Modelling of extreme uniform temperature for high-speed railway bridge piers using maximum entropy and field monitoring

Abstract

Due to the atmospheric temperature and solar radiation, the effects of temperature variation in bridge structures should be considered. Such variation induces notable deformations and movements, jeopardizing the safety of bridges and high-speed trains operations. However, the temperature action is a random process and its distribution is difficult to determine. The existing methods for analyzing structural temperatures are insufficient to meet the precision requirement. Therefore, the accurate prediction of extreme structural temperatures relates to the accurate evaluation on the bridge safety. This paper proposes a robust and accurate model for predicting the extreme structural temperature of a bridge. A field experiment, spanning over 2 years, was carried out on a high-speed railway bridge; and the long-term (56-years) atmospheric temperature data was adopted. Probabilistic models for the structural temperature were established using the Maximum Entropy (MaxEnt) model and the Generalized Pareto distribution (GPD) model; and the predictions on the uniform structural temperature ( T u) with 50 and 100 years return periods are presented. Additionally, the performance between the MaxEnt model and the GPD model is compared, based on the estimates with different return levels. The results show that the MaxEnt model is more stable and is significantly robust to the variation of sample sizes; and indicates that the MaxEnt model reduces the uncertainty of outcomes and avoids the high risk of bias. The MaxEnt model has a great potential to the applications of the extreme value analysis with small sample size. It offers a wider applicability and helps solve practical problems.

Thermal behaviors of bridges — A literature review

“…The uniform components and the gradients are mainly concerned. Similar studies on temperature distributions in beam bridges were also conducted by other researchers (Abid, 2015; Branco and Mendes, 1993; Dai et al, 2022; Fu et al, 1990; Froli et al, 1996; Ho and Liu, 1989; Kennedy and Soliman, 1987; Kromanis et al, 2015; Mirambell and Aguado, 1990; Potgieter and Gamble, 1983; Roeder, 2003; Tong et al, 2001; Wollman et al, 2002; Zhang et al, 2021a). These studies are summarized in Table 2.…”

Investigation of the Temperature Actions of Bridge Cables Based on Long-Term Measurement and the Gradient Boosted Regression Trees Method

“…Compared with the GEV, the MaxEnt model is more stable and significantly more robust in the variation in sample sizes, indicating that the MaxEnt model reduces the outcome uncertainty and avoids the high risk of bias. This robustness of the MaxEnt for the sample sizes has also been demonstrated by Dai et al [ 37 ]. Therefore, the MaxEnt model is adopted in this paper to determine the extreme temperatures of cables.…”

“…According to Dai et al [ 37 ], the MaxEnt model is expressed as where ln represents the natural logarithm and f ( x ) is a probability distribution function that satisfies the following constraint conditions: where D is the integration interval, r is the order of the moments used, and m i is the i -th order origin moment of the sample. Then, by introducing the Lagrangian function and corresponding multipliers λ i , the expression of the MaxEnt probability density function (PDF) is obtained as whose cumulative distribution function (CDF) is …”

Temperature behavior of cable-stayed bridges. Part I — Global 3D temperature distribution by integrating heat-transfer analysis and field monitoring data

“…Exposed to ambient temperature and solar radiation, bridges are subjected to daily and seasonal thermal effects (Dai et al, 2022; Xia et al, 2022; Li et al, 2023). Variations in structural temperature are likely to induce deformations and stresses, especially for long-span cable-stayed bridges.…”