Investigation of the Temperature Actions of Bridge Cables Based on Long-Term Measurement and the Gradient Boosted Regression Trees Method
Abstract
:1. Introduction
2. Research Background
2.1. Description of the Bridge and Segment Test
2.2. Experiment Process
2.3. Sensor Arrangement
3. The Cross-Sectional Distribution and the Time-History Curve of Cables
3.1. The Cross-Sectional Distribution of Cables
3.2. The Time-History Curve of Cable Temperature
3.3. Annual Cycle Variation in Uniform Temperatures on a Cable Section
3.4. Daily Cycle Variation in Uniform Temperatures of Cable Section
3.4.1. Statistical Analysis of Daily Cycle Variation
3.4.2. Theoretical Method of Extreme Value Analysis
3.4.3. Extreme Value Analysis of Daily Cycle Variation
4. Relationship between the Cable Temperature and Environmental Variables
4.1. Regression via the Gradient Boosted Regression Trees (GBRT) Algorithm
4.1.1. Description of the GBRT Algorithm
4.1.2. Construction of the Prediction Model
4.2. Training and Testing of Tu Prediction Model
4.3. Hyperparameter Optimization
4.4. Testing of the GBRT
4.5. Representative Values of Temperature Actions of Cables
5. Conclusions
- No temperature gradient distribution is noted inside the cable, suggesting a uniform temperature distribution on the cross-section. The temperature on the cable cross-section can be decomposed into a daily uniform temperature (Tu) and a daily fluctuating temperature (Tf) to portray the annual cycle and daily cycle variation patterns of cable temperatures, respectively.
- For the annual cycle variation pattern, the time-history curve of Tu,d (daily average uniform temperature) can be fitted to the Fourier formula. Due to the effect of Tu,d, the cable contracts and expands seasonally. The daily cycle of temperature variations can be represented by the fluctuation temperature envelope curve with an exceedance probability of 0.01, and the variation in the cable’s fluctuating temperatures is more noticeable throughout the year. Therefore, to accurately determine the temperature deformation of the cable, it is important to consider both the daily temperature fluctuations and the annual cycle of uniform temperatures.
- This study establishes the use of the GBRT model to predict Tu in the cable considering four environmental variables (air temperature, solar radiation intensity, wind speed, and wind direction) at the bridge site. As for Tu prediction, the prediction accuracy of the GBRT model is significantly higher than that of the univariate linear regression (ULR) model that considers a single environmental factor only.
- A complete EVA method based on the machine learning simulation and one-year measured data is proposed for determining the representative values of temperature effects. This method can compensate for the deficiency of measured data and determine the representative values of bridges’ temperature effects quickly and efficiently. For the measured stayed-cable segment, the representative maximum uniform temperatures are 38.82 °C and 39.51 °C and the representative values of the minimum uniform temperature are 1.12 °C and 0.27 °C for the 50- and 100-year return periods, respectively.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Season | Minimum Fluctuating Temperature, Tf | Maximum Fluctuating Temperature, Tf | ||
---|---|---|---|---|
Main Time of Occurrence | Percentage of All Data | Main Time of Occurrence | Percentage of All Data | |
Hot season | 5:30–7:00 | 65.57% | 13:00–15:00 | 70.49% |
Cold season | 6:00–7:30 | 51.87% | 13:00–15:00 | 73.76% |
Number | Featured Engineering | Units |
---|---|---|
1~48 | Air temperature for the past 48 h | °C |
49~96 | Solar radiation intensity for the past 48 h | W/m2 |
97~144 | Wind speed for the past 48 h | m/s |
145~192 | Wind direction for the past 48 h | ° |
193 | Date | - |
194 | Time | - |
Hyperparameters | Meanings | Search Ranges | Optimal Values |
---|---|---|---|
n_estimators | Number of trees | (150, 500) | 220 |
learning_rate | Shrinkage coefficient of each tree | (0.01, 0.2) | 0.14 |
subsample | Subsample ratio of training samples | (0.1, 1) | 0.8 |
max_depth | Maximum depth of a tree | (2, 20) | 7 |
Dataset | MAE | R2 |
---|---|---|
Training set | 0.053 | 0.998 |
Test set | 0.381 | 0.986 |
Year | Temperature Tu (°C) | Year | Temperature Tu (°C) | Year | Temperature Tu (°C) | |||
---|---|---|---|---|---|---|---|---|
Maximum Temperature | Minimum Temperature | Maximum Temperature | Minimum Temperature | Maximum Temperature | Minimum Temperature | |||
1987 | 35.84 | 5.01 | 1999 | 35.63 | 1.91 | 2011 | 37.35 | 4.89 |
1988 | 35.68 | 6.39 | 2000 | 36.51 | 4.25 | 2012 | 36.79 | 3.75 |
1989 | 35.03 | 5.86 | 2001 | 37.02 | 5.99 | 2013 | 36.60 | 5.35 |
1990 | 35.14 | 5.89 | 2002 | 38.89 | 4.27 | 2014 | 37.65 | 4.53 |
1991 | 37.18 | 1.39 | 2003 | 37.75 | 5.45 | 2015 | 36.49 | 5.74 |
1992 | 36.06 | 3.30 | 2004 | 37.56 | 4.59 | 2016 | 37.11 | 0.33 |
1993 | 36.04 | 3.57 | 2005 | 37.41 | 2.75 | 2017 | 38.05 | 7.39 |
1994 | 35.41 | 4.95 | 2006 | 37.06 | 4.45 | 2018 | 36.95 | 3.74 |
1995 | 36.39 | 4.78 | 2007 | 36.91 | 6.41 | 2019 | 38.81 | 8.45 |
1996 | 36.92 | 4.29 | 2008 | 36.62 | 5.54 | 2020 | 37.32 | 5.28 |
1997 | 35.13 | 5.55 | 2009 | 36.81 | 4.69 | |||
1998 | 36.56 | 5.53 | 2010 | 37.14 | 2.37 |
The Exceeding Probability | 2% | 1% |
---|---|---|
The return period | 50-year | 100-year |
Maximum uniform temperature Tu,max (°C) | 38.82 | 39.51 |
Minimum uniform temperature Tu,min (°C) | 1.12 | 0.27 |
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Wang, F.; Dai, G.; Liu, Y.; Ge, H.; Rao, H. Investigation of the Temperature Actions of Bridge Cables Based on Long-Term Measurement and the Gradient Boosted Regression Trees Method. Sensors 2023, 23, 5675. https://doi.org/10.3390/s23125675
Wang F, Dai G, Liu Y, Ge H, Rao H. Investigation of the Temperature Actions of Bridge Cables Based on Long-Term Measurement and the Gradient Boosted Regression Trees Method. Sensors. 2023; 23(12):5675. https://doi.org/10.3390/s23125675
Chicago/Turabian StyleWang, Fen, Gonglian Dai, Yonglu Liu, Hao Ge, and Huiming Rao. 2023. "Investigation of the Temperature Actions of Bridge Cables Based on Long-Term Measurement and the Gradient Boosted Regression Trees Method" Sensors 23, no. 12: 5675. https://doi.org/10.3390/s23125675