基于小波的Volterra模型对黄河源区径流混沌预测的研究

Study on chaotic prediction of runoff in the source region of the Yellow River by wavelet-based Volterra model

为进行黄河流域水文系统的混沌特性研究和预测,深入了解黄河流域水文系统的运行机制和规律,基于相空间重构、混沌识别与混沌预测理论,对黄河源区唐乃亥水文站1956—2021年月径流时间序列进行分析,利用互信息法求时间序列的时间延迟τ,利用改进虚假邻近点法(CAO法)求该序列的嵌入维数m,并利用改进C-C法对时间延迟τ与嵌入维数m的计算结果进行验证,最终确定时间延迟τ为3,嵌入维数m为5。通过小数据量法计算最大Lyapunov指数,并对月径流量时间序列进行定量的混沌分析,得出最大Lyapunov指数λmax=0.0481>0,确定唐乃亥月径流量时间序列具有混沌特征。通过基于小波分析的二阶Volterra级数一步模型对混沌时间序列进行模拟预测,并与单纯二阶Volterra级数一步模型进行对比,发现基于小波分析的二阶Volterra级数一步模型模拟结果的纳什效率系数可达0.8551,比未经小波分析的模型更好模拟出唐乃亥站月径流量时间序列的演变规律。

In order to study and predict the chaotic characteristics of the Yellow River Basin hydrological system,the operation mechanism and law of the Yellow River Basin hydrological system are deeply studied.Based on the theory of phase space reconstruction,chaos recognition and chaos prediction,the time series of monthly runoff from 1956 to 2021 at Tangnaihai Hydrologic station in the source region of the Yellow River is analyzed.The time delayτof the time series is obtained by mutual information method,and the embedded dimension m of the series is obtained by improved false adjacent point method(CAO method).The modified C-C method is used to verify the calculation result of the time delayτembedding dimension m,and finally the time delayτis 3 and the embedding dimension m is 5.The maximum Lyapunov index is calculated by small data quantity method,and the maximum Lyapunov indexλmax=0.0481>0 is obtained by quantitative chaotic analysis of the monthly runoff time series,which indicates that the monthly runoff time series has chaotic characteristics.The second order Volterra series one-step model based on wavelet analysis is used to simulate and predict chaotic time series,and is compared with the simple second order Volterra series one-step model.The results show that the Nash efficiency coefficient of the second-order Volterra series one-step model based on wavelet analysis can reach 0.8551,which is better than the unanalyzed model to simulate the evolution law of the time series of monthly runoff at Tangnaihai Station.