摘要
非线性是水环境中普遍的现象,污染物在水中的迁移、转化等过程容易受各种内部、外部因素的影响。作为城市排污的渠道,城市河涌是一类特殊的水环境,更易受到工业废水、生活污水等污染,某些受严重污染的河段,水体中溶解氧浓度偏低,影响污染物的耗氧降解过程,使污染物耗氧降解过程呈现非线性特征。本文以城市河涌为研究对象,研究河涌水质的非线性特征,并在水质预测、误差非线性补偿、河涌水质非线性建模、水质非线性性态分析、河涌模型存在正解的条件、河流曝气过程的脉冲描述等方面进行了研究,主要成果有：
1.针对河涌水质预测中出现的误差,提出利用混沌理论分析河涌水质的混沌特性,并利用相空间重构理论确定水质预测误差的相空间,在此基础上,将相空间与神经网络进行对比,确定神经网络单层神经元个数,进而建立误差补偿的神经网络,并与水质模型相结合建立误差补偿水质模型,此方法突破单一类型水质模型在预测中的局限性,通过对河涌检测结果的模拟与仿真,结果表明,模型预测相对误差由2.4%降到1.65%,提高了水质预测精度。
2.根据城市河涌水体中溶解氧浓度过低这一现象,在分析稳态SP模型假设、Shastry模型假设的基础上,确定河涌水质建模的条件,针对河涌水体中溶解氧不足及BOD沉降等因素,建立了河涌水质非线性微分方程模型。仿真结果得SP模型相对误差Er,sp,=0.8291,Shastry模型相对误差Er,shatry=0.2498,河涌模型相对误差Er,hc=0.2426,即河涌非线性模型具有更高的预测精度。
3.为了分析河涌水质非线性微分方程模型的性态,借鉴了微分方程定性分析理论,对所建立的城市河涌水质非线性微分方程模型进行稳定性分析,证明了：河涌水质非线性模型在其解空间中具有唯一解,即模型在理论上可用于水质预测；利用数值仿真技术,分析模型参数对模型解的影响,发现模型解的特性(稳定性、正解)依赖于模型参数的选取。
4.河涌水质非线性模型的应用,通过分析模型参数在实际应用中的取值范围,证明了：当模型参数都大于零时,模型存在正解,即BOD、DO浓度不会出现负值；通过对模型解的渐进性态分析得到：排污稳定时,在距离污染源足够远处,BOD浓度最终将趋于零,而溶解氧浓度(D0)最终将趋于饱和,即河涌水质终将因污染物降解和水体复氧而得到净化。
5.针对河流治理中常用的曝气过程,分别在SP水质模型、河涌水质非线性微分方程模型的基础上,利用脉冲原理对曝气过程进行描述,建立了基于脉冲的河涌曝气模型,通过模拟与仿真得：当河涌曝气时,水质预测平均相对误差为5.21%,当对河涌不曝气时水质平均相对误差为3.114%,因此河涌曝气过程在近距离上对水质预测精度有一定影响。
论文主要针对水体中污染物迁移、转化过程之间的非线性行为进行了研究与建模,其中还有一些有待深入研究的问题。
(1)模型的水质组分需要增加：论文只对BOD、DO两种水质组分进行建模,由于河涌水体中各水质组分之间存在一定的迁移转化关系,如氨碳、磷等,其降解过程会影响水体中溶解氧浓度,在以后的研究中,可根据研究的需要增加相应水质组分,建立基于多水质的河涌水质数学模型。
(2)在空间上进行拓展：论文所建立的河涌水质模型为一维水质模型,其适应水流速率缓慢的河涌,如果河涌污染在各方向迁移、扩散差异较大,则需要拓展到二维或三维情形。
(3)由于水环境的复杂性,模型假设还存在可改善的空间,如利用脉冲过程描述河流曝气过程,在近距离上模型预测精度有待进一步提高,在以后的工作中,需进一步研究水体中污染物迁移、转化的规律,对模型进行改善,提高模型的预测精度
Nonlinear is the universal phenomenon about pollution water quality, the migration and transformation of pollutants in water is easy to be affected by a variety of internal or external factors. City river is a special kind of water environment, it is easy to be polluted by city sewage, domestic sewage and other types of pollution, at some polluted section, there is few oxygen in water, the process of pollutant's migration and transformation in water has non-linear characteristic. In this paper, some studies include water quality model of nonlinear compensation, non-linear differential equation water quality model, water quality analysis of low oxygen river, impulse model of river aeration are researched.
1. According to prediction errors of water quality, chaos theory alwalys to be used to analysis water quality, the errors is reconstructed to a new phase space with chaos theory, and neuron number of neural network layer is given by the phase space, base on it, an error compensation model of the neural network is established, that's breakthrough a single water quality model limitations, the results show that, the relative prediction error is reduced from2.4%to1.65%, it show that the neural network error compensation model is effective.
2. According to low dissolved oxygen phenomenon of urban heavy polluted river, the assumptions of SP model and Shastry model are analyzed, on the base of it, assumptions is modified to establish a new nonlinear differential equation model, and the results is Ersp=0.829, Er,shastry,=0.2498Er,hc=0.2426by simulate with Matlab, it show that the new model has more effectivly.
3. In order to analyze the state of nonlinear water quality differential equation, methed of differential equations has used to analysis the behavior of City river nonlinear differential equation model, and some results are given, firstly, the City river water quality model has a unique solution in its solution space, it means the model can be used for water quality's prediction. Secondly, the stability of the City river model is dependent on its parameters.
4. On the application of City river water quality model, positive solution should be proved to avoid negative phenomenon of the water quality prediction, so the existence of positive solutions of a model condition is discussed in the paper, the conclusion is that the City river water quality model has positive solutions when the model parameter is greater than zero, it means BOD, DO concentration will not be negative, it also means that the model is effectively in water quality prediction; the other conclusion is that the concentration of BOD will eventually approach to zero, and oxygen (DO) will eventually approach to saturation when there is enough distance, it means that the water will self-purification by itself ability of purification.
5. On the management of River aeration process, impulse models base on the SP model and City river model have been established to describe aeration process, its average relative error is5.21%by simulated with practical rive data, it means that the describe is validity; at the same time, SP model's average relative error is3.114%(less than5.21%), it means that the prediction accuracy of water quality will be influenced by impulse process.
In this paper, a new nonlinear model has been established about nonlinear characteristic of pollutant migration, conversion in City river,but there is also some questions to be studied in the further.
(1) Components of City river model should to be increased, in the paper, only BOD and DO has been studied, in the future more components water quality model should be studied if it necessed.
(2) In the pape, only one-dimensional water quality model has been established on City river water quality, in the future, the two-dimensional or three-dimensional City river water quality model should been studied.
(3) Due to the complex of water environment, there is many assumptions should be revised, such as the description of river aeration process, the assumptions of water quality model, the migration and transformation of pollutants in water and so on, all of it will improve model's prediction accuracy.
引文
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