Abstract
This study introduces methodologies for constructing joint probability distribution functions utilizing the Copula function and neural networks, and evaluates their efficacy in marine and civil engineering projects. Through an analytical comparison of both models using a numerical example, it is revealed that the neural network model exhibits superior adaptability to large sample sizes. This adaptability is attributed to the neural network's ability to learn complex relationships within the data, which is especially beneficial when dealing with large datasets. The neural network model also demonstrates higher accuracy in constructing joint probability distribution functions compared to the Copula function model. In marine and civil engineering, the adaptability and accuracy of neural networks are of paramount importance due to the variable and complex nature of weather patterns. A practical engineering application is presented, wherein a joint probabilistic distribution neural network model of wind velocity and rain intensity is established for the Lanzhou–Xinjiang high-speed railroad in China. This model illustrates the promising application of neural networks in engineering projects where weather factors play a critical role. Subsequent to the construction of the joint probability distribution functions, a feature importance analysis is incorporated to quantify the contribution of different weather parameters such as wind velocity and rain intensity to the joint distribution function. This analysis provides an objective assessment of the relative importance of various weather factors and offers data-driven insights that are essential for engineering applications where weather conditions are a significant consideration. The study concludes by highlighting the potential benefits of neural network models in marine and civil engineering, suggesting areas for future exploration.
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Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
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Funding
This research was supported by the National Natural Science Foundation of China (Grant No.11962021), the Natural Science Foundation of Inner Mongolia (Grant No.2021MS05020, 2022MS05021) and the Basic scientific research business expenses of universities directly under the autonomous region No. JY20220383.
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YY, HL: designed the study and conducted the neural network model development. YY, DL: performed the comparative analysis and contributed to the literature review, focusing on the Copula function and neural network methodologies. DL: prepared figures 1, 2 and 3 and assisted in data analysis. YY, DL: analyzed the case study of the Lanzhou–Xinjiang high-speed railroad and contributed to the discussion of practical applications. All four authors reviewed, revised, and approved the final manuscript.
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Yang, Y., Li, D., Li, H. et al. Joint probability distribution of weather factors: a neural network approach for environmental science. Stoch Environ Res Risk Assess 37, 4385–4397 (2023). https://doi.org/10.1007/s00477-023-02513-1
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DOI: https://doi.org/10.1007/s00477-023-02513-1