Threshold selection for extreme value estimation of vehicle load effect on bridges

Abstract

In the design and condition assessment of bridges, the extreme vehicle load effects are necessary to be taken into consideration, which may occur during the service period of bridges. In order to obtain an accurate extrapolation of the extreme value based on limited duration, threshold selection is a critical step in the peak-over-threshold method. Overly high threshold results in little information to be used and excessively low threshold leads to large bias in parameters estimation of generalized Pareto distribution. To investigate this issue, 417 days of strain data acquired from the long-term structural health monitoring system of Taiping Lake Bridge in China are employed in this article. According to the tail distribution of the strain data induced by vehicle loads, four homothetic distributions are chosen as its parent distribution, from which lots of random samples are generated by the Monte Carlo method. For each parent distribution, the 100-yearly extreme values at different thresholds are estimated and compared with the theoretical value based on those samples. Then a simple and empirical threshold selection method is proposed and applied to estimate the weekly extreme strain due to vehicle loads on the Taiping Lake Bridge. Results show that the estimate on the basis of the threshold obtained by the proposed method is closer to the measured result than the commonly used methods. The proposed method can be an effective threshold selection tool for the extreme value estimation of vehicle load effect in future engineering practice.

Does extreme rainfall lead to heavy losses in the food industry?

“…Thus, the Hill graph is constructed by the Hill estimator in a range of variation of the values of k vs the threshold. The value of X k,n where the Hill estimator tends to become stable will be chosen as the optimal threshold (Yang et al, 2018). It is also possible to use the mean square error (MSE) method (Longin and Solnik, 2001;Giles et al, 2016;Silva-González et al, 2017), which consists in selecting several possible thresholds where for each of them, the excess of the returns is calculated for the adjustment of the respective GPD.…”

“…Thus, the parameter of the GPD is estimated several times by the bootstrap method, and the MSE of the estimated parameter is estimated. The threshold chosen will be the one with the lowest MSE (Yang et al, 2018). Lima et al (2018), in turn, used a non-parametric approach to 250 ARLA 32,2 estimate the GPD parameters.…”

Bayesian Updates for an Extreme Value Distribution Model of Bridge Traffic Load Effect Based on SHM Data

“…Threshold selection is an important step in the application of the POT method. An appropriate threshold is critical for estimating the EV distribution [33,43]. To choose an appropriate threshold, the mean excess function (MEF) [44] of the GPD is defined as follows:…”

Modelling of traffic load effects in the assessment of existing road bridges

“…More on the general methods for threshold definition can be found in the book by Coles [70], while Zhou et al [71] focus on threshold selection in Mixture POT method for estimation of extreme traffic loads on bridges. A more recent discussion on threshold selection in traffic load analysis can be found in the work by Yang et al [72].…”