School of Computing, Mathematics and Engineering, Charles Sturt University, Bathurst, New South Wales, Australia.
Gulbali Institute for Agriculture, Water and Environment, Charles Sturt University, Albury, NSW, 2640, Australia.
Environ Sci Pollut Res Int. 2023 Sep;30(44):98907-98921. doi: 10.1007/s11356-022-23194-3. Epub 2022 Oct 10.
This study furthers the utilisation of the parametric group method of data handling (GMDH) in assessing the possibility of rainfall modelling and prediction, using publicly available temperature and rainfall data. In using ordinary GMDH approaches, the modelling is inconclusive with no clear consistency demonstrated through coefficients of determination and analysis of variance. Hence, an empirical assessment has been undertaken to provide an explanation of the inconsistency. In doing so, state variable distribution, their classification within the fuzzy context, and the need to integrate the principle of incompatibility into the GMDH modelling format are all assessed. The mathematical foundations of GMDH are discussed within the heuristic framework of data partitioning, partial description synthesis, the limitations of the least-squares coefficient of determination, incompleteness theorem, and the necessity for an external criterion in the selection procedure for polynomials. Methods for modelling improvement include the potential for hybridisation with least square support vector machines (LSSVM), the application of filters for parameter estimation, and the combination with signal processing techniques, ensemble empirical mode decomposition (EEMD), wavelet transformation (WT), and wavelet packet transformation (WPT). These have been investigated in addition to the implementation of enhanced GMDH (eGMDH) and fuzzy GMDH (FGMDH). The inclusion of exogenous data and its application within the GMDH modelling paradigm are also discussed. The study concludes with recommendations to enhance the potential for future rainfall modelling study success using parametric GMDH.
本研究进一步利用参数群数据处理方法（GMDH），利用公开的温度和降雨量数据，评估降雨量建模和预测的可能性。在使用普通 GMDH 方法时，建模结果不一致，通过确定系数和方差分析没有显示出明显的一致性。因此，进行了实证评估，以解释不一致的原因。在这样做的过程中，评估了状态变量分布、它们在模糊环境中的分类，以及将不兼容性原则集成到 GMDH 建模格式中的必要性。在数据分区、部分描述综合、最小二乘确定系数的局限性、不完整性定理和选择多项式的外部标准的启发式框架内讨论了 GMDH 的数学基础。改进建模的方法包括与最小二乘支持向量机（LSSVM）杂交的潜力、参数估计滤波器的应用，以及与信号处理技术的结合，例如集合经验模态分解（EEMD）、小波变换（WT）和小波包变换（WPT）。除了实施增强型 GMDH（eGMDH）和模糊 GMDH（FGMDH）外，还对这些方法进行了研究。此外，还讨论了包含外生数据及其在 GMDH 建模范例中的应用。本研究最后提出了建议，以提高使用参数 GMDH 进行未来降雨建模研究的成功潜力。
