arXiv:2502.13190cs.LGphysics.flu-dyn2025-02

用少量测点数据精准重建水库温度场,降低监测成本。

Application of machine learning algorithm in temperature field reconstruction

  • 结合POD与稀疏表示,从少样本数据重构温度场。
  • 2个基函数+10个测点时误差稳定在0.15左右。
  • 适用于水库温升分析,适合水利/环境领域研究者。

本研究聚焦水库水体分层特征与温度动态演变,旨在利用有限且含噪的局部测温数据估算与重构温度场。由于测量环境复杂及技术限制,获取完整水库温度信息极具挑战,因此基于少量测点实现高精度温度场重构成为关键科学问题。为此,研究采用本征正交分解(POD)与稀疏表示方法,基于有限测点温度数据重构温度场。结果表明,当POD基函数数量设为2、测点数为10时,可实现满意重构效果;在不同取水深度下,两种方法的重构误差均稳定在约0.15,充分验证了其有效性。此外,研究还分析了不同水位区间下两种方法的误差分布特征,探讨了最优测点布局方案及其方法局限性。该研究不仅显著降低监测成本与计算资源消耗,也为水库温度分析提供新方法,具有重要理论与实践价值。

原文摘要 · Abstract (English)

This study focuses on the stratification patterns and dynamic evolution of reservoir water temperatures, aiming to estimate and reconstruct the temperature field using limited and noisy local measurement data. Due to complex measurement environments and technical limitations, obtaining complete temperature information for reservoirs is highly challenging. Therefore, accurately reconstructing the temperature field from a small number of local data points has become a critical scientific issue. To address this, the study employs Proper Orthogonal Decomposition (POD) and sparse representation methods to reconstruct the temperature field based on temperature data from a limited number of local measurement points. The results indicate that satisfactory reconstruction can be achieved when the number of POD basis functions is set to 2 and the number of measurement points is 10. Under different water intake depths, the reconstruction errors of both POD and sparse representation methods remain stable at around 0.15, fully validating the effectiveness of these methods in reconstructing the temperature field based on limited local temperature data. Additionally, the study further explores the distribution characteristics of reconstruction errors for POD and sparse representation methods under different water level intervals, analyzing the optimal measurement point layout scheme and potential limitations of the reconstruction methods in this case. This research not only effectively reduces measurement costs and computational resource consumption but also provides a new technical approach for reservoir temperature analysis, holding significant theoretical and practical importance.

温度场重建POD方法水库监测数据稀疏

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