scholarly journals Introduction to the Theory of Imprecise Probability

2021 ◽  
pp. 37-50
Author(s):  
Erik Quaeghebeur
Keyword(s):  
Probability Theory ◽  
Uncertainty Modeling ◽  
Basic Knowledge ◽  
Imprecise Probabilities ◽  
Imprecise Probability ◽  
Limited Information ◽  
Practical Advantage ◽  
Uncertainty Model ◽  
Uncertainty Models ◽  
Modeling Task

AbstractThe theory of imprecise probability is a generalization of classical ‘precise’ probability theory that allows modeling imprecision and indecision. This is a practical advantage in situations where a unique precise uncertainty model cannot be justified. This arises, for example, when there is a relatively small amount of data available to learn the uncertainty model or when the model’s structure cannot be defined uniquely. The tools the theory provides make it possible to draw conclusions and make decisions that correctly reflect the limited information or knowledge available for the uncertainty modeling task. This extra expressivity however often implies a higher computational burden. The goal of this chapter is to primarily give you the necessary knowledge to be able to read literature that makes use of the theory of imprecise probability. A secondary goal is to provide the insight needed to use imprecise probabilities in your own research. To achieve the goals, we present the essential concepts and techniques from the theory, as well as give a less in-depth overview of the various specific uncertainty models used. Throughout, examples are used to make things concrete. We build on the assumed basic knowledge of classical probability theory.

Development of Conceptual Model for Uncertainty Management on Project Completion Late Delivery in Environmental Issues

2014 ◽  
Vol 666 ◽  
pp. 363-370 ◽  
Author(s):  
Baharum Zirawani ◽  
M. Ngadiman Salihin ◽  
H. Mustaffa Noorfa
Keyword(s):  
Conceptual Model ◽  
Construction Industry ◽  
Time Management ◽  
Uncertainty Modeling ◽  
Environmental Issues ◽  
Fractional Factorial ◽  
Project Completion ◽  
Uncertainty Model ◽  
Late Delivery ◽  
Water Supply Company

The construction industry has many underlying causes of uncertainty that impact on late delivery of project completion's performance as well as in time management. Most of researchers proposed a modelling and simulation techniques to solve these uncertainties problem nevertheless not tackling the uncertainty in environmental issues (EI). Yet, the environmental issues were also leading significant deviations for project completion performance, which means it is important to be studied. Therefore, the comprehensive sturvey is discussed in this paper in purpose to develop the uncertainty modeling model on late delivery in environmental issues. The development of conceptual model through a comprehensive survey involving piping's construction industry for water supply company with multi-project construction environment is developed to show the relationship for each cause and affects that underlying uncertainty on late project delivery in environmental issues. Further research is to verify and validate the conceptual model as has been analyzed through fractional factorial design with ANOVA, through the development of uncertainty model via modeling and simulation using MATLAB.

Application of Parametric Uncertainty Modeling to a Flexible Structure

1997 ◽  
Author(s):  
G. Wolodkin ◽  
V. Nalbantoğlu ◽  
K. B. Lim ◽  
G. J. Balas
Keyword(s):  
Closed Loop ◽  
Additional Data ◽  
Parametric Uncertainty ◽  
Uncertainty Modeling ◽  
Flexible Structure ◽  
University Of Minnesota ◽  
Output Data ◽  
Norm Model ◽  
Uncertainty Models ◽  
The University

Abstract We present the results of a study in uncertainty modeling applied to the flexible structure at the University of Minnesota. In addition to additive and multiplicative uncertainty models, we examine parametric uncertainty descriptions in which the weights are obtained directly from input-output data. Two methods are examined, one based on a minimum norm model validation (MNMV) test and another in which the estimated co-variance of the parameters is used to arrive at the uncertainty weights. The resulting uncertainty models are then used to design μ-synthesis controllers, and the resulting closed-loop performance is evaluated. Additional data is taken in a closed-loop setting, and this data is used to refine the model. For the flexible structure studied, we show that the use of parametric uncertainty leads to higher performance than that attainable with purely additive or multiplicative uncertainty. Refinement of the model based on closed-loop data is also shown to result in increased performance.

Parameter Uncertainty Modeling Using the Multidimensional Principal Curves

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
M. Sepasi ◽  
F. Sassani ◽  
R. Nagamune
Keyword(s):  
Transfer Functions ◽  
Linear Time ◽  
Optimization Technique ◽  
Parametric Uncertainty ◽  
Uncertainty Modeling ◽  
Principal Component ◽  
Linear Matrix ◽  
Linear Time Invariant ◽  
Uncertain Variables ◽  
Uncertainty Model

This paper proposes a technique to model uncertainties associated with linear time-invariant systems. It is assumed that the uncertainties are only due to parametric variations caused by independent uncertain variables. By assuming that a set of a finite number of rational transfer functions of a fixed order is given, as well as the number of independent uncertain variables that affect the parametric uncertainties, the proposed technique seeks an optimal parametric uncertainty model as a function of uncertain variables that explains the set of transfer functions. Finding such an optimal parametric uncertainty model is formulated as a noncovex optimization problem, which is then solved by a combination of a linear matrix inequality and a nonlinear optimization technique. To find an initial condition for solving this nonconvex problem, the nonlinear principal component analysis based on the multidimensional principal curve is employed. The effectiveness of the proposed technique is verified through both illustrative and practical examples.

Uncertainties Revisited

2019 ◽  
pp. 216-237
Author(s):  
Liesbeth Huybrechts ◽  
Katrien Dreessen ◽  
Selina Schepers
Keyword(s):  
Network Theory ◽  
Actor Network Theory ◽  
Social Processes ◽  
Actor Network ◽  
Uncertainty Model ◽  
The Social ◽  
Matters Of Concern ◽  
Uncertainty Models ◽  
Do So

In this chapter, the authors use actor-network theory (ANT) to explore the relations between uncertainties in co-design processes and the quality of participation. To do so, the authors investigate Latour's discussion uncertainties in relation to social processes: the nature of actors, actions, objects, facts/matters of concern, and the study of the social. To engage with the discussion on uncertainties in co-design and, more specific in infrastructuring, this chapter clusters the diversity of articulations of the role and place of uncertainty in co-design into four uncertainty models: (1) the neoliberal, (2) the management, (3) the disruptive, and (4) the open uncertainty model. To deepen the reflections on the latter, the authors evaluate the relations between the role and place of uncertainty in two infrastructuring processes in the domain of healthcare and the quality of these processes. In the final reflections, the authors elaborate on how ANT supported in developing a “lens” to assess how uncertainties hinder or contribute to the quality of participation.

Multiscale Variability and Uncertainty Quantification Based on a Generalized Multiscale Markov Model

2010 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Probability Theory ◽  
Bayesian Inference ◽  
Markov Model ◽  
Uncertainty Quantification ◽  
System Analysis ◽  
Scale Validation ◽  
Uncertainty Propagation ◽  
Bayes Rule ◽  
Imprecise Probability ◽  
Modal Extension

Variability is inherent randomness in systems, whereas uncertainty is due to lack of knowledge. In this paper, a generalized multiscale Markov (GMM) model is proposed to quantify variability and uncertainty simultaneously in multiscale system analysis. The GMM model is based on a new imprecise probability theory that has the form of generalized interval, which is a Kaucher or modal extension of classical set-based intervals to represent uncertainties. The properties of the new definitions of independence and Bayesian inference are studied. Based on a new Bayes’ rule with generalized intervals, three cross-scale validation approaches that incorporate variability and uncertainty propagation are also developed.

scholarly journals On the Potential use of Index Paths for Avalanche Assessment

1983 ◽  
Vol 29 (101) ◽  
pp. 178-184 ◽  
Author(s):  
A. Judson
Keyword(s):  
Probability Theory ◽  
Diagnostic Value ◽  
Conditional Probabilities ◽  
Limited Information ◽  
Joint Occurrence ◽  
Potential Use

AbstractThe possible use of index paths to assess avalanche potential in large avalanche samples was evaluated with probability theory on 56 uncontrolled avalanche paths in Colorado. Results showed the technique yields limited information of little diagnostic value because of low conditional probabilities of joint occurrence and high yearly variance. 90% of pairs tested had probabilities ≦0.20 for a six-year period. Implications for researchers and field personnel are discussed.

Uncertainty Modeling in Robust Control of Active Magnetic Suspension

2008 ◽  
Vol 144 ◽  
pp. 22-26 ◽  
Author(s):  
Arkadiusz Mystkowski ◽  
Zdzisław Gosiewski
Keyword(s):  
Robust Control ◽  
Digital Signal Processor ◽  
Experimental Studies ◽  
Uncertainty Modeling ◽  
Digital Signal ◽  
Magnetic Suspension ◽  
Robust Controller ◽  
Quality Of Control ◽  
Uncertainty Parameters ◽  
Uncertainty Models

Stabilization of a plant in case of uncertainty parameters and unmodeled dynamics are the main problems considered in this paper. A robust control of motion of a rigid shaft that is supported by magnetic bearings was used as an example. The dynamics of the active magnetic suspension system is characterized by instability and uncertainty. The uncertainty is modeled as an additive and multiplicative. Robust controller H∞ was designed for the defined plant with the uncertainty models. The robust controller assures high quality of control despite the uncertainty models. Robust control of vibrations of a rigid rotor is confirmed by experimental studies. A digital signal processor is used to execute the control algorithm in real time.

scholarly journals An improved approach by introducing copula functions for structural reliability analysis under hybrid uncertainties

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878583 ◽  
Author(s):  
Zheng Liu ◽  
Xin Liu
Keyword(s):  
Probability Theory ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Field Tests ◽  
Copula Function ◽  
Working Environment ◽  
Imprecise Probability ◽  
Copula Functions ◽  
Structural Reliability Analysis ◽  
Reliability Method

The structural composition of the oil platform is very complicated, and its working environment is harsh, thus conducting a large number of reliability tests is not feasible, and the field tests are also hard to accomplish. So the reliability of the oil platform cannot be analyzed and calculated by the traditional reliability method which needs a lot of test data, and new methods should be studied. In recent years, imprecise probability theory has attracted more and more attention because when unified, it can quantify hybrid uncertainty. Structural reliability analysis on the basis of imprecise probability theory has made remarkable achievements in theoretical aspects, but it is scarcely used in practical engineering domains due to the complexity in the developed methods and the unavailability of suitable or specific modeling steps for applications. In this regard, we propose a unified quantification method for statistical data, fuzzy data, incomplete information, and the like, which can handle the issue of hybrid uncertainties, and then, we construct an improved imprecise structural reliability model aiming at the practical problems by introducing copula function. To verify the existing methodology, we also consider a cantilever beam widely applied in the oil platform here for the structural reliability analysis.

Subsurface-to-Economics Closing the Loop on Uncertainty Analysis

2021 ◽  
Author(s):  
Galvin Shergill ◽  
Adrian Anton ◽  
Kwangwon Park
Keyword(s):  
Measurement Errors ◽  
Oil And Gas ◽  
Uncertainty Modeling ◽  
Weather Forecast ◽  
Oil And Gas Industry ◽  
Development Planning ◽  
Gas Field ◽  
Field Development ◽  
Development Scenarios ◽  
Uncertainty Model

Abstract We are all aware that our future is uncertain. Although some aspects can be predicted with more certainty and others with less, essentially everything is uncertain. Uncertainty exists because of lack of data, lack of resources, and lack of understanding. We cannot measure everything, so there are always unknowns. Even measurements include measurement errors. Also, we do not always have enough resources to analyze the data obtained. In addition, we do not have a full understanding of how the world, or the universe, works (Park 2011). Every day we find ourselves in situations where we must make many decisions, big or small. We tend to make the decisions based on a prediction, despite knowing that it is uncertain. For instance, imagine how many decisions are made by people every day based on the probability of it raining tomorrow (i.e., based on the weather forecast). To have a good basis for making a decision, it is of critical importance to correctly model the uncertainty in the forecast. In the oil and gas industry, uncertainties are large and complex. Oil and gas fields have been developed and operated despite tremendous uncertainty in a variety of areas, including undiscovered media and unpredictable fluid in the subsurface, wells, unexpected facility and equipment costs, and economic, political, international, environmental, and many other risks. Another important aspect of uncertainty modeling is the feasibility of verifying the uncertainty model with the actual results. For example, in the weather forecast it was announced that the probability of raining the next day was 20%. And the next day it rained. Do we say the forecast was wrong? Can we say the forecast was right? In order to make sure the uncertainty model is correct; we should strictly verify all the assumptions and follow the mathematically, statistically, proven-to-be-correct methodology to model the uncertainty (Caers et al. 2010; Caers 2011). In this paper, we show an effective, rigorous method of modeling uncertainty in the expected performance of potential field development scenarios in the oil and gas field development planning given uncertainties in various domains from subsurface to economics. The application of this method is enabled by using technology as described in a later section.

Probabilistic Uncertainty Modeling of Obstacle Motion for Robot Motion Planning

2002 ◽  
Vol 14 (4) ◽  
pp. 349-356 ◽  
Author(s):  
Jun Miura ◽  
◽  
Yoshiaki Shirai
Keyword(s):  
Motion Planning ◽  
Uncertainty Modeling ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Probabilistic Uncertainty ◽  
Probabilistic Distribution ◽  
Uncertainty Model ◽  
Observation Uncertainty ◽  
Moving Obstacle ◽  
Time Point

This paper describes a method of modeling the motion uncertainty of moving obstacles and its application to mobile robot motion planning. The method explicitly considers three sources of uncertainty: path ambiguity, velocity uncertainty, and observation uncertainty. In the uncertainty model, the position of an obstacle at a certain time point is represented by a probabilistic distribution over possible positions on each possible path of the moving obstacle. Using this model, the best robot motion is selected in a decision-theoretic way. By considering the distribution, not the range, of uncertainty, more efficient behavior of the robot is realized.

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