Dynamic Uncertain Causality Graph Applied to the Intelligent Evaluation of a Shale-Gas Sweet Spot

Shale-gas sweet-spot evaluation as a critical part of shale-gas exploration and development has always been the focus of experts and scholars in the unconventional oil and gas field. After comprehensively considering geological, engineering, and economic factors affecting the evaluation of shale-gas sweet spots, a dynamic uncertainty causality graph (DUCG) is applied for the first time to shale-gas sweet-spot evaluation. A graphical modeling scheme is presented to reduce the difficulty in model construction. The evaluation model is based on expert knowledge and does not depend on data. Through rigorous and efficient reasoning, it guarantees exact and efficient diagnostic reasoning in the case of incomplete information. Multiple conditional events and weighted graphs are proposed for specific problems in shale-gas sweet-spot evaluation, which is an extension of the DUCG that defines only one conditional event for different weighted function events and relies only on the experience of a single expert. These solutions make the reasoning process and results more objective, credible, and interpretable. The model is verified with both complete data and incomplete data. The results show that compared with other methods, this methodology achieves encouraging diagnostic accuracy and effectiveness. This study provides a promising auxiliary tool for shale-gas sweet spot evaluation.

A Method to Avoid Underestimated Risks in Seismic SUPSA and MUPSA for Nuclear Power Plants Caused by Partitioning Events

Seismic probabilistic safety assessment (PSA) models for nuclear power plants (NPPs) have many non-rare events whose failure probabilities are proportional to the seismic ground acceleration. It has been widely accepted that minimal cut sets (MCSs) that are calculated from the seismic PSA fault tree should be converted into exact solutions, such as binary decision diagrams (BDDs), and that the accurate seismic core damage frequency (CDF) should be calculated from the exact solutions. If the seismic CDF is calculated directly from seismic MCSs, it is drastically overestimated. Seismic single-unit PSA (SUPSA) models have random failures of alternating operation systems that are combined with seismic failures of components and structures. Similarly, seismic multi-unit PSA (MUPSA) models have failures of NPPs that undergo alternating operations between full power and low power and shutdown (LPSD). Their failures for alternating operations are modeled using fraction or partitioning events in seismic SUPSA and MUPSA fault trees. Since partitioning events for one system are mutually exclusive, their combinations should be excluded in exact solutions. However, it is difficult to eliminate the combinations of mutually exclusive events without modifying PSA tools for generating MCSs from a fault tree and converting MCSs into exact solutions. If the combinations of mutually exclusive events are not deleted, seismic CDF is underestimated. To avoid CDF underestimation in seismic SUPSAs and MUPSAs, this paper introduces a process of converting partitioning events into conditional events, and conditional events are then inserted explicitly inside a fault tree. With this conversion, accurate CDF can be calculated without modifying PSA tools. That is, this process does not require any other special operations or tools. It is strongly recommended that the method in this paper be employed for avoiding CDF underestimation in seismic SUPSAs and MUPSAs.

Low- and High-Drag Intermittencies in Turbulent Channel Flows

Recent direct numerical simulations (DNS) and experiments in turbulent channel flow have found intermittent low- and high-drag events in Newtonian fluid flows, at Reτ=uτh/ν between 70 and 100, where uτ, h and ν are the friction velocity, channel half-height and kinematic viscosity, respectively. These intervals of low-drag and high-drag have been termed “hibernating” and “hyperactive”, respectively, and in this paper, a further investigation of these intermittent events is conducted using experimental and numerical techniques. For experiments, simultaneous measurements of wall shear stress and velocity are carried out in a channel flow facility using hot-film anemometry (HFA) and laser Doppler velocimetry (LDV), respectively, for Reτ between 70 and 250. For numerical simulations, DNS of a channel flow is performed in an extended domain at Reτ = 70 and 85. These intermittent events are selected by carrying out conditional sampling of the wall shear stress data based on a combined threshold magnitude and time-duration criteria. The use of three different scalings (so-called outer, inner and mixed) for the time-duration criterion for the conditional events is explored. It is found that if the time-duration criterion is kept constant in inner units, the frequency of occurrence of these conditional events remain insensitive to Reynolds number. There exists an exponential distribution of frequency of occurrence of the conditional events with respect to their duration, implying a potentially memoryless process. An explanation for the presence of a spike (or dip) in the ensemble-averaged wall shear stress data before and after the low-drag (or high-drag) events is investigated. During the low-drag events, the conditionally-averaged streamwise velocities get closer to Virk’s maximum drag reduction (MDR) asymptote, near the wall, for all Reynolds numbers studied. Reynolds shear stress (RSS) characteristics during these conditional events are investigated for Reτ = 70 and 85. Except very close to the wall, the conditionally-averaged RSS is higher than the time-averaged value during the low-drag events.

Tail conditional probabilities to predict academic performance

In this paper, we estimate tail conditional probabilities by incorporating copula models and adopting a Bayesian estimation process for the copula’s parameter. Based on the records of student’s classifications in (a) Mathematics and (b) Natural Sciences/Physics (of the entrance exam to the University of Campinas, from 2013 to 2015), by means of tail conditional probabilities we predict the performance, of the same students, in Calculus I which is a mandatory subject of the undergraduate course of Statistics, and we compare the conditional probabilities year after year. We see that (a), (b) and Calculus I show maximal trivariate correlations in tail events given by classifications which are jointly high/low in the three subjects. We compare the evolution of the tail conditional probabilities from 2013 to 2015 and, according to our results there has been an improvement (from 2013 to 2015) of at most 12%. This improvement being more incisive in the settings with conditional events given by jointly high classifications in comparison with settings with conditional events given by jointly lower classifications.

Human Understandings of Probability

In this chapter developments in theories and research on human understandings and judgements of probability are examined. The concept of probability as a degree of belief and the systematic study of human probability judgements have emerged only recently, but have stimulated numerous fruitful debates about the nature of rationality, belief formation, decision-making, and uncertainty itself. The chapter begins with a review of how the connection between probability and degrees of belief was developed and elaborated to form a prescriptive framework, followed by a brief summary of debates concerning rationality and uncertainty. It then surveys models of human probability judgements based on probability weighting functions, ways in which these judgements depend on how relevant information is presented, mental shortcuts (or “heuristics”) underpinning such judgements, the extent to which probability judgements are miscalibrated, fallacies in judgements of probabilities of compound and conditional events, and debates concerning the effective communication of probabilistic information.