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

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 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:

S

n

=

{

0

if

x

n

≤

T

1

if

x

n

>

T

wherein said transition probabilities p(i|j) are switching probabilities from state j to state i, characterized by the probability that S n =i given that S n−1 =j, being a total of four transition probabilities;

computing said four transition probabilities for a 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 two-dimensional feature vectors f i ={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 f f ={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 (f i ) n and (f f ) 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.

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; and

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

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 indicating 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 an 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 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:

S

n

=

{

0

if

x

n

≤

T

1

if

x

n

>

T

wherein said transition probabilities p(i|j) are switching probabilities from state j to state i, characterized by the probability that S n =i given that S n−1 =j, being a total of four transition probabilities;

computing said four transition probabilities for a 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 two independent probabilities p(1|1) and p(1|0), said training session comprising:

computing two-dimensional feature vectors f i ={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 f f ={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 (f i ) n and (f f ) 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.

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; and

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

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

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

7. 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 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:

S

n

=

{

0

if

x

n

≤

T

1

if

x

n

>

T

wherein said transition probabilities p(i|j) are switching probabilities from state j to state i, characterized by the probability that S n =i given that S n−1 =j, being a total of four transition probabilities;

means for computing said four transition probabilities for a 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 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 a final N number of scans, thereby forming a second vector set,

computing two-dimensional feature vectors f f ={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 (f i ) n and (f f ) 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.