Time-variant reliability analysis via approximation of the first-crossing PDF

Yu, Shui; Zhang, Yanwei; Li, Yun; Wang, Zhonglai

doi:10.1007/s00158-020-02635-y

Cited by 23 publications

(7 citation statements)

References 48 publications

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“…Based on the Poisson hypothesis model, Markov hypothesis model, or other improved models, the strategy transforms the cross-crossing rate into time-variant reliability. 31,32 Compared with MCS, the second strategy is more efficient. The third strategy is the surrogate model method.…”

Section: Time-variant Reliability Analysismentioning

confidence: 99%

Dynamic response and time-variant reliability analysis of an eight-rod shock isolator

Liu

Huang

Yan

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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The operation of a warship is commonly affected by shock loads in different directions during sailing in a rough sea, which can decrease the precision of the shipboard equipment. To improve the shock resistance performance of the shipboard equipment, an isolator is usually installed to isolate it from the vibration of the ship deck. The paper proposes a method for dynamic response and time-variant reliability analysis of an eight-rod shock isolator (ERSI). ERSI has a novel symmetrical structure, which can improve the utilization of the isolation rods compared with the classical parallel mechanism. The isolator is modeled using Denavit-Hartenberg (D-H) convention and screw theory. Then, Duhamel integral is employed to derive the dynamic response to the isolator after decoupling the governing equation using the modal analysis method. Considering impacts of uncertain factors, this paper also presents a practical method for time-variant reliability analysis of ERSI. Finally, a discussion of the practical example of this method along with a detailed analysis to evaluate the efficiency of the proposed method is presented.

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Section: Time-variant Reliability Analysismentioning

confidence: 99%

Dynamic response and time-variant reliability analysis of an eight-rod shock isolator

Liu

Huang

Yan

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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show abstract

“…The failure rate, on the other hand, is evaluated using concepts from FORM (First Order Reliability Method) [Madsen et al, 1986, Ditlevsen andMadsen, 1996a]. Some additional methods on the subject were later proposed by Li and Mourelatos [2009], Singh et al [2010], Hu and Du [2013a], Hu and Du [2013b], Hu and Du [2014], Jiang et al [2014], Jiang et al [2017], Jiang et al [2018], Hawchar et al [2015], Hawchar et al [2017], Moarefzadeh and Sudret [2018], Nie and Ellingwood [2005], Gong and Frangopol [2019], Zhou et al [2017], Yu et al [2020], Wu et al [2020], Hu et al [2021], Zhang et al [2021]. However, it must be emphasized that all these methods are based on a discretization of the stochastic processes using expansion techniques such as EOLE or KL.…”

Section: Literature Overviewmentioning

confidence: 99%

Time Series Models and Expansion Optimal Linear Estimation for Time-Dependent Reliability Analysis

Torii¹,

Medeiros²,

Kroetz³

et al. 2022

Uncertainty Modeling: Fundamental Concepts and Models

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This chapter presents conceptual and computational comparisons between EOLE (Expansion Optimal Linear Estimation) and AR (Auto-Regressive) models to represent stochastic processes in the context of time-dependent reliability analysis. Even though expansion techniques, such as EOLE, are appropriate for problems where the properties of the stochastic process are explicitly known, such information is rarely available in practical situations. On the other hand, time series models, such as AR, are widely employed to represent stochastic processes from real time monitoring or available historical data. For this reason, here we compare EOLE and AR in the context of time-dependent reliability analysis. We first demonstrate how AR models can be calibrated to represent a given stochastic process with known properties. It is then demonstrated that similar results for time-dependent reliability can be obtained using the two approaches. This is an important contribution from both conceptual and practical reasons, since it demonstrates that existing AR models (and likely other types of time series models) can be directly employed for time-dependent reliability analysis, without the need to first obtain an equivalent EOLE model.

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“…Jiang et al [13] presented an outcrossing rate model and efficient calculation approach for timedependent system reliability analysis. Yu et al [14] presented a combined method to approximate the PDF of the first-crossing point. The first-crossing based method is the most popular method for the time-dependent reliability analysis.…”

Section: Introductionmentioning

confidence: 99%

Active Learning Kriging Model With Adaptive Uniform Design for Time-Dependent Reliability Analysis

Li²

2021

IEEE Access

Self Cite

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Due to uncertainties and time-varying parameters in design, manufacturing, and commissioning, many structural systems often exhibit uncertain and dynamic properties. The timedependent reliability analysis structural systems can effectively estimate the safe state during their lifecycle. However, one of its critical challenging issues lies in computational efficiency. This paper develops an active learning Kriging technique to improve the computational efficiency of time-dependent reliability analysis. The Kriging model is first employed as a response surface to fit the extreme value response of time-dependent limit state functions. The Most Probable Point (MPP) of the Kriging response surface is then determined by solving an optimization problem in terms of the cumulative distribution function (CDF). Further, an adaptive iterative algorithm is developed to prepare the sampling points for updating the Kriging model based on the adaptive uniform design. The Monte Carlo simulation (MCS) can thus facilitate evaluation based on the final generated Kriging response surface. Several case studies are performed to test and validate the effectiveness of the proposed method and its applicability to practical engineering problems.

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Time-variant reliability analysis via approximation of the first-crossing PDF

Cited by 23 publications

References 48 publications

Dynamic response and time-variant reliability analysis of an eight-rod shock isolator

Dynamic response and time-variant reliability analysis of an eight-rod shock isolator

Time Series Models and Expansion Optimal Linear Estimation for Time-Dependent Reliability Analysis

Active Learning Kriging Model With Adaptive Uniform Design for Time-Dependent Reliability Analysis

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