2015
DOI: 10.1115/1.4029326
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Time-Dependent Reliability Analysis Using the Total Probability Theorem

Abstract: A new reliability analysis method is proposed for time-dependent problems with explicit in time limit-state functions of input random variables and input random processes using the total probability theorem and the concept of composite limit state. The input random processes are assumed Gaussian. They are expressed in terms of standard normal variables using a spectral decomposition method. The total probability theorem is employed to calculate the time-dependent probability of failure using time-dependent con… Show more

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Cited by 65 publications
(25 citation statements)
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“…Based on the training points and the associated responses, a surrogate modelĜ t ð Þ ¼ĝ X; t ð Þ is built using the Kriging method reviewed in the appendix. For any untrained point x; t ½ , the surrogate model prediction is Ĝ t ð Þ $ Nĝ x; t ð Þ; rĝ 2 x; t ð Þ (11) in which N Á; Á ð Þ stands for normal distribution, andĝ x; t ð Þ and rĝ 2 x; t ð Þ are the expected value and variance of the prediction, which are obtained from Eqs. (A4) and (A5), respectively.…”
Section: Surrogate Modeling Ofĝ X; T ð þmentioning
confidence: 99%
See 1 more Smart Citation
“…Based on the training points and the associated responses, a surrogate modelĜ t ð Þ ¼ĝ X; t ð Þ is built using the Kriging method reviewed in the appendix. For any untrained point x; t ½ , the surrogate model prediction is Ĝ t ð Þ $ Nĝ x; t ð Þ; rĝ 2 x; t ð Þ (11) in which N Á; Á ð Þ stands for normal distribution, andĝ x; t ð Þ and rĝ 2 x; t ð Þ are the expected value and variance of the prediction, which are obtained from Eqs. (A4) and (A5), respectively.…”
Section: Surrogate Modeling Ofĝ X; T ð þmentioning
confidence: 99%
“…This paper focuses on component reliability, which has been extensively studied in recent years. For instance, a PHI2 method has been developed to compute the time-variant reliability by estimating the upcrossing rate at each time instant [6]; Singh and Mourelatos [7] proposed a composite limit-state function method and investigated importance sampling [8], Markov Chain Monte Carlo simulation (MCS) [9], subset simulation [10], and total probability theory [11] for this estimation; Hagen and Tvedt [12,13] proposed a parallel system approach to solve timedependent problems with binomial distributions; Li and Chen developed a reliability analysis method for dynamic response using a new probability density evolution approach [14]; Along with these methods, Zhang and Du [15] derived analytical expressions for the upcrossing rate of function generator mechanisms; Du [16] proposed an envelope function method based on firstorder approximation; Hu and Du investigated the upcrossing rate method [17], joint upcrossing rate method [18], and the first-order sampling approach [19]; Wang and Wang [20,21] presented a nested extreme value response method to estimate the timedependent reliability; and Jiang et al [22] studied the strategy of time-dependent reliability assessment through stochastic process discretization.…”
Section: Introductionmentioning
confidence: 99%
“…To handle time dependency of system failures, various approaches have been developed, which can be generally categorized into two types, the first-passage based approaches [12][13][14][15][16][17][18] and the extreme value based approaches [19][20][21][22][23]. In the first-passage based approaches, outcrossing events will occur if the system performance exceeds the upper bound or falls below the lower bound of the safety threshold, and thus the first order derivative of reliability with respect to time can be approximated by an out-crossing rate measure.…”
Section: Nomenclaturementioning
confidence: 99%
“…Therefore, to improve products reliability, reliability modeling methods, and reliability estimation methods have been widely developed and used in reality. For reliability estimation, two types of methods, namely, instantaneous reliability estimation approaches [2][3][4] and time-dependent reliability estimation methods, [5][6][7] have been studied in the field. Since the mechanical systems become more and more complex, multi-failure modes occurring and time-consuming design of experiments (DOE), instantaneous reliability estimation techniques by data-driven technology combining with physics of failure modeling methods have been developed and widely used in aerospace, transportation, oil and gas exploration, and petrochemical industries.…”
Section: Introductionmentioning
confidence: 99%