An Importance Sampling Approach for Time-Dependent Reliability

2011 ◽  
Author(s):  
Amandeep Singh ◽  
Zissimos P. Mourelatos ◽  
Efstratios Nikolaidis
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Random Process ◽  
Importance Sampling ◽  
Sampling Technique ◽  
Process Time ◽  
Cumulative Probability ◽  
Repairable Systems ◽  
Importance Sampling Method ◽  
True Value

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. The reliability usually degrades with time increasing the lifecycle cost due to potential warranty costs, repairs and loss of market share. Reliability is the probability that the system will perform its intended function successfully for a specified time. In this article, we consider the first-passage reliability which accounts for the first time failure of non-repairable systems. Methods are available which provide an upper bound to the true reliability which may overestimate the true value considerably. The traditional Monte-Carlo simulation is accurate but computationally expensive. A computationally efficient importance sampling technique is presented to calculate the cumulative probability of failure for random dynamic systems excited by a stationary input random process. Time series modeling is used to characterize the input random process. A detailed example demonstrates the accuracy and efficiency of the proposed importance sampling method over the traditional Monte Carlo simulation.

Reliability Assessment of Power System Using Importance Sampling Technique Based on Layer Optimization Simulation

2011 ◽  
Vol 88-89 ◽  
pp. 554-558 ◽  
Author(s):  
Bin Wang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Power System ◽  
Importance Sampling ◽  
System Reliability ◽  
Sampling Method ◽  
Sampling Technique ◽  
Test System ◽  
Importance Sampling Method ◽  
Importance Sampling Technique

An improved importance sampling method with layer simulation optimization is presented in this paper. Through the solution sequence of the components’ optimum biased factors according to their importance degree to system reliability, the presented technique can further accelerate the convergence speed of the Monte-Carlo simulation. The idea is that the multivariate distribution’ optimization of components in power system is transferred to many steps’ optimization based on importance sampling method with different optimum biased factors. The practice is that the components are layered according to their importance degree to the system reliability before the Monte-Carlo simulation, the more forward, the more important, and the optimum biased factors of components in the latest layer is searched while the importance sampling is carried out until the demanded accuracy is reached. The validity of the presented is verified using the IEEE-RTS79 test system.

A Simulation-Based Random Process Method for Time-Dependent Reliability of Dynamic Systems

2010 ◽  
Author(s):  
Amandeep Singh ◽  
Zissimos P. Mourelatos ◽  
Efstratios Nikolaidis
Keyword(s):  
Random Process ◽  
Operating Conditions ◽  
Time Dependent ◽  
Process Time ◽  
Cumulative Probability ◽  
Repairable Systems ◽  
First Passage ◽  
True Value ◽  
Warranty Costs ◽  
Short Time

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. As time progresses, a product may fail due to time-dependent operating conditions and material properties, and component degradation. The reliability degradation with time may significantly increase the lifecycle cost due to potential warranty costs, repairs and loss of market share. In this work, we consider the first-passage reliability, which accounts for the first time failure of non-repairable systems. Methods are available that provide an upper bound to the true reliability, but they may overestimate the true value considerably. This paper proposes a methodology to calculate the cumulative probability of failure (probability of first passage or upcrossing) of a dynamic system with random properties, driven by an ergodic input random process. Time series modeling is used to characterize the input random process based on data from a “short” time period (e.g. seconds) from only one sample function of the random process. Sample functions of the output random process are calculated for the same “short” time because it is usually impractical to perform the calculation for a “long” duration (e.g. hours). The proposed methodology calculates the time-dependent reliability, at a “long” time using an accurate “extrapolation” procedure of the failure rate. A representative example of a quarter car model subjected to a stochastic road excitation demonstrates the improved accuracy of the proposed method compared with available methods.

A Comprehensive Procedure to Estimate the Probability of Extreme Vibration Levels Due to Mistuning

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Y.-J. Chan ◽  
D. J. Ewins
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Distribution Function ◽  
Importance Sampling ◽  
Gradient Method ◽  
Sampling Method ◽  
Optimization Analysis ◽  
Amplification Factors ◽  
Bladed Disk ◽  
Importance Sampling Method

A new procedure is developed to find the probabilities of extremely high amplification factors in mistuned bladed disk vibration levels, typical of events which occur rarely. While a rough estimate can be made by curve-fitting the distribution function generated in a Monte Carlo simulation, the procedure presented here can determine a much more accurate upper bound and the probabilities of amplification factors near to that bound. The procedure comprises an optimization analysis based on the conjugate gradient method and a stochastic simulation using the importance sampling method. Two examples are provided to illustrate the efficiency of the procedure, which can be 2 or 3 orders of magnitude more efficient than Monte Carlo simulations.

Estimating Weights of Evaluation Factors on Basis of Monte Carlo Simulation

2012 ◽  
Vol 268-270 ◽  
pp. 1735-1740
Author(s):  
Yan Fei Tian ◽  
Li Wen Huang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Random Process ◽  
Stochastic Simulation ◽  
Research Work ◽  
Simulation Method ◽  
Distribution Functions ◽  
Probability Process ◽  
Evaluation Work

Although the value of factor weight in an evaluation work is deterministic, the solving process is random, so connection between weight solution with digital characteristics or distribution functions of specific random variables or random process could be build. Using stochastic simulation method to get a lot of random solutions to the problem, expectation of the random solutions can be used as a estimation solution. On basis of idea of Monte Carlo simulation, this paper analyzed the probability process of calculating factor weight, and provided the procedures of estimating factor weight by means of Monte Carlo simulation. Through discussion and example in this paper, feasibility and validity of this method were proved, which may make foreshadowing for follow-up research work.

Optimal importance sampling for the Laplace transform of exponential Brownian functionals

2016 ◽  
Vol 53 (2) ◽  
pp. 531-542 ◽  
Author(s):  
Je Guk Kim
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Performance Analysis ◽  
Laplace Transform ◽  
Importance Sampling ◽  
Pricing Model ◽  
Asymptotically Optimal ◽  
Closed Form Solutions ◽  
The Laplace Transform ◽  
Exponential Brownian Functionals

Abstract We present an asymptotically optimal importance sampling for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals which plays a prominent role in many disciplines. To this end we utilize the theory of large deviations to reduce finding an asymptotically optimal importance sampling measure to solving a calculus of variations problem. Closed-form solutions are obtained. In addition we also present a path to the test of regularity of optimal drift which is an issue in implementing the proposed method. The performance analysis of the method is provided through the Dothan bond pricing model.

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