scholarly journals Uncertainty Evaluation of Water Inrush in Karst Tunnels Based on Epistemic Uncertainty with Possibility Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yiqing Hao ◽  
Hao Lu ◽  
Yehui Shi ◽  
Hao Geng ◽  
Xi J ◽  
...  
Keyword(s):  
Probability Theory ◽  
Mechanical Model ◽  
Poisson Ratio ◽  
Epistemic Uncertainty ◽  
Water Inrush ◽  
Possibility Theory ◽  
Mathematical Structure ◽  
Karst Tunnel ◽  
Uncertainty Analyses ◽  
Aleatory And Epistemic Uncertainty

In the risk assessment of water inrush in karst tunnel, it is most important to provide an available theoretical model for qualifying the epistemic uncertainties due to a lack of knowledge and information. Firstly, a mechanical model dependent on geology is introduced associating with four parameters, i.e., the elastic modulus E, the Poisson ratio μ, the water differential pressure q, and the tunnel radius a. Then, a mathematical model representing epistemic uncertainty is represented with probability theory and possibility theory. The methodology was computerized to calculate the distribution of the margin and uncertainty and then to determine the ratio of “margin/uncertainty.” Analyses involving possibility theory and possibility theory are illustrated with the same engineering example used in the presentation indicated above to illustrate the use of probability to represent aleatory and epistemic uncertainty in QMU analyses. The comparison between the uses of possibility theory and probability theory for the representation of aleatory and epistemic uncertainty indicates that the possibility is not only has a better mathematical structure than probability theory but also has some challenges.

Study on Safe Thickness of Comparatively Intact Rock Ahead of Karst Tunnel Face

2011 ◽  
Vol 90-93 ◽  
pp. 2456-2459 ◽  
Author(s):  
Jia Qi Guo ◽  
Lian Wei Ren ◽  
Xi Liang Liu
Keyword(s):  
Mechanical Model ◽  
Water Pressure ◽  
Water Inrush ◽  
Intact Rock ◽  
Tensile Fracture ◽  
Karst Tunnel ◽  
Tunnel Face ◽  
Rock Wall ◽  
Safe Thickness ◽  
Tension Strength

Under the effect of water pressure in karst cave before tunnel face, water inrush happens when excavation face enters into the minimal value of safe thickness. Aiming at comparatively intact rock ahead of karst tunnel face, rock wall often appears to be tensile fracture. With some hypotheses, a mechanical model of water inrush for tunnel face instability has been established, furthermore, the analytical expression to calculate safe thickness of rock wall has been given based on the criteria of tension strength through elastical theories. Combined with Maluqing tunnel in Yiwan line, applicability and reliability of formula is discussed.

scholarly journals Evolution Pattern and Matching Mode of Precursor Information about Water Inrush in a Karst Tunnel

Water ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1579
Author(s):  
Jie Song ◽  
Diyang Chen ◽  
Jing Wang ◽  
Yufeng Bi ◽  
Shang Liu ◽  
...  
Keyword(s):  
Rock Mass ◽  
Stress Field ◽  
Displacement Field ◽  
Water Inrush ◽  
Seepage Field ◽  
Karst Tunnel ◽  
Rock Mass Structure ◽  
Evolution Pattern ◽  
Water Blocking ◽  
Precursor Information

The water inrush of the Shangjiawan karst tunnel is used to study the evolution pattern of precursor water inrush information in water-filled caves and to further reveal the matching mode of the information. The three-dimensional numerical method FLAC3D was used to simulate the evolution process of water inrush after damage to a water-blocking rock mass structure in a water-filled cave and to obtain the evolution pattern of precursor water-inrush information caused by the damage. The results show that the multifield response to the characteristic precursor information of the water-inrush pattern after the fracture of the water-blocking rock mass follows the order of stress-field displacement-field seepage-field. Further, the matching pattern of the information shows that the stress field increased first and then decreased, the displacement field always increased, and the seepage field increased first and then decreased.

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

POSSIBILISTIC SONAR DATA MODELING FOR MOBILE ROBOTS

1999 ◽  
Vol 07 (02) ◽  
pp. 173-198 ◽  
Author(s):  
K. DEMIRLI ◽  
M. MOLHIM ◽  
A. BULGAK
Keyword(s):  
Probability Theory ◽  
Mobile Robots ◽  
Data Modeling ◽  
Possibility Theory ◽  
Sensor Design ◽  
Map Building ◽  
Sonar Sensors ◽  
New Models ◽  
Possibility Distributions ◽  
Target Characteristics

Sonar sensors are widely used in mobile robots applications such as navigation, map building, and localization. The performance of these sensors is affected by the environmental phenomena, sensor design, and target characteristics. Therefore, the readings obtained from these sensors are uncertain. This uncertainity is often modeled by using Probability Theory. However, the probablistic approach is valid when the available knowledge is precise which is not the case in sonar readings. In this paper, the behavior of sonar readings reflected from walls and corners are studied, then new models of angular uncertainty and radial imprecision for sonar readings obtained from corners and walls are proposed. These models are represented by using Possibility Theory, mainly possibility distributions.

scholarly journals Epistemic Uncertainty Analysis: An Approach Using Expert Judgment and Evidential Credibility

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Patrick Hester
Keyword(s):  
Decision Making ◽  
Probability Theory ◽  
Air Force ◽  
Subject Matter ◽  
Epistemic Uncertainty ◽  
Expert Judgment ◽  
Decision Makers ◽  
Expert Analysis ◽  
Physical Attributes ◽  
The Subject

When dealing with complex systems, all decision making occurs under some level of uncertainty. This is due to the physical attributes of the system being analyzed, the environment in which the system operates, and the individuals which operate the system. Techniques for decision making that rely on traditional probability theory have been extensively pursued to incorporate these inherent aleatory uncertainties. However, complex problems also typically include epistemic uncertainties that result from lack of knowledge. These problems are fundamentally different and cannot be addressed in the same fashion. In these instances, decision makers typically use subject matter expert judgment to assist in the analysis of uncertainty. The difficulty with expert analysis, however, is in assessing the accuracy of the expert's input. The credibility of different information can vary widely depending on the expert’s familiarity with the subject matter and their intentional (i.e., a preference for one alternative over another) and unintentional biases (heuristics, anchoring, etc.). This paper proposes the metric of evidential credibility to deal with this issue. The proposed approach is ultimately demonstrated on an example problem concerned with the estimation of aircraft maintenance times for the Turkish Air Force.

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