Evaluation on Safety of In-Service Structures Concerning Earthquake Resistance Based on Fourth-Order Moment of Limit State Function

2014 ◽  
Vol 1065-1069 ◽  
pp. 2319-2322
Author(s):  
Yu Ying Wang ◽  
Ya Zhou Sun ◽  
Le Yang Feng
Keyword(s):  
Bearing Capacity ◽  
Fourth Order ◽  
Structural Damage ◽  
Limit State ◽  
Decisive Role ◽  
Order Moment ◽  
State Function ◽  
Limit State Function ◽  
Engineering Structures ◽  
Internal Factors

During the process of being used, engineering structures will undergo material aging and structural damage with time passing by under the combined influence of internal factors including load, environment and structural material[1], and accumulation of such damages will cause decrease of bearing capacity, durability and reliability. Among various factors influencing the reliability of in-service structures, ultimate bearing capacity plays the decisive role in safety. In this paper, the fourth-order moment of limit state function is inferred through calculation of failure probability of in-service structures, and thus safety and durability of in-service structures can be ensured.

Reliability Analysis of Mechanical Systems Based on the First Four Moments of Input Parameters

2020 ◽  
Author(s):  
Singiresu S. Rao ◽  
Yang Zhou
Keyword(s):  
Reliability Analysis ◽  
Fourth Order ◽  
Probability Distributions ◽  
Limit State ◽  
Moment Function ◽  
Design Parameters ◽  
Order Moment ◽  
State Function ◽  
Exact Probability ◽  
First Four Moments

Abstract The performance of a mechanical or structural system can be improved through a proper selection of its design parameters such as the geometric dimensions, external actions (loads) and material characteristics. The computation of the reliability of a system, in general, requires a knowledge of the probability distributions of the parameters of the system. It is known that for most practical systems, the exact probability distributions of the parameters are not known. However, the first few moments of the parameters of the system may be readily available in many cases from experimental data. The determination of the reliability and the sensitivity of reliability to variations or fluctuations in the parameters of the system starts with the establishment of a suitable limit state equation. This work presents a reliability analysis approach for mechanical and structural systems using the fourth order moment function for approximating the first four moments of the limit state function. By combining the fourth-order moment function with the probabilistic perturbation method, numerical methods are developed for finding the reliability and sensitivity of reliability of the system. An automobile brake and a power screw are considered for demonstrating the methodology and effectiveness of the proposed computational approach. The results of the automobile brake are compared with those given by the Monte Carlo method.

scholarly journals Méthode du gradient projeté avec contrôle d’erreur

2008 ◽  
pp. 1039-1056
Author(s):  
Xuan Son Nguyen ◽  
Frédéric Duprat ◽  
Alain Sellier ◽  
Gérard Pons
Keyword(s):  
Gradient Method ◽  
Error Control ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Gradient Vector ◽  
Projected Gradient Method ◽  
Engineering Structures ◽  
Projected Gradient ◽  
Durability Analysis

Probabilistic approaches are today frequently used in the design of new civil engineering structures and durability analysis of existing constructions. The so-called Hasofer-Lind’s reliability index is the most popular reliability measure in design codes. This index can be determined by several minimizations under constraint algorithms, such as Rackwitz-Fiessler’s algorithm which is based on the projected gradient method. The drawback of this method lies in the estimation of the gradient vector of the limit state function which is often carried out by finite differences. If the perturbation chosen for this estimation gives a variation of the result lower than the accuracy of the limit state function, the algorithm could give erroneous results, not even to converge. In order to circumvent this drawback, we propose a method called projected gradient method with error control. The principle is to add to Rackwitz-Fiessler’s algorithm a procedure for choosing judiciously the perturbation for calculating the gradient vector accounting for the numerical accuracy of the limit state function. The efficiency of the proposed method can be judged from examples taken from the literature.

An Efficient Response Surface Method Using Givens Transformation for Structural Reliability Analysis

2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Mathematical Techniques ◽  
Input Variables ◽  
Improved Accuracy

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.

Development of Ultimate Strength Evaluation Method for Piping Subjected to Seismic Loads

2013 ◽  
Author(s):  
Hideo Machida ◽  
Hiromasa Chitose ◽  
Tatsuhiro Yamazaki
Keyword(s):  
Power Plants ◽  
Evaluation Method ◽  
Failure Modes ◽  
Limit State ◽  
Seismic Loading ◽  
Earthquake Resistance ◽  
State Function ◽  
Limit State Function ◽  
Input Acceleration ◽  
Resistance Tests

This paper reports the results of the study on the failure modes and limit loads of piping in nuclear power plants subjected to cyclic seismic loading. By investigating the past fracture tests and earthquake resistance tests, it became clear that dominant failure mode of piping was fatigue, and the effect of ratchet strain was negligible. Until now, the stress generated with the acceleration of an earthquake was classified into the primary stress. However, the relationship between the input acceleration and the seismic response displacement of the pipe observed from earthquake resistance tests is non-linear, and increasing rate of displacement is lower than that of input acceleration in elastic-plastic stress condition. Therefore, the seismic loading can be treated as displacement controlled loading. To evaluate the reliability-based critical acceleration, a limit state function was defined taking the variations in the fatigue strength or some parameters into consideration. By using the limit state function, the reliability was evaluated for the typical piping of boiling water reactor (BWR) plants subjected to cyclic seismic loading, and a partial safety factors were calculated. Based on these results, a fatigue curve corresponding to the target reliability was proposed.

A New Reliability Evaluation Algorithm Using Response Surface Methodology Combined With Space Mapping Technique

2006 ◽  
Author(s):  
Lixin Zhang ◽  
Zhijun Jian ◽  
Zhaohui Xu
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Limit State ◽  
Space Mapping ◽  
Mapping Technique ◽  
State Function ◽  
Limit State Function ◽  
New Approach ◽  
Successive Response ◽  
Evaluation Algorithm

A new method is proposed to tackle the huge computation cost involved in Successive Response Surface Methodology applied to the reliability analysis, in which Space Mapping technique is combined with Response Surface Methodology. While the new approach is performed, the limit state function is only fitted at the first iteration; at other iterations Space Mapping technique is employed to map the original limit state function into the new ones. Experimental design, corresponding model evaluations and response surface fitting of the limit state function are not done repetitively as what we do while SRSM is used, which leads to the great cutting down of computational efforts.

scholarly journals Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

2022 ◽  
Vol 10 (1) ◽  
pp. 102
Author(s):  
Zhiyao Zhu ◽  
Huilong Ren ◽  
Xiuhuan Wang ◽  
Nan Zhao ◽  
Chenfeng Li
Keyword(s):  
Least Squares ◽  
Residual Strength ◽  
Least Squares Method ◽  
Limit State ◽  
Nonlinear Least Squares ◽  
State Function ◽  
Limit State Function ◽  
Distribution Models ◽  
Sample Distribution ◽  
Fitting Method

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

Fatigue Design Margin Evaluation for Carbon and Low-Alloy Steels by Reliability-Based Load and Resistance Factor Method

2011 ◽  
Author(s):  
Masahiro Takanashi ◽  
Makoto Higuchi ◽  
Junki Maeda ◽  
Shinsuke Sakai
Keyword(s):  
Applied Stress ◽  
Limit State ◽  
State Function ◽  
Low Alloy Steels ◽  
Limit State Function ◽  
Safety Factors ◽  
Fatigue Data ◽  
Alloy Steels ◽  
Partial Safety Factors ◽  
Two Parameters

This paper discusses the margins of the design fatigue curve in the ASME Boiler and Pressure Vessel Codes Section III from a reliability analysis point of view. It is reported that these margins were developed so as to cover uncertainties of fatigue data scatter, size effect, and surface condition[1], but the reasons for them remain unclear. In order to investigate the physical implications of the design margin, a probabilistic approach is taken for the collected fatigue data of carbon and low-alloy steels. In this approach, these three parameters are treated as random variables, and an applied stress is also taken into consideration as a random variable. For the analysis, to begin with, a limit state function for fatigue is proposed. Next, reliability index contours of the design fatigue curves for carbon and low-alloy steels are obtained based on the proposed limit state function. The contours indicate that the margins 2 on stress and 20 on life do not provide equal reliability. The margin 20 on life is more conservative and the margin became a minimum near intersections of the design curves with margins 2 on stress and 20 on life. For practical applications, the partial safety factors (PSF) for the target reliability are computed for all materials and several levels of coefficients of variation (COV) of the applied stress. A sensitivity analysis of the PSFs clarifies that only two parameters, the strength (or the life) and the applied stress, are predominant. Thus, the partial safety factors for these two parameters are proposed in a tabular form.

An Upheaval Buckling Limit State Function for Onshore Natural Gas Pipelines

2008 ◽  
Author(s):  
Ian Matheson ◽  
Wenxing Zhou ◽  
Joe Zhou ◽  
Rick Gailing
Keyword(s):  
Natural Gas ◽  
Elevated Temperatures ◽  
Limit State ◽  
State Function ◽  
Operating Pressure ◽  
Limit State Function ◽  
Gas Pipelines ◽  
Upheaval Buckling ◽  
Natural Gas Pipelines ◽  
Axial Forces

The reliability-based design and assessment (RBDA) methodology has gained increasing acceptance in the pipeline industry, largely due to a multi-year PRCI program aimed at establishing RBDA as a viable alternative for the design and assessment of onshore natural gas pipelines. A key limit state of buried pipelines that operate at elevated temperatures is upheaval buckling. The elevated temperatures generate large compressive axial forces that can cause Euler buckling susceptibility. The tendency to buckle is increased at vertical imperfections (i.e. a series of cold formed bends) that primarily occur due to topography. Upheaval buckling in itself is not an ultimate limit state but can lead to high strains, local buckling, high cycle fatigue, expensive remediation measures, and even loss of pressure integrity. The critical forces at which upheaval buckling occurs for typical hill-crest type imperfections present in onshore pipelines cannot be readily predicted using analytical methods. A parametric study is therefore undertaken using non-linear finite element analyses to generate a matrix of upheaval buckling responses. The critical force for the onset of upheaval buckling is then developed using a series of empirical relationships to capture the influences of all key parameters. An upheaval buckling limit state function is subsequently developed by comparing the critical buckling force with applied compressive force, which is a function of operating pressure and temperature differential between the operating and tie-in conditions. The limit state function can be readily implemented in a reliability analysis framework to calculate the pipeline failure probability due to upheaval buckling.

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