混沌序列WA-VOLTERRA耦合模型在月降水量预测中的应用

摘要: 由于月降水量时间序列含有大量噪声, 并表现出明显的混沌特性, 现有预测模型均存在一定程度的不足.基于混沌理论的小波分析-VOLTERRA级数自适应(WA-VOLTERRA)耦合预测模型, 在对月降水量时间序列进行混沌特性识别的基础上, 先用小波分析对月降水序列进行时频分解, 再分别对各频率分量进行相空间重构并用3阶VOLTERRA级数自适应模型建模预测, 最后综合得到原始序列的预测值.以相近区域杭州市和南通市的月降水序列为例, 并通过与小波分析-支持向量机(WA-SVM)模型进行比较, 发现该模型具有较强的适用性和更高的预测精度.
- 月降水时间序列 /
- 混沌理论 /
- 小波分解 /
- VOLTERRA级数自适应模型
Abstract: To address the inefficiency of exsiting prediction models of monthly precipitation time series due to large amount of noises and obvious characteristics of chaos, a coupling model is proposed in this study, which takes full advantages of wavelet analysis and VOLTERRA adaptive model. The monthly precipitation time series is firstly mapped into several time-frequency domains, and then a third-order VOLTERRA adaptive model is established for each domain based on the phase-space reconstruction. The final forecasting results are the algebraic sums of all the forecasted components obtained by respective VOLTERRA adaptive model corresponding to different time-frequency domains. An experiment has been conducted by applying different models to estimate the monthly precipitation time series in Hangzhou and Nantong, and the comparison of the data obtained by the conventional model with the results obtained using wavelet analysis and support vector machine (WA-SVM) coupling prediction model confirms that this new WA-VOLTERRA coupling method can achieve higher accuracy. The new model offers a new approach for monthly precipitation forecasting.
- monthly precipitation time series /
- chaos theory /
- wavelet analysis /
- VOLTERRA adaptive model

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图 1 WA-VOLTERRA自适应耦合预测模型示意图

Fig. 1. The diagram of WA-VOLTERRA adaptive coupling forecast model

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图 2 杭州市月降水序列log₂(r)-log₂c(r)关系

Fig. 2. Relational curves of log₂(r)-log₂c(r) for monthly precipitation series of Hangzhou

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图 3 杭州市月降水序列饱和关联维图

Fig. 3. Relational curves of saturation correlation dimension for monthly precipitation series of Hangzhou

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图 4 小数据量法计算得到的Lyapunov值

Fig. 4. The calculation chart of Lyapunov value

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图 5 小波分解后的各个分量序列

Fig. 5. Wavelet decomposition of the monthly precipitation of Hangzhou City

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图 6 杭州市月降水量预测值与实测值对比

Fig. 6. One month ahead precipitation forecasts using WA-VOLTERRA model and WA-SVM model of Hangzhou

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图 7 南通市月降雨量模型预测值与真实值对比

Fig. 7. The comparison of Nantong monthly precipitation predicted and measured values

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表 1 杭州市月降水量预测结果对比

Table 1. Comparison of different models for 1 month ahead precipitation forecasting at Hangzhou

模型 RMSE MAPE(%)

WA-VOLTERRA 22.9 24.5

WA-SVM 28.2 30.1

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表 2 南通市模型预测结果对比

Table 2. Comparison of different models for 1 month ahead precipitation forecasting at Nantong

模型 RMSE MAPE(%)

WA-VOLTERRA 16.9 31.8

WA-SVM 24.9 36.9

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