Epistemic Uncertainty Modeling of Johnson-Cook Plasticity Model Using Evidence Theory

2010 ◽  
Author(s):  
Shahabedin Salehghaffari ◽  
Masoud Rais-Rohani
Keyword(s):  
Epistemic Uncertainty ◽  
Evidence Theory ◽  
Uncertainty Modeling ◽  
Plasticity Model

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.

Evidence-Based Uncertainty Modeling

2014 ◽  
pp. 54-74
Author(s):  
Tazid Ali
Keyword(s):  
Evidence Theory ◽  
Uncertainty Modeling ◽  
Possibility Theory ◽  
Dempster Shafer Theory ◽  
Uncertainty Measurement ◽  
Frame Work ◽  
Shafer Theory ◽  
Relationship Of ◽  
Different Sources ◽  
Fuzzy Setting

Evidence is the essence of any decision making process. However in any situation the evidences that we come across are usually not complete. Absence of complete evidence results in uncertainty, and uncertainty leads to belief. The framework of Dempster-Shafer theory which is based on the notion of belief is overviewed in this chapter. Methods of combining different sources of evidences are surveyed. Relationship of probability theory and possibility theory to evidence theory is exhibited. Extension of the classical Dempster-Shafer Structure to fuzzy setting is discussed. Finally uncertainty measurement in the frame work of Dempster-Shafer structure is dealt with.

Uncertainty Analysis Using Fuzzy Random Set Theory

2016 ◽  
pp. 384-418
Author(s):  
Debabrata Datta
Keyword(s):  
Uncertainty Analysis ◽  
Set Theory ◽  
Practical Problem ◽  
Epistemic Uncertainty ◽  
Uncertainty Modeling ◽  
Random Set ◽  
Uncertain Variables ◽  
Definition Of ◽  
Hydrological Applications ◽  
Fuzzy Random

Uncertainty analysis of any physical model is always an essential task from the point of decision making analysis. Two kinds of uncertainties exist: (1) aleatory uncertainty which is due to randomness of the parameters of models of interest and (2) the epistemic uncertainty which is due to fuzziness of the parameters of the same models. So far both these uncertainties are addressed independently; however since in any practical problem both the types of uncertain variables present, it is required to address them jointly. In order to solve practical problems on uncertainty modeling, it is required to replace the abstract definition of hybrid set by fuzzy random set. Since uncertainty modeling using fuzzy random set has not been carried out so far, the present chapter will address the utility of fuzzy random set for uncertainty modeling on geotechnical and hydrological applications. This chapter will present the fundamentals of fuzzy random set and their application in uncertainty analysis.

scholarly journals Evidence-Theory-Based Robust Optimization and Its Application in Micro-Electromechanical Systems

2019 ◽  
Vol 9 (7) ◽  
pp. 1457 ◽  
Author(s):  
Zhiliang Huang ◽  
Jiaqi Xu ◽  
Tongguang Yang ◽  
Fangyi Li ◽  
Shuguang Deng
Keyword(s):  
Probabilistic Model ◽  
Epistemic Uncertainty ◽  
Evidence Theory ◽  
Robustness Analysis ◽  
Force Sensor ◽  
Image Sensor ◽  
Optimization Approach ◽  
Electromechanical Systems ◽  
Capacitive Accelerometer ◽  
Robustness Optimization

The conventional engineering robustness optimization approach considering uncertainties is generally based on a probabilistic model. However, a probabilistic model faces obstacles when handling problems with epistemic uncertainty. This paper presents an evidence-theory-based robustness optimization (EBRO) model and a corresponding algorithm, which provide a potential computational tool for engineering problems with multi-source uncertainty. An EBRO model with the twin objectives of performance and robustness is formulated by introducing the performance threshold. After providing multiple target belief measures (Bel), the original model is transformed into a series of sub-problems, which are solved by the proposed iterative strategy driving the robustness analysis and the deterministic optimization alternately. The proposed method is applied to three problems of micro-electromechanical systems (MEMS), including a micro-force sensor, an image sensor, and a capacitive accelerometer. In the applications, finite element simulation models and surrogate models are both given. Numerical results show that the proposed method has good engineering practicality due to comprehensive performance in terms of efficiency, accuracy, and convergence.

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.

scholarly journals A Novel Evidence Conflict Measurement for Multi-Sensor Data Fusion Based on the Evidence Distance and Evidence Angle

Sensors ◽  
2020 ◽  
Vol 20 (2) ◽  
pp. 381 ◽  
Author(s):  
Zhan Deng ◽  
Jianyu Wang
Keyword(s):  
Measurement Method ◽  
Evidence Theory ◽  
Weighted Average ◽  
Uncertainty Modeling ◽  
New Method ◽  
Sensor Data ◽  
Mutual Support ◽  
Combination Rule ◽  
Practical Applications ◽  
Multi Sensor Data Fusion

As an important method for uncertainty modeling, Dempster–Shafer (DS) evidence theory has been widely used in practical applications. However, the results turned out to be almost counter-intuitive when fusing the different sources of highly conflicting evidence with Dempster’s combination rule. In previous researches, most of them were mainly dependent on the conflict measurement method between the evidence represented by the evidence distance. However, it is inaccurate to characterize the evidence conflict only through the evidence distance. To address this issue, we comprehensively consider the impacts of the evidence distance and evidence angle on conflicts in this paper, and propose a new method based on the mutual support degree between the evidence to characterize the evidence conflict. First, the Hellinger distance measurement method is proposed to measure the distance between the evidence, and the sine value of the Pignistic vector angle is used to characterize the angle between the evidence. The evidence distance indicates the dissimilarity between the evidence, and the evidence angle represents the inconsistency between the evidence. Next, two methods are combined to get a new method for measuring the mutual support degree between the evidence. Afterward, the weight of each evidence is determined by using the mutual support degree between the evidence. Then, the weights of each evidence are utilized to modify the original evidence to achieve the weighted average evidence. Finally, Dempster’s combination rule is used for fusion. Some numerical examples are given to illustrate the effectiveness and reasonability for the proposed method.

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