Novelty detection

• US 20090187381A1
• Filed: 07/11/2008
• Published: 07/23/2009
• Est. Priority Date: 01/18/2008
• Status: Active Grant

• Current Assignee: Oxford Biosignals (Us) Incorporated, Rolls-Royce Controls & Data Services Ltd. (Rolls-Royce Holdings Plc)
• Original Assignee: Oxford Biosignals (Us) Incorporated, Rolls-Royce PLC (Rolls-Royce Holdings Plc)
• Inventors: King, Dennis M., King, Stephen P., Slater, Robert W., Tarassenko, Lionel, Clifton, David, Anuzis, Paul
• Granted Patent: US 7,925,470 B2
• Time in Patent Office: Days
• US Class Current: 702/181
• CPC Class Codes: G06F 18/2433 Single-class perspective, e.g. one-against-all classification; Novelty detection; Outlier detection

Abstract

A method and apparatus for detecting an abnormality in e.g. in operating characteristics or function of a machine, apparatus or system, the method including providing a data sample set comprising n values of a measured physical parameter associated with the apparatus or system generated by repeating a measurement of the physical parameter n times. An extremal measured parameter value is selected from amongst the data sample set, determining a probability of observing the selected parameter value (e.g. of observing a value not exceeding the selected parameter value) by applying the selected parameter value to an extreme value probability distribution function having a location parameter and a scale parameter. The value of the location parameter and the value of the scale parameter are each constructed using an integer value m (e.g. notionally representing the size of a sub-sample data set comprising m of said measured parameter values) in which m is less than n (i.e. m<n). A conditional indication is given that the selected parameter value is abnormal according to the value of the probability.

Claims

1. A method for detecting an abnormality in an apparatus or system including:

providing a data sample set comprising n values of a measured physical parameter associated with the apparatus or system generated by repeating a measurement of the physical parameter n times;

selecting an extremal measured parameter value from amongst the data sample set;

determining a probability of observing the selected parameter value by applying the selected parameter value to an extreme value probability distribution function having a location parameter and a scale parameter wherein the value of the location parameter and the value of the scale parameter are each constructed using an integer value m (e.g. notionally representing the size of a sub-sample data set comprising m of said measured parameter values) in which m is less than n (i.e. m<

n);

conditionally indicating that the selected parameter value is abnormal according to the value of said probability.

2. A method according to claim 1 in which the measured parameter values of a sub-sample data set of size m comprising m of said measured parameter values, and including the extremal value, conform to a distribution which approximates a Gaussian distribution more closely than the distribution of the values of such a sub-sample data set of a different size.

3. A method according to claim 1 in which each of the measured parameter values of the sub-sample data set is greater in value than any measured parameter value of the data sample set not also comprised in the sub-sample data set.

4. A method according to claim 1 in which the extreme value probability distribution function is a Gumbel (Type I) distribution.

5. A method according to claim 1 in which the extremal value is the maximum value of the data sample set.

6. A method according to claim 1 in which the extremal value is the minimum value of the data sample set.

7. A method according to claim 1 in which the integer value (m) is a value selected from following integers:

3 to 10.

8. A method according to claim 1 in which the value (m) is 3 (m=3).

9. A method according to claim 1 including constructing the location parameter (μ

m) of the extreme value probability distribution function with a magnitude given according to the following equation;

${\mathrm{\mu <br><br>}}_m=\sqrt{2<br><br><br><br>\ln <br><br>\left(m\right)}-\frac{\ln <br><br>\left(\ln <br><br>\left(m\right)\right)+\ln <br><br>\left(4<br><br>\mathrm{\pi <br><br>}\right)}{2<br><br>\sqrt{2<br><br><br><br>\ln <br><br>\left(m\right)}}$

10. A method according to claim 1 including constructing the scale parameter (σ

m) of the extreme value probability distribution function according to the following equation;

11. A method according to claim 1 including repeating n times a measurement of a physical parameter associated with the apparatus of system thereby to generate said data sample set comprising said n measured parameter values.

79. A computer-implemented method according to claim 1.

80. A computer means containing computer program instructions executable thereon to implement the method according to claim 1.

81. A computer program product containing computer program instructions executable on a computer means to implement the method according to claim 1.

82. A method for detecting an abnormality in an apparatus or system utilizing a computer system according to the method of claim 1.

12. A method for detecting an abnormality in an apparatus or system including:

providing a data sample set comprising a plurality of values of a measured physical parameter associated with the apparatus or system generated by repeating a measurement of the physical parameter a plurality of times;

selecting an extremal measured parameter value from amongst the sample set;

determining a probability of observing the selected parameter value by applying the selected parameter value to a probability distribution function comprising a weighted sum of a plurality of extreme value probability distribution functions each having a location parameter and a scale parameter wherein the value of the location parameter and the value of the scale parameter are determined according to an estimation of the probability thereof;

conditionally indicating that the selected parameter value is abnormal according to the value of said probability of observing the selected parameter value.

13. A method according to claim 12 including generating the estimation using a plurality of measured physical parameter values from the data sample set to recursively update a prior said estimation.

14. A method according to claim 12 including generating the estimation using a plurality of measured physical parameter values from another data sample set which is independent of said data sample set and which comprises a plurality of values of said physical parameter generated by repeating said measurement of said physical parameter a corresponding plurality of times.

15. A method according to claim 12 in which the value of the weight associated with a given extreme value probability distribution function in said weighted sum is determined according to the estimation.

16. A method according to claim 12 including generating a joint posterior probability distribution function comprising the product of a first component probability distribution function for the value of the location parameter, and a second component probability distribution function for the value of the scale parameter, and generating said estimation using the joint posterior probability distribution function.

17. A method according to claim 16 including selecting coordinates of a point in the coordinate space of the random variables of the joint posterior probability distribution function, the coordinates being selected from amongst a predetermined finite plurality of different such coordinates surrounding the coordinates corresponding to the location of the peak of the joint posterior probability distribution function, and using the value of the selected coordinates to determine the value of a location parameter and the value of a scale parameter of a said extreme value probability distribution function.

18. A method according to claim 17 including defining a plurality of separate regions in said coordinate space having a common associated probability mass according to the joint posterior probability distribution function within that region, wherein a given said selected coordinates are selected to be the coordinates of the centroid of probability mass in a given said region.

19. A method according to claim 18 in which neighbouring said regions are contiguous.

20. A method according to claim 16 including selecting a plurality of the measured parameter values from amongst the data sample set and generating a value for a hyper-parameter of the joint posterior probability distribution function using the measured values so selected.

21. A method according to claim 16 including generating a value for a hyper-parameter of the joint posterior probability distribution function using an integer value (j) representing the size of a sample data set comprising j of the measured parameter values of the data sample set.

22. A method according to claim 21 in which the integer value j is less than the integer value n (i.e. j<

n) representing the size of the data sample set, and the sample data set is a sub-sample data set.

23. A method according to claim 21 including generating the value of each hyper-parameter using the integer value j.

24. A method according to claim 16 in which a hyper-parameter of the joint posterior probability distribution function is the value of the mean of the first component probability distribution function, the method including generating a value of said mean using the values of a plurality of measured parameter values selected from amongst the data sample set.

25. A method according to claim 16 in which a hyper-parameter of the joint posterior probability distribution function is the value of the scale parameter of the second component probability distribution function, the method including generating a value of the scale parameter of the second component probability distribution function using the values of a plurality of measured parameter values selected from amongst the data sample set.

26. A method according to claim 16 wherein second component probability distribution function is a Gamma probability distribution function and the first component probability distribution function is a Gaussian probability distribution function the value of the variance of which is determined according to a value(s) of the scale parameter (A) of the joint posterior probability distribution function.

27. A method according to claim 26 in which hyper-parameters of the joint posterior probability distribution include the mean and variance of the first component probability distribution function, the method including generating the mean (μ

_m) and variance ([σ

_m]²) of the first component probability distribution function using m (m=integer) measured parameter values (x_i;

i=1, . . . , m) according to the following equations in which β

₀ and μ

₀ are predefined constants;

${\mathrm{\mu <br><br>}}_m=\frac{{\mathrm{\beta <br><br>}}_0<br><br>{\mathrm{\mu <br><br>}}_0+\stackrel{m}{\underset{i=1}{\sum <br><br>}}<br><br>x_i}{{\mathrm{\beta <br><br>}}_m},<br><br>\mathrm{and}$ ${\mathrm{\sigma <br><br>}}_m^2={\left({\mathrm{\beta <br><br>}}_m<br><br>\mathrm{\lambda <br><br>}\right)}^{-1}$

where β

_m=β

₀+m.

28. A method according to claim 26 in which hyper-parameters of the joint posterior probability distribution include the shape and scale parameters of the second component probability distribution function the method including generating the shape hyper-parameter value (a_m) and scale hyper-parameter value (b_m) of the second component probability distribution function using m (m=integer) measured parameter values (x_i;

i=1, . . . , m) according to the following equations in which a₀, b₀, β

₀ and μ

₀ are predefined constants;

$a_m=a_0+\frac{m}{2}$ $b_m=b_0+\frac{1}{2}<br><br>\left[\stackrel{m}{\underset{i=1}{\sum <br><br>}}<br><br>x_i^2-\frac{1}{m}<br><br>{\left(\stackrel{m}{\underset{i=1}{\sum <br><br>}}<br><br>x_i\right)}^2+\frac{{\mathrm{\beta <br><br>}}_0<br><br>m}{{\mathrm{\beta <br><br>}}_0+m}<br><br>{\left(\frac{1}{m}<br><br>\stackrel{m}{\underset{i=1}{\sum <br><br>}}<br><br>\left(x_i-{\mathrm{\mu <br><br>}}_0\right)\right)}^2\right].$

29. A method according to claim 22 in which the sub-sample data set includes the extremal value and the distribution of the j measured parameter values thereof approximates a Gaussian distribution more closely than the distribution of the values of such a sub-sample data set of a different size.

30. A method according to claim 22 in which each of the measured parameter values of the sub-sample data set is greater in value than any measured parameter value of the data sample set not also comprised in the sub-sample data set.

31. A method according to claim 12 in which the extreme value probability distribution function is a Gumbel (Type I) distribution.

32. A method according to claim 12 in which the extremal value is the maximum value of the data sample set.

33. A method according to claim 12 in which the extremal value is the minimum value of the data sample set.

34. A method according to claim 22 in which the value (j) of the size of the sub-sample data-set is a value selected from following integers:

3 to 10.

35. A method according to claim 22 in which the value (j) of the size of the sub-sample data set is 3, or 4 or 5 (j=3, or j=4, or j=5).

36. A method according to claim 12 including repeating a plurality of times a measurement of a physical parameter associated with the apparatus or system thereby to generate said data sample set comprising said plurality of measured parameter values.

37. Apparatus for detecting an abnormality in an apparatus or system including:

data acquisition means for acquiring a data sample set comprising n (n=integer) values of a measured physical parameter associated with the apparatus or system generated by repeating a measurement of the physical parameter n times;

selector means for selecting an extremal measured parameter value from amongst the data sample set;

calculation means for determining a probability of observing the selected parameter value by applying the selected parameter value to an extreme value probability distribution function having a location parameter and a scale parameter wherein the value of the location parameter and the value of the scale parameter are each constructed using an integer value m (e.g. notionally representing the size of a sub-sample data set comprising m of said measured parameter values) in which m is less than n (i.e. m<

n);

indicator means for conditionally indicating that the selected parameter value is abnormal according to the value of said probability.

38. Apparatus according to claim 37 in which the measured parameter values of a sub-sample data set of size m comprising m of said measured parameter values, including the extremal value, conform to a distribution which approximates a Gaussian distribution more closely than the distribution of the values of such a sub-sample data set of a different size.

39. Apparatus according to claim 37 in which each of the measured parameter values of the sub-sample data set is greater in value than any measured parameter value of the data sample set not also comprised in the sub-sample data set.

40. Apparatus according to claim 37 in which the extreme value probability distribution function is a Gumbel (Type I) distribution.

41. Apparatus according to claim 37 in which the extremal value is the maximum value of the data sample set.

42. Apparatus according to claim 37 in which the extremal value is the minimum value of the data sample set.

43. Apparatus according to claim 37 in which the integer value (m) is a value selected from following integers:

3 to 10.

44. Apparatus according to claim 37 in which the integer value (m) is 3, or 4, or 5 (m=3, or m=4, or m=5).

45. Apparatus according to claim 37 in which the calculation means is arranged to construct the location parameter (μ

_m) of the extreme value probability distribution function with a magnitude given according to the following equation;

${\mathrm{\mu <br><br>}}_m=\sqrt{2<br><br><br><br>\ln <br><br>\left(m\right)}-\frac{\ln <br><br>\left(\ln <br><br>\left(m\right)\right)+\ln <br><br>\left(4<br><br>\mathrm{\pi <br><br>}\right)}{2<br><br>\sqrt{2<br><br><br><br>\ln <br><br>\left(m\right)}}$

46. Apparatus according to claim 37 in which the calculation means is arranged to construct the scale parameter (σ

_m) of the extreme value probability distribution function according to the following equation;

${\mathrm{\sigma <br><br>}}_m=\frac{1}{\sqrt{2<br><br><br><br>\ln <br><br>\left(m\right)}}$

47. Apparatus according to claim 37 in which the data acquisition means is arranged to repeating n times a measurement of a physical parameter associated with the apparatus of system thereby to generate said data sample set comprising said n measured parameter values.

60. Apparatus according to claim 42 in which a hyper-parameter of the joint posterior probability distribution function is the value of the mean of the first component probability distribution function, the calculation means being arranged to generate a value of said mean using the values of a plurality of measured parameter values selected from amongst the data sample set.

61. Apparatus according to claim 42 in which a hyper-parameter of the joint posterior probability distribution function is the value of the scale parameter of the second component probability distribution function, the calculation means be arranged to generate a value of the scale parameter of the second component probability distribution function using the values of a plurality of measured parameter values selected from amongst the data sample set.

73. Apparatus according to claim 37 in which the calculation means is a computer means.

74. Apparatus according to claim 37 in which the indicator means is arranged to provide a visual said conditional indication.

75. Apparatus according to claim 37 in which the data acquisition means includes a data storage means arranged to receive data and to retrievably store received data.

76. Apparatus according to claim 37 in which the data acquisition means includes data measurement means arranged to measure values of said physical parameter.

77. A detector for detecting an abnormality in an apparatus or system including an apparatus according to claim 37.

78. An engine in combination with a detector according to claim 77 arranged to detect an abnormality in operating characteristics of the engine.

48. Apparatus for detecting an abnormality in an apparatus or system including:

data acquisition means for acquiring a data sample set comprising a plurality of values of a measured physical parameter associated with the apparatus or system generated by repeating a measurement of the physical parameter a plurality of times;

selector means for selecting an extremal measured parameter value from amongst the sample set;

calculation means for determining a probability of observing the selected parameter value by applying the selected parameter value to a probability distribution function comprising a weighted sum of a plurality of extreme value probability distribution functions each having a location parameter and a scale parameter wherein the value of the location parameter and the value of the scale parameter are determined according to an estimation of the probability thereof;

indicator means for conditionally indicating that the selected parameter value is abnormal according to the value of said probability of observing the selected parameter value.

49. Apparatus according to claim 48 in which the calculation means is arranged to generate the estimation using a plurality of measured physical parameter values from the data sample set to recursively update a prior said estimation.

50. Apparatus according to claim 48 in which the calculation means is arranged to generate the estimation using a plurality of measured physical parameter values from another data sample set which is independent of said data sample set and which comprises a plurality of values of said physical parameter generated by repeating said measurement of said physical parameter a corresponding plurality of times.

51. Apparatus according to claim 48 in which the calculation means is arranged to determine the value of the weight associated with a given extreme value probability distribution function in said weighted sum according to the estimation.

52. Apparatus according to claim 48 in which the calculation means is arranged to generate the estimation using a joint posterior probability distribution function comprising the product of a first component probability distribution function for the value of the location parameter, and a second component probability distribution function for the value of the scale parameter.

53. Apparatus according to claim 52 in which the calculation means is arranged to select coordinates of a point in the coordinate space of the random variables of the joint posterior probability distribution function, the coordinates being selected from amongst a predetermined finite plurality of different such coordinates surrounding the coordinates corresponding to the location of the peak of the joint posterior probability distribution function, and to use the value of the selected coordinates to determine the value of a location parameter and the value of a scale parameter of a said extreme value probability distribution function.

54. Apparatus according to claim 53 in which the calculation means is arranged to define a plurality of separate regions in said coordinate space having a common associated probability mass according to the joint posterior probability distribution function within that region, to determine the centroid of probability mass within each region and wherein a given said selected coordinates are selected to be the coordinates of the centroid of probability mass in a given said region.

55. Apparatus according to claim 54 in which neighbouring said regions are contiguous.

56. Apparatus according to claim 52 in which the calculation means is arranged to select a plurality of the measured parameter values from amongst the data sample set and to generate a value for a hyper-parameter of the joint posterior probability distribution function using the measured values so selected.

57. Apparatus according to claim 48 in which the calculation means is arranged to generate a value for a hyper-parameter of the joint posterior probability distribution function using an integer value (j) representing the size of a sample data set comprising j of said n measured parameter values.

58. Apparatus according to claim 57 in which the integer value j is less than the integer value n (i.e. j<

n) representing the number of measured parameter values comprised in the data sample set such that the sample data set is a sub-sample data set.

59. Apparatus according to claim 57 in which the calculation means is arranged to generate the value of each hyper-parameter using the integer value j.

62. Apparatus according to claim 48 wherein second component probability distribution function is a Gamma probability distribution function and the first component probability distribution function is a Gaussian probability distribution function the value of the variance of which the calculation means is arranged to determine according to a value(s) of the scale parameter (A) of the joint posterior probability distribution function.

63. Apparatus according to claim 48 in which hyper-parameters of the joint posterior probability distribution include the mean and variance of the first component probability distribution function, the calculation means being arranged to generate the mean (μ

_m) and variance ([σ

_m]²) of the first component probability distribution function using m (m=integer) measured parameter values (x_i;

i=1, . . . , m) of the data sample set according to the following equations in which (β

₀ and μ

₀ are predefined constants;

${\mathrm{\mu <br><br>}}_m=\frac{{\mathrm{\beta <br><br>}}_0<br><br>{\mathrm{\mu <br><br>}}_0+\stackrel{m}{\underset{i=1}{\sum <br><br>}}<br><br>x_i}{{\mathrm{\beta <br><br>}}_m},<br><br>\mathrm{and}$ ${\mathrm{\sigma <br><br>}}_m^2={\left({\mathrm{\beta <br><br>}}_m<br><br>\mathrm{\lambda <br><br>}\right)}^{-1}$

where β

_m=β

₀+m.

64. Apparatus according to claim 62 in which hyper-parameters of the joint posterior probability distribution include the shape and scale parameters of the second component probability distribution function the calculation means being arranged to generate the shape hyper-parameter value (a_m) and scale hyper-parameter value (b_m) of the second component probability distribution function using m (m=integer) measured parameter values (x_i;

i=1, . . . , m) of the data sample set according to the following equations in which a₀, b₀, β and

uo are predefined constants;

$a_m=a_0+\frac{m}{2}$ $b_m=b_0+\frac{1}{2}<br><br>\left[\stackrel{m}{\underset{i=1}{\sum <br><br>}}<br><br>x_i^2-\frac{1}{m}<br><br>{\left(\stackrel{m}{\underset{i=1}{\sum <br><br>}}<br><br>x_i\right)}^2+\frac{{\mathrm{\beta <br><br>}}_0<br><br>m}{{\mathrm{\beta <br><br>}}_0+m}<br><br>{\left(\frac{1}{m}<br><br>\stackrel{m}{\underset{i=1}{\sum <br><br>}}<br><br>\left(x_i-{\mathrm{\mu <br><br>}}_0\right)\right)}^2\right].$

65. Apparatus according to claim 58 in which the sub-sample data set includes the extremal value and the distribution of the j measured parameter values thereof approximates a Gaussian distribution more closely than the distribution of the values of such a sub-sample data set of a different size.

66. Apparatus according to claim 58 in which each of the measured parameter values of the sub-sample data set is greater in value than any measured parameter value of the data sample set not also comprised in the sub-sample data set.

67. Apparatus according to claim 48 in which the extreme value probability distribution function is a Gumbel (Type I) distribution.

68. Apparatus according to claim 48 in which the extremal value is the maximum value of the data sample set.

69. Apparatus according to claim 48 in which the extremal value is the minimum value of the data sample set.

70. Apparatus according to claim 58 in which the value (j) of the size of the sub-sample data-set is a value selected from following integers:

3 to 10.

71. Apparatus according to claim 58 in which the value (j) of the size of the sub-sample data set is 3, or 4 or 5 (j=3, or j=4, or j=5).

72. Apparatus according to claim 48 including repeating a plurality of times a measurement of a physical parameter associated with the apparatus or system thereby to generate said data sample set comprising said plurality of measured parameter values.