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Inter occurrence time statistics of successive large earthquakes: analyses of the global CMT dataset

Bantidi Thystere Matondo

Acta Geophysica

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2022

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Vol. 70, no 6

2603--2619

EN

The purpose of this study is to discuss the statistical distributions of the inter-occurrence times of successive large earthquakes. We examine the Global Centroid Moment Tensor Catalog from 1976 to 2021 to analyze shallow earthquakes with a moment magnitude, Mw ≥ 7.0. After removing the aftershocks that occur in and around the faults of the mainshock within a given time–space window, we select the main events and search for successive ones in the space–time window to group them in clusters. We use four renewal models (Brownian passage time, gamma, lognormal, and Weibull) to fit the data. We estimate the models’ parameters using the maximum likelihood estimation method. Then, we perform two goodness-of-fit tests: the Akaike information criterion and the Kolmogorov–Smirnov test to evaluate the suitability of the model distributions to the observed data. The results reveal that the lognormal distribution provides the best fit to the observed data in at least 50% of the regions under consideration. An intermediate fit comes from the Weibull distribution, whereas the Brownian passage time and gamma distributions exhibit a poor fit. Then, we estimated the conditional probability of the occurrence of successive large earthquakes for the 10-year period between 2022 and 2032. Estimates range from 16 to 96%. To evaluate the usefulness of the interevent time-dependent earthquake modeling, we compared the results with the time-independent Poisson distribution. The results show that the renewal model, associated with a time-dependent earthquake hazard, is significantly better than a time-independent Poisson model.

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On explainable fuzzy recommenders and their performance evaluation

Rutkowski Tomasz, Łapa Krystian, Nielek Radosław

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 3

595--610

EN

This paper presents a novel approach to the design of explainable recommender systems. It is based on the Wang–Mendel algorithm of fuzzy rule generation. A method for the learning and reduction of the fuzzy recommender is proposed along with feature encoding. Three criteria, including the Akaike information criterion, are used for evaluating an optimal balance between recommender accuracy and interpretability. Simulation results verify the effectiveness of the presented recommender system and illustrate its performance on the MovieLens 10M dataset.

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Critical values of driver response time and its impact on reducing reliability and safety in road traffic

Kornacki A., Wawrzosek J., Bochniak A., Szymanek A., Pawlak H.

Eksploatacja i Niezawodność

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2017

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Vol. 19, no. 1

142--148

EN

Road traffic is among the most dangerous types of human activity. The main causes of road accidents are driver fatigue, poor physical and mental condition of drivers and overestimating one’s skills while driving. This study focuses on the estimation of driver response time, as the basis of a hypothetical system that uses short and long-range radars, which determines the physical and mental condition of a driver, based on the analysis of „acceleration noise” of the vehicle following its predecessor. This work highlights serious consequences of the fact that driver response time is described by means of a distribution with heavy tails, and thus may be a source of hazard in the driver-vehicle system. Extremes of driver response time were treated as outliers in this study. Their detection was attained by using the Akaike information criterion [1, 2], which is an alternative to conventional methods of testing hypotheses. Untypical, on account of their outlying nature, values are interpreted as critical driver response time values which potentially endanger the reliability of driving.

PL

Ruch drogowy należy do najbardziej niebezpiecznych rodzajów działalności człowieka. Główne przyczyny wypadków drogowych to zmęczenie kierowców, zły stan psychofizyczny kierujących oraz przecenianie swoich umiejętności podczas prowadzenia pojazdu. W niniejszej pracy skupiono uwagę na estymacji czasu reakcji kierowców, jako podstawie hipotetycznego systemu wykorzystującego radary dalekiego i krótkiego zasięgu a określającego stan psychofizyczny kierowcy w oparciu o analizę „szumu przyspieszeń” pojazdu podążającego za poprzednikiem. Wskazuje się na groźne konsekwencje faktu, że czas reakcji kierowcy jest opisywany rozkładem z ciężkimi ogonami, gdyż z tego powodu może być źródłem zagrożenia w układzie kierowca-pojazd. Skrajne wartości czasu reakcji kierowców potraktowano w pracy, jako wartości odstające. Do ich wykrycia zastosowano kryterium informacyjne Akaike [1, 2] co stanowi alternatywę w stosunku do klasycznych metod testowania hipotez. Nietypowe, bo odstające wartości interpretuje się, jako krytyczne czasy reakcji kierowców potencjalnie zagrażające niezawodności jazdy.