scholarly journals Sensitivity Analysis in Probabilistic Structural Design: A Comparison of Selected Techniques

2020 ◽  
Vol 12 (11) ◽  
pp. 4788 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Limit State ◽  
Information Value ◽  
Ultimate Limit State ◽  
State Function ◽  
Sensitivity Indices ◽  
Small Failure Probability ◽  
Input Variables

Although more and more reliability-oriented sensitivity analysis (ROSA) techniques are now available, review and comparison articles of ROSA are absent. In civil engineering, many of the latest indices have never been used to analyse structural reliability for very small failure probability. This article aims to analyse and compare different sensitivity analysis (SA) techniques and discusses their strengths and weaknesses. For this purpose, eight selected sensitivity indices are first described and then applied in two different test cases. Four ROSA type indices are directly oriented on the failure probability or reliability index beta, and four other indices (of a different type) are oriented on the output of the limit state function. The case study and results correspond to cases under common engineering assumptions, where only two independent input variables with Gaussian distribution of the load action and the resistance are applied in the ultimate limit state. The last section of the article is dedicated to the analysis of the different results. Large differences between first-order sensitivity indices and very strong interaction effects obtained from ROSA are observed for very low values of failure probability. The obtained numerical results show that ROSA methods lack a common platform that clearly interprets the relationship of indices to their information value. This paper can help orientate in the selection of which sensitivity measure to use.

scholarly journals Global sensitivity analysis of failure probability caused by fatigue crack propagation

2019 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Global Sensitivity Analysis ◽  
Limit State ◽  
Random Variables ◽  
Probability Of Failure ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Stress Changes

The probability of failure of a load bearing steel member is investigated using a new type of global sensitivity analysis subordinated to contrasts. The main objective of the probability-oriented sensitivity analysis is structural reliability. The structural reliability methodology uses random variables as inputs. The subject of interest is the identification of those random variables that are most important when the limit state of a steel bridge member is reached. The limit state is defined by the occurrence of brittle fracture, which results from stress changes caused by multiple repeated loads. The propagation of a single-edge crack from initial to critical size is analysed using linear fracture mechanics. The failure probability and sensitivity indices are calculated using sampling-based methods. The sensitivity indices are estimated using double-nested-loop simulation of the Latin Hypercube Sampling method. New findings indicate that interaction effects among input variables strongly influence the probability of failure especially at the beginning of the operating period.

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.

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

scholarly journals From Probabilistic to Quantile-Oriented Sensitivity Analysis: New Indices of Design Quantiles

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1720 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Structural Reliability ◽  
Building Design ◽  
Design Standards ◽  
Average Value ◽  
Sensitivity Indices ◽  
Before And After ◽  
Input Variables ◽  
Total Sensitivity

In structural reliability analysis, sensitivity analysis (SA) can be used to measure how an input variable influences the failure probability Pf of a structure. Although the reliability is usually expressed via Pf, Eurocode building design standards assess the reliability using design quantiles of resistance and load. The presented case study showed that quantile-oriented SA can provide the same sensitivity ranking as Pf-oriented SA or local SA based on Pf derivatives. The first two SAs are global, so the input variables are ranked based on total sensitivity indices subordinated to contrasts. The presented studies were performed for Pf ranging from 9.35 × 10−8 to 1–1.51 × 10−8. The use of quantile-oriented global SA can be significant in engineering tasks, especially for very small Pf. The proposed concept provided an opportunity to go much further. Left-right symmetry of contrast functions and sensitivity indices were observed. The article presents a new view of contrasts associated with quantiles as the distance between the average value of the population before and after the quantile. This distance has symmetric hyperbola asymptotes for small and large quantiles of any probability distribution. Following this idea, new quantile-oriented sensitivity indices based on measuring the distance between a quantile and the average value of the model output are formulated in this article.

scholarly journals Structural reliability-based assessment of Nigerian Anogeissus schimperi timber bridge beam in shear and bearing forces

2021 ◽  
Vol 39 (4) ◽  
pp. 1011-1020
Author(s):  
P. Abubakar ◽  
A. Iorkar ◽  
A.A. Adedeji ◽  
J.I. Aguwa ◽  
U.N. Wilson
Keyword(s):  
Sensitivity Analysis ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Safety Margin ◽  
Physical And Mechanical Properties ◽  
Ultimate Limit State ◽  
Safety Level ◽  
Ultimate Limit ◽  
North Western

This research investigates the reliability of Anogeissus schimperi timber specie grown in North Western Nigeria as a bridge beam in shear and bearing forces. Specimens for laboratory tests were prepared using the timber specie in accordance with BS 373 (1957). Tests were carried out to determine the physical and mechanical properties at 12% moisture content in line with BS 5268 (2002). Statistical analysis was carried out using strength properties obtained and the specie was classified to strength class D60, confirmed to be Hardwood. Anogeissus schimperi timber bridge beam was designed in accordance to BS5268 (2002), using deterministicapproach. While, reliability analysis to confirm the safety level of the timber bridge beam designed was carried out using constant failure rate model in accordance with Jimoh, (2018). Sensitivity analysis to ascertain the safety margin of a simply supported timber bridge beam subjected to Shear and bearing by varying the span, depth, width and live load was carried out. Results of reliability analysis showed that Anogeissus schimperi met the minimum reliability index of 0.5 under ultimate state of loading in Shear and bearing. Safety index was found to be directly proportional to the depth and width but inversely proportional to the span and live loadof the timber bridge beam during Sensitivity Analysis. The result confirmed that Anogeissus schimperi specie from north western Nigeria at 400mm depth, 150mm breadth and 5000mm span under ultimate limit state loading in Shear and bearing can be used as a reliable timber bridge beam material. Keywords: Bridge Beam, Nigerian Anogeissus schimperi Reliability, Structural Material, Timber, Ultimate Limit State.

scholarly journals Limit States of Structures and Global Sensitivity Analysis Based on Cramér-von Mises Distance

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Sensitivity Analysis ◽  
Lognormal Distribution ◽  
Goodness Of Fit ◽  
Global Sensitivity Analysis ◽  
Limit State ◽  
State Function ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Von Mises ◽  
Cramer Von Mises

This article presents a stochastic computational model for the analysis of the reliability of a drawn steel bar. The whole distribution of the limit state function is studied using global sensitivity analysis based on Cramér-von Mises distance. The algorithm for estimating the sensitivity indices is based on one loop of the Latin Hypercube Sampling method in combination with numerical integration. The algorithm is effective due to the approximation of resistance using a threeparameter lognormal distribution. Goodness-of-fit tests and other comparative studies demonstrate the significant accuracy and suitability of the three-parameter lognormal distribution, which provides better results and faster response than sampling-based methods. Global sensitivity analysis is evaluated for two load cases with proven dominant effect of the long-term variation load action, which is introduced using Gumbel probability density function. The Cramér-von Mises indices are discussed in the context of other types of probability-oriented sensitivity indices whose performance has been studied earlier.

scholarly journals An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 209
Author(s):  
Bolin Liu ◽  
Liyang Xie
Keyword(s):  
Reliability Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Limit State ◽  
Local Approximation ◽  
State Function ◽  
Limit State Function ◽  
Enrichment Technique ◽  
Reliability Method ◽  
Multiple Sample

The Kriging-based reliability method with a sequential design of experiments (DoE) has been developed in recent years for implicit limit state functions. Such methods include the efficient global reliability analysis, the active learning reliability method combining Kriging and MCS Simulations. In this research, a novel local approximation method based on the most probable failure point (MPFP) is proposed to improve such methods. In this method, the MPFP calculated in the last iteration is the center of the next sampling region. The size of the local region depends on the reliability index obtained by the First Order Reliability Method (FORM) and the deviation distance of the standard deviation. The proposed algorithm, which approximates the limit state function accurately near MPFP rather than in the whole design space, can avoid selecting samples in regions that have negligible effects on the reliability analysis results. In addition, a multi-point enrichment technique is also introduced to select multiple sample points in each iteration. After the high-quality approximation of limit state function is obtained, the failure probability is calculated by the Monte Carlo method. Four numerical examples are used to validate the accuracy and efficiency of the proposed method. Results show that the proposed method is very effective for an accurate evaluation of the failure probability.

Reliability and reliability-based sensitivity analysis of self-centering buckling restrained braces using meta-models

2021 ◽  
pp. 1045389X2110263
Author(s):  
Seyede Vahide Hashemi ◽  
Mahmoud Miri ◽  
Mohsen Rashki ◽  
Sadegh Etedali
Keyword(s):  
Failure Probability ◽  
Limit State ◽  
Computational Cost ◽  
Sensitivity Analyses ◽  
State Function ◽  
Reliability Indices ◽  
Buckling Restrained Brace ◽  
Polynomial Response Surface ◽  
Nonlinear Dynamic Analyses ◽  
High Computational Cost

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.

Response surface method strategies coupled with NLFEA for structural reliability analysis of prestressed bridges

2021 ◽  
Author(s):  
Silvia J. Sarmiento Nova ◽  
Jaime Gonzalez-Libreros ◽  
Gabriel Sas ◽  
Rafael A. Sanabria Díaz ◽  
Maria C. A. Texeira da Silva ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Material Behavior ◽  
Nonlinear Material ◽  
State Function ◽  
Surface Method ◽  
Highly Nonlinear

<p>The Response Surface Method (RSM) has become an essential tool to solve structural reliability problems due to its accuracy, efficacy, and facility for coupling with Nonlinear Finite Element Analysis (NLFEA). In this paper, some strategies to improve the RSM efficacy without compromising its accuracy are tested. Initially, each strategy is implemented to assess the safety level of a highly nonlinear explicit limit state function. The strategy with the best results is then identified and used to carry out a reliability analysis of a prestressed concrete bridge, considering the nonlinear material behavior through NLFEA simulation. The calculated value of &#120573; is compared with the target value established in Eurocode for ULS. The results showed how RSM can be a practical methodology and how the improvements presented can reduce the computational cost of a traditional RSM giving a good alternative to simulation methods such as Monte Carlo.</p>

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.

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