﻿ 基于LSTM模型模拟安康水库洪水过程

基于LSTM模型模拟安康水库洪水过程Simulation of Ankang Reservoir Inflow Based on LSTM Model

Abstract: The underlying surface conditions have changed greatly in the Ankang river basin due to human activities, and the error of the flood forecasting system is relatively large. Considering that hydrological data is a complex time series, it is difficult for ordinary hydrological models to capture its changing laws. LSTM (Long-short term memory), as a learning network with memory ability, can learn the complex and chan-geable time of hydrological data well by continuously inputting new data and learning the main features and changes of time series sequence. The LSTM network model is used to simulate the flood process of Ankang reservoir and compare with the Xinanjiang model. The adaptability of LSTM model in reservoir flood prediction is also discussed.

1. 概述

1.1. 研究背景

1.2. 研究对象

Figure 1. Location map of the meteorological and hydrological stations in the Ankang River basin

2. 模型介绍

2.1. LSTM模型

Hochreiter和Schmidhuber引入长短期记忆(LSTM)神经网络，是一种特殊的循环神经网络(Recurrent Neural Network, RNN) [3]，其结构如图2所示，许多人进行了改进和普及，解决了RNN的长期记忆能力上的缺陷。LSTM神经网络通过在神经网络的隐藏层(Hidden layer)中引入存储单元(Memory cell)，即输入门(Input gate)、忘记门(Forget gate)、内部回馈连结(Self-recurrent connection)、和输出门(Output gate)来选择记忆当前信息或遗忘过去记忆信息，以增强神经网络的长期记忆能力 [4]。

${h}_{t}=\delta \left(U{x}_{t}+W{h}_{t-1}+b\right)$ (1)

Figure 2. Recurrent neural network structure

Figure 3. Complete RNN unit diagram

LSTM神经网络是一种在RNN (如图3)基础上改进的递归神经网络，用来解决RNN使用过程中所产生的梯度消失、梯度爆炸以及缺乏长期记忆能力等问题。Bengio等 [7] 已经表明，传统的RNN几乎不能记住长度超过10的序列，对于日流量模拟，这就意味着我们只能使用最近10天的气象数据作为输入来预测第二天的流量。考虑到地下水，积雪甚至冰川储存等集水区的记忆，这段时间太短，降水和排放之间的滞后时间达到几年。为解决RNN在计算过程中出现梯度消失的问题，LSTM神经网络在原有的RNN神经网络结构的基础上，将隐含层的RNN计算单元换成结构更加复杂的LSTM计算单元，更新了计算网络的节点。LSTM神经网络通过设置多个不同门的开关实现时间轴上的记忆和遗忘功能，解决梯度消失问题，在每个LSTM神经网络计算单元设置3个门控制器，分别为输入门、输出门和遗忘门，形成一个新的计算单元。输入门控制特征值的信息输入，遗忘门控制计算单元状态信息的保留，输出门控制信息输出。

LSTM神经网络的构建思想是在RNN网络的基础上，将RNN中每个隐藏计算单元换成具有记忆功能的计算单元。LSTM层的计算可以表示如下(若干个计算单元组成一个LSTM层)：

Figure 4. Complete LSTM unit diagram

${g}^{\left(t\right)}=\varphi \left({W}_{gx}{x}^{\left(t\right)}+{W}_{ih}{h}^{\left(t-1\right)}+{b}_{g}\right)$ (2)

${i}^{\left(t\right)}=\sigma \left({W}_{ix}{x}^{\left(t\right)}+{W}_{ih}{h}^{\left(t-1\right)}+{b}_{i}\right)$ (3)

${f}^{\left(t\right)}=\sigma \left({W}_{fx}{x}^{\left(t\right)}+{W}_{fh}{h}^{\left(t-1\right)}+{b}_{f}\right)$ (4)

${o}^{\left(t\right)}=\sigma \left({W}_{ox}{x}^{\left(t\right)}+{W}_{oh}{h}^{\left(t-1\right)}+{b}_{o}\right)$ (5)

${h}^{\left(t\right)}={s}^{\left(t\right)}$ (6)

Figure 5. LSTM calculation flow chart

2.2. 新安江模型

3. 实例计算与分析

3.1. 模型评价指标

$NS=1-\frac{{\sum }_{t=1}^{n}{\left({Q}_{ot}-{Q}_{pt}\right)}^{2}}{{\sum }_{t=1}^{n}{\left({Q}_{ot}-\stackrel{¯}{{Q}_{o}}\right)}^{2}}$ (7)

3.2. LSTM模拟计算结果

LSTM神经网络需要构建多层复杂网络结构，并且选取不同特征值来适配最优模拟目标结果，本文在尝试多种网络结构以及不同的特征值后，最终选取双层LSTM网络结构，选取时间、降雨、前一天入库流量作为特征值，模拟安康水库的入库洪水过程。

3.3. 新安江模拟计算结果

Figure 6. Flood seasonal runoff hydrograph simulated by LSTM model

Table 1. Calibrated parameters of Xinanjiang model

Figure 7. Flood seasonal runoff hydrograph simulated by Xinanjiang model

3.4. 结果对比分析

Table 2. Comparison of annual and flood seasonal Nash efficiency coefficients simulated by LSTM model and Xinanjiang model

4. 结论

1) LSTM模型对安康水库洪水过程模拟时，仅使用降雨与径流的历史过程，相对于新安江模型在一定程度上更简便，模拟效果也明显优于新安江模型。

2) 在日洪水过程模拟的基础上，进一步研究LSTM模型在时段洪水过程的模拟，以便将LSTM模型应用于安康水库实时洪水预报。

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