System and Method for Importance Sampling Based Time-Dependent Reliability Prediction

• US 20130035822A1
• Filed: 08/04/2011
• Published: 02/07/2013
• Est. Priority Date: 08/04/2011
• Status: Active Grant

• Current Assignee: United States Secretary of the Army
• Original Assignee: The United States Of America As Represented By The Secretary Of The Army
• Inventors: Singh, Amandeep, Nikolaidis, Efstatios, Mourelatos, Zissimos P.
• Granted Patent: US 8,781,672 B2
• Time in Patent Office: Days
• US Class Current: 701/29.9
• CPC Class Codes: G07C 5/0841 Registering performance data recording measured values G01D; information storage G11B

Abstract

A system and a method of generating a reliability prediction for components of a vehicle. The system and the method include implementing importance sampling in dynamic vehicle systems when the vehicle is subjected to time-dependent random terrain input. Alternatively, simulation data may be implemented. The system and the method include determining a decorrelation length, scaling up the standard deviation of white noise, and calculation of a likelihood ratio.

Claims

1. A system for generating a reliability prediction for components of a vehicle, the system comprising:

sensors electrically coupled to a data acquisition system for obtaining data related to the components from a random input process; and

a data analysis system, wherein the data analysis system comprises a computer processor electrically coupled to a computer memory, and the computer memory includes programming for the computer processor to perform the steps of;

(A) retrievably storing the data in the computer memory;

(B) characterizing the random input process;

(C) determining a decorrelation length;

(D) scaling up the standard deviation of a white noise level of the data;

(E) computing a covariance matrix of an original time series and of a scaled time series;

(F) beginning evaluation of a sample function;

(G) generating a scaled up sample function to produce an inflated domain;

(H) performing at least one of running a test or running a simulation model of the vehicle;

(I) computing a scaled vehicle response at a series of time steps until a first occurrence of a failure;

(J) when the failure occurs, computing a likelihood ratio based on an original joint probability density function and a sampling joint probability density function;

(K) determining whether an estimated vehicle response is equal to or greater than a threshold response, and when the estimated vehicle response is not equal to or greater than the threshold response, incrementing the time step and returning to the step (I), and when the estimated vehicle response is equal to or greater than the threshold response;

(L) incrementing a failure counter by 1 at the current time step;

(M) determining whether the number of the sample functions has exceeded a target number of sample functions and when the target number of sample functions is not exceeded, incrementing to the next sample evaluation and returning to the step (G), and when the target number of sample functions is exceeded;

(N) computing a safe number of the sample functions;

(O) calculating a failure rate estimation; and

(P) determining whether the failure rate estimation variance exceeds a predetermined value and the scale factor is greater than a predetermined amount, and when the failure rate estimation variance exceeds a predetermined estimation variance value and the scale factor is greater than a predetermined amount, reducing the scale factor by a predetermined amount and returning to the step (D), and when the failure rate estimation variance exceeds the predetermined estimation variance value;

(Q) providing the reliability prediction to a user, and ending the method.

2. The system of claim 1 wherein, the step of characterizing the random input process further comprises time series modeling of the data.

3. The system of claim 1 wherein, the step of characterizing the random input process further comprises generating an autoregressive integrated moving average (ARIMA) model of the data.

4. The system of claim 3 wherein, the step of characterizing the random input process further comprises estimating feedback parameters of the data.

5. The system of claim 4 wherein, the step of characterizing the random input process further comprises estimating a standard deviation of the white noise in the data.

6. The system of claim 1 wherein, a scaling factor in the range of 1.2 to 1.5 is implemented to inflate the standard deviation of the white noise level of the data.

7. The system of claim 1 wherein, the covariance matrix is computed via Yule-Walker equations.

8. The system of claim 1 further comprising the step of storing the covariance matrix in the computer memory.

9. The system of claim 1 further comprising the step of computing a likelihood ratio.

10. The system of claim 9 further comprising the step of adding the likelihood ratio to a previous sum at the same time step.

11. A method of generating a reliability prediction for components of a vehicle, the method comprising the steps of:

(A) obtaining data related to the components from a random input process and retrievably storing the data in a computer memory, and via programming stored in the computer memory implementing a computer processor to perform the steps of;

(B) characterizing the random input process;

(C) determining a decorrelation length;

(D) scaling up the standard deviation of a white noise level of the data;

(E) computing a covariance matrix of an original time series and of a scaled time series;

(F) beginning evaluation of a sample function;

(G) generating a scaled up sample function to produce an inflated domain;

(H) performing at least one of running a test or running a simulation model of the vehicle;

(I) computing a scaled vehicle response at a series of time steps until a first occurrence of a failure;

(J) when the failure occurs, computing a likelihood ratio based on an original joint probability density function and a sampling joint probability density function;

(K) determining whether an estimated vehicle response is equal to or greater than a threshold response, and when the estimated vehicle response is not equal to or greater than the threshold response, incrementing the time step and returning to the step (I), and when the estimated vehicle response is equal to or greater than the threshold response;

(L) incrementing a failure counter by 1 at the current time step;

(M) determining whether the number of the sample functions has exceeded a target number of sample functions and when the target number of sample functions is not exceeded, incrementing to the next sample evaluation and returning to the step (G), and when the target number of sample functions is exceeded;

(N) computing a safe number of the sample functions;

(O) calculating a failure rate estimation; and

(P) determining whether the failure rate estimation variance exceeds a predetermined value and the scale factor is greater than a predetermined amount, and when the failure rate estimation variance exceeds a predetermined estimation variance value and the scale factor is greater than a predetermined amount, reducing the scale factor by a predetermined amount and returning to the step (D), and when the failure rate estimation variance exceeds the predetermined estimation variance value;

(Q) providing the reliability prediction to a user, and ending the method.

12. The method of claim 11 wherein, the step of characterizing the random input process further comprises time series modeling of the data.

13. The method of claim 11 wherein, the step of characterizing the random input process further comprises generating an autoregressive integrated moving average (ARIMA) model of the data.

14. The method of claim 13 wherein, the step of characterizing the random input process further comprises estimating feedback parameters of the data.

15. The method of claim 14 wherein, the step of characterizing the random input process further comprises estimating a standard deviation of the white noise in the data.

16. The method of claim 11 wherein, a scaling factor in the range of 1.2 to 1.5 is implemented to inflate the standard deviation of the white noise level of the data.

17. The method of claim 11 wherein, the covariance matrix is computed via Yule-Walker equations.

18. The method of claim 11 further comprising the step of storing the covariance matrix in the computer memory.

19. The method of claim 11 further comprising the step of computing a likelihood ratio.

20. The method of claim 19 further comprising the step of adding the likelihood ratio to a previous sum at the same time step.