Possibilistic Uncertainty Quantification in 1-D Consolidation Problems

2021 ◽  
Author(s):  
Djamalddine Boumezerane
Keyword(s):  
Uncertainty Quantification ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Possibility Distribution ◽  
Coefficient Of Consolidation ◽  
Consolidation Process ◽  
Possibility Distributions ◽  
Coverage Function ◽  
The One ◽  
Measure Of Uncertainty

Abstract In this study, we use possibility distribution as a basis for parameter uncertainty quantification in one-dimensional consolidation problems. A Possibility distribution is the one-point coverage function of a random set and viewed as containing both partial ignorance and uncertainty. Vagueness and scarcity of information needed for characterizing the coefficient of consolidation in clay can be handled using possibility distributions. Possibility distributions can be constructed from existing data, or based on transformation of probability distributions. An attempt is made to set a systematic approach for estimating uncertainty propagation during the consolidation process. The measure of uncertainty is based on Klir's definition (1995). We make comparisons with results obtained from other approaches (probabilistic…) and discuss the importance of using possibility distributions in this type of problems.

scholarly journals EMPIRICAL COMPARISON OF METHODS FOR THE HIERARCHICAL PROPAGATION OF HYBRID UNCERTAINTY IN RISK ASSESSMENT, IN PRESENCE OF DEPENDENCES

2012 ◽  
Vol 20 (04) ◽  
pp. 509-557 ◽  
Author(s):  
NICOLA PEDRONI ◽  
ENRICO ZIO
Keyword(s):  
Risk Analysis ◽  
Epistemic Uncertainty ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Random Sets ◽  
Uncertain Parameters ◽  
Random Events ◽  
Possibility Distributions ◽  
Hybrid Uncertainty ◽  
Analysis Models

Risk analysis models describing aleatory (i.e., random) events contain parameters (e.g., probabilities, failure rates, …) that are epistemically-uncertain, i.e., known with poor precision. Whereas aleatory uncertainty is always described by probability distributions, epistemic uncertainty may be represented in different ways (e.g., probabilistic or possibilistic), depending on the information and data available. The work presented in this paper addresses the issue of accounting for (in)dependence relationships between epistemically-uncertain parameters. When a probabilistic representation of epistemic uncertainty is considered, uncertainty propagation is carried out by a two-dimensional (or double) Monte Carlo (MC) simulation approach; instead, when possibility distributions are used, two approaches are undertaken: the hybrid MC and Fuzzy Interval Analysis (FIA) method and the MC-based Dempster-Shafer (DS) approach employing Independent Random Sets (IRSs). The objectives are: i) studying the effects of (in)dependence between the epistemically-uncertain parameters of the aleatory probability distributions (when a probabilistic/possibilistic representation of epistemic uncertainty is adopted) and ii) studying the effect of the probabilistic/possibilistic representation of epistemic uncertainty (when the state of dependence between the epistemic parameters is defined). The Dependency Bound Convolution (DBC) approach is then undertaken within a hierarchical setting of hybrid (probabilistic and possibilistic) uncertainty propagation, in order to account for all kinds of (possibly unknown) dependences between the random variables. The analyses are carried out with reference to two toy examples, built in such a way to allow performing a fair quantitative comparison between the methods, and evaluating their rationale and appropriateness in relation to risk analysis.

Pacific Salmon Environmental and Life History Models: Advancing Science for Sustainable Salmon in the Future

2009 ◽  
Keyword(s):  
Model Uncertainty ◽  
Pacific Salmon ◽  
Probability Distributions ◽  
Cultural Resources ◽  
Policy Makers ◽  
Recovery Planning ◽  
Habitat Recovery ◽  
Alternative Scenarios ◽  
The One

<em>Abstract.</em>—Natural resource management requires difficult decisions, broad societal costs, and sacrifices from private landowners and public agencies. With so many financial, ecological and cultural resources at stake, policy-makers, managers, and citizens need scientific predictions that can help resolve conflicts and balance the often competing needs of ecosystems and communities. Modeled information is essential for meeting this need. The words “model uncertainty” are often misinterpreted as describing a lack of knowledge about model output. In fact, they describe knowledge, not only of the one most likely modeled estimate, but also of all the other possible estimates that the model might have provided, and their likelihood. We present six case studies, from salmon habitat recovery planning, illustrating how scientists can provide more useful products by describing distributions of possible outcomes as formal probability distributions, as confidence intervals, or as descriptions of alternative scenarios. In terms of management effectiveness, the communication and use of model uncertainty can be at least as important as the quality of the original model.

scholarly journals Experimental insights into consolidation rates during one-dimensional loading with special reference to excess pore water pressure

2020 ◽  
Vol 15 (12) ◽  
pp. 3571-3591
Author(s):  
Bartłomiej Szczepan Olek
Keyword(s):  
Pore Water ◽  
Large Scale ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Small Scale ◽  
Coefficient Of Consolidation ◽  
Consolidation Process ◽  
Factors Affecting ◽  
Fine Grained ◽  
Fine Grained Soil

AbstractConsolidation rate has significant influence on the settlement of structures founded on soft fine-grained soil. This paper presents the results of a series of small-scale and large-scale Rowe cell consolidation tests with pore water pressure measurements to investigate the factors affecting the consolidation process. Permeability and creep/resistance structure factors were considered as the governing factors. Intact and reconstituted marine clay from the Polish Carpathian Foredeep basin as well as clay–sand mixtures was examined in the present study. The fundamental relationship correlating consolidation degrees based on compression and pore water pressure was assessed to indicate the nonlinear soil behaviour. It was observed that the instantaneous consolidation parameters vary as the process progresses. The instantaneous coefficient of consolidation first drastically increases or decreases with increase in the degree of consolidation and stabilises in the middle stage of the consolidation; it then decreases significantly due to viscoplastic effects occurring in the soil structure. Based on the characteristics of the relationship between coefficient of consolidation and degree of dissipation at the base, the consolidation range that complies with theoretical assumptions was established. Furthermore, the influence of coarser fraction in clay–sand mixtures in controlling the consolidation rates is discussed.

scholarly journals An Improved Algorithm for Low-Level Turbulence Forecasting

2018 ◽  
Vol 57 (6) ◽  
pp. 1249-1263 ◽  
Author(s):  
Domingo Muñoz-Esparza ◽  
Robert Sharman
Keyword(s):  
Probability Distributions ◽  
Atmospheric Stability ◽  
Energy Dissipation Rate ◽  
Probability Of Detection ◽  
Percentage Error ◽  
Unmanned Aerial Systems ◽  
Low Level ◽  
Forecasting System ◽  
The One ◽  
Aerial Systems

AbstractA low-level turbulence (LLT) forecasting algorithm is proposed and implemented within the Graphical Turbulence Guidance (GTG) turbulence forecasting system. The LLT algorithm provides predictions of energy dissipation rate (EDR; turbulence dissipation to the one-third power), which is the standard turbulence metric used by the aviation community. The algorithm is based upon the use of distinct log-Weibull and lognormal probability distributions in a statistical remapping technique to represent accurately the behavior of turbulence in the atmospheric boundary layer for daytime and nighttime conditions, respectively, thus accounting for atmospheric stability. A 1-yr-long GTG LLT calibration was performed using the High-Resolution Rapid Refresh operational model, and optimum GTG ensembles of turbulence indices for clear-air and mountain-wave turbulence that minimize the mean absolute percentage error (MAPE) were determined. Evaluation of the proposed algorithm with in situ EDR data from the Boulder Atmospheric Observatory tower covering a range of altitudes up to 300 m above the surface demonstrates a reduction in the error by a factor of approximately 2.0 (MAPE = 55%) relative to the current operational GTG system (version 3). In addition, the probability of detection of typical small and large EDR values at low levels is increased by approximately 15%–20%. The improved LLT algorithm is expected to benefit several nonconventional turbulence-prediction sectors such as unmanned aerial systems and wind energy.

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 Application of Asymmetrical Statistical Distributions for 1D Simulation of Solute Transport in Streams

Water ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 2145
Author(s):  
Sokáč ◽  
Velísková ◽  
Gualtieri
Keyword(s):  
Probability Distributions ◽  
New Approach ◽  
Dead Zones ◽  
Advection Dispersion ◽  
Small Streams ◽  
Computational Speed ◽  
Transient Storage Zones ◽  
The One ◽  
Published Research ◽  
Substance Transport

Analytical solutions of the one-dimensional (1D) advection–dispersion equations, describing the substance transport in streams, are often used because of their simplicity and computational speed. Practical computations, however, clearly show the limits and the inaccuracies of this approach. These are especially visible in cases where the streams deform concentration distribution of the transported substance due to hydraulic and morphological conditions, e.g., by transient storage zones (dead zones), vegetation, and irregularities in the stream hydromorphology. In this paper, a new approach to the simulation of 1D substance transport is presented, adapted, and tested on tracer experiments available in the published research, and carried out in three small streams in Slovakia with dead zones. Evaluation of the proposed methods, based on different probability distributions, confirmed that they approximate the measured concentrations significantly better than those based upon the commonly used Gaussian distribution. Finally, an example of the application of the proposed methods to an iterative (inverse) task is presented.

Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
M. Li ◽  
S. Azarm
Keyword(s):  
Robust Optimization ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Multiple Objectives ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Solution Approach ◽  
Time In Literature ◽  
Collaborative Robust Optimization ◽  
First Time

We present a new solution approach for multidisciplinary design optimization (MDO) problems that, for the first time in literature, has all of the following characteristics: Each discipline has multiple objectives and constraints with mixed continuous-discrete variables; uncertainty exists in parameters and as a result, uncertainty propagation exists within and across disciplines; probability distributions of uncertain parameters are not available but their interval of uncertainty is known; and disciplines can be fully (two-way) coupled. The proposed multiobjective collaborative robust optimization (McRO) approach uses a multiobjective genetic algorithm as an optimizer. McRO obtains solutions that are as best as possible in a multiobjective and multidisciplinary sense. Moreover, for McRO solutions, the variation of objective and/or constraint functions can be kept within an acceptable range. McRO includes a technique for interdisciplinary uncertainty propagation. The approach can be used for robust optimization of MDO problems with multiple objectives, or constraints, or both together at system and subsystem levels. Results from an application of McRO to a numerical and an engineering example are presented. It is concluded that McRO can solve fully coupled MDO problems with interval uncertainty and obtain solutions that are comparable to a single-disciplinary robust optimization approach.

scholarly journals Investigation of the Effects of Anisotropic Flow of Pore Water and Multilayered Soils on Three-Dimensional Consolidation Characteristics

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Arpan Laskar ◽  
Sujit Kumar Pal
Keyword(s):  
Pore Water ◽  
Three Dimensional ◽  
Surface Settlement ◽  
Coefficient Of Consolidation ◽  
Consolidation Process ◽  
Soil Layers ◽  
Anisotropic Flow ◽  
Practical Engineering ◽  
Consolidating Soil ◽  
Multilayered Soils

Many practical engineering problems are seriously different from the assumptions which are considered for one-dimensional consolidation test and need to concentrate on three-dimensional consolidation of soil under different boundary conditions. In this study three-dimensional consolidation tests are performed with four different anisotropic flow conditions of pore water and fifteen different combinations of horizontal layered soils. Twelve different three-dimensional consolidation tests are also performed with different soils, surrounded by anisotropic vertical soil layers on two opposite sides. From these studies, it is observed that the anisotropic flow of pore water does not have any effect on initial and final surface settlement of soil but has a significant effect during the consolidation process. The anisotropic flow of pore water during the consolidation process has an immense effect on the coefficient of consolidation. Horizontal layered soil has a great effect on both surface settlement and the rate of settlement. Vertical soil layers on two opposite sides of consolidative soil have an immense effect on the horizontal movements of consolidating soil, finally affecting the resultant vertical settlement of soil. Vertical anisotropic surrounding soil layers also have an effect on the rate of consolidation settlement.

scholarly journals Optimization results for a generalized coupon collector problem

2016 ◽  
Vol 53 (2) ◽  
pp. 622-629 ◽  
Author(s):  
Emmanuelle Anceaume ◽  
Yann Busnel ◽  
Ernst Schulte-Geers ◽  
Bruno Sericola
Keyword(s):  
Probability Distribution ◽  
Uniform Distribution ◽  
Closed Subset ◽  
Probability Distributions ◽  
Fixed Number ◽  
Coupon Collector ◽  
The One

Abstract In this paper we study a generalized coupon collector problem, which consists of analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we prove that the almost uniform distribution, for which all the nonnull coupons have the same drawing probability, is the distribution which stochastically minimizes the time needed to collect a fixed number of distinct coupons. Moreover, we show that in a given closed subset of probability distributions, the distribution with all its entries, but one, equal to the smallest possible value is the one which stochastically maximizes the time needed to collect a fixed number of distinct coupons.

scholarly journals ESTIMATIONS OF EXPECTEDNESS AND POTENTIAL SURPRISE IN POSSIBILITY THEORY

1994 ◽  
Vol 02 (04) ◽  
pp. 417-428 ◽  
Author(s):  
HENRI PRADE ◽  
RONALD R. YAGER
Keyword(s):  
Possibility Theory ◽  
Point Of View ◽  
Possibility Distribution ◽  
Owa Operators ◽  
Set Functions ◽  
Basic Set ◽  
Potential Applications ◽  
Possibility Distributions

This note investigates how various ideas of "expectedness" can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying "I would not be surprised that…" before an event takes place, or by saying "I knew it" after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of possibility of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined.

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