Method and apparatus for providing predictive maintenance of a device by using markov transition probabilities
First Claim
1. A method for providing predictive maintenance of a device, comprising the steps of:
- modeling as a time series xn of a discretely sampled signal representative of occurrences of a defined event in the operation of said device, said time series xn being modeled as two-state first order Markov processes with associated transition probabilities p(i|j), wherein state 1 applies when a number of said occurrences exceeds a certain threshold T, and state 0 applies when a number of said occurrences falls below said certain threshold T, being represented as;
wherein said transition probabilities p(i|j) are switching probabilities from state j to state i, characterized by the probability that Sn=i given that Sn−
1=j, being a total of four transition probabilities;
computing said four transition probabilities for a last N states Sn, where N is a predetermined number;
conducting a supervised training session utilizing a set of J devices, which have failed due to known causes and considering the two independent probabilities p(1|1) and p(1|0), said training session comprising;
computing two-dimensional feature vectors fi={p(1|1), p(1|0)}i for an initial M windows of N scans, thereby a first vector set, computing two-dimensional feature vectors ff={p(1|1), p(1|0)f for o final N number of scans, thereby forming a second vector set, plotting a scatter-diagram of all two-dimensional feature vectors (fi)n and (ff)n, (n=1 . . . J), and deriving from the scatter-diagram a pattern classifier by estimating an optimal linear discriminant which separates the first and second vector sets; and
applying said classifier to monitor a persistence of occurrences of said defined event in an operation of said device.
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Abstract
A method for providing predictive maintenance of a device, comprises the steps of modeling as a time series of a discretely sampled signal representative of occurrences of a defined event in the operation of the device, the time series being modeled as two-state first order Markov processes with associated transition probabilities, wherein one state applies when the number of the occurrences exceeds a certain threshold, and the other state applies when the number of the occurrences falls below the certain threshold; computing the four transition probabilities the last N states Sn, where N is a predetermined number, conducting a supervised training session utilizing a set of J devices, which have failed due to known causes and considering the two independent probabilities and, the training session comprising computing the two-dimensional feature vectors for the initial M windows of N scans, computing the two-dimensional feature vectors for the final N number of scans, plotting a scatter-diagram of all 2D feature vectors, and deriving a pattern classifier by estimating the optimal linear discriminant which separates the two foregoing sets of vectors; and applying the classifier to monitor the persistence of occurrences of the defined event in the operation of the device.
20 Citations
7 Claims
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1. A method for providing predictive maintenance of a device, comprising the steps of:
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modeling as a time series xn of a discretely sampled signal representative of occurrences of a defined event in the operation of said device, said time series xn being modeled as two-state first order Markov processes with associated transition probabilities p(i|j), wherein state 1 applies when a number of said occurrences exceeds a certain threshold T, and state 0 applies when a number of said occurrences falls below said certain threshold T, being represented as;
wherein said transition probabilities p(i|j) are switching probabilities from state j to state i, characterized by the probability that Sn=i given that Sn−
1=j, being a total of four transition probabilities;computing said four transition probabilities for a last N states Sn, where N is a predetermined number;
conducting a supervised training session utilizing a set of J devices, which have failed due to known causes and considering the two independent probabilities p(1|1) and p(1|0), said training session comprising;
computing two-dimensional feature vectors fi={p(1|1), p(1|0)}i for an initial M windows of N scans, thereby a first vector set, computing two-dimensional feature vectors ff={p(1|1), p(1|0)f for o final N number of scans, thereby forming a second vector set, plotting a scatter-diagram of all two-dimensional feature vectors (fi)n and (ff)n, (n=1 . . . J), and deriving from the scatter-diagram a pattern classifier by estimating an optimal linear discriminant which separates the first and second vector sets; and
applying said classifier to monitor a persistence of occurrences of said defined event in an operation of said device. - View Dependent Claims (2, 3)
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4. A method for providing predictive maintenance of an X-ray tube, comprising the steps of:
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modeling as a time series xn of a discretely sampled signal representative of occurrences of arcing in an operation of said tube, said time series xn being modeled as two-state first order Markov processes with associated transition probabilities p(i|j), wherein state 1 applies when a number of said occurrences exceeds a certain threshold T, and state 0 applies when a number of said occurrences falls below said certain threshold T, being represented as;
wherein said transition probabilities p(i|j) are switching probabilities from state j to state i, characterized by the probability that Sn=i given that Sn−
1=j, being a total of four transition probabilities;
computing said four transition probabilities for a last N states Sn, where N is a predetermined number;
conducting a supervised training session utilizing a set of J X-ray tubes, which have failed due to known causes and considering two independent probabilities p(1|1) and p(1|0), said training session comprising;
computing two-dimensional feature vectors fi={p(1|1), p(1|0)}i for an initial M windows of N scans, thereby forming a first vector set, computing the two-dimensional feature vectors ff={p(1|1), p(1|0)f for a final N number of scans, thereby forming a second vector set, plotting a scatter-diagram of all two-dimensional feature vectors (fi)n and (ff)n, (n=1 . . . J), and deriving a pattern classifier by estimating an optimal linear discriminant which separates the first and second vector sets; and
applying said classifier to monitor a persistence of occurrences of said arcing in an operation of said X-ray tube. - View Dependent Claims (5, 6)
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7. Apparatus for providing predictive maintenance of a device, comprising:
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means for modeling as a time series xn of a discretely sampled signal representative of occurrences of a defined event in the operation of said device, said time series xn being modeled as two-state first order Markov processes with associated transition probabilities p(i|j), wherein state 1 applies when a number of said occurrences exceeds a certain threshold T, and state 0 applies when a number of said occurrences falls below said certain threshold T, being represented as;
wherein said transition probabilities p(i|j) are switching probabilities from state j to state i, characterized by the probability that Sn=i given that Sn−
1=j, being a total of four transition probabilities;
means for computing said four transition probabilities for a last N states Sn, where N is a predetermined number;
means for conducting a supervised training session utilizing a set of J devices, which have failed due to known causes and considering two independent probabilities p(1|1) and p(1|0), said means for conducting a supervised training session comprising means for;
computing the two-dimensional feature vectors fi={p(1|1), p(1|0)}i for a final N number of scans, thereby forming a second vector set, computing two-dimensional feature vectors ff={p(1|1), p(1|0)f for a final N number of scans, thereby forming a second vector set, plotting a scatter-diagram of all two-dimensional feature vectors (fi)n and (ff)n, (n=1 . . . J), and deriving a pattern classifier by estimating an optimal linear discriminant which separates the first and second vector sets; and
means for applying said classifier to monitor a persistence of occurrences of said defined event in the operation of said device.
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Specification