System and method for importance sampling based time-dependent reliability prediction

• US 8,781,672 B2
• Filed: 08/04/2011
• Issued: 07/15/2014
• 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, Mourelatos, Zissimos P., Nikolaidis, Efstratios
• Primary Examiner(s): Black, Thomas G
• Assistant Examiner(s): NELSON, SARA J
• Application Number:
  US13/198,337
• Publication Number:
  US 20130035822A1
• Time in Patent Office: 1,076 Days
• Field of Search: 701/29.1, 701/29.7, 701/29.8, 701/29.9, 701/30.3, 701/30.4, 701/30.5, 701/31.3, 701/31.7, 701/31.9, 701/33.6, 703/22
• 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 (2000) of;

(A) (2010) retrievably storing the data in the computer memory;

(B) (2020) characterizing the random input process, wherein the step of characterizing the random input process further comprises time series modeling of the data, generating an autoregressive integrated moving average (ARIMA) model of the data, estimating feedback parameters of the data, and estimating a standard deviation of white noise of the data;

(C) (2030) determining a decorrelation length;

(D) (2040) scaling up the standard deviation of the white noise of the data;

(E) (2050) computing a covariance matrix of an original time series and of a scaled time series;

(F) (2060) beginning evaluation of a sample function;

(G) (2070) generating a scaled up sample function wherein, a scale factor in the range of 1.2 to 1.5 is implemented to inflate the standard deviation of the white noise of the data to produce an inflated domain;

(H) (2080) performing at least one of running a test or running a simulation model of the vehicle to generate the data;

(I) (2090) computing a scaled vehicle response in response to the inflated domain at a series of time steps until a first occurrence of a failure;

(J) (2100) when the failure occurs, (2102) computing a likelihood ratio based on an original joint probability density function and a sampling joint probability density function, and further comprising (2104) adding the likelihood ratio to a sum of the previous likelihood ratios;

(K) (2110) determining whether the scaled vehicle response is equal to or greater than a threshold response, and (i) when the scaled vehicle response is not equal to or greater than the threshold response, (2112) incrementing the time step and returning to the step (I), and alternatively, (ii) when the scaled vehicle response is equal to or greater than the threshold response;

(L) (2120) incrementing a failure counter by 1 at the current time step to generate a number of the sample functions;

(M) (2130) 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, (2132) incrementing to the next sample evaluation and returning to the step (G), and alternatively, when the target number of sample functions is exceeded;

(N) (2140) computing a safe number of the sample functions, wherein the safe number of the sample functions comprises the number of sample functions minus the number of the sample functions that has exceeded the target number of sample functions;

(O) (2150) calculating a failure rate estimation in response to the safe number of the sample functions and the sum of the previous likelihood ratios; and

(P) (2160) determining whether variance of the failure rate estimation exceeds a predetermined estimation variance value and the scale factor is greater than a predetermined scale factor amount, and when the variance of the failure rate estimation exceeds the predetermined estimation variance value and the scale factor is greater than the predetermined scale factor amount, (2162) reducing the scale factor by a predetermined scale factor reduction amount and returning to the step (D), and alternatively, when the variance of the failure rate estimation exceeds the predetermined estimation variance value;

(Q) (2170) providing the failure rate estimation as the reliability prediction to a user, and ending the method.

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

3. The system of claim 1, the step (E) further comprising (2054) a sub-step of storing the covariance matrix in the computer memory.

4. A method (2000) of generating a reliability prediction for components of a vehicle, the method comprising the steps of:

(A) (2010) 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) (2020) characterizing the random input process, wherein the step of characterizing the random input process further comprises time series modeling of the data, generating an autoregressive integrated moving average (ARIMA) model of the data, estimating feedback parameters of the data, and estimating a standard deviation of white noise of the data;

(C) (2030) determining a decorrelation length;

(D) (2040) scaling up the standard deviation of the white noise of the data;

(E) (2050) computing a covariance matrix of an original time series and of a scaled time series;

(F) (2060) beginning evaluation of a sample function;

(G) (2070) generating a scaled up sample function wherein, a scale factor in the range of 1.2 to 1.5 is implemented to inflate the standard deviation of the white noise of the data to produce an inflated domain;

(H) (2080) performing at least one of running a test or running a simulation model of the vehicle to generate the data;

(I) (2090) computing a scaled vehicle response in response to the inflated domain at a series of time steps until a first occurrence of a failure;

(J) (2100) when the failure occurs, (2102) computing a likelihood ratio based on an original joint probability density function and a sampling joint probability density function, and further comprising (2104) adding the likelihood ratio to a sum of the previous likelihood ratios;

(K) (2110) determining whether the scaled vehicle response is equal to or greater than a threshold response, and (i) when the scaled vehicle response is not equal to or greater than the threshold response, (2112) incrementing the time step and returning to the step (I), and alternatively, (ii) when the scaled vehicle response is equal to or greater than the threshold response;

(L) (2120) incrementing a failure counter by 1 at the current time step to generate a number of the sample functions;

(M) (2130) 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, (2132) incrementing to the next sample evaluation and returning to the step (G), and alternatively, when the target number of sample functions is exceeded;

(N) (2140) computing a safe number of the sample functions, wherein the safe number of the sample functions comprises the number of sample functions minus the number of the sample functions that has exceeded the target number of sample functions;

(O) (2150) calculating a failure rate estimation in response to the safe number of the sample functions and the sum of the previous likelihood ratios; and

(P) (2160) determining whether variance of the failure rate estimation exceeds a predetermined estimation variance value and the scale factor is greater than a predetermined scale factor amount, and when the variance of the failure rate estimation exceeds the predetermined estimation variance value and the scale factor is greater than the predetermined scale factor amount, (2162) reducing the scale factor by a predetermined scale factor reduction amount and returning to the step (D), and alternatively, when the variance of the failure rate estimation exceeds the predetermined estimation variance value;

(Q) (2170) providing the failure rate estimation as the reliability prediction to a user, and ending the method.

5. The method of claim 4 wherein, the covariance matrix is computed via Yule-Walker equations.

6. The method of claim 4, the step (E) further comprising (2054) a sub-step of storing the covariance matrix in the computer memory.