scholarly journals Global Sensitivity Analysis of Ultimate Limit States of Stainless Steel Structural Members

2021 ◽  
Vol 1203 (2) ◽  
pp. 022142
Author(s):  
Abayomi Omishore
Keyword(s):  
Sensitivity Analysis ◽  
Stainless Steel ◽  
Yield Strength ◽  
Higher Order ◽  
Carbon Steels ◽  
Sensitivity Analyses ◽  
Statistical Characteristics ◽  
Limit States ◽  
Sensitivity Indices ◽  
Input Variables

Abstract The article presents global Sobol sensitivity analysis of a rolled member in tension made from austenitic chromium-nickel stainless steel of type 1.4307/AISI 304 L. The statistical characteristics of yield strength and of the geometry of the rolled steel IPE cross-section are presented on the basis of published experimental research. The sensitivity analysis showed the dominant effect of the yield strength on the static resistance. The second dominant variable is the flange thickness. Higher-order sensitivity indices oriented at detecting the presence of interaction effects between input variables are very small. The characteristics of other types of sensitivity analyses oriented at quantiles or the probability of failure are discussed, especially in terms of a higher proportion of higher-order sensitivity indices. The results of Sobol sensitivity analysis of stainless steel are compared with similar results of carbon steels.

Comprehensive global sensitivity analysis of a repository model using different types of transformations and metamodeling techniques

2021 ◽  
Author(s):  
Sabine M. Spiessl ◽  
Dirk-A. Becker ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Higher Order ◽  
Model Parameters ◽  
High Dimensional Model Representation ◽  
Model Output ◽  
Global Sensitivity ◽  
Sparse Polynomial ◽  
Sensitivity Indices ◽  
Highly Nonlinear

<p>Due to their highly nonlinear, non-monotonic or even discontinuous behavior, sensitivity analysis of final repository models can be a demanding task. Most of the output of repository models is typically distributed over several orders of magnitude and highly skewed. Many values of a probabilistic investigation are very low or even zero. Although this is desirable in view of repository safety it can distort the evidence of sensitivity analysis. For the safety assessment of the system, the highest values of outputs are mainly essential and if those are only a few, their dependence on specific parameters may appear insignificant. By applying a transformation, different model output values are differently weighed, according to their magnitude, in sensitivity analysis. Probabilistic methods of higher-order sensitivity analysis, applied on appropriately transformed model output values, provide a possibility for more robust identification of relevant parameters and their interactions. This type of sensitivity analysis is typically done by decomposing the total unconditional variance of the model output into partial variances corresponding to different terms in the ANOVA decomposition. From this, sensitivity indices of increasing order can be computed. The key indices used most often are the first-order index (SI1) and the total-order index (SIT). SI1 refers to the individual impact of one parameter on the model and SIT represents the total effect of one parameter on the output in interactions with all other parameters. The second-order sensitivity indices (SI2) describe the interactions between two model parameters.</p><p>In this work global sensitivity analysis has been performed with three different kinds of output transformations (log, shifted and Box-Cox transformation) and two metamodeling approaches, namely the Random-Sampling High Dimensional Model Representation (RS-HDMR) [1] and the Bayesian Sparse PCE (BSPCE) [2] approaches. Both approaches are implemented in the SobolGSA software [3, 4] which was used in this work. We analyzed the time-dependent output with two approaches for sensitivity analysis, i.e., the pointwise and generalized approaches. With the pointwise approach, the output at each time step is analyzed independently. The generalized approach considers averaged output contributions at all previous time steps in the analysis of the current step. Obtained results indicate that robustness can be improved by using appropriate transformations and choice of coefficients for the transformation and the metamodel.</p><p>[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.</p><p>[2] Q. Shao, A. Younes, M. Fahs, T.A. Mara (2017). Bayesian sparse polynomial chaos expansion for global sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 318: 474-496.</p><p>[3] S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus (2018). Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004.</p><p>[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.</p>

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 QUANTILE-ORIENTED GLOBAL SENSITIVITY ANALYSIS OF DESIGN RESISTANCE

2019 ◽  
Vol 25 (4) ◽  
pp. 297-305 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Latin Hypercube Sampling ◽  
Higher Order ◽  
Lateral Torsional Buckling ◽  
Sensitivity Indices ◽  
Order Polynomial ◽  
New Type ◽  
Design Resistance ◽  
Design Value ◽  
Higher Sensitivity

The article investigates the application of a new type of global quantile-oriented sensitivity analysis (called QSA in the article) and contrasts it with established Sobol’ sensitivity analysis (SSA). Comparison of QSA of the resistance design value (0.1 percentile) with SSA is performed on an example of the analysis of the resistance of a steel IPN 200 beam, which is subjected to lateral-torsional buckling. The resistance is approximated using higher order polynomial metamodels created from advanced non-linear FE models. The main, higher order and total effects are calculated using the Latin Hypercube Sampling method. Noticeable differences between the two methods are found, with QSA apparently revealing higher sensitivity of the resistance design value to random input second and higher order interactions (compared to SSA). SSA cannot identify certain reliability aspects of structural design as comprehensively as QSA, particularly in relation to higher order interactions effects of input imperfections. In order to better understand the reasons for the differences between QSA and SSA, two simple examples are presented, where QSA (median) and SSA show a general agreement in the calculation of certain sensitivity indices.

Moment Matching for Sensitivity Analysis of Probabilistic Model Output

2004 ◽  
Author(s):  
Mahmoud Awad ◽  
Agus Sudjianto ◽  
Nanua Singh
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Models ◽  
Moment Matching ◽  
Model Output ◽  
Sensitivity Indices ◽  
Variance Contribution ◽  
Complex Engineering ◽  
Input Variables ◽  
The Relationship ◽  
Effective Sensitivity

With the advent of highly complex engineering simulation models that describe the relationship between input variables and output response, the need for an efficient and effective sensitivity analysis is more demanding. In this article, a generalized approach that can provide efficient as well as accurate global sensitivity indices is developed. The approach consists of two steps: running an orthogonal array based experiment using moment-matched levels of the input variables and followed by a variance contribution analysis. The benefits of the approach are demonstrated through three different examples.

scholarly journals New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2425
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Binary Outcome ◽  
Global Sensitivity ◽  
First Order ◽  
Sensitivity Measure ◽  
Sensitivity Indices ◽  
Alternative Measures ◽  
Input Variables ◽  
Dome Shape

This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

Material Performance in Laser Cladding of a Laminated Plate with Wavy Bond Interface

2016 ◽  
Vol 861 ◽  
pp. 159-165
Author(s):  
Zi Hui Li ◽  
Mei Na Gao ◽  
Xu Yue Wang
Keyword(s):  
Mechanical Properties ◽  
Stainless Steel ◽  
Yield Strength ◽  
Laser Cladding ◽  
Carbon Steels ◽  
National Standard ◽  
304 Stainless Steel ◽  
Tensile Fracture ◽  
Laminated Plate ◽  
Bond Interface

A laminated plate with excellent mechanical properties is commonly used for a bulkhead part in which the interface structure of diffusion bonded is detrimental to the bending quality. In this study, 304 stainless steel and Q235 carbon steel were cladded by laser cladding technique. Microstructure, yield strength, elements diffusion, hardness and tensile fracture morphology of the clad metals were evaluated. The bond interface of the cladded metals demonstrated a wavy morphology in this work. Tensile test results shows that yield strength reaches 400-410MPa and tensile strength reaches 405-419MPa. They are higher than the standard value 235MPa and 370MPa, respectively. In wavy interface region, transition layer of metallurgical bond was formed as a result of mutual diffusion of Fe, Cr and Ni. The hardness is increased in the substrate and cladding plate near the bond interface. The mechanical properties of the low-carbon steels is increased by laser cladding with austenitic stainless steel, which are far beyond the national standard and other bending methods.

scholarly journals A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2489
Author(s):  
Zhiwei Bai ◽  
Hongkui Wei ◽  
Yingying Xiao ◽  
Shufang Song ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Joint Probability ◽  
Copula Functions ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method ◽  
Input Variables ◽  
Vine Copula ◽  
Bivariate Copula

For multidimensional dependent cases with incomplete probability information of random variables, global sensitivity analysis (GSA) theory is not yet mature. The joint probability density function (PDF) of multidimensional variables is usually unknown, meaning that the samples of multivariate variables cannot be easily obtained. Vine copula can decompose the joint PDF of multidimensional variables into the continuous product of marginal PDF and several bivariate copula functions. Based on Vine copula, multidimensional dependent problems can be transformed into two-dimensional dependent problems. A novel Vine copula-based approach for analyzing variance-based sensitivity measures is proposed, which can estimate the main and total sensitivity indices of dependent input variables. Five considered test cases and engineering examples show that the proposed methods are accurate and applicable.

scholarly journals Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 263
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Structural Reliability ◽  
Sensitivity Analyses ◽  
Importance Measure ◽  
Mathematical Function ◽  
Output Resistance ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
The Difference ◽  
Comparison Of The Results

The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance.

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 A Sampling-Based Sensitivity Analysis Method Considering the Uncertainties of Input Variables and Their Distribution Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1095
Author(s):  
Xiang Peng ◽  
Xiaoqing Xu ◽  
Jiquan Li ◽  
Shaofei Jiang
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Method ◽  
Transformation Method ◽  
Unscented Transformation ◽  
Performance Function ◽  
Gaussian Integration ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method ◽  
Distribution Parameters ◽  
Input Variables

For engineering products with uncertain input variables and distribution parameters, a sampling-based sensitivity analysis methodology was investigated to efficiently determine the influences of these uncertainties. In the calculation of the sensitivity indices, the nonlinear degrees of the performance function in the subintervals were greatly reduced by using the integral whole domain segmentation method, while the mean and variance of the performance function were calculated using the unscented transformation method. Compared with the traditional Monte Carlo simulation method, the loop number and sampling number in every loop were decreased by using the multiplication approximation and Gaussian integration methods. The proposed algorithm also reduced the calculation complexity by reusing the sample points in the calculation of two sensitivity indices to measure the influence of input variables and their distribution parameters. The accuracy and efficiency of the proposed algorithm were verified with three numerical examples and one engineering example.

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