关键词: 时序分解, 阶段式粒度重构, 集成预测, 供水量, 深度储备池计算

Abstract: A stable water supply is the cornerstone of social stability and economic development, and accurately forecasting the water supply enables cities to allocate resources more effectively, so as to avoid waste and unnecessary costs in the water supply planning and management.
Inspired by the ideas of “division and conquest” and “granularity reconstruction”, this paper proposes a decomposition integration forecasting model with staged granularity reconstruction. First, we decompose the original time series into multiple intrinsic mode functions (IMF). Then, we perform staged granularity reconstruction on IMF, which include the first reconstruction in terms of time-frequency features (identifying different granularity information) and the second reconstruction based on complexity evaluation (improving the representativeness of high-frequency granularity). Finally, we construct deep reservoir computing networks (DeepLiESN) on each granularity after staged granularity reconstruction and integrate the results as the final forecast. The staged granularity reconstruction method proposed in this paper improves the performance of local feature extraction (especially high-frequency features), thereby improving the accuracy of decomposition-integration model.
To verify the effectiveness of the proposed model, this work investigates two types of tests (i.e., four independent models and two reconstruction patterns). The comparative analysis of independent models reveals that the DeepLiESN, by introducing leaky integrated spiking neurons and a deep learning framework, improves its ability to describe nonlinear systems and temporal features, enhances short-term memory capacity, captures rich inherent information from the data, and is more capable of tracking the dynamic evolution of daily urban water supply. The comparative analysis of reconstruction patterns reveals that the staged reconstruction is advantageous for enhancing feature representation, particularly in overcoming the problem of mixed-frequency features. It enhances the effective utilization of high-frequency granularity information while reducing random interference in high-frequency granularity. The proposed models in this paper comprehensively consider the advantages of single-model forecasting and staged granularity reconstruction. As a result, it achieves the best forecasting performance with (1)the global error MAE=1053m³/d, RMSE=1397m³/d, and MAPE=0.577%; and (2)the individual error distribution (0,1%) accounts for 81.74%, (1,2%) for 97%, and (2%,3%) for 100%.
In summary, the proposed decomposition-integration model with staged granularity reconstruction is enhanced from three perspectives: (1)converting one-dimensional mixed information into multidimensional components to reduce temporal complexity, (2)learning time-frequency features and entropy probability features of multidimensional components for granularity reconstruction, particularly for mitigating high-frequency noise interference, and (3)integrating deep reservoir computing networks to improve the learning of complex nonlinear system characteristics. This model can offer accurate decision-making support for urban daily water supply management.

Key words: sequence decomposition, staged granularity reconstruction, integration forecasting, water supply, deep reservoir computing