Reliability Analysis of Two-Dimensional Series Portal-Framed Bridge System Based on Mixed Copula Functions

2013 ◽  
Vol 574 ◽  
pp. 95-105 ◽  
Author(s):  
Yue Fei Liu ◽  
Da Gang Lu
Keyword(s):  
Failure Modes ◽  
Copula Function ◽  
Monte Carlo Sampling ◽  
Two Dimensional ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Performance Function ◽  
Mcs Method ◽  
Dimensional Series ◽  
Bridge System

In this paper, several commonly-used Elliptical copulas and Archimedean copulas were introduced, and their application in the correlation analysis were also described in detal. For the two failure modes of two-dimensional series portal-framed bridge system, the performance function values with respect to the failure modes were considered as the analysis variables of the chosen copula functions, and the Baysian copula selection method was applied to select the proper copula functions. And then, the two-dimension mixed copula function was built. Thereinto, the uncertain parameters of copula function were determined with Monte Carlo Sampling (MCS) method, so the numerical modeling of the mixed copula fuction about the failure mode of two-dimensional series portal-framed bridge system was achieved. Finally the reliability of this system was analyzed with the built mixed copula function, and the structural system failure probability was obtained.

Research on Function Reliability of Gear Door Lock System With Correlated Failure Models Based on Mixed Copula

2016 ◽  
Author(s):  
Linjie Shen ◽  
Yugang Zhang ◽  
Xinchen Zhuang
Keyword(s):  
Failure Modes ◽  
Tail Dependence ◽  
Copula Function ◽  
Large Error ◽  
Copula Model ◽  
Copula Functions ◽  
Copula Theory ◽  
Reliability Models ◽  
Dynamic Simulation Model ◽  
Door Lock

The gear door lock system (GDLS) is a mechanism with multi-failure modes. It often leads to a large error when ignoring the correlation between failure modes. Copula theory in this work is applied to research the correlation between two failure modes. A dynamic simulation model is constructed to acquire the joint statistics characteristics of the two failure modes. Gumbel and Clayton Copula functions are chosen to establish the reliability model respectively, which shows that the single Copula model cannot fully capture the tail dependence. To solve the problem, a mixed Copula function is constructed. The minimum squared Euclidean distance is adopted to estimate the parameters of the reliability models. It shows that the result of mixed Copula model is the closest to that of the Monte Carlo simulation, and it presents the relative error is at least 46% lower than the single Copula.

scholarly journals System Reliability Evaluation of a Bridge Structure Based on Multivariate Copulas and the AHP–EW Method That Considers Multiple Failure Criteria

2020 ◽  
Vol 10 (4) ◽  
pp. 1399 ◽  
Author(s):  
Hanbing Liu ◽  
Xirui Wang ◽  
Guojin Tan ◽  
Xin He
Keyword(s):  
System Reliability ◽  
Failure Modes ◽  
Failure Criteria ◽  
Reliability Evaluation ◽  
Bridge Structure ◽  
Copula Functions ◽  
Entropy Weight ◽  
Joint Failure ◽  
Simply Supported ◽  
Bridge System

The system reliability evaluation of a bridge structure is a complicated problem. Previous studies have commonly used approximate estimation methods, such as the wide bounds method and the narrow bounds method, but neither could obtain an accurate result. In recent years, the copula theory has been introduced into the system reliability evaluation, which can obtain more accurate results than the approximate methods. However, most studies simply construct binary copula functions to consider the joint failure of two failure modes. For a complex bridge structure composed of multiple components and failure modes, the joint failure of multiple failure modes needs to be considered. Before evaluating the system reliability, it is necessary to determine the failure criteria of the system. Different failure criteria for simply supported beam bridges have been proposed. However, there is no standard available to determine which failure criterion to choose, and the selection of failure criteria is ambiguous. In this paper, a novel method is proposed to evaluate the system reliability of a simply supported beam bridge by considering multiple failure criteria based on multivariate copulas and the analytic hierarchy process entropy weight (AHP–EW) method. The method first considers multiple failure criteria comprehensively and constructs multivariate copulas for the joint failure of multiple components in a bridge system reliability evaluation. The AHP–EW method is a comprehensive weighting method combining the analytic hierarchy process and entropy weight methods, which is used to establish the hierarchical analysis model between system reliability and multiple failure criteria. By considering the joint failure of multiple failure modes in the system reliability evaluation under a single failure criterion, multivariate copula functions were constructed. In order to verify the applicability of the proposed bridge system reliability method, a simply supported reinforced concrete (RC) hollow slab bridge composed of nine slab segments was selected as the numerical example. The results indicate that the method proposed in this paper could evaluate the bridge system reliability more comprehensively and reasonably.

scholarly journals Probabilistic analysis of coincident sums of precipitation at two measurement stations. Introduction to the method and an example

2018 ◽  
Vol 23 ◽  
pp. 00002
Author(s):  
Gabriela Biel
Keyword(s):  
Rank Correlation ◽  
Random Variable ◽  
Analysis Data ◽  
Botanical Garden ◽  
Copula Function ◽  
Rain Gauge ◽  
Two Dimensional ◽  
Copula Functions ◽  
Frank Copula ◽  
Definition Of

This article proposes the use of copula (copula function) for the purpose of two-dimensional analysis of the sums of precipitation as measured with a Hellman rain-gauge. The sums of precipitation are characterized by a two-dimensional random variable: the sum of uninterrupted sequence of rainfalls which were measured in Jelcz-Laskowice and the corresponding (coincident) sum of precipitation at the Botanical Garden in Wrocław. Several problems occur from the very start: debonding from time and lack of precipitation on one of stations. For the purpose of greater precision and correction it should be stated that in order to apply the two-dimensional copula functions we will use a random vector determining the sum of uninterrupted sequences of rainfalls at two simultaneous stations. In that way, this will not be a characteristics of the phenomenon, but rather the definition of two-dimensional random variable under analysis. Data for analysis has been derived from observational logs of the Institute of Meteorology and Water Management, branch in Wrocław. The results obtained in years 1980-2014 were subject to analysis. The aim of the work was to find the best two-dimensional probability distribution of a random variable (OpadJelcz, OpadOgród). The following were analysed from among the known copulas: the Archimedean copulas (the Gumbel copula, the Frank copula and the Clayton copula) and the Gaussian elliptical copula. The study of fitting of copulas to observed variables was carried out using the Spearmann's rank correlation coefficient and the best fitting was obtained for the Frank's copula.

scholarly journals Compound Archimedean Copulas

2021 ◽  
Vol 10 (3) ◽  
pp. 126
Author(s):  
Moshe Kelner ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Random Variables ◽  
Copula Function ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Unique Structure ◽  
The Family ◽  
The Many

The copula function is an effective and elegant tool useful for modeling dependence between random variables. Among the many families of this function, one of the most prominent family of copula is the Archimedean family, which has its unique structure and features. Most of the copula functions in this family have only a single dependence parameter which limits the scope of the dependence structure. In this paper we modify the generator of Archimedean copulas in a way which maintains membership in the family while increasing the number of dependence parameters and, consequently, creating new copulas having more flexible dependence structure.

Copula Simulation of Mechanical Structural Systems Failure Mode

2012 ◽  
Vol 462 ◽  
pp. 844-849 ◽  
Author(s):  
Wen Qin Han ◽  
Jin Yu Zhou
Keyword(s):  
Failure Modes ◽  
Joint Probability ◽  
Copula Function ◽  
Joint Probability Distribution ◽  
Structural Systems ◽  
Practical Case ◽  
Structural System ◽  
Probability Models ◽  
Copula Functions ◽  
Unknown Parameters

As a new and efficient tool of statistical analysis, Copula has the capability of putting multivariate random probability models into practice, and describing time-varying and nonlinear feature of statistcal dependence of random variables. Aiming at mechanical structural systems with failure-dependence, a new method is put forward for reliability modeling by introducing mixed copula, in which giving a reference to several copula functions and its applicable feature of the correlation. Copula model of joint probability distribution function is build between every functions, in which every functions value are chosen as the analytic variables of copula function and unknown parameters of copula are estimated by means of the random sampling data generated by Monte Carlo simulation in MATLAB software, thereby failure probability of the structural system is got by copula function. Finally, a practical case of copula demonstrates the feasibility of the method , which give a new path for the reliability analysis of mechanical structural system with correlated failure modes.

scholarly journals Composite hollow truss with multiple vierendeel panels

2013 ◽  
Vol 66 (4) ◽  
pp. 431-438
Author(s):  
Augusto Ottoni Bueno da Silva ◽  
Newton de Oliveira Pinto Júnior ◽  
João Alberto Venegas Requena
Keyword(s):  
Bearing Capacity ◽  
Failure Modes ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Two Dimensional ◽  
Shear Forces ◽  
Vertical Displacements ◽  
New System ◽  
The Ideal

The aim of this study was to evaluate through analytical calculation, two-dimensional elastic modeling, and three-dimensional plastic modeling, the bearing capacity and failure modes of composite hollow trusses bi-supported with a 15 meter span, varying the number of central Vierendeel panels. The study found the proportion span/3 - span/3 - span/3, as the ideal relationship for the truss - Vierendeel - truss lengths, because by increasing the proportion of the length occupied by the central Vierendeel panels, the new system loses stiffness and no longer supports the load stipulated in the project. Furthermore, they can start presenting excessive vertical displacements and insufficient resistance to external shear forces acting on the panels.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

Lifetime assessment method for products with dependent competing failures based on copula theory

2013 ◽  
Vol 228 (9) ◽  
pp. 1622-1633 ◽  
Author(s):  
Xiangpo Zhang ◽  
Jianzhong Shang ◽  
Xun Chen ◽  
Chunhua Zhang ◽  
Yashun Wang
Keyword(s):  
Statistical Inference ◽  
Failure Modes ◽  
Likelihood Estimation ◽  
Copula Function ◽  
Assessment Method ◽  
Distribution Functions ◽  
Life Testing ◽  
Copula Theory ◽  
Dependent Relationship ◽  
Margin Distribution

Based on copula theory and methods, we construct the dependent relationship between the margin distribution functions of the competing failure modes and their joint distribution function through copula function. With the dependent relationship, we study statistical inference method of the life testing with dependent competing failure modes, and found the maximum likelihood estimation (MLE) model for the parameter estimations to evaluate the lifetime of the products. The results and analysis of case studies prove that sample size, proportion of censored samples, proportion of failure samples with masked failure mode, and copula model types have great impact on the accuracy of the lifetime assessment of the products with dependent competing failure modes. And with appropriate test data and right copula modes, method developed in this paper has very good accuracy for the lifetime assessment with dependent competing failure modes. It provides an effective and accurate way to solve the problems of statistical inference of life testing with dependent competing failure modes, and also an accurate way of lifetime assessment for products.

Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions

2009 ◽  
Vol 465 (2109) ◽  
pp. 2725-2749 ◽  
Author(s):  
M. J. Ablowitz ◽  
T. S. Haut
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Asymptotic Series ◽  
High Order ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Small Surface ◽  
Petviashvili Equation ◽  
Dimensional Series

High-order asymptotic series are obtained for two- and three-dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known sech 2 solution of the Korteweg–de Vries equation; in three dimensions, the first term is the rational lump solution of the Kadomtsev–Petviashvili equation I. The two-dimensional series is used (with nine terms included) to investigate how small surface tension affects the height and energy of large-amplitude waves and waves close to the solitary version of Stokes’ extreme wave. In particular, for small surface tension, the solitary wave with the maximum energy is obtained. For large surface tension, the two-dimensional series is also used to study the energy of depression solitary waves. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. In three dimensions, analytic solutions for the high-order perturbation terms are computed numerically, and the resulting asymptotic series (to three terms) is used to obtain the speed versus maximum amplitude curve for solitary waves subject to sufficiently large surface tension. Finally, the above asymptotic method is applied to the Benney–Luke (BL) equation, and the resulting asymptotic series (to three terms) is verified to agree with the solitary-wave solution of the BL equation.

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