Safety analysis of passing maneuvers using extreme value theory

This paper tests the Generalized Extreme Value (GEV) distribution as an EV method using the minimum time-to-collision with the opposing vehicle during passing maneuvers. Detailed trajectory data of the passing, passed and opposite vehicles from a fixed-based driving simulator experiment were used in this study. One hundred experienced drivers from different demographic strata participated in this experiment on a voluntary base. Raw data were collected at a resolution of 0.1 s and included the longitudinal and lateral position, speed and acceleration of all vehicles in the scenario. From this raw data, the minimum time-to-collision with the opposing vehicle at the end of the passing, maneuver was calculated. GEV distribution based on the Block Maxima approach was tested for the estimation of head-on collision probabilities in passing maneuvers. The estimation results achieved good fit with respect to head-on collisions' prediction indicating that this is a promising approach for safety evaluation.

A cross-comparison of different extreme value modeling techniques for traffic conflict-based crash risk estimation

ABSTRACTThe block maxima approach, which consists of dividing a series of observations into equal‐sized blocks to extract the block maxima, is commonly used for identifying and modeling extreme events using the generalized extreme value (GEV) distribution. In the analysis of coastal wave surge levels, the underlying data that generate the block maxima typically have missing observations. Consequently, the observed block maxima may not correspond to the true block maxima, yielding biased estimates of the GEV distribution parameters. Various parametric modeling procedures are proposed to account for the presence of missing observations under a block maxima framework. The performance of these estimators is compared through an extensive simulation study and illustrated by an analysis of extreme wave surges in Atlantic Canada.

Climate change has brought about unprecedented new weather patterns, one of which is changes in extreme rainfall. In Kenya, heavy rains and severe flash floods have left people dead and displaced hundreds from their settlements. In order to build a resilient society and achieve sustainable development, it is paramount that adequate inference about extreme rainfall be made. To this end, this research modelled and predicted extreme rainfall events in Kenya using Extreme Value Theory for rainfall data from 1901-2016. Maximum Likelihood Estimation was used to estimate the model parameters and block maxima approach was used to fit the Generalized Extreme Value Distribution (GEVD) while the Peak Over Threshold method was used to fit the Generalized Pareto Distribution (GPD). The Gumbel distribution was found to be the optimal model from the GEVD while the Exponential distribution gave the optimal model over the threshold value. Furthermore, prediction for the return periods of 10, 20, 50 and 100 years were made using the return level estimates and their corresponding confidence intervals were presented. It was found that increase in return periods leads to a corresponding increase in return levels. However, the GPD gave higher return levels for 10 and 20 years compared to GEVD. While, for higher return periods 50 and 100 years, the GEVD gave higher return levels compared to the GPD. Model diagnostics using probability, density, quantile and return level plots indicated that the models provided were a good fit for the data.

The block maxima approach is an important method in univariate extreme value analysis. While assuming that block maxima are independent results in straightforward analysis, the resulting inferences maybe invalid when a series of block maxima exhibits dependence. We propose a model, based on a first‐order Markov assumption, that incorporates dependence between successive block maxima through the use of a bivariate logistic dependence structure while maintaining generalized extreme value (GEV) marginal distributions. Modeling dependence in this manner allows us to better estimate extreme quantiles when block maxima exhibit short‐ranged dependence. We demonstrate via a simulation study that our first‐order Markov GEV model performs well when successive block maxima are dependent, while still being reasonably robust when maxima are independent. We apply our method to two polar annual minimum air temperature data sets that exhibit short‐ranged dependence structures, and find that the proposed model yields modified estimates of high quantiles.

Some events are difficult to avoid and gives considerable influence to humans and the environment is extreme weather and climate change. Many of the problems that require knowledge about the behavior of extreme values and one of the methods used are the Extreme Value Theory (EVT). EVT used to draw up reliable systems in a variety of conditions, so as to minimize the risk of a major disaster. There are two methods for identifying extreme value, Block Maxima with Generalized Extreme Value (GEV) distribution approach and Peaks over Threshold (POT) with Generalized Pareto Distribution (GPD) approach. This research in Indramayu with January 1961-December 2003 period, the method used is Block Maxima with GEV distribution approach. The result showed that there is no climate change in Indramayu with January 1961-December 2003 period.

The Development of Conflict Index for the Safety Assessment of Intersections Considering Crash Probability and Severity

Crash prediction for freeway work zones in real time: A comparison between Convolutional Neural Network and Binary Logistic Regression model

On the probabilistic prediction for extreme geometrical defects induced by laser-based powder bed fusion

Orientation: In light of the global financial instabilities, investors and risk analysts need extreme risk management tools to help them accurately monitor and reduce market exposure in an investment portfolio. Research purpose: The main aim of the study was to apply extreme value theory results to quantify the extreme downside risk and upside risk of the South African Financial Index (J580). Motivation for the study: Financial markets have been characterised by significant instabilities caused by occurrence of extreme events. This means there is a need to develop proper risk management models that can accurately assess these extreme events. Research approach, design and method: The peak over threshold approach was used to obtain the excess returns over the threshold. The generalised Pareto distribution (GPD) was fitted to the excess returns over the threshold to estimate the parameters, which were used to quantify the downside and upside risk in the form of value at risk and expected shortfall. Main findings: The findings indicate that the upside risk of the Financial Index (J580) outweighs the downside risk. Practical/managerial implications: These findings would be important for hedging purposes, investment decision-making and help risk analysts to monitor the exposure of market risk and protect their investment portfolios accordingly. Contribution/value-add: This article will contribute to empirical evidence of the research into the behaviour of the extreme returns on the Johannesburg Stock Exchange. The GPD model formulated will be used to assess tail-related risk.

The classical extreme value theory based on generalized extreme value (GEV) distribution and generalized Pareto distribution (GPD) is applied to the wave height estimate based on wave hindcast data covering a period of 31 years for a location in the eastern Arabian Sea. Practical concern such as the threshold selection and model validation is discussed. Estimates of wave height having different return periods are compared with estimates obtained from different distributions. On comparing the distributions fitted to the GEV with annual maximum approach and GPD with peaks over threshold approach have indicated that both GEV and GPD models gave similar or comparable wave height for the study area since there is no multiple storm event in a year. Influence of seasonality on wave height having different return period is also studied.

Melting of the land-based ice and warming of the oceans around the world has resulted in acceleration of the pace of global mean sea level rise. Higher mean sea level causes more frequent extreme sea levels. This forces coastal cities urgently to do major preparedness and adaptation measures. In Finland, preparedness for coastal flooding hazards is relevant even though protection given by the post-glacial land uplift is helpful. This is especially true on the Finnish southern coast, where mean sea level rise is foreseen and increase of probability of high sea levels within the 21st century is expected (Pellikka et al., 2023, 2018). In the Finnish coastal area, the extreme sea level estimates are used e.g. to support infrastructure planning, flood maps and safe operation of nuclear power plants. On a short timescale, sea level variations are driven on the Finnish coast by storm surges, wind induced oscillations within the bays, and tides (playing a minor role). On the long-term side, global mean sea level rise, land uplift and the water inflow and outflow in the Danish straits (which change the total amount of Baltic Sea water) are the main factors controlling the sea level behaviour. In this presentation, a study aiming at improving extreme sea level estimates in Finland will be illustrated. Tentative results on how different sampling techniques and extrapolation approaches affect the probability estimates of coastal floods will be presented. Altogether 90 years of observations from the 13 Finnish tide gauges are analysed. We apply two different well-known sampling methods (Block Maxima and Peak Over Threshold) to the high tail of the sea level distribution and investigate which extrapolation function belonging to the family of Generalized Extreme Value (GEV) distribution matches best to the Finnish tide gauge observations. The results will be grouped into four coastal regions in Finland: the Gulf of Finland and Archipelago Sea in the south, and the Bothnian Sea and Bay of Bothnia in the west.   Pellikka, H., Johansson, M. M., Nordman, M., and Ruosteenoja, K., 2023: Probabilistic projections and past trends of sea level rise in Finland, Nat. Hazards Earth Syst. Sci., 23, 1613–1630, https://doi.org/10.5194/nhess-23-1613-2023 Pellikka, H., Leijala, U., Johansson, M. M., Leinonen, K., Kahma, K. K., 2018: Future probabilities of coastal floods in Finland, Continental Shelf Research, 157, 32-42, https://doi.org/10.1016/j.csr.2018.02.

The current safety management program in Indiana uses a method based on aggregate crash data for conditions averaged over several-year periods with consideration of only major roadway features. This approach does not analyze the risk of crashes potentially affected by time-dependent conditions such as traffic control, operations, weather and their interaction with road geometry. With the rapid development of data collection techniques, time-dependent data have emerged, some of which have become available for safety management. This project investigated the feasibility of using emerging and existing data sources to supplement the current safety management practices in Indiana and performed a comprehensive evaluation of the quality of the new data sources and their relevance to traffic safety analysis. In two case studies, time-dependent data were acquired and integrated to estimate their effects on the hourly probability of crash and its severity on two selected types of roads: (1) rural freeways and (2) signalized intersections. The results indicate a considerable connection between hourly traffic volume, average speeds, and weather conditions on the hourly probability of crash and its severity. Although some roadway geometric features were found to affect safety, the lack of turning volume data at intersections led to some counterintuitive results. Improvements have been identified to be implemented in the next phase of the project to eliminate these undesirable results.

A great challenge has been appeared on if the assumption of data stationary for flood frequency analysis is justifiable. Results for frequency analysis (FA) could be substantially different if non-stationarity is incorporated in the data analysis. In this study, extreme water levels (annual maximum and daily instantaneous maximum) in a coastal part of New York City were considered for FA. Annual maximum series (AMS) and peak-over threshold (POT) approaches were applied to build data timeseries. The resulted timeseries were checked for potential trend and stationarity using statistical tests including Man-Kendall, Augmented Dickey–Fuller (ADF) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS). Akaike information criterion (AIC) was utilized to select the most appropriate probability distribution models. Generalized Extreme Value (GEV) distribution and Generalized Pareto Distribution (GPD) were then applied as the probability distribution functions on the selected data based on AMS and POT methods under non-stationary assumption. Two methods of maximum likelihood and penalized maximum likelihood were applied and compared for the estimation of the distributions’ parameters. Results showed that by incorporating non-stationarity in FA, design values of extreme water levels were significantly different from those obtained under the assumption of stationarity. Moreover, in the non-stationary FA, consideration of time-dependency for the distribution parameters resulted in a range of variation for design floods. The findings of this study emphasize on the importance of FA under the assumptions of data stationarity and non-stationarity, and taking into account the worst case flooding scenarios for future planning of the watershed against the probable flood events. There is a need to update models developed for stationary flood risk assessment for more robust and resilient hydrologic predictions. Applying non-stationary FA provides an advanced method to extrapolate return levels up to the desired future time perspectives.

<p>Storm surges caused by extreme meteorological conditions are a major natural risk in coastal areas, especially in the context of global climate change. The increase of future sea-levels caused by continuing global warming, may endanger human lives and infrastructure through inundation, erosion and salinization.<br>Hence, the reliable estimation of the occurrence probability of these extreme events is crucial to quantify risk and to design adequate coastal defense structures. The probability of event occurrence is typically estimated by modelling observed sea-level records using one of a few statistical approaches.<br>The traditional Extreme Value Theory is based on the use of the Generalized Extreme Value distribution (GEV),  fitted either by considering block (typically yearly) maxima, or values exceeding a high threshold (POT). This approach does not make full use of all observational information, and thereby does not minimize estimation uncertainty.<br>The recently proposed Metastatistical Extreme Value Distribution (MEVD), instead, makes use of most of the available observations and has been shown to outperform the classical GEV distribution in several applications, including hourly and daily rainfall, flood peak discharge and extreme hurricane intensity.<br>Here, we comparatively apply the MEVD and the GEV distribution to long time series of sea-level observations distributed along European coastlines (Venice (IT), Hornbaek (DK), Marseille (FR), Newlyn (UK)). A cross-validation approach, dividing available data in separate calibration and test sub-samples, is used to compare their performances in high-quantile estimation.<br>The MEVD approach is based on the definition of an “ordinary values” distribution (here a Generalized Pareto distribution), whose parameters are estimated using the Probability Weighted Moments method on non-overlapping sub-samples of fixed size (5 years). To address the problems posed by observational samples of different sizes, we explore the effect on uncertainty of different calibration sample sizes, from 5 to 30 years. In this application, we find that the GEVD-POT and MEVD approaches perform similarly, once the above parameter choices are optimized. In particular, when considering short samples (5 years) and events with a high return time, the estimation errors show no significant differences in their median value across methods and sites, all approaches producing a similar underestimation of the actual quantile. When larger calibration sample sizes are considered (10-30 yrs), the median error of MEVD estimates tends to be closer to zero than those obtained from the traditional methods.<br>Future projections of sea-level rise until 2100 are also analyzed, with reference to intermediate and extreme representative concentration pathways (RCP 4.5 and RCP 8.5). The probability of future storm surges along European coastlines are then estimated assuming a changing mean sea-level and an unchanged storm regime. The projections indicate future changes in mean sea-level lead to increases in the height of storm surges for a fixed return period that are spatially heterogeneous across the coastal locations explored.</p>