Adaptation of fast Fourier transformations to estimate the structural failure probability

2000 ◽  
Author(s):  
Ravi Penmetsa ◽  
Liwu Zhou ◽  
Ramana Grandhi
Keyword(s):  
Failure Probability ◽  
Structural Failure

ON RELIABILITY-BASED STRUCTURAL OPTIMISATION USING STOCHASTIC QUASIGRADIENT METHODS/ZUR ZUVERLÄSSIGKEITSTHEORETISCH GESTÜTZTEN TRAGWERKS-OPTIMIERUNG MIT VERFAHREN DER STOCHASTISCHEN QUASIGRA-DIENTEN

1995 ◽  
Vol 1 (2) ◽  
pp. 43-64
Author(s):  
E. R. Vaidogas
Keyword(s):  
Objective Function ◽  
Lagrange Multiplier ◽  
Failure Probability ◽  
Stochastic Gradient ◽  
Lagrange Multiplier Method ◽  
Time Dependent ◽  
Multiplier Method ◽  
Structural Failure ◽  
Structural Optimisation ◽  
Constraint Function

Methodical aspects of the reliability-based structural optimisation using stochastic quasigradient methods are considered. For an example of the simply supported reinforced concrete beam, the employment of the Lagrange multiplier method that belongs to the class of stochastic quasigradient methods is demonstrated. The classical optimum design goal to minimise structural cost or weight under the constraint on the structural failure probability is taken for consideration. Optimisation problems solved with the Lagrangemultiplier method are formulated in form of general stochastic programming problem. The mathematical expectation of the concrete volume reduced with respect to the in-place cost of the beam materials is taken as the objective function. Constraint function is the limitation placed on the beam failure probability. The beam is considered as a series structural system. Values of the prescribed allowable failure probability belongs to the interval in which the estimation of the failure probabilities by the simple Monte-Carlomethod is possible with an acceptable confidence. The time-independent case as well as the time-dependent one is considered in the optimisation problems. The generalisation on the time-dependent case is undertaken through the introduction into the constraint function of the quasi-linear distribution law of the random variables. In the time-dependent case, the objective function is associated with beginning and the constraint function with end of the service period. An expression of the stochastic gradient based on the differentiation under the integral sign is used for calculations with the Lagrange multiplier method. The stochastic gradient used is computationally more effective in comparison with stochastic finite-difference formulae usual in stochastic quasigradient methods because it requires only one computation of the structure in search iteration of the optimisation process. Three rules based on statistical argumentation are used for the stopping of the seat according to the procedure of the Lagrange multiplier method. The optimising of the beam shows that the Lagrange multiplier method is applicable for the optimal design of structures in that cases when the structural reliability can be estimated by means of the simple Monte-Carlo method. Additional research is needed for integration in the Lagrange multiplier method of statistical simulation techniques for the estimation of small structural failure probabilities.

scholarly journals Structural Safety Assessment of Marine Operations From a Long-Term Perspective: A Case Study of Offshore Wind Turbine Blade Installation

2019 ◽  
Author(s):  
Amrit Shankar Verma ◽  
Zhen Gao ◽  
Zhiyu Jiang ◽  
Zhengru Ren ◽  
Nils Petter Vedvik
Keyword(s):  
Failure Probability ◽  
Safety Assessment ◽  
Routine Activity ◽  
Structural Safety ◽  
Offshore Wind Turbine ◽  
Structural Failure ◽  
Blade Root ◽  
Extreme Response

Abstract A marine operation is a complex non-routine activity of limited duration carried out in offshore environment. Due to safety reasons, these operations are normally performed within specific sea state limits, which are derived from numerical modelling and analysis of hazardous events. In view of the uncertainties in the assessment of structural responses under stochastic environmental conditions, these limiting curves correspond to a target structural failure probability recommended in offshore standards (for example, 10−4 per operation as specified by DNV-GL). However, one of the main limitations is that these curves do not reflect site-specific safety assessment. The current paper presents a novel methodology for assessing the structural safety level of marine operations from a long-term perspective. The methodology includes estimation of extreme response distribution under all possible operational sea states (i.e. the operational domain under the limiting sea states) for a given offshore site and is compared to the response limit to obtain an average failure probability. A case study is also presented for a blade root mating process onto preassembled hub using a jack-up crane vessel and risk of impact between root and hub is considered critical. Global time-domain simulations are performed using multibody dynamics, and extreme value distributions for impact velocities are derived for different wind-wave conditions. The allowable impact velocity between the blade root and the hub is determined by an explicit finite element analysis of the damage at the blade root. Finally, the average failure probabilities considering the operational domain are obtained for four different European offshore sites and are compared to the target level of structural failure probability considered for the limiting sea states.

scholarly journals A Bayesian updating of crack distributions in steam generator tubes

2021 ◽  
Vol 30 (2) ◽  
pp. 33-44
Author(s):  
Alexandre Santos Francisco ◽  
Tiago Simões
Keyword(s):  
Steam Generator ◽  
Failure Probability ◽  
Nuclear Power ◽  
Power Plants ◽  
Plastic Collapse ◽  
Structural Failure ◽  
Maintenance Strategies ◽  
Threshold Size ◽  
Steam Generator Tubes ◽  
Good Agreement

The structural failure of steam generator tubes is a common problem that can a ect the availability and safety of nuclear power plants. To minimize the probability of occurrence of failure, it is needed to implement maintenance strategies such as periodic nondestructive inspections of tubes. Thus, a tube is repaired or plugged whenever it has detected a crack which a threshold size is overtaken. In general, uncertainties and errors in crack sizes are associated with the nondestructive inspections. These uncertainties and errors should be appropriately characterized to estimate the actual crack distribution. This work proposes a Bayesian approach for updating crack distributions, which in turn allows computing the failure probability of steam generator tubes at current and future times. The failure criterion is based on plastic collapse phenomenon, and the failure probability is computed by using the Monte-Carlo simulation. The failure probability at current and future times is in good agreement with the ones presented in the literature.

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