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Autoregressive conditional duration modeling and forecasting the earthquakes temporal data of the different regions of Pakistan

Khan Muhammad Yousaf, Mittnik Stefan, Tahir Mohammad, Shah Muhammad Ali, Iqbal Talat

Acta Geophysica

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2024

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Vol. 72, no. 3

1543--1559

EN

Pakistan is situated in an earthquake-prone area, and in the past, many destructive earthquakes have occurred including the most destructive 1935 Quetta, and 2005 Kashmir, earthquakes. Therefore, it is of vital importance to investigate the statistical properties of the earthquake temporal data of Pakistan. The present study brings novelty through the vast extension of the linear and nonlinear autoregressive conditional duration models in the field of seismology. A simple duration model capable of describing and forecasting the earthquake elapsed times data has been developed. Different specifications of the duration models were considered to completely extract the time-dependent structure in earthquake data. This study aims to identify the most suitable in-sample fitted and out-of-sample forecasting models for the earthquake elapsed times data of Pakistan. A variety of autoregressive conditional duration models were applied to the complete and updated earthquake catalog of Pakistan. The most suitable model was chosen through statistical model evaluation techniques. The method of maximum likelihood was used to estimate the model parameters. The adequacy of fitted models is assessed through residual analysis. The obtained results suggest that the Logarithmic Autoregressive Conditional Duration model of type 2 (LACD2) appeared as the most suitable in-sample fitted model for describing the earthquake temporal data of the different zones of Pakistan. Further, the simple autoregressive conditional duration (ACD) model outperforms the remaining considered models regarding 1-through-4 steps-ahead out-of-sample forecasting performance for both India-Eurasia collision (IEC) and Makran subduction (MS) zones. Autoregressive models with Burr and exponential distributions as assumed error distributions have appeared as the most suitable fitted models for IEC and MS zones, respectively. The residuals analysis results show that the most suitable fitted models are correctly identified. The results show that the earthquake short-term (h = 1) forecasting with duration models is more accurate in comparison with earthquake long-term (h = 1, 2, 3) forecasting. The forecasted elapsed times for IEC and MS zones are 0.60 and 2.94 years, respectively. The obtained results show that the autoregressive conditional models are a more useful tool for forecasting the earthquake elapsed times for short term in comparison with the long-term forecasting. Hence, autoregressive conditional models are capable of modeling and forecasting the earthquake temporal data of the different regions of Pakistan. Among the competing models, the best fit model can serve the purpose of data description, missing value estimation in earthquake catalogs and uncertainty quantification in the earthquake occurrence process. The most suitable forecasted model yields the future earthquake occurrence trend in the study region.

2

From structural analysis to observer-based residual generation for fault detection

Pröll S., Lunze J., Jarmolowitz F.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 2

233--245

EN

This paper combines methods for the structural analysis of bipartite graphs with observer-based residual generation. The analysis of bipartite structure graphs leads to over-determined subsets of equations within a system model, which make it possible to compute residuals for fault detection. In observer-based diagnosis, by contrast, an observability analysis finds observable subsystems, for which residuals can be generated by state observers. This paper reveals a fundamental relationship between these two graph-theoretic approaches to diagnosability analysis and shows that for linear systems the structurally over-determined set of model equations equals the output connected part of the system. Moreover, a condition is proved which allows us to verify structural observability of a system by means of the corresponding bipartite graph. An important consequence of this result is a comprehensive approach to fault detection systems, which starts with finding the over-determined part of a given system by means of a bipartite structure graph and continues with designing an observer-based residual generator for the fault-detectable subsystem found in the first step.

3

Adaptation of the south-west wing of Collegium Chemicum of Adam Mickiewicz University in Poznań for storage facilities

Ścigałło J.

Civil and Environmental Engineering Reports

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2015

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No. 17

137--145

EN

The article refers to the problems of adaptation of Collegium Chemicum facilities belonging to Adam Mickiewicz Uniwersity in Poznań to its storage needs. The subject building is situated in Grunwaldzka Street in Poznań. In the introduction part, the building and its structural solutions are described. The results of the materials research and the measurements of the used reinforcement have been presented. The structure diagnostic analyses were performed basing on measurements and research. The analysis allowed the determination of the limit loads. The results of the performed analysis of the current state turned out to be unsatisfactory, not only in terms of the planned storage load but also in terms of the current load state, as was shown by the construction analysis.

PL

W pracy przedstawiono problemy związane z adaptacją budynku dydaktycznego Collegium Chemicum przy ul. Grunwaldzkiej w Poznaniu na cele magazynowe Biblioteki Głównej UAM. Na wstępie opisano badany budynek oraz scharakteryzowano zastosowane w nim rozwiązania konstrukcyjne. Przedstawiono wyniki wykonanych badań materiałowych oraz pomiarów inwentaryzacyjnych zastosowanego zbrojenia. Na podstawie wykonanych pomiarów i badań przeprowadzono analizę diagnostyczną konstrukcji, która pozwoliła na wyznaczenie dopuszczalnych wartości obciążeń powierzchni stropowych. Wyniki wykonanej analizy konstrukcji w stanie istniejącym okazały się dalece niezadowalające nie tylko z punktu widzenia planowanych, znacznych obciążeń magazynowych. Analiza wykazała bowiem, że konstrukcja jest już znacznie przeciążona w aktualnym stanie jej obciążenia.

4

Analiza wyznaczenia rozkładu ciśnienia w łożysku korbowym

Kyureghyan K., Piekarski W.

Eksploatacja i Niezawodność

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2008

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nr 4

19-24

PL

Praca przedstawia analityczną metodę wyznaczenia rozkładu ciśnienia oleju w łożysku korbowym, stanowiące rozwiązanie równania Reynoldsa. Odpowiednie warunki brzegowe rozważono adekwatnie do modelu klasycznego ślizgowego łożyska poprzecznego zgodnie z parametrami technicznymi, charakteryzującymi łożysko wału korbowego silników S-4002/4003 stosowanych w ciągnikach rolniczych. Celem pracy było przeprowadzenie analizy porównawczej teoretycznych parametrów charakteryzujących pracę łożyska ślizgowego, jako wartości parametrów sygnału diagnostycznego. Równanie Reynoldsa ( przy stałym współczynniku lepkości dynamicznej) metodą rozdzielenia zmiennych, sprowadzono do układu równań różniczkowych zwyczajnych, ostateczne rozwiązanie zapisano w postaci ogólnej.

EN

The paper presents an analytical method of determining oil pressure distribution in a crank bearing, which makes a solution of the Reynold's equation. Proper boundary conditions were considered according to the classic model of a radial slide in agreement with technical parameters typical for the crankshaft bearing of S-4002/4003 engines used in agriculture tractors. The goal of this work was to conduct a comparative analysis of theoretical parameters characterizing the work of the slide bearing as the value of the diagnostic signal parameters. By using the method of seperation of variables, the Reynold's equation(with constant coeffi cient of dynamic viscosity) was brought to the system of ordinary differential equations, and the ultimate solution was written in general form.