Method and apparatus for providing predictive maintenance of a device by using markov transition probabilities

• US 20020128799A1
• Filed: 12/14/2001
• Published: 09/12/2002
• Est. Priority Date: 12/14/2000
• Status: Active Grant

• Current Assignee: Siemens Corp. (Siemens AG)
• Original Assignee: Siemens Corporate Research Incorporated (Siemens AG)
• Inventors: Loecher, Markus
• Granted Patent: US 6,847,918 B2
• Time in Patent Office: Days
• US Class Current: 702/181
• CPC Class Codes: G06Q 10/06 Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling

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 S_n, 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.

Claims

1. A method for providing predictive maintenance of a device, comprising the steps of:

modeling as a time series x_n of a discretely sampled signal representative of occurrences of a defined event in the operation of said device, said time series x_n being modeled as two-state first order Markov processes with associated transition probabilities p(i|j), wherein state 1 applies when the number of said occurrences exceeds a certain threshold T, and state 0 applies when the number of said occurrences falls below said certain threshold T, being represented as;

$S_n=\{\begin{array}{ccc}0& \mathrm{if}& x_n\le <br><br>T\\ 1& \mathrm{if}& x_n><br><br>T\end{array}$

wherein said transition probability p(i|j) is the switching probability from state j to state i, that is, the probability that S_n=i given that S<sub>n−

1</sub>=j, being a total of 4 transition probabilities;

computing said four transition probabilities the last N states S_n, 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 the two-dimensional feature vectors f_i={p(1|1), p(1|0)}_i for the initial M windows of N scans,

computing the two-dimensional feature vectors f_f={p(1|1), p(1|0)_f for the final N number of scans,

plotting a scatter-diagram of all 2D feature vectors (f_i)_n and (f_f)_n, (n=1 . . . J), and

deriving a pattern classifier by estimating the optimal linear discriminant which separates the two foregoing sets of vectors; and

applying said classifier to monitor the persistence of occurrences of said defined event in the operation of said device.

2. A method for providing predictive maintenance of a device as recited in claim 1, including the steps of:

updating said transition probabilities at each scan are updated; and

constructing the feature vector f={p(1|1), p(1|0)} constructed.

3. A method for providing predictive maintenance of a device as recited in claim 2, including the step of:

providing a warning of imminent failure of said device if f falls into a region of said classifier corresponding indicating such failure prediction.

4. A method for providing predictive maintenance of an X-ray tube, comprising the steps of:

modeling as a time series x_n of a discretely sampled signal representative of occurrences of arcing in the operation of said tube, said time series x_n being modeled as two-state first order Markov processes with associated transition probabilities p(i|j), wherein state 1 applies when the number of said occurrences exceeds a certain threshold T, and state 0 applies when the number of said occurrences falls below said certain threshold T, being represented as;

$S_n=\{\begin{array}{ccc}0& \mathrm{if}& x_n\le <br><br>T\\ 1& \mathrm{if}& x_n><br><br>T\end{array}$

wherein said transition probability p(i|j) is the switching probability from state j to state i, that is, the probability that S_n=i given that S<sub>n−

1</sub>=j, being a total of 4 transition probabilities;

computing said four transition probabilities the last N states S_n, 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 the two independent probabilities p(1|1) and p(1|0), said training session comprising;

computing the two-dimensional feature vectors f_i={p(1|1), p(1|0)}_i for the initial M windows of N scans,

computing the two-dimensional feature vectors f_f={p(1|1), p(1|0)_f for the final N number of scans,

plotting a scatter-diagram of all 2D feature vectors (f_i)_n and (f_f)_n, (n=1 . . . J), and

deriving a pattern classifier by estimating the optimal linear discriminant which separates the two foregoing sets of vectors; and

applying said classifier to monitor the persistence of occurrences of said arcing in the operation of said X-ray tube.

5. A method for providing predictive maintenance of an X-ray tube as recited in claim 4, including the steps of:

updating said transition probabilities at each scan are updated; and

constructing the feature vector f={p(1|1), p(1|0)} constructed.

6. A method for providing predictive maintenance of an X-ray tube as recited in claim A5, including the step of:

providing a warning of imminent failure of said X-ray tube if f falls into a region of said classifier corresponding indicating such failure prediction.

7. 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 said device, said time series being modeled as two-state first order Markov processes with associated transition probabilities, wherein one state applies when the number of said occurrences exceeds a certain threshold, and the other state applies when the number of said occurrences falls below said certain threshold;

computing said four transition probabilities the last N states S_n, 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, said 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 said classifier to monitor the persistence of occurrences of said defined event in the operation of said device.

8. Apparatus for providing predictive maintenance of a device, comprising:

means for modeling as a time series x_n of a discretely sampled signal representative of occurrences of a defined event in the operation of said device, said time series x_n being modeled as two-state first order Markov processes with associated transition probabilities p(i|j), wherein state 1 applies when the number of said occurrences exceeds a certain threshold T, and state 0 applies when the number of said occurrences falls below said certain threshold T, being represented as;

$S_n=\{\begin{array}{ccc}0& \mathrm{if}& x_n\le <br><br>T\\ 1& \mathrm{if}& x_n><br><br>T\end{array}$

wherein said transition probability p(i|j) is the switching probability from state j to state i, that is, the probability that S_n=i given that S<sub>n−

1</sub>=j, being a total of 4 transition probabilities;

means for computing said four transition probabilities the last N states S_n, 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 the 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 f_i={p(1|1), p(1|0)}_i for the initial M windows of N scans,

computing the two-dimensional feature vectors f_f={p(1|1), p(1|0)_f for the final N number of scans,

plotting a scatter-diagram of all 2D feature vectors (f_i)_n and (f_f)_n, (n=1 . . .J), and

deriving a pattern classifier by estimating the optimal linear discriminant which separates the two foregoing sets of vectors; and

means for applying said classifier to monitor the persistence of occurrences of said defined event in the operation of said device.