Evidence-Theory-Based Analysis for Structural-Acoustic Field with Epistemic Uncertainties

2017 ◽  
Vol 14 (02) ◽  
pp. 1750012 ◽  
Author(s):  
Longxiang Xie ◽  
Jian Liu ◽  
Jinan Zhang ◽  
Xianfeng Man
Keyword(s):  
Interval Analysis ◽  
Interpolation Method ◽  
Epistemic Uncertainty ◽  
Computational Cost ◽  
Evidence Theory ◽  
System Response ◽  
Response Analysis ◽  
Acoustic System ◽  
Response Characteristics ◽  
Focal Element

Evidence theory has a strong capacity to deal with epistemic uncertainty, in view of the overestimation in interval analysis, the responses of structural-acoustic problem with epistemic uncertainty could be untreated. In this paper, a numerical method is proposed for structural-acoustic system response analysis under epistemic uncertainties based on evidence theory. To improve the calculation accuracy and reduce the computational cost, the interval analysis technique and radial point interpolation method are adopted to obtain the approximate frequency response characteristics for each focal element, and the corresponding formulations of structural-acoustic system for interval response analysis are deduced. Numerical examples are introduced to illustrate the efficiency of the proposed method.

An Efficient Reliability Analysis Method for Structures With Epistemic Uncertainty Using Evidence Theory

2014 ◽  
Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Computational Cost ◽  
Evidence Theory ◽  
State Function ◽  
Limited Information ◽  
Design Point ◽  
Engineering Problems

Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the heavy computational cost caused by its discrete property severely influences the practicability of evidence theory, which has become a main difficulty in structural reliability analysis using evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with evidence variables, and hence improves the applicability of evidence theory for engineering problems. A non-probabilistic reliability index approach is introduced to obtain a design point on the limit-state surface. An assistant area is then constructed through the obtained design point, based on which a small number of focal elements can be picked out for extreme analysis instead of using all the elements. The vertex method is used for extreme analysis to obtain the minimum and maximum values of the limit-state function over a focal element. A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

Unified Uncertainty Analysis by the First Order Reliability Method

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Probability Theory ◽  
Interval Analysis ◽  
Probabilistic Analysis ◽  
Epistemic Uncertainty ◽  
Evidence Theory ◽  
Black Box ◽  
Aleatory Uncertainty ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method

Two types of uncertainty exist in engineering. Aleatory uncertainty comes from inherent variations while epistemic uncertainty derives from ignorance or incomplete information. The former is usually modeled by the probability theory and has been widely researched. The latter can be modeled by the probability theory or nonprobability theories and is much more difficult to deal with. In this work, the effects of both types of uncertainty are quantified with belief and plausibility measures (lower and upper probabilities) in the context of the evidence theory. Input parameters with aleatory uncertainty are modeled with probability distributions by the probability theory. Input parameters with epistemic uncertainty are modeled with basic probability assignments by the evidence theory. A computational method is developed to compute belief and plausibility measures for black-box performance functions. The proposed method involves the nested probabilistic analysis and interval analysis. To handle black-box functions, we employ the first order reliability method for probabilistic analysis and nonlinear optimization for interval analysis. Two example problems are presented to demonstrate the proposed method.

Evidential uncertainty quantification of the Park–Ang damage model in performance based design

2018 ◽  
Vol 35 (7) ◽  
pp. 2480-2501
Author(s):  
Hesheng Tang ◽  
Dawei Li ◽  
Lixin Deng ◽  
Songtao Xue
Keyword(s):  
Uncertainty Quantification ◽  
Earthquake Engineering ◽  
Epistemic Uncertainty ◽  
Damage Model ◽  
Computational Cost ◽  
Damage Index ◽  
Evidence Theory ◽  
Optimization Strategy ◽  
Content Type ◽  
Whole Process

Purpose This paper aims to develop a comprehensive uncertainty quantification method using evidence theory for Park–Ang damage index-based performance design in which epistemic uncertainties are considered. Various sources of uncertainty emanating from the database of the cyclic test results of RC members provided by the Pacific Earthquake Engineering Research Center are taken into account. Design/methodology/approach In this paper, an uncertainty quantification methodology based on evidence theory is presented for the whole process of performance-based seismic design (PBSD), while considering uncertainty in the Park–Ang damage model. To alleviate the burden of high computational cost in propagating uncertainty, the differential evolution interval optimization strategy is used for efficiently finding the propagated belief structure throughout the whole design process. Findings The investigation results of this paper demonstrate that the uncertainty rooted in Park–Ang damage model have a significant influence on PBSD design and evaluation. It might be worth noting that the epistemic uncertainty present in the Park–Ang damage model needs to be considered to avoid underestimating the true uncertainty. Originality/value This paper presents an evidence theory-based uncertainty quantification framework for the whole process of PBSD.

Optimization Based Algorithms for Uncertainty Propagation Through Functions With Multidimensional Output Within Evidence Theory

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Christian Gogu ◽  
Youchun Qiu ◽  
Stéphane Segonds ◽  
Christian Bes
Keyword(s):  
Convex Function ◽  
Optimization Problems ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Evidence Theory ◽  
Uncertainty Modeling ◽  
Preliminary Design ◽  
One Dimensional ◽  
Special Cases ◽  
Focal Element

Evidence theory is one of the approaches designed specifically for dealing with epistemic uncertainty. This type of uncertainty modeling is often useful at preliminary design stages where the uncertainty related to lack of knowledge is the highest. While multiple approaches for propagating epistemic uncertainty through one-dimensional functions have been proposed, propagation through functions having a multidimensional output that need to be considered at once received less attention. Such propagation is particularly important when the multiple function outputs are not independent, which frequently occurs in real world problems. The present paper proposes an approach for calculating belief and plausibility measures by uncertainty propagation through functions with multidimensional, nonindependent output by formulating the problem as one-dimensional optimization problems in spite of the multidimensionality of the output. A general formulation is first presented followed by two special cases where the multidimensional function is convex and where it is linear over each focal element. An analytical example first illustrates the importance of considering all the function outputs at once when these are not independent. Then, an application example to preliminary design of a propeller aircraft then illustrates the proposed algorithm for a convex function. An approximate solution found to be almost identical to the exact solution is also obtained for this problem by linearizing the previous convex function over each focal element.

scholarly journals Quantification of Margins and Uncertainties Approach for Structure Analysis Based on Evidence Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Chaoyang Xie ◽  
Guijie Li
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Evidence Theory ◽  
Aleatory Uncertainty ◽  
Engineering Systems ◽  
Kriging Surrogate Model ◽  
Structure Reliability

Quantification of Margins and Uncertainties (QMU) is a decision-support methodology for complex technical decisions centering on performance thresholds and associated margins for engineering systems. Uncertainty propagation is a key element in QMU process for structure reliability analysis at the presence of both aleatory uncertainty and epistemic uncertainty. In order to reduce the computational cost of Monte Carlo method, a mixed uncertainty propagation approach is proposed by integrated Kriging surrogate model under the framework of evidence theory for QMU analysis in this paper. The approach is demonstrated by a numerical example to show the effectiveness of the mixed uncertainty propagation method.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

scholarly journals The temperature dependence of gradient system response characteristics

2019 ◽  
Vol 83 (4) ◽  
pp. 1519-1527 ◽  
Author(s):  
Manuel Stich ◽  
Christiane Pfaff ◽  
Tobias Wech ◽  
Anne Slawig ◽  
Gudrun Ruyters ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
System Response ◽  
Gradient System ◽  
Response Characteristics
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