摘要
径流预报不仅是水资源研究领域中的一项重要内容,而且是水资源规划及综合开发利用、防洪抗旱、水利枢纽运行管理等重大决策问题的基本依据,对国民经济发展具有十分重要的意义。作为自然学科与技术科学领域内的一个研究热点,径流预报存在的主要难点在于预报精度较低,并且由于较少考虑水文系统不确定性,在实际工作中难以有效指导生产实践,国内外众多学者一直致力于研究能有效解决上述问题的各种方法。然而,水文系统是一个复杂的巨系统,其水文要素时空变化的高度非线性和不确定性使得问题的描述和模型的求解极为困难,至今缺乏令人满意的解决方法,亟待进一步发展新的理论并探索其技术实现方法。因此,径流预报先进理论与方法的研究始终是学术和工程界的研究前沿。本文通过对水文要素的非线性、历史数据误差和模型误差的不确定性分析,采用小波分析和相关向量机方法,对径流预报的理论与方法进行了深入研究。针对水文系统的非线性特征,研究并提出了Biased小波网络,并通过对自适应Metropolis算法的改进和基于相关向量机的不确定性分析方法的研究,建立了非线性径流预报模型。研究结论不仅证明了算法处理参数估计问题的有效性,而且体现了Biased小波网络处理非线性数据样本的能力及减少计算冗余的特点,显示了相关向量机处理不确定信息的优势,进一步发展了径流预报的理论。研究成果成功应用于凤滩和三峡流域径流预报工程实践,为水库优化运行和调度决策提供了科学依据。主要研究工作和创新性成果如下:
针对小波变换的冗余问题,提出Biased小波网络(Biased Wavelet Neural Network,BWNN)结构及其学习算法。BWNN是一种自适应小波网络,其核心是利用Biased小波函数,根据不同的训练样本优化网络结构参数,减少计算冗余。基于梯度下降的网络学习算法,具有简单、清晰、有效的特点。通过对凤滩水库月径流预报的研究表明,BWNN能够克服陷入局部极小、引起振荡效应等问题,达到提高径流预报精度的目标,为非线性预报建模提供了一条有效的新途径。
针对传统MCMC算法不能自适应地给出“建议分布”的问题,提出一种改进的MCMC算法(Improved Adaptive Metropolis,IAM)。IAM算法选取正态分布做为“建议分布”来实现对目标函数的取样,通过改进协方差的求解方法,加速了算法收敛速度,减少了不稳定因素,研究成果不仅丰富了MCMC理论,而且为径流频率预报问题的解决提供了有力的工具。
建立基于IAM的径流量频率参数估计方法。结合径流频率预报中线型选择和参数估计问题,采用IAM算法对P-III型分布曲线进行参数估计。IAM算法不仅能够获得参数的后验分布等统计信息,而且可以使样本多样性得以丰富和保持,减少收敛于局部最优区域的可能性,提高参数估计的质量和计算速度。以凤滩水库年、最大旬径流量频率分析为应用背景,得到了满意的参数估计结果,能够反映与模型参数不确定性相关的频率预报范围,验证了算法的良好性能。
建立基于相关向量机(Relevance Vector Machine,RVM)的径流预报不确定性研究框架。针对一般非线性预报方法较少考虑模型本身不确定性的问题,提出小波消噪、相关向量回归建模、基于IAM模型选择和递推循环多步预报的径流预报框架。该框架充分利用了相关向量机能够输出预测值分布、使用更少数量的相关向量和对核函数没有限制等特点,并且,通过提出有效的模型选择方法,实现了训练精度和模型复杂度的有效权衡。宜昌站日径流预报的应用实例表明,该模型不仅能够提供较好的预报结果,而且为后期调度决策提供了更多的信息,使得预报人员在决策中能够考虑预报的不确定性,定量地估计各种决策的风险和后果。
As one of the most important facets in water resources research, streamflow forecast not only plays the great role in national economy, but also is the basis for crucial decisions, such as water resources planning and its comprehensive utilization, flood control, and hydropower station operation. Since streamflow forecast is a tough topic in both science and technology research area, low forecast precision, and less concern of hydrology system uncertainty, are the main obstacles in streamflow forecast, which lead to difficulities in supervising engineering practice. Thereby researchers at domain and abroad are always dedicated to seeking for effective methods to solve above problems. However, hydrology system is a complex and huge system, and its high nonlinearity and uncertainty when changing in space and time make it hard to describe and resolve proposed models, which are lake of satisfying results so far and starve for new theories and technology. Consequently, the research of advanced theory and technology of streamflow forecast is a hot science topic all the time. Based on the ananlysis of nonlinear hydrology factors, and uncertain historical records and modeling, the thesis explores thorough streamflow forecast research by adopting modern nonlinear scientific techniques. Focusing on the built nonlinear streamflow forecast models, biased wavelet neural network, improved adaptive Metropolis algorithm, and uncertain research frame using relevance vector machine are put forward, which exhibit the performance of wavelet neural network in managing data samples amd reducing calculation redundancy, testify the validity of algorithm in parameter estimation, acquire the predominance of relevance vector machin in treating with uncertain information, and develop streamflow forecast theory. The research results are successfully applied in engineering practice of streamflow forecast in Fengtan and Three Gorges valleys, and supplies good references for hydropower optimal regulation and decision-makers. The study work and innovations are listed as follows:
By studying the nonlinear modeling abilities of wavelet analysis theory and relevance vector machine, annual streamflow forecast model is established with the combination of wavelet analysis and AR, as the wavelet decomposition can reveal the details of streamflow time series and explore their evolving process and characteristics. The simulation results show that such coupled method supplies good forecasts results, which are also better than single AR. According to the application of wavelet theory into“Choangyang Water”, trends of the streamflow time series are detected. The uncertainty analysis capability of relevance vector machine is then validated by function regression example.
Biased wavelet neural network (BWNN) and its corresponding learning algorithm are proposed for the purpose of dealing with the redundancy in wavelet transform. BWNN is an adaptive wavelet network constructed by biased wavelets, and the form of such wavelets can adapt to special applications during learning period, while not just regulate the parameters of fixed wavelets, which reduce the redundancy to certain extent. The presented learning algorithm based on gradient decent also holds the treats of simple, clarity and efficiency. When applied to month streamflow forecast of Fengtan reservoir, BWNN can not only reach the goal of increasing forecast precision, but also avoid falling into local minimum and arising oscillation, which furnishes a new effective approach to nonlinear forecast modeling.
Aiming at resolving the issue of designing appropriate“proposal distribution”in Markov Chain Monte Carlo (MCMC), an improved adaptive Metropolis algorithm (IAM) is developed in the thesis. IAM selects normal density distribution to sample in objective function, and ameliorates the way of computing covariance matrix, which accelerate the algorithm convergence speed and lessen uncertainty factors influence. The achievements enrich the MCMC theory, and as well as provide a powerful tool for streamflow frequency forecast.
Parameter estimation of Pearson-III distribution using IAM is brought forward to figure out the problems of curve selection and parameter estimation in streamflow frequency forecast. IAM can obtain certain useful statistical information such as posterior distribution of parameters. By keeping the richness of sample data, IAM is able to reduce the probability of converging at the local optimal area, which advances the quality and speed of final estimators. Based on the instances of annual and a period of ten days streamflow frequency calculation in Fengtan reservoir, satisfying results are obtained, and can reflect the forecast range related to uncertainty of model parameters, which simultaneously verify the better performance of IAM.
The research frame of stramflow forecast uncertainty based on relevance vector machine (RVM) is established in allusion to the less attention of model uncertainty in most nonlinear forecast methods. With the analysis of components in streamflow time series, the frame is composed of wavelet denoising, RVM modeling, model selection based on IAM, and multi-step forecast by recursive calculation. The proposed frame avails of the prominent characteristics of RVM in outputting forecast distribution, using less relevance vectors, and confining no limitation to kernel function. Further more, the valid presented model selection method implements the trade-off between training precision and model complexity. The application to daily streamflow forecast of Yichan station indicated that, the frame is capable of supplying good forecast results, and the equipped uncertainty distribution offers more information for reservoir regulation decision, which redounds to quantitatively estimate different risks when concerning forecast uncertainty.
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