Optimal Calculation of Non-Probabilistic Structure Reliability Index

2014 ◽  
Vol 1048 ◽  
pp. 560-566
Author(s):  
Jia Zhao ◽  
Chang Hua Li ◽  
Jun Lian
Keyword(s):  
Reliability Index ◽  
Present Method ◽  
Minimum Distance ◽  
Limit State ◽  
Normal Space ◽  
Numerical Examples ◽  
Structure Reliability ◽  
Standard Normal ◽  
Probabilistic Structure ◽  
Optimal Calculation

The optimal calculaion of non-probabilistic structure reliability index is researched, where the minimum distance from the origin to the limit-state surface in the standard normal space is required. From the viewpoints of the global nolinear and local linear, it build the global approximate variational inequality. The primal coupled potential function is used to decide direction and step of searching. It is more effective in convergence and polynomials than the other methods in the related references. After a brief review, the method are compared through two numerical examples. It shows that the present method is effective and feasibility.

scholarly journals Reliability Analysis via an Optimal Covariance Matrix Adaptation Evolution Strategy: Emphasis on Applications in Civil Engineering

2020 ◽  
Author(s):  
Ali Kaveh ◽  
Seyed Mohammad Javadi ◽  
Roya Mahdipour Moghanni
Keyword(s):  
Reliability Index ◽  
Civil Engineering ◽  
Limit State ◽  
Normal Space ◽  
State Function ◽  
Optimization Approach ◽  
Covariance Matrix Adaptation ◽  
Highly Nonlinear ◽  
Standard Normal ◽  
Reliability Based Optimization

In this paper, a reliability-based optimization approach is applied using a recently proposed CMA-ES with optimal covariance update and storage complexity. Cholesky-CMA-ES gives a significant increase in optimization speed and reduces the runtime complexity of the standard CMA-ES. The reliability index is the shortest distance between the surface of Limit-State Function (LSF) and the origin of the standard normal space. Hence, finding the reliability index can be expressed as a constrained optimization problem. To verify the concept and test the feasibility of this algorithm, several numerical examples consisting of mathematical and highly nonlinear civil engineering problems are investigated. The reliability indexes obtained agree reasonably well with reported values from some existing approximation methods and Monte Carlo simulation.

Reliability Assessment of Existing Reinforced Concrete Arch Bridge

2013 ◽  
Vol 405-408 ◽  
pp. 1687-1690 ◽  
Author(s):  
Wei Peng ◽  
Wen Ya Ye ◽  
Jia Jia ◽  
Zhao Hui Lu ◽  
Hai Tao Hou
Keyword(s):  
Reinforced Concrete ◽  
Reliability Index ◽  
Structural Characteristics ◽  
Limit State ◽  
Element Model ◽  
Ansys Software ◽  
Arch Bridge ◽  
Structure Reliability ◽  
Main Arch ◽  
State Functions

A finite element model of an existing reinforced concrete arch bridge was established. The reliability index was investigated based on the PDF module in ANSYS software. Taking the maximum concrete stress and tendon stress as limit state, the limit state functions of main arch, upright column and deck are established respectively. There are taken as series system to study the bridge system reliability according to the structural characteristics of reinforced concrete arch bridge. The lowest reliability index superstructure is selected as the whole structure reliability index. Based on JC method and made-up MATLAB program, the reliability index of the example bridge is calculated.

Time-Dependent Reliability Analysis Using the Total Probability Theorem

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vijitashwa Pandey ◽  
Igor Baseski
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Processes ◽  
Time Dependent ◽  
Normal Space ◽  
Total Probability ◽  
Conditional Probabilities ◽  
Reliability Method ◽  
Standard Normal ◽  
Total Probability Theorem

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 conditional probabilities which are computed accurately and efficiently in the standard normal space using the first-order reliability method (FORM) and a composite limit state of linear instantaneous limit states. If the dimensionality of the total probability theorem integral is small, we can easily calculate it using Gauss quadrature numerical integration. Otherwise, simple Monte Carlo simulation (MCS) or adaptive importance sampling are used based on a Kriging metamodel of the conditional probabilities. An example from the literature on the design of a hydrokinetic turbine blade under time-dependent river flow load demonstrates all developments.

Most-Probable-Point-Locus Reliability Method in Standard Normal Space

1991 ◽  
Author(s):  
M. R. Khalessi ◽  
Y.-T. Wu ◽  
T. Y. Torng
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Search Algorithm ◽  
Limit State ◽  
Iteration Procedure ◽  
Normal Space ◽  
State Function ◽  
Most Probable Point ◽  
Reliability Method ◽  
Standard Normal

Abstract This paper describes a new structural reliability analysis iteration procedure based on the concept of most probable point locus (MPPL). Using a new quadratic search algorithm, the proposed procedure examines the global behavior of the limit-state function, g, along the MPPL in the standard normal space in search of the most probable point (MPP) on the g = o surface, and identifies unusual conditions such as multiple MPPs. During the iteration procedure, the generated information is updated after each sensitivity analysis. This action helps the analyst to minimize the number of computer runs and determine the next step. By adopting two efficient convergence criteria, the proposed procedure is demonstrated to be significantly more efficient than the commonly used reliability analysis procedures, and is suitable to be integrated with existing general-purpose finite element computer programs for nondeterministic structural analysis.

Improved bat algorithm for structural reliability assessment: application and challenges

2016 ◽  
Vol 12 (2) ◽  
pp. 218-253 ◽  
Author(s):  
Asma Chakri ◽  
Rabia Khelif ◽  
Mohamed Benouaret
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Structural Reliability ◽  
Limit State ◽  
Computing Time ◽  
Bat Algorithm ◽  
Normal Space ◽  
Content Type ◽  
Reliability Method ◽  
Adaptive Penalty

Purpose – The first order reliability method requires optimization algorithms to find the minimum distance from the origin to the limit state surface in the normal space. The purpose of this paper is to develop an improved version of the new metaheuristic algorithm inspired from echolocation behaviour of bats, namely, the bat algorithm (BA) dedicated to perform structural reliability analysis. Design/methodology/approach – Modifications have been embedded to the standard BA to enhance its efficiency, robustness and reliability. In addition, a new adaptive penalty equation dedicated to solve the problem of the determination of the reliability index and a proposition on the limit state formulation are presented. Findings – The comparisons between the improved bat algorithm (iBA) presented in this paper and other standard algorithms on benchmark functions show that the iBA is highly efficient, and the application to structural reliability problems such as the reliability analysis of overhead crane girder proves that results obtained with iBA are highly reliable. Originality/value – A new iBA and an adaptive penalty equation for handling equality constraint are developed to determine the reliability index. In addition, the low computing time and the ease implementation of this method present great advantages from the engineering viewpoint.

Time-Dependent Reliability Analysis Using the Total Probability Theorem

2014 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vijitashwa Pandey ◽  
Igor Baseski
Keyword(s):  
Reliability Analysis ◽  
Conditional Probability ◽  
Limit State ◽  
Random Variables ◽  
Random Processes ◽  
Time Dependent ◽  
Normal Space ◽  
Total Probability ◽  
Standard Normal ◽  
Total Probability Theorem

A new reliability analysis method is proposed for time-dependent problems with limit-state functions of input random variables, input random processes and explicit in time 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 a time-dependent conditional probability which is computed accurately and efficiently in the standard normal space using FORM and a composite limit state of linear instantaneous limit states. If the dimensionality of the total probability theorem integral (equal to the number of input random variables) is small, we can easily calculate it using Gauss quadrature numerical integration. Otherwise, simple Monte Carlo simulation or adaptive importance sampling is used based on a pre-built Kriging metamodel of the conditional probability. An example from the literature on the design of a hydrokinetic turbine blade under time-dependent river flow load demonstrates all developments.

A Comprehensive Investigation of Ensembles of Gaussian-Based and Gradient-Based Transformed Reliability Analyses: When and How to Use Them

2016 ◽  
Author(s):  
Po Ting Lin ◽  
Wei-Hao Lu ◽  
Shu-Ping Lin
Keyword(s):  
Design Optimization ◽  
Design Space ◽  
Optimization Problems ◽  
Nonlinear Problems ◽  
Kernel Functions ◽  
Sensitivity Analyses ◽  
Normal Space ◽  
Highly Nonlinear ◽  
Standard Normal ◽  
Gradient Based

In the past few years, researchers have begun to investigate the existence of arbitrary uncertainties in the design optimization problems. Most traditional reliability-based design optimization (RBDO) methods transform the design space to the standard normal space for reliability analysis but may not work well when the random variables are arbitrarily distributed. It is because that the transformation to the standard normal space cannot be determined or the distribution type is unknown. The methods of Ensemble of Gaussian-based Reliability Analyses (EoGRA) and Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) have been developed to estimate the joint probability density function using the ensemble of kernel functions. EoGRA performs a series of Gaussian-based kernel reliability analyses and merged them together to compute the reliability of the design point. EGTRA transforms the design space to the single-variate design space toward the constraint gradient, where the kernel reliability analyses become much less costly. In this paper, a series of comprehensive investigations were performed to study the similarities and differences between EoGRA and EGTRA. The results showed that EGTRA performs accurate and effective reliability analyses for both linear and nonlinear problems. When the constraints are highly nonlinear, EGTRA may have little problem but still can be effective in terms of starting from deterministic optimal points. On the other hands, the sensitivity analyses of EoGRA may be ineffective when the random distribution is completely inside the feasible space or infeasible space. However, EoGRA can find acceptable design points when starting from deterministic optimal points. Moreover, EoGRA is capable of delivering estimated failure probability of each constraint during the optimization processes, which may be convenient for some applications.

RELIABILITY OF CORRODED STIFFENED PLATE SUBJECTED TO UNIAXIAL COMPRESSIVE LOADING

2021 ◽  
Vol 162 (A4) ◽  
Author(s):  
K Woloszyk ◽  
Y Garbatov
Keyword(s):  
Mechanical Properties ◽  
Reliability Index ◽  
Structural Reliability ◽  
Limit State ◽  
Plate Thickness ◽  
Thickness Reduction ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Initial Imperfections ◽  
Subsequent Decrease

The work is focused on the reliability of corroded stiffened plates subjected to compressive uniaxial load based on the progressive collapse approach as stipulated by the Common Structural Rules for Bulk Carriers and Oil Tankers, employing the limit state design. Two different cases have been investigated. In the first model, the corrosion degradation led to uniform thickness loss, whereas the mechanical properties were unchanged, as given in the Rules. In the second model, the plate thickness degradation was followed by mechanical properties reduction. The uncertainties related to the mechanical properties, thicknesses, and initial imperfections of the corroded stiffened plate were taken into account. Several initial design solutions of stiffened plates, as well as different severity levels of corrosion degradation were investigated. The results show that structural reliability significantly decreases with corrosion development, especially when in addition to the initial imperfections and corrosion plate thickness reduction, corroded plate surface roughness and the changes in the mechanical properties were considered. The uncertainties, their origins and confidence levels are discussed. It was found that non-linear time-dependent corrosion degradation accounting not only for the thickness reduction due to corrosion wastage but also the subsequent decrease of mechanical properties lead to a significant reduction in the reliability index. Additionally, it was defined that the reliability estimate is very sensitive to the uncertainties related to the initial thickness and the spread of corrosion degradation as a function of the time. Incorporating the probability of corrosion detection into the original reliability model introduces additional information about the validity of structural degradation that may lead to a higher beta reliability index estimate compared to the original model.

Determination of Basic Wind Velocity for Wind Load-Governed Limit State

2019 ◽  
Author(s):  
Ji Hyeon Kim ◽  
Hae-Sung Lee
Keyword(s):  
Wind Velocity ◽  
Reliability Index ◽  
General Procedure ◽  
Limit State ◽  
Wind Load ◽  
Wind Pressure ◽  
Load Factor ◽  
Load Effect ◽  
Design Life ◽  
Target Reliability Index

<p>This paper proposes a general procedure for evaluating a nominal value of wind velocity for a wind load- governed limit state to secure a target reliability index during the design life of a structure. The nominal value of wind velocity, referred to as a basic wind velocity, and wind load factor should be determined so that the factored wind load effect secures a target reliability index for a wind load-governed limit state. In this study, the analytical form of the return period of the basic wind velocity is expressed as a function of the target reliability index, wind load factor, and statistical parameters of wind pressure, which are derived as linear functions of the coefficient of wind velocity. The proposed approach is applied to the Korean Highway Bridge Design Code-Cable supported Bridge, which specifies the design life of a structure as 100- and 200-year.</p>

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