said first set of said plurality of condition indicators;
determining differences between expected values for a plurality of health classes for use in a between health class scatter matrix;
determining a whitened transformation of said between health class scatter matrix using said whitening transformation matrix; and
selecting a portion of said plurality of condition indicators in accordance with those condition indicators which have a largest corresponding value in said whitened transformation of said between health class scatter matrix.
8. The computer program product of claim 7 , wherein said whitened transformation of said between health class scatter matrix has diagonal values, each of said diagonal values corresponds to one of said condition indicators, and the computer program product further comprising machine executable code for:
sorting said diagonals in descending order.
9. The computer program product of claim 7 , wherein said first plurality of condition indicators correspond to an observed data acquisition.
10. A computer program product for ranking condition indicators used in determining a health indicator for a component comprising machine executable code for:
determining a first set of a plurality of said condition indicators;
determining a covariance matrix corresponding to said plurality of condition indicators;
determining a whitening transformation matrix that whitens the covariance matrix;
using said whitening transformation matrix to determine differences between said first plurality of condition indicators and expected values for said condition indicators belonging to a health class, each health class having a corresponding health indicator;
selecting a portion of said plurality of condition indicators in accordance with those condition indicators which have the smallest of said differences; and
determining a measure of between class scatter, Sb, represented as:
S
b
=
∑
i
=
1
L
P
i
(
M
i
-
M
0
)
(
M
i
-
M
0
)
T
,
M
0
=
∑
i
=
1
L
P
i
M
i
,
where M0 is an expected value of all L classes, Mi represents an expected value of a particular class, and Pi is the probability of a class i.
11. The computer program product of claim 10 , further comprising machine executable code for:
determining a whitening transformation of Sb as Sbw represented as:
S bw =A T S b A, for the whitening transformation matrix A.
12. The computer program product of claim 11 , wherein said whitening transformation matrix A is:
Λ −1/2 Φ T with a corresponding eigenvalue matrix Λ and a corresponding eigenvector matrix Φ.
13. The method of claim 4 , further comprising:
determining a measure of within class scatter, S w , as a weighted average of class covariance represented as:
S
W
=
∑
i
=
1
L
P
i
∑
i
for each class, i, where P 1 is a probability of occurrence of a covariance Σ i for the ith class.
14. The method of claim 13 , further comprising:
using diagonal values of S w −1 S b in selecting said portion of said plurality of indicators.
15. A method for selecting one or more condition indicators used in determining a health indicator corresponding to a health class for a component comprising:
determining a first set of one or more condition indicators;
determining a covariance matrix for said first set of condition indicators;
determining a whitening transformation matrix that whitens the covariance matrix;
using said whitening transformation matrix that whitens the covariance matrix to normalize differences between mean values of different health classes producing a whitened between class scatter matrix; and
selecting a portion of said first set of condition indicators in accordance with corresponding diagonals of said whitened between class scatter matrix.
16. The method of claim 15 , further comprising:
sorting diagonals of said whitened between class scatter matrix; and
selecting said portion of said first set of condition indicators wherein said portion has “n” condition indicators corresponding to the largest “n” diagonals of said whitened between class scatter matrix.
17. The method of claim 15 , wherein said whitening transformation matrix is:
Λ −1/2 Φ T with a corresponding eigenvalue matrix Λ and a corresponding eigenvector matrix Φ for a matrix of said first set of one or more condition indicators.
18. The method of claim 15 , further comprising:
determining a measure of within class scatter, S w , as a weighted average of class covariance represented as:
S
W
=
∑
i
=
1
L
P
i
∑
i
for each class, i, where P i is a probability of occurrence of a covariance Σ i for the ith class.
19. The method of claim 18 , further comprising: determining said whitening transformation matrix, A, of said within class scatter, Sw, where A t S w A=I.
20. A method for ranking condition indicators used in determining a health indicator for a component comprising:
determining a first set of a plurality of said condition indicators;
determining a covariance matrix for said plurality of condition indicators;
determining a whitening transformation matrix that whitens the covariance matrix;
using said whitening transformation matrix to determine differences between said first plurality of condition indicators and expected values for said condition indicators belonging to a health class, each health class having a corresponding health indicator; and
selecting a portion of said plurality of condition indicators in accordance with those condition indicators which have the smallest of said differences,
wherein said whitening transformation matrix is represented as: Λ −1/2 Φ T with a corresponding eigenvalue matrix Λ and a corresponding eigenvector matrix Φ for a matrix of said first set of a plurality of condition indicators.
21. The method of claim 20 , further comprising:
using said whitening transformation matrix to normalize differences between mean values of different health classes.
22. A computer program product for ranking condition indicators used in determining a health indicator for a component comprising machine executable code for:
determining a first set of a plurality of said condition indicators;
determining a covariance matrix corresponding to said plurality of condition indicators;
determining a whitening transformation matrix that whitens the covariance matrix;
using said whitening transformation matrix to determine differences between said first plurality of condition indicators and expected values for said condition indicators belonging to a health class, each health class having a corresponding health indicator; and
selecting a portion of said plurality of condition indicators in accordance with those condition indicators which have the smallest of said differences
wherein said whitening transformation matrix is represented as: Λ −1/2 Φ T with a corresponding eigenvalue matrix Λ and a corresponding eigenvector matrix Φ for a matrix of said first set of a plurality of condition indicators.
23. The computer program product of claim 22 , further comprising:
machine executable code for using said whitening transformation matrix to normalize differences between mean values of different health classes.
24. The computer program product of claim 10 , further comprising:
machine executable code for determining a measure of within class scatter, S w , as a weighted average of class covariance represented as:
S
W
=
∑
i
=
1
L
P
i
∑
i
for each class, i, where P i is a probability of occurrence of a covariance Σ i for the ith class.
25. The computer program product of claim 24 , further comprising:
machine executable code for using diagonal values of S w −1 S b in selecting said portion of said plurality of indicators.
26. A computer program product for selecting one or more condition indicators used in determining a health indicator corresponding to a health class for a component comprising machine executable code for:
determining a first set of one or more condition indicators;
determining a covariance matrix for said first set of condition indicators;
determining a whitening transformation matrix that whitens the covariance matrix;
using said whitening transformation matrix that whitens the covariance matrix to normalize differences between mean values of different health classes producing a whitened between class scatter matrix; and
selecting a portion of said first set of condition indicators in accordance with corresponding diagonals of said whitened between class scatter matrix.
27. The computer program product of claim 26 , further comprising machine executable code for:
sorting diagonals of said whitened between class scatter matrix; and
selecting said portion of said first set of condition indicators wherein said portion has “n” condition indicators corresponding to the largest “n” diagonals of said whitened between class scatter matrix.
28. The computer program product of claim 26 , wherein said whitening transformation matrix is:
Λ 1/2 Φ T with a corresponding eigenvalue matrix Λ and a corresponding eigenvector matrix Φ for a matrix of said first set of one or more condition indicators.
29. The computer program product of claim 26 , further comprising:
machine executable code for determining a measure of within class scatter, S w , as a weighted average of class covariance represented as:
S
W
=
∑
i
=
1
L
P
i
∑
i
for each class, i, where P i is a probability of occurrence of a covariance Σ i for the ith class.
30. The computer program product of claim 29 , further comprising:
machine executable code for determining said whitening transformation matrix, A, of said within class scatter, Sw, where A t S w A=I.
31. The method of claim 2 , wherein said between health class scatter matrix is Sb, represented as:
S
b
=
∑
i
=
1
L
P
i
(
M
i
-
M
0
)
(
M
i
-
M
0
)
T
,
M
0
=
∑
i
=
1
L
P
i
M
i
,
where M0 is an expected value of all L classes, Mi represents an expected value of a particular class, and Pi is the probability of a class i.
32. The method of claim 31 , wherein said whitened transformation of Sb is Sbw represented as S bw =A T S b A, for the whitening transformation matrix A.
33. The method of claim 32 , wherein said whitening transformation matrix A is:
Λ −1/2 Φ T with a corresponding eigenvalue matrix Λ and a corresponding eigenvector matrix Φ for said plurality of condition indicators.
34. The method of claim 31 , further comprising:
determining a measure of within class scatter, S w , as a weighted average of class covariance represented as:
S
W
=
∑
i
=
1
L
P
i
∑
i
for each class, i, where P i is a probability of occurrence of a covariance Σ i for the ith class.
35. The method of claim 34 , further comprising:
using diagonal values of S w −1 S b in selecting said portion of said plurality of indicators.
36. The method of claim 34 , wherein said covariance matrix is said weighted average of class covariance, S w , said whitening transformation matrix is A, and A t S w A=I.
37. The computer program product of claim 8 , wherein said between health class scatter matrix is Sb, represented as:
S
b
=
∑
i
=
1
L
P
i
(
M
i
-
M
0
)
(
M
i
-
M
0
)
T
,
M
0
=
∑
i
=
1
L
P
i
M
i
,
where M0 is an expected value of all L classes, Mi represents an expected value of a particular class, and Pi is the probability of a class i.
38. The computer program product of claim 37 , wherein said whitened transformation of Sb is Sbw represented as S bw =A T S b A, for the whitening transformation matrix A.
39. The computer program product of claim 38 , wherein said whitening transformation matrix A is:
Λ −1/2 Φ T with eigenvalue matrix Λ and a corresponding eigenvector matrix Φ for said plurality of condition indicators.
40. The computer program product of claim 37 , further comprising code that:
determines a measure of within class scatter, S w , as a weighted average of class covariance represented as:
S
W
=
∑
i
=
1
L
P
i
∑
i
for each class, i, where P i is a probability of occurrence of a covariance Σ i for the ith class.
41. The computer program product of claim 40 , further comprising code that:
uses diagonal values of S w −1 S b in selecting said portion of said plurality of indicators.
42. The computer program product of claim 40 , wherein said covariance matrix is said weighted average of class covariance, S w , said whitening transformation matrix is A, and A t S w A=I.