Threshold Selection for POT Framework in the Extreme Vehicle Loads Analysis Based on Multiple Criteria

Abstract

Extreme value of vehicle load plays an important role in bridge design and risk assessment. Peaks over threshold (POT) is a method commonly used in extreme load estimation. The selection of thresholds for the POT method is extremely crucial, but the selected optimal threshold varies under different test criteria. Therefore, a method to select the suitable threshold is developed based on multiple criteria decision analysis (MCDA) in the paper. In MCDA, Chi-Square (χ2) test, Kolmogorov–Smirnov (K–S) test, and Root Mean Square Error (RMSE) in probability distribution functions (PDF) are employed as the test criteria and the weight of these criteria is calculated using the entropy method. Finally, vehicle loads obtained from simulation and field measurement are adopted to validate the effectiveness and feasibility of the proposed method. The results indicate that the proposed MCDA is a useful and complementary tool for threshold selection in the extreme value analysis.

Assessing the importance of the choice threshold in quantifying market risk under the POT approach (EVT)

“…The Extreme Value Theory (EVT) studies the asymptotic behaviour of extreme values of a random variable. This theory has wide applications in many fields, such as, civil engineering (Wu and Qiu 2018), climatology (Davison and Smith 1990;Kharin et al 2013), seismology (Beirlant et al 2018), hydrology (Katz et al 2002;Carreau et al 2017;Bader et al 2018), insurance (Reiss and Thomas 2007) and finance (Embrechts et al 1997), among others.…”

“…Recently, new methods have been developed to automate some of the existing proposals, especially those based on visual data inspection, see for instance Wu and Qiu (2018), Bader et al (2018), Caballero-Megido et al (2018 and Queensley et al (2019), Schneider et al (2021) among others. Wu and Qiu (2018) propose a method to select the suitable threshold based on multiple criteria decision analysis (MCDA).…”

“…Extreme value analysis has wide applications in many fields, such as civil engineering (Wu and Qiu 2018), climatology (Davison and Smith 1990;Kharin et al 2013), seismology (Beirlant et al 2018), hydrology (Katz et al 2002;Carreau et al 2017;Bader et al 2018), insurance (Reiss and Thomas 2007) and finance (Embrechts et al 1997;Fontnouvelle et al 2007;Abad and Benito 2013, among others). For instance, the extreme value of vehicle load plays an important role in bridge design and risk assessment (Wu and Qiu 2018). In seismology and climatology, extreme value analysis is used to study earthquakes (Beirlant et al 2018) and extreme precipitation (Bader et al 2018).…”

“…Those methods can be divided into two groups: (i) graphical approaches, based on a visual inspection of plots, such as the mean excess plot (Davison and Smith 1990), stability parameters plot (Coles 2001) and Hill plot (Drees et al 2000) among others and (ii) numerical approaches (Ferreira et al 2003;Thompson et al 2009;Northrop and Coleman 2014;Li et al 2014;Wadsworh and Tawn 2012;Naveau et al 2016) which are more objective methods. Recently, new methods have been developed with the aim of automating some of the existing proposals, especially those based on visual data inspection, see for instance Wu and Qiu (2018), Bader et al (2018), Caballero-Megido et al (2018) and Queensley et al (2019) among others.…”

Prediction of Extreme Conditional Quantiles of Electricity Demand: An Application Using South African Data

“…In peaks-over-threshold models, the threshold is normally estimated first before fitting the desired model to the exceedances [38]. A sufficiently high threshold is vital to guarantee the stability of the parameters.…”