Low-probability Events Research Articles

Reliability of Supply and the Impact of Weather Exposure and Protection System Failures

Extreme weather is known to cause failure bunching in electrical transmission systems. However, protection systems can also contribute to the worsening of the system state through various failure modes—spontaneous, missing or unwanted operation. The latter two types of failures only occur when an initial failure has happened, and thus are more likely to happen when the probability of failure of transmission lines is high, such as in an extreme weather scenario. This causes an exacerbation of failure bunching effects, increasing the risk of blackouts, or High Impact Low Probability (HILP) events. This paper describes a method to model transmission line failure rates, considering both protection system reliability and extreme weather exposure. A case study is presented using the IEEE 24 bus Reliability Test System (RTS) test system. The case study, using both an approximate method as well as a time-series approach to calculate reliability indices, demonstrates both a compact generalization of including protection system failures in reliability analysis, as well as the interaction between weather exposure and protection system failures and its impact on power system reliability indices. The results show that the inclusion of protection system failures can have a large impact on the estimated occurrence of higher order contingencies for adjacent lines, especially for lines with correlated weather exposure.

Probabilistic–proactive distribution network scheduling against a hurricane as a high impact–low probability event considering chaos theory

High impact–low probability (HILP) incidents, such as hurricanes, usually and gravely damage electric distribution networks. A resilient distribution network must have an ability to recover itself with a fast restoration methodology against the effects of HILP events. Due to improve the electric distribution network resiliency against HILP incidents, this paper suggests a probabilistic–proactive distribution network operation model based upon the chaos theory (P-PDNOMC(. Here, a resilience index based upon operational cost and load shedding cost is employed to decrease the effects of a hurricane as an HILP incident. P-PDNOMC is formulated as a framework that consists of a novel hurricane modelling and operation scheduling in normal and emergency conditions with uncertainties considering. It should be noted that a prediction approach based on the chaos theory and the least-squares support vector machine (LS-SVM) is also designed to consider the provisional and spatial behaviour of the hurricane. Furthermore, this paper proposes a novel optimization framework for damaged lines determination based upon the P-PDNOM C (DLsP-PDNOM C) by considering multi-zone and multi-period damaged equipment budget constraints. Here, the load shedding cost is applied to present the efficiency of the proposed model. The numerical results indicate the resiliency enhancement of the electric distribution network in the face of HILP incidents.

Artificial intelligence for resilience enhancement of power distribution systems

The threat of high impact low probability (HILP) events on power distribution system is substantial but quite unpredictable. Enhancing the resilience of power distribution grids against such events requires solving combinatorial planning and operational problems in stochastic spaces, as well as classifying system conditions based on high-dimensional input data. Since traditional mathematical solutions struggle with both uncertainty and the curse of dimensionality, data-driven techniques based on artificial intelligence (AI) are gaining momentum for solving those problems. This paper reviews AI capabilities for decision making in uncertain and high-dimensional spaces in general, and their particular application in resilient enhancement problems such as damage detection and estimation, cyber-physical anomaly detection, stochastic operation, and cyber security enhancement. Efficient data structures and AI approaches are suggested for each problem, which depend on the type of input signals, search-based or game-based structure of the problem, as well as the uncertainty sources involved. In particular, potential applications of supervised and unsupervised deep learning combined with Monte Carlo Tree Search and ε-greedy search is explored to find near optimal operational decisions that help enhance the resilience of power distribution systems.

Jiamusi pulsar observations

Aims. Most pulsar nulling observations have been conducted at frequencies lower than 1400 MHz. We aim to understand the nulling behaviors of pulsars at relatively high frequencies, and to decipher whether or not nulling is caused by a global change in the pulsar magnetosphere. Methods. We used the Jiamusi 66 m telescope to observe 20 bright pulsars at 2250 MHz with unprecedented lengths of time. We estimated the nulling fractions of these pulsars, and identified the null and emission states of the pulses. We also calculated the nulling degrees and scales of the emission-null pairs to describe the distributions of emission and null lengths. Results. Three pulsars, PSRs J0248+6021, J0543+2329, and J1844+00, are found to null for the first time. The details of null-to-emission and emission-to-null transitions within the pulse window are observed for the first time for PSR J1509+5531, which is a low-probability event. A complete cycle of long nulls with timescales of hours is observed for PSR J1709−1640. For most of these pulsars, the K-S tests of nulling degrees and nulling scales reject the hypothesis that null and emission are caused by random processes at high significance levels. Emission-null sequences of some pulsars exhibit quasi-periodic, low-frequency or featureless modulations, which might be related to different origins. During transitions between emission and null states, pulse intensities have diverse tendencies for variation. Significant correlations are found between respectively nulling fraction, nulling cadence, and nulling scale and the energy loss rate of the pulsars. Combined with the nulling fractions reported in the literature for 146 nulling pulsars, we find that statistically large nulling fractions are more tightly related to pulsar period than to characteristic age or energy-loss rate.

Broad bracketing for low probability events

Individuals tend to underprepare for rare, catastrophic events because of biases in risk perception. A simple form of broad bracketing—presenting the cumulative probability of loss over a longer time horizon—has the potential to alleviate these barriers to accurate risk perception and increase protective actions such as purchasing flood insurance. However, it is an open question whether broad bracketing effects last over time: There is evidence that descriptive probability information is ignored when decisions are based on “experience” (repeatedly and in the face of feedback), which characterizes many protective decisions. Across six incentive-compatible experiments with high stakes, we find that the broad bracketing effect does not disappear or change size when decisions are made from experience. We also advance our understanding of the mechanisms underlying broad bracketing, finding that, while cumulative probability size is a strong driver of the effect, this is dampened for larger brackets leading people to be less sensitive to probability size.

Household Portfolio Underdiversification and Probability Weighting: Evidence from the Field

AbstractWe test whether probability weighting affects household portfolio choice in a representative survey. On average, people display inverse-S-shaped probability weighting, overweighting low probability events. As theory predicts, probability weighting is positively associated with portfolio underdiversification and significant Sharpe ratio losses. Analyzing respondents’ individual stock holdings, we find higher probability weighting is associated with owning lottery-type stocks and positively skewed equity portfolios. People with higher probability weighting are less likely to own mutual funds and more likely to either avoid equities or hold individual stocks. We are the first to empirically link individuals’ elicited probability weighting and real-world decisions under risk.

Multi-hazard perceptions at Long Valley Caldera, California, USA

Caldera systems such as Long Valley Caldera, California; Taupo, New Zealand; and Campi Flegrei, Italy, experience centuries to millennia without eruption, but have the potential for large eruptions. This raises questions about how local residents' behavioral responses to these low-probability high-consequence events differ from their responses to events, such as wildfires and earthquakes, that have higher probabilities. To examine this issue, a multi-hazard mail survey of 229 households explored perceptions of—and responses to—volcano, earthquake and wildfire hazards in the Long Valley Volcanic Region. Response efficacy was the only significant predictor of emergency preparedness, which suggests that hazard managers can increase household emergency preparedness by emphasizing this attribute of protective actions. In addition to response efficacy, expected personal consequences, hazard intrusiveness, and affective responses were all significantly related to information seeking. This indicates that hazard managers can also increase households’ information seeking about local hazards and appropriate protective actions by communicating the certainty and severity of hazard impacts (thus increasing expected personal consequences) and that they communicate this information repeatedly (thus increasing hazard intrusiveness) to produce significant emotional involvement (thus increasing affective response).

Risk Management Solutions for Climate Change-Induced Disasters.

In honor of the 40th anniversary of Risk Analysis, this article suggests ways of linking risk assessment and risk perception in developing risk management strategies that have a good chance of being implemented, focusing on the problem of reducing losses from natural hazards in the face of climate change. Following a checklist for developing an implementable risk management strategy, Section 2 highlights the impact that exponential growth of CO2 emissions is likely to have on future disaster losses as assessed by climate and social scientists. Section 3 then discusses how people perceive the risks of low-probability adverse events and the cognitive biases that lead them to underprepare for future losses. Based on this empirical evidence, Section 4 proposes a risk management strategy for reducing future losses using the principles of choice architecture to communicate the likelihood and consequences of disasters, coupled with economic incentives and well-enforced regulations.

The CoViD-19 Pandemic and the End of Corporate Risk Management as we know it

Aim: The article is intended to contribute to a discussion on risks related to the CoViD-19 pandemic, which was started in the last issues of this journal.
 Findings: The article discusses the thesis that conventional risk management is reaching its limits in its application in companies, particularly with regard to low-probability but high-impact events its applications seems nor appropriate. In complex and tightly coupled systems like global supply chains, catastrophic events must be considered "normal". The risk of a global pandemic is well known, and at the end of 2019 the first signs of an impending outbreak were also evident. Nevertheless, the global pandemic and the gradual lockdown was surprising in that no precautionary measures were taken. Therefore, this paper argues for a change of perspective from traditional risk management to BCM and for increasing the resilience of supply chains.
 Keywords: CoViD-19, risk management, black swans, business continuity, supply chain resilience

Methodology to incorporate stuck condition of the circuit breaker in reliability evaluation of electrical distribution networks

The random failure of a circuit breaker (CB) in a power distribution network adversely impacts its ability to maintain supply continuity to its electricity customers. Among different CB failure modes, the failure to open, or the stuck condition, of a normally closed CB causes the operation of its backup breaker(s) leading to outages of multiple healthy feeders. Stuck condition is a low-probability failure event, but has wide-spread consequences when it occurs. This study proposes a generalised analytical methodology to identify the failure events due to the stuck breaker condition. The complexity of the reliability evaluation of a modern distribution system involving multiple switching arrangements is achieved through a search algorithm and repeated matrix operations that can readily be implemented in a computer program. The methodology is illustrated using a test distribution network. The usefulness of the methodology is demonstrated by quantifying the impact of the stuck breaker condition on load point and system reliability indices. The developed methodology can be a useful tool for industrial/commercial customers and utilities to incorporate the impact of breaker failures, including stuck breaker conditions, and make wise investment decisions in the upgrade and maintenance of the distribution network components and the protection system.

A Review of the Measures to Enhance Power Systems Resilience

Rare and extreme climate events may result in wide power outages or blackouts. The concept of power system resilience has been introduced for focusing on high-impact and low-probability (HILP) events such as a hurricane, heavy snow, and floods. Power system resilience is the ability of a system to reduce the likelihood of blackout or wide power outages due to HILP events. Indeed, in a resilient power system, as the severity of HILP events increases, the rate (but not the amount) of unserved loads diminishes. Suitable measures for managing power system resilience can be classified into three categories in terms of time, known as “resilience-based planning,” “resilience-based response,” and “resilience-based restoration.” The most widely used approaches, methods, and techniques in each of these categories, as well as the future trends for improving the power system resilience are reviewed in this article. The challenges of resilience in power systems with high penetration of renewable energy sources are also discussed in each of these categories.

Future changes in heatwave severity, duration and frequency due to climate change for the most populous cities

A novel approach to quantify the present and future heatwave hazard is presented which can discern characteristics beyond what can be achieved from current approaches, such as distributions of severity, duration and frequency, including very low probability events that may not have been seen. A statistical model is built that represents the seasonal cycle, climate change, magnitude and temporal behaviour of all temperatures above a moderately high time varying threshold at a site from which very large samples of temperature time series can be drawn. From these, user defined heatwaves can be extracted and precise empirical statistics calculated, allowing application to a wide range of problems such as heatwave impact on the pollination of food crops. Fitting the heatwave model to climate model simulations allows the changing severity, duration and frequency of heatwaves from the past to the future to be quantified. This approach is validated by reproducing the heatwave climatology of a pre-industrial 3 500 year GCM control run from a 110 year future emission run of the same GCM. Using this methodology, future heatwave changes for the most populous cities from 20 countries are derived from a 44 member ensemble of 28 GCMs from the CMIP5 archive forced with the RCP 8.5 emission scenario. Compared to 2006, absolute temperatures of 4–10 day long heatwaves are projected to be between 3.4 to 6.6 °C hotter in 2099, though the magnitude of the increases are independent of heatwave rarity and duration. For 13 of the cities no significant future changes in the distribution of durations are found relative to a contemporaneous threshold. Six cities show future heatwaves will have a tendency to be longer and one to be shorter. Half of the cities show increases in severity, the time integrated temperature anomalies above the contemporaneous threshold. The largest changes are found for Paris with 100 year return level severity changes equivalent to mean heatwave temperatures increasing by 3.4 °C or by 1.7 °C for 5 and 10 day heatwaves respectively, and the rate of 10 day heatwaves increasing by 130%.

Reliability Evaluation on a Joint Machine Learning and Optimization Framework

Coordinately embedding machine learning and optimization in the Monte Carlo simulation is proposed as a new framework for reliability evaluation, which is becoming more challenging due to the joining of variability and intermittency of the renewable generation and components’ ageing. As a machine learning method, the dynamic Bayesian belief network predicts the renewable outputs by generating their probability distributions through historical data to overcome the defect of rarely grasping the low-probability events in the traditional methods, which either predict a single-point value or presume a parametric probability distribution. As the internal operation module of the framework, the rolling-horizon unit commitment maintains the complexity of the operation model and meantime punctually updates the predicted renewable generation and the components’ ageing. The dynamic Bayesian belief network and the rolling-horizon unit commitment traverse time step after time step throughout the horizon, and thus form one bid of the Monte Carlo simulation. In each time step, the dynamic Bayesian belief network extracts the probability distributions of the renewable generation, from which the boundary of the commitment is sampled, and the impact of scheduling the generators on their ageing is then accumulated from the commitment. The proposed framework has its effectiveness proved on a microgrid.

Blackouts, Restoration, and Islanding: A System Resilience Perspective

The resilience (or resiliency) of a system is characterized by its resistive, anticipative, absorptive, adaptive, and restorative capacities when facing adverse events. Resilience is an umbrella term that goes beyond related concepts like robustness and protection, redundancy and fallback options, or reliability. A system is considered resilient when it can provide a high level of service, even after highimpact, low-probability events. For every system, resilience regarding a specific event can be analyzed by studying the system's performance over time.

High-Fidelity Potential Energy Surfaces for Gas-Phase and Gas-Surface Scattering Processes from Machine Learning.

In this Perspective, we review recent advances in constructing high-fidelity potential energy surfaces (PESs) from discrete ab initio points, using machine learning tools. Such PESs, albeit with substantial initial investments, provide significantly higher efficiency than direct dynamics methods and/or high accuracy at a level that is not affordable by on-the-fly approaches. These PESs not only are a necessity for quantum dynamical studies because of delocalization of wave packets but also enable the study of low-probability and long-time events in (quasi-)classical treatments. Our focus here is on inelastic and reactive scattering processes, which are more challenging than bound systems because of the involvement of continua. Relevant applications and developments for dynamical processes in both the gas phase and at gas-surface interfaces are discussed.

Prospect Theory and due process paranoia: what behavioural models say about arbitrators’ assessment of risk and uncertainty

Abstract The term ‘due process paranoia’ is used to describe a perceived reluctance by arbitral tribunals to act decisively in certain situations for fear of the arbitral award being challenged on the basis of a party not having had the chance to present its case fully. This article approaches due process paranoia from the perspective of Prospect Theory, which is a behavioural model describing how individuals make decisions under risk and uncertainty. The authors examine how Prospect Theory’s insight that decision makers tend to overweight low-probability events in their decision-making (the ‘possibility effect’) affects decision-making by arbitrators when faced with the threat of challenge to their awards on due process grounds (the ‘enforcement risk’). The article concludes that the possibility effect is prone to contribute to an overweighting by arbitrators of the enforcement risk, thereby explaining the perceived tendency by tribunals to make sub-optimal decisions when faced with due process-related complaints or threats.

Insurance Purchase for Low-Probability Losses

It is widely accepted that individuals tend to underinsure against low-probability, high-loss events relative to high-probability, low-loss events. This conventional wisdom is based largely on field studies, as there is very little experimental evidence. We reexamine this issue with an experiment that accounts for possible confounds in prior insurance experiments. Our results are counter to the prior experimental evidence, as we observe subjects buying more insurance for low-probability events than the higher-probability events, given a constant expected loss and load factor. Our results suggest that, to the extent underinsurance for catastrophic risk is observed in the field, it can be attributed to factors other than the relative probability of the loss events.

Accelerating quantum optics experiments with statistical learning

Quantum optics experiments, involving the measurement of low-probability photon events, are known to be extremely time-consuming. We present a methodology for accelerating such experiments using physically motivated ansatzes together with simple statistical learning techniques such as Bayesian maximum a posteriori estimation based on few-shot data. We show that it is possible to reconstruct time-dependent data using a small number of detected photons, allowing for fast estimates in under a minute and providing a one-to-two order of magnitude speed-up in data acquisition time. We test our approach using real experimental data to retrieve the second order intensity correlation function, G(2)(τ), as a function of time delay τ between detector counts, for thermal light as well as anti-bunched light emitted by a quantum dot driven by periodic laser pulses. The proposed methodology has a wide range of applicability and has the potential to impact the scientific discovery process across a multitude of domains.

Analytic regularity and stochastic collocation of high-dimensional Newton iterates.

In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the solution with respect to the random variables. This justifies the application of sparse grids for the computation of statistical measures. Convergence rates are derived and are shown to be subexponential or algebraic with respect to the number of realizations of random perturbations. Due the accuracy of the method, sparse grids are well suited for computing low probability events with high confidence. We apply our method to the power flow problem. Numerical experiments on the non-trivial 39 bus New England power system model with large stochastic loads are consistent with the theoretical convergence rates. Moreover, compared to the Monte Carlo method our approach is at least 1011 times faster for the same accuracy.

Functional Series Expansions and Quadratic Approximations for Enhancing the Accuracy of the Wiener Path Integral Technique

A novel Wiener path integral (WPI) technique is developed for determining the response of stochastically excited nonlinear oscillators. This is done by employing functional series expansions in conjunction with quadratic approximations. The technique can be construed as an extension and enhancement in terms of accuracy of the standard (semiclassical) WPI solution approach where only the most probable path connecting initial and final states is considered for determining the joint response probability density function (PDF). In contrast, the technique developed herein accounts also for fluctuations around the most probable path, thus yielding an increased accuracy degree. An additional significant advantage of the proposed enhancement as compared to the most probable path approach relates to the fact that low-probability events (e.g., failure probabilities) can be estimated directly in a computationally efficient manner by determining only a few points of the joint response PDF. Specifically, the normalization step in the standard approach, which requires the evaluation of the joint response PDF over its entire effective domain, is circumvented. The performance of the technique is assessed in several numerical examples pertaining to various oscillators exhibiting diverse nonlinear behaviors, where analytical results are set vis-à-vis pertinent Monte Carlo simulation data.