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Mathematics
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Sensitivity Analysis
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Sensitivity Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 8149

Special Issue Editor

Prof. Dr. Zdeněk Kala

E-Mail Website
Guest Editor
Department of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, Veveri Str. 95, 602 00 Brno, Czech Republic
Interests: sensitivity analysis; reliability analysis; structural mechanics; stability; buckling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to advances in research on sensitivity analysis methods and their interdisciplinary applications. Sensitivity analysis investigates the effect of varying the inputs of a mathematical model on the output of the model itself. The scope of opportunities for engaging with sensitivity analysis is large, ranging from partial derivatives, regression, scatter plots, sampling-based methods, correlations, variance-based techniques, distribution-based methods, entropy, and fuzzy sets to many other methods. The application areas are numerous in all disciplines of science using mathematical models, including computer science, chemistry, biology, medicine, physics, engineering, economics and finance, environmental science, and many others. In the midst of all this are computational models, metamodels, and analytical and simulation methods that potentially augment outcomes. Local and global methods of sensitivity analysis are welcome. This Special Issue welcomes articles that address the challenges and opportunities of sensitivity analysis, in all its facets.

Prof. Dr. Zdeněk Kala
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • sensitivity analysis
  • uncertainty analysis
  • decision making under uncertainty
  • reliability analysis
  • importance measures
  • model
  • model output
  • model calibration
  • model validation
  • quantification
  • Monte Carlo
  • analytical and simulation methods

Published Papers (4 papers)

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Research

17 pages, 623 KiB  
Article
Preventive Maintenance of k-out-of-n System with Dependent Failures
by Vladimir Rykov and Olga Kochueva
Mathematics 2023, 11(2), 422; https://doi.org/10.3390/math11020422 - 13 Jan 2023
Cited by 1 | Viewed by 959
Abstract
The paper investigates a model of a k-out-of-n system, the residual lifetime of which changes after failures of any of its components. The problem of a Preventive Maintenance (PM) organization as advice to the Decision Maker (DM) for such a system [...] Read more.
The paper investigates a model of a k-out-of-n system, the residual lifetime of which changes after failures of any of its components. The problem of a Preventive Maintenance (PM) organization as advice to the Decision Maker (DM) for such a system is considered. The purpose of this paper is to propose a mathematical model of the k-out-of-n system to support DM about PM. For most practical applications, it is usually possible to estimate the lifetime distribution parameters of the system components with limited accuracy (only one or two moments), which is why special attention is paid to the sensitivity analysis of the system reliability characteristics and decisions about PM to the shape of system components lifetime distributions. In the numerical examples, we consider the 3-out-of-6 model discussed in our previous works for two real systems. The novelty, significance, and features of this study consist of the following, after the failure of one of the system components, the load on all the others increases, which leads to a decrease in their residual lifetime. We model this situation with order statistics and study the quality of PM strategies with respect to the availability maximization criterion. At the same time, we are focusing on the study of the sensitivity of decision-making to the type of lifetime distribution of system components. Full article
(This article belongs to the Special Issue Sensitivity Analysis)
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19 pages, 6979 KiB  
Article
Quantification of Model Uncertainty Based on Variance and Entropy of Bernoulli Distribution
by Zdeněk Kala
Mathematics 2022, 10(21), 3980; https://doi.org/10.3390/math10213980 - 26 Oct 2022
Cited by 3 | Viewed by 2499
Abstract
This article studies the role of model uncertainties in sensitivity and probability analysis of reliability. The measure of reliability is failure probability. The failure probability is analysed using the Bernoulli distribution with binary outcomes of success (0) and failure (1). Deeper connections between [...] Read more.
This article studies the role of model uncertainties in sensitivity and probability analysis of reliability. The measure of reliability is failure probability. The failure probability is analysed using the Bernoulli distribution with binary outcomes of success (0) and failure (1). Deeper connections between Shannon entropy and variance are explored. Model uncertainties increase the heterogeneity in the data 0 and 1. The article proposes a new methodology for quantifying model uncertainties based on the equality of variance and entropy. This methodology is briefly called “variance = entropy”. It is useful for stochastic computational models without additional information. The “variance = entropy” rule estimates the “safe” failure probability with the added effect of model uncertainties without adding random variables to the computational model. Case studies are presented with seven variants of model uncertainties that can increase the variance to the entropy value. Although model uncertainties are justified in the assessment of reliability, they can distort the results of the global sensitivity analysis of the basic input variables. The solution to this problem is a global sensitivity analysis of failure probability without added model uncertainties. This paper shows that Shannon entropy is a good sensitivity measure that is useful for quantifying model uncertainties. Full article
(This article belongs to the Special Issue Sensitivity Analysis)
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24 pages, 1352 KiB  
Article
Behavioral Study of Software-Defined Network Parameters Using Exploratory Data Analysis and Regression-Based Sensitivity Analysis
by Mobayode O. Akinsolu, Abimbola O. Sangodoyin and Uyoata E. Uyoata
Mathematics 2022, 10(14), 2536; https://doi.org/10.3390/math10142536 - 21 Jul 2022
Cited by 3 | Viewed by 1647
Abstract
To provide a low-cost methodical way for inference-driven insight into the assessment of SDN operations, a behavioral study of key network parameters that predicate the proper functioning and performance of software-defined networks (SDNs) is presented to characterize their alterations or variations, given various [...] Read more.
To provide a low-cost methodical way for inference-driven insight into the assessment of SDN operations, a behavioral study of key network parameters that predicate the proper functioning and performance of software-defined networks (SDNs) is presented to characterize their alterations or variations, given various emulated SDN scenarios. It is standard practice to use simulation environments to investigate the performance characteristics of SDNs, quantitatively and qualitatively; hence, the use of emulated scenarios to typify the investigated SDN in this paper. The key parameters studied analytically are the jitter, response time and throughput of the SDN. These network parameters provide the most vital metrics in SDN operations according to literature, and they have been behaviorally studied in the following popular SDN states: normal operating condition without any incidents on the SDN, hypertext transfer protocol (HTTP) flooding, transmission control protocol (TCP) flooding, and user datagram protocol (UDP) flooding, when the SDN is subjected to a distributed denial-of-service (DDoS) attack. The behavioral study is implemented primarily via univariate and multivariate exploratory data analysis (EDA) to characterize and visualize the variations of the SDN parameters for each of the emulated scenarios, and linear regression-based analysis to draw inferences on the sensitivity of the SDN parameters to the emulated scenarios. Experimental results indicate that the SDN performance metrics (i.e., jitter, latency and throughput) vary as the SDN scenario changes given a DDoS attack on the SDN, and they are all sensitive to the respective attack scenarios with some level of interactions between them. Full article
(This article belongs to the Special Issue Sensitivity Analysis)
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20 pages, 3966 KiB  
Article
A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables
by Zhiwei Bai, Hongkui Wei, Yingying Xiao, Shufang Song and Sergei Kucherenko
Mathematics 2021, 9(19), 2489; https://doi.org/10.3390/math9192489 - 04 Oct 2021
Cited by 5 | Viewed by 1666
Abstract
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. [...] Read more.
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. Full article
(This article belongs to the Special Issue Sensitivity Analysis)
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