Research Papers

Time-Dependent Reliability Analysis Using a Vine-ARMA Load Model

[+] Author and Article Information
Zhen Hu

Department of Civil and Environmental Engineering,
Vanderbilt University,
279 Jacobs Hall, Nashville, TN 37235
e-mail: zhen.hu@vanderbilt.edu

Sankaran Mahadevan

Department of Civil and Environmental Engineering,
Vanderbilt University,
272 Jacobs Hall, Nashville, TN 37235
e-mail: sankaran.mahadevan@vanderbilt.edu

1Corresponding author.

Manuscript received April 6, 2016; final manuscript received September 12, 2016; published online November 21, 2016. Assoc. Editor: Michael Beer.

ASME J. Risk Uncertainty Part B 3(1), 011007 (Nov 21, 2016) (12 pages) Paper No: RISK-16-1078; doi: 10.1115/1.4034805 History: Received April 06, 2016; Accepted September 13, 2016

A common strategy for the modeling of stochastic loads in time-dependent reliability analysis is to describe the loads as independent Gaussian stochastic processes. This assumption does not hold for many engineering applications. This paper proposes a Vine-autoregressive-moving average (Vine-ARMA) load model for time-dependent reliability analysis, in problems with a vector of correlated non-Gaussian stochastic loads. The marginal stochastic processes are modeled as univariate ARMA models. The correlations among different univariate ARMA models are captured using the Vine copula. The ARMA model maintains the correlation over time. The Vine copula represents not only the correlation among different ARMA models but also the tail dependence of different ARMA models. Therefore, the developed Vine-ARMA model can flexibly model a vector of high-dimensional correlated non-Gaussian stochastic processes with the consideration of tail dependence. Due to the complicated structure of the Vine-ARMA model, new challenges are introduced in time-dependent reliability analysis. In order to overcome these challenges, the Vine-ARMA model is integrated with a single-loop Kriging (SILK) surrogate modeling method. A hydrokinetic turbine blade subjected to a vector of correlated river flow loads is used to demonstrate the effectiveness of the proposed method.

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Fig. 1

Four-variable (node) Vine models: (a) D-Vine, (b) C-Vine, and (c) a regular Vine

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Fig. 2

Illustration of a hydrokinetic turbine

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Fig. 3

Geometry configuration of the turbine blade: (a) side view locations, (b) front view, and (c) top view

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Fig. 4

Chord length distribution of the turbine blade

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Fig. 5

Twist angle distribution of the turbine blade

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Fig. 6

Flowchart of the stress analysis for the turbine blade

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Fig. 7

von Mises stress response of the turbine blade

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Fig. 8

One realization of simulated river velocities at four stations

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Fig. 9

Velocity at station i versus velocity at location j, ∀i,j=2,5,8,11




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