scholarly journals HLRF-BFGS-Based Algorithm for Inverse Reliability Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Rakul Bharatwaj Ramesh ◽  
Olivia Mirza ◽  
Won-Hee Kang
Keyword(s):  
Computational Efficiency ◽  
Hybrid Algorithm ◽  
Limit State ◽  
Final Solution ◽  
Bfgs Update ◽  
Inverse Form ◽  
Reliability Method ◽  
Improved Performance ◽  
Bfgs Update Formula ◽  
Modified Algorithm

This study proposes an algorithm to solve inverse reliability problems with a single unknown parameter. The proposed algorithm is based on an existing algorithm, the inverse first-order reliability method (inverse-FORM), which uses the Hasofer Lind Rackwitz Fiessler (HLRF) algorithm. The initial algorithm analyzed in this study was developed by modifying the HLRF algorithm in inverse-FORM using the Broyden-Fletcher-Goldarb-Shanno (BFGS) update formula completely. Based on numerical experiments, this modification was found to be more efficient than inverse-FORM when applied to most of the limit state functions considered in this study, as it requires comparatively a smaller number of iterations to arrive at the solution. However, to achieve this higher computational efficiency, this modified algorithm sometimes compromised the accuracy of the final solution. To overcome this drawback, a hybrid method by using both the algorithms, original HLRF algorithm and the modified algorithm with BFGS update formula, is proposed. This hybrid algorithm achieves better computational efficiency, compared to inverse-FORM, without compromising the accuracy of the final solution. Comparative numerical examples are provided to demonstrate the improved performance of this hybrid algorithm over that of inverse-FORM in terms of accuracy and efficiency.

In-Plane Creep Stability Design of Concrete Filled Steel Tubular Arches Using Inverse Reliability Method

2013 ◽  
Vol 351-352 ◽  
pp. 1601-1604
Author(s):  
Wei Jiang ◽  
Da Gang Lu
Keyword(s):  
Limit State ◽  
Time Dependent ◽  
Safety Factors ◽  
State Equations ◽  
Stability Range ◽  
Good Efficiency ◽  
Reliability Indices ◽  
Inverse Form ◽  
Dependent Behavior ◽  
Reliability Method

An inverse first order reliability method (FORM) is presented to solve the safety factors for the in-plane creep stability of concrete filled steel tubular (CFST) arches. In the inverse analysis, the safety factors with or without considering the time-dependent behavior of concrete are introduced into limit state equations for the in-plane stability design of CFST arches. For different target reliability indices and steel ratios, the time-independent and time-dependent safety factors are solved. The results show that the inverse FORM is of good efficiency and applicability. The target reliability indices have little effect on the safety factors for the creep stability of CFST arches. The effects of steel ratios are significant which should be considered in design. For the commonly used steel ratios of CFST arches, the in-plane safety factors for creep stability range from 1.17 to 1.43.

Reliability Method to Estimate Shear Strength Parameters

2011 ◽  
Vol 52-54 ◽  
pp. 1752-1756
Author(s):  
Li Hong Chen ◽  
Yu Fei Zhao
Keyword(s):  
Shear Strength ◽  
Linear Regression ◽  
Moment Method ◽  
Limit State ◽  
Safety Evaluation ◽  
Regression Method ◽  
Linear Regression Method ◽  
Shear Strength Parameters ◽  
Strength Parameters ◽  
Reliability Method

The design and safety evaluation of a geotechnical project is influenced by the shear strength parameters of geo-material. Moment method and linear regression method are the mainly used methods to estimate the shear strength parameters. But moment method is always over estimate the variation of strength parameters due to the smaller sample size, meanwhile the conventional linear regression method cannot obtain the standard deviation. Base on the reliability theory, a new method employing Solver add-in of spreadsheet was developed to calculate the shear strength parameters. The method was simplified by the principle that the shortest distance form origin point to the limit state surface in the normalization space was the reliability index. Four hundred and four samples of direct shear tests of rock mass from many large hydraulic projects in China were analyzed by four statistic methods including the new proposed one. Comparing results of different methods indicated that the new reliability statistic method had good performance than the traditional ways.

scholarly journals Computer-aided SPT-based reliability model for probability of liquefaction using hybrid PSO and GA

2020 ◽  
Vol 7 (1) ◽  
pp. 107-127 ◽  
Author(s):  
Maral Goharzay ◽  
Ali Noorzad ◽  
Ahmadreza Mahboubi Ardakani ◽  
Mostafa Jalal
Keyword(s):  
Engineering Design ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Probabilistic Method ◽  
Limit State ◽  
Soil Liquefaction ◽  
Probability Models ◽  
Reliability Indices ◽  
Hybrid Particle Swarm Optimization ◽  
Reliability Method

Abstract In this paper, an approach for soil liquefaction evaluation using probabilistic method based on the world-wide SPT databases has been presented. In this respect, the parameters’ uncertainties for liquefaction probability have been taken into account. A calibrated mapping function is developed using Bayes’ theorem in order to capture the failure probabilities in the absence of the knowledge of parameter uncertainty. The probability models provide a simple, but also efficient decision-making tool in engineering design to quantitatively assess the liquefaction triggering thresholds. Within an extended framework of the first-order reliability method considering uncertainties, the reliability indices are determined through a well-performed meta-heuristic optimization algorithm called hybrid particle swarm optimization and genetic algorithm to find the most accurate liquefaction probabilities. Finally, the effects of the level of parameter uncertainty on liquefaction probability, as well as the quantification of the limit state model uncertainty in order to incorporate the correct model uncertainty, are investigated in the context of probabilistic reliability analysis. The results gained from the presented probabilistic model and the available models in the literature show the fact that the developed approach can be a robust tool for engineering design and analysis of liquefaction as a natural disaster.

Reliability analysis of wood I-joists

1993 ◽  
Vol 20 (4) ◽  
pp. 564-573 ◽  
Author(s):  
R. O. Foschi ◽  
F. Z. Yao
Keyword(s):  
Reliability Analysis ◽  
Carrying Capacity ◽  
Failure Modes ◽  
Limit State ◽  
Load Carrying Capacity ◽  
Limit States ◽  
Element Analysis ◽  
Strength Limit ◽  
Reliability Method ◽  
Load Carrying

This paper presents a reliability analysis of wood I-joists for both strength and serviceability limit states. Results are obtained from a finite element analysis coupled with a first-order reliability method. For the strength limit state of load-carrying capacity, multiple failure modes are considered, each involving the interaction of several random variables. Good agreement is achieved between the test results and the theoretical prediction of variability in load-carrying capacity. Finally, a procedure is given to obtain load-sharing adjustment factors applicable to repetitive member systems such as floors and flat roofs. Key words: reliability, limit state design, wood composites, I-joist, structural analysis.

Reliability Methods for Bimodal Distribution With First-Order Approximation1

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Probability Density ◽  
Order Approximation ◽  
Limit State ◽  
Random Variables ◽  
Random Variable ◽  
State Function ◽  
First Order ◽  
Reliability Method ◽  
Reliability Methods ◽  
Basic Random Variable

In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. When binomial variables are involved, traditional reliability methods, such as the first-order second moment (FOSM) method and the first-order reliability method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation (SPA) for bimodal variables and then employs SPA-based reliability methods with first-order approximation to predict the reliability. A limit-state function is at first approximated with the first-order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The SPA is then applied to estimate the reliability. Examples show that the SPA-based reliability methods are more accurate than FOSM and FORM.

Probabilistic Optimum Design of Composite Laminates

1998 ◽  
Vol 32 (1) ◽  
pp. 68-82 ◽  
Author(s):  
S. Mahadevan ◽  
X. Liu
Keyword(s):  
Objective Function ◽  
Optimum Design ◽  
Composite Laminates ◽  
Plate Theory ◽  
Limit State ◽  
Strength Criterion ◽  
System Level ◽  
State Function ◽  
Practical Procedure ◽  
Reliability Method

This paper proposes a procedure for the optimum design of composite laminates under probabilistic considerations. The problem is formulated to consider the minimization of laminate weight as the objective function and the reliability requirements as the constraints. Both system-level and element-level reliabilities are considered. The first-order reliability method (FORM) is used to estimate the reliability of each ply group, and system reliability is computed based on series or parallel system assumptions. The Tsai-Wu strength criterion is adopted to derive the limit state function of individual ply groups in the laminate. The gradient and sensitivity information of the objective function and the constraints with respect to the design variables are obtained by using sensitivity analysis based on the composite plate theory. Thus the proposed procedure brings together modern concepts of reliability analysis, composite laminate behavior and nonlinear optimization to develop a rational and practical procedure for the optimum design of composite laminates. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

Second-Order Reliability Method With First-Order Efficiency

2010 ◽  
Author(s):  
Xiaoping Du ◽  
Junfu Zhang
Keyword(s):  
Limit State ◽  
Saddlepoint Approximation ◽  
Quadratic Function ◽  
Second Order ◽  
State Function ◽  
Limit State Function ◽  
First Order ◽  
Reliability Method ◽  
Order Of Magnitude ◽  
Univariate Function

The widely used First Order Reliability Method (FORM) is efficient, but may not be accurate for nonlinear limit-state functions. The Second Order Reliability Method (SORM) is more accurate but less efficient. To maintain both high accuracy and efficiency, we propose a new second order reliability analysis method with first order efficiency. The method first performs the FORM and identifies the Most Probable Point (MPP). Then the associated limit-state function is decomposed into additive univariate functions at the MPP. Each univariate function is further approximated as a quadratic function, which is created with the gradient information at the MPP and one more point near the MPP. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied for computing the probability of failure. The accuracy of the new method is comparable to that of the SORM, and its efficiency is in the same order of magnitude as the FORM.

First-Order Reliability Method for Structural Reliability Analysis in the Presence of Random and Interval Variables

2015 ◽  
Vol 1 (4) ◽  
Author(s):  
Umberto Alibrandi ◽  
C. G. Koh
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Computational Cost ◽  
Computational Effort ◽  
Stochastic Dynamic ◽  
First Order Reliability Method ◽  
First Order ◽  
Structural Reliability Analysis ◽  
Reliability Method

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis in the presence of random parameters and interval uncertain parameters. In the proposed formulation, the hybrid problem is reduced to standard reliability problems, where the limit state functions are defined only in terms of the random variables. Monte Carlo simulation (MCS) for hybrid reliability analysis (HRA) is presented, and it is shown that it requires a tremendous computational effort; FORM for HRA is more efficient but still demanding. The computational cost is significantly reduced through a simplified procedure, which gives good approximations of the design points, by requiring only three classical FORMs and one interval analysis (IA), developed herein through an optimization procedure. FORM for HRA and its simplified formulation achieve a much improved efficiency than MCS by several orders of magnitude, and it can thus be applied to real-world engineering problems. Representative examples of stochastic dynamic analysis and performance-based engineering are presented.

Reliability Analysis of Piles in Multilayer Soil in Mooring Dolphin Structures

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Reda Farag ◽  
Achintya Haldar ◽  
Mahmoud El-Meligy
Keyword(s):  
Nile Delta ◽  
Limit State ◽  
Large Diameter ◽  
Hybrid Approach ◽  
Element Model ◽  
Limit States ◽  
Soil System ◽  
Sea Bed ◽  
Contact Nonlinearity ◽  
Reliability Method

Reliability of complicated mooring dolphin structures (MDS) is estimated using few deterministic evaluations and an improved response surface method denoted as IRSM-second-order reliability method (SORM). It is a hybrid approach consisting of an IRSM, SORM, and several advanced factorial schemes. For this type of sophisticated analysis, simulation-based algorithm is impractical to implement. The concept is applied to estimate the risk of an existing MDS at the shore of Nile Delta. It is a large diameter steel-pile embedded in the sea bed. The Pile–Soil-System is represented by a nonlinear finite element model (NLFEM). In NLFEM, the steel pile is assumed to behave linearly under the considered working loads, but the soil is considered to behave nonlinearly. Moreover, the contact nonlinearity between the pile and the soil is taken into account. It is demonstrated that the reliability information on MDS can be extracted using tens of deterministic evaluations. It has been found that incorporation of the contact nonlinearity into analysis has no effect on the pile behavior. In the probabilistic analysis, the uncertainties in loading, material properties, and geometric details are taken into account. Both operational and structural limit states are considered. For the MDS considered in this study, it has been observed that the strength limit state (flexural) is more critical than the operational limit state (drift). The most important variables are the mooring loads, the radius and thickness of the pile, and the modulus of elasticity of steel.

Reliability of TLP Tethers Using Evolutionary Strategies

2008 ◽  
Author(s):  
Federico Barranco Cicilia ◽  
Alberto Omar Va´zquez Herna´ndez
Keyword(s):  
Limit State ◽  
Evolutionary Strategies ◽  
Economic Losses ◽  
State Function ◽  
Safety Level ◽  
Reliability Method ◽  
Reliability Methods ◽  
New Codes ◽  
Monte Carlo Importance Sampling ◽  
Von Mises

Tether system is a critical component for the TLPs, since its failure may lead to the collapse of the whole structure involving human lives, economic losses and damages to the environment. Due to this fact, reliability methods have been proposed to design TLP tethers and new codes are being developed to increase their safety level. The objective of this paper is to compare the probability of failure for TLP tethers considering the maximum tension limit state obtained with three methods, which are: a methodology based on Evolutionary Strategies and the Monte Carlo Importance Sampling, the First Order Reliability Method, and the Second Order Reliability Method. Von-Mises failure criterion is used as limit state function for the most loaded tether of a TLP submitted to different sea states. Efficiency of the ES algorithm to find design points and probabilities of failure obtained with the reliability methods are discussed.

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