基于复杂性理论的河湖环境系统模型研究
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摘要
本论文首先综述了复杂性理论及其在河湖环境系统模型应用中的研究进展,指出复杂环境系统模型现状研究中存在的问题,并具体针对复杂河湖环境系统的水环境质量模型、水环境容量计算模型、水环境风险模型、湖泊富营养化模型、水环境时序变化机制探讨和酸沉降子系统时空分布特征模拟等方面,从数学理论、方法和应用相结合的角度出发,系统的研究了基于复杂性理论的河湖环境系统建模的新理论、新方法,以期建立的复杂环境系统模型更符合客观规律和事实。
本文的研究工作和研究成果包括以下内容:(1)针对缺乏河流流场和参数资料的环境系统,建立了基于区间有限单元法的二维水质模型,通过对规则河流采用数值实验(最优化的区间解析解)方法验证基于区间有限单元法的二维区间水质模型的可靠性和精度,并以区间数“度”的测度描述水环境风险。研究发现该模型为传统的随机理论和模糊理论研究水环境模拟、预测和风险评价提供了有益的补充。(2)针对湖泊富营养化Chlorophyll-a与环境参数、生物参数之间的非线性关系,建立了基于贝叶斯神经网络(BRBPNN)和贝叶斯最小二乘支持向量机(BEFLSSVM)的Chlorophyll-a预测模型。实例数据研究表明基于贝叶斯推断理论自动获取后验分布意义上的最大值,大大方便了神经网络训练和支持向量机估计算法的规整化参数、核参数的选择,且具有优良的稳健性和泛化能力,可以为有效及时的控制湖泊富营养化变化趋势提供科学依据。(3)基于未确知数学的盲数理论和皮尔逊III型曲线的Monte-Carlo模拟,以出湖水体水质超标风险率小于10%的污染物浓度均值作为水质控制目标,提出了不确定信息下湖泊富营养化水环境容量的计算方法,可以获得理论上较为可行且计算结果偏于安全的水环境容量。(4)根据频率幂律分布分析、功率谱分析和消除趋势波动分析三种统计方法和自组织临界系统的三个基本特征,研究发现湖泊溶解氧序列的频率分布在一定区间内遵从幂律分布(尺度不变性)且在时域上具有1 /fβ噪声特性,分析了可将水体的饱和溶解氧浓度作为水环境系统临界状态的原因,探讨了自组织临界性可能是水环境系统溶解氧时序形成与演化的内在机制之一。(5)在Streeter-Phelps和Shastry水质模型的基础上引入随机力,建立了基于线性和非线性随机微分方程的突发性水环境风险计算模型,并以数值方法求解多维随机偏微分方程得到概率密度分布函数,获得污染物超标风险率与超标时间长短的关系。研究表明一个微小的随机扰动都有可能改变系统的“命运”,环境风险管理者和规划者应充分重视环境系统中的非线性效应和不确定效应。(6)基于酸沉降系统中存在的非线性和不确定性特征,建立了酸沉降时空分布特征的BRBPNN和BEFLSSVM模型,模拟结果明显优于传统多元线性回归(MLR)模型,改善提高了酸沉降化学组分的月平均浓度的时空分析模型的模拟精度,有利于解释酸沉降时空分布特征的机理。
本文基于环境系统的复杂性特征,较为系统、深入地提出了基于复杂性理论的河湖环境系统模型的预测、模拟、评价和规划的理论与方法。一方面,有助于发展一套较完整的针对复杂环境系统的建模理论与方法,在本质上加深了对复杂河湖环境系统客观规律性的认识,具有一定的理论意义。另一方面,本文以三峡水库、洞庭湖等实例研究证明,基于复杂性理论的环境系统模型能够更加准确、有效的预测、模拟复杂的环境系统行为,可以为环境管理、规划和管理提供定量理论依据和技术支持,更有效的指导和协调环境系统的可持续发展,具有一定的实践意义。
This dissertation first reviews the research progresses on complexity theory and its applications to the models of water environmental system, and accounts for the current problems on complex environmental models. Then from the respective of the mathematic theories, methodologies and applications and based on complexity theory, the focus is given on the development of new theory and new methodology for the water environmental modeling establishment. This dissertation systematically studies the modeling problems in such areas as follows: water quality model, calculation of water environmental capacity, risk analysis of water environment, mechanism discussion of water environmental time series, lake eutrophication model and temporal distribution simulation of acid precipitation. By means of complexity theory, we hope to found some environmental system models which are more accorded with the objective rules and facts.
The main work and novel results of this dissertation includes the following elements. (1) Under the condition of unclear water environment, inexact cognition of parameters, without the detailed monitoring flow field and to avoid full dependence of practical monitoring data of river, an interval two-dimensional water quality model, its numerical algorithm and interval risk (denoted by“degree”of interval number) have been proposed, the availability and reliability of which were calibrated by numerical experiment of the ideal regular river reach. The results of a case study indicated that the interval water quality model offered a realistic approach for dealing with uncertainties in real-world problems compared with traditional stochastic or fuzzy methods. (2) Based on the non-linear relationship between Chlorophyll-a and environmental parameters as well as biological parameters in the lake eutrophication, the Bayesian regularized BP neural network (BRBPNN) and the least squares support vector machine within Baysiean evidence framework (BEFLSSVM) were proposed to predict Chlorophyll-a concentration. The results showed that BRBPNN and BEFLSSVM models were capable of automated selection of regularization and kernel parameters, and thus it may ensure the excellent generation ability and robustness. (3) Based on the pollutant concentration distribution in lake effluent (the risk of exceeding standard was lower than 10%, which was considered as the control goal of water quality), with the unascertained mathematics theory and Monte-Carlo method by the Pearson-III distribution curve, a new model for the calculation of water environmental capacity in eutrophic lake under unascertained information was proposed. This modeling could offer the feasible and reliable capacity of the water environment. (4) Three statistical methods were used to examine the self-organized criticality (SOC) of weekly dissolved oxygen (DO) series: empirical probability distribution function, power spectrum analysis and detrended fluctuation analysis (DFA). We found evidence that DO events were analogous to avalanches of granular piles exhibiting SOC properties. The weekly DO events complied with double power-law in two different regimes separated by a characteristic scale, X c, and could be described as 1 /fβnoise with long-range persistence. Then additionally, we argued that the critical state of DO events referred to the concentration of the saturated dissolved oxygen ( O s). Therefore, DO evolution was consistent with the three criteria of complex SOC systems. We thus suggested that SOC might be a possible mechanism underlying weekly DO evolution. (5) On the basis of Streeter-Phelps and Shastry's water quality model, the concept of stochastic force was introduced to develop the stochastic differential equation of water environment. The probability density distribution function was deduced by numerically solving the multi-dimensional stochastic partial differential equation. Accordingly, the relationship between the risk and duration of pollution exceeding standard could be obtained. The calculation of case study showed that a very small stochastic vibration maybe changed the“fate”of water environment and thus the managers and planners should fully attach importance to the non-linear and uncertain effect in the environment. (6) Based on the nonlinear and uncertain characteristics of acid precipitation, the BRBPNN and BEFLSSVM models of Chapter 3 were applied to the trend analysis, acidity and chemical composition of precipitation. And the simulation results were obviously better than those of multiple linear regression (MLR), which proved that the environmental system modeling based on complexity theory had the excellent applicability and practicality and was helpful to explain the mechanism of trend analysis of precipitation.
Due to the complexity characteristics of environmental system, this dissertation systematically and further developed the theory and methodology in prediction, simulation and assessment of the water environmental system models. To sum up, on one hand, this dissertation has been helpful to develop a set of environmental system modeling based on complexity theory and essentially deepen to recognize the objective rules. On the other hand, the results of the typical case study, such as Three-Gorge Reservoir and Dongting Lake, proved that the models based on complexity theory could more accurately and effectively account for the complex behaviors of water environment. And these offered theoretical and technical bases for environmental management and planning, and thus would more effectively boost the sustainable development of environmental system.
本文的研究工作和研究成果包括以下内容:(1)针对缺乏河流流场和参数资料的环境系统,建立了基于区间有限单元法的二维水质模型,通过对规则河流采用数值实验(最优化的区间解析解)方法验证基于区间有限单元法的二维区间水质模型的可靠性和精度,并以区间数“度”的测度描述水环境风险。研究发现该模型为传统的随机理论和模糊理论研究水环境模拟、预测和风险评价提供了有益的补充。(2)针对湖泊富营养化Chlorophyll-a与环境参数、生物参数之间的非线性关系,建立了基于贝叶斯神经网络(BRBPNN)和贝叶斯最小二乘支持向量机(BEFLSSVM)的Chlorophyll-a预测模型。实例数据研究表明基于贝叶斯推断理论自动获取后验分布意义上的最大值,大大方便了神经网络训练和支持向量机估计算法的规整化参数、核参数的选择,且具有优良的稳健性和泛化能力,可以为有效及时的控制湖泊富营养化变化趋势提供科学依据。(3)基于未确知数学的盲数理论和皮尔逊III型曲线的Monte-Carlo模拟,以出湖水体水质超标风险率小于10%的污染物浓度均值作为水质控制目标,提出了不确定信息下湖泊富营养化水环境容量的计算方法,可以获得理论上较为可行且计算结果偏于安全的水环境容量。(4)根据频率幂律分布分析、功率谱分析和消除趋势波动分析三种统计方法和自组织临界系统的三个基本特征,研究发现湖泊溶解氧序列的频率分布在一定区间内遵从幂律分布(尺度不变性)且在时域上具有1 /fβ噪声特性,分析了可将水体的饱和溶解氧浓度作为水环境系统临界状态的原因,探讨了自组织临界性可能是水环境系统溶解氧时序形成与演化的内在机制之一。(5)在Streeter-Phelps和Shastry水质模型的基础上引入随机力,建立了基于线性和非线性随机微分方程的突发性水环境风险计算模型,并以数值方法求解多维随机偏微分方程得到概率密度分布函数,获得污染物超标风险率与超标时间长短的关系。研究表明一个微小的随机扰动都有可能改变系统的“命运”,环境风险管理者和规划者应充分重视环境系统中的非线性效应和不确定效应。(6)基于酸沉降系统中存在的非线性和不确定性特征,建立了酸沉降时空分布特征的BRBPNN和BEFLSSVM模型,模拟结果明显优于传统多元线性回归(MLR)模型,改善提高了酸沉降化学组分的月平均浓度的时空分析模型的模拟精度,有利于解释酸沉降时空分布特征的机理。
本文基于环境系统的复杂性特征,较为系统、深入地提出了基于复杂性理论的河湖环境系统模型的预测、模拟、评价和规划的理论与方法。一方面,有助于发展一套较完整的针对复杂环境系统的建模理论与方法,在本质上加深了对复杂河湖环境系统客观规律性的认识,具有一定的理论意义。另一方面,本文以三峡水库、洞庭湖等实例研究证明,基于复杂性理论的环境系统模型能够更加准确、有效的预测、模拟复杂的环境系统行为,可以为环境管理、规划和管理提供定量理论依据和技术支持,更有效的指导和协调环境系统的可持续发展,具有一定的实践意义。
This dissertation first reviews the research progresses on complexity theory and its applications to the models of water environmental system, and accounts for the current problems on complex environmental models. Then from the respective of the mathematic theories, methodologies and applications and based on complexity theory, the focus is given on the development of new theory and new methodology for the water environmental modeling establishment. This dissertation systematically studies the modeling problems in such areas as follows: water quality model, calculation of water environmental capacity, risk analysis of water environment, mechanism discussion of water environmental time series, lake eutrophication model and temporal distribution simulation of acid precipitation. By means of complexity theory, we hope to found some environmental system models which are more accorded with the objective rules and facts.
The main work and novel results of this dissertation includes the following elements. (1) Under the condition of unclear water environment, inexact cognition of parameters, without the detailed monitoring flow field and to avoid full dependence of practical monitoring data of river, an interval two-dimensional water quality model, its numerical algorithm and interval risk (denoted by“degree”of interval number) have been proposed, the availability and reliability of which were calibrated by numerical experiment of the ideal regular river reach. The results of a case study indicated that the interval water quality model offered a realistic approach for dealing with uncertainties in real-world problems compared with traditional stochastic or fuzzy methods. (2) Based on the non-linear relationship between Chlorophyll-a and environmental parameters as well as biological parameters in the lake eutrophication, the Bayesian regularized BP neural network (BRBPNN) and the least squares support vector machine within Baysiean evidence framework (BEFLSSVM) were proposed to predict Chlorophyll-a concentration. The results showed that BRBPNN and BEFLSSVM models were capable of automated selection of regularization and kernel parameters, and thus it may ensure the excellent generation ability and robustness. (3) Based on the pollutant concentration distribution in lake effluent (the risk of exceeding standard was lower than 10%, which was considered as the control goal of water quality), with the unascertained mathematics theory and Monte-Carlo method by the Pearson-III distribution curve, a new model for the calculation of water environmental capacity in eutrophic lake under unascertained information was proposed. This modeling could offer the feasible and reliable capacity of the water environment. (4) Three statistical methods were used to examine the self-organized criticality (SOC) of weekly dissolved oxygen (DO) series: empirical probability distribution function, power spectrum analysis and detrended fluctuation analysis (DFA). We found evidence that DO events were analogous to avalanches of granular piles exhibiting SOC properties. The weekly DO events complied with double power-law in two different regimes separated by a characteristic scale, X c, and could be described as 1 /fβnoise with long-range persistence. Then additionally, we argued that the critical state of DO events referred to the concentration of the saturated dissolved oxygen ( O s). Therefore, DO evolution was consistent with the three criteria of complex SOC systems. We thus suggested that SOC might be a possible mechanism underlying weekly DO evolution. (5) On the basis of Streeter-Phelps and Shastry's water quality model, the concept of stochastic force was introduced to develop the stochastic differential equation of water environment. The probability density distribution function was deduced by numerically solving the multi-dimensional stochastic partial differential equation. Accordingly, the relationship between the risk and duration of pollution exceeding standard could be obtained. The calculation of case study showed that a very small stochastic vibration maybe changed the“fate”of water environment and thus the managers and planners should fully attach importance to the non-linear and uncertain effect in the environment. (6) Based on the nonlinear and uncertain characteristics of acid precipitation, the BRBPNN and BEFLSSVM models of Chapter 3 were applied to the trend analysis, acidity and chemical composition of precipitation. And the simulation results were obviously better than those of multiple linear regression (MLR), which proved that the environmental system modeling based on complexity theory had the excellent applicability and practicality and was helpful to explain the mechanism of trend analysis of precipitation.
Due to the complexity characteristics of environmental system, this dissertation systematically and further developed the theory and methodology in prediction, simulation and assessment of the water environmental system models. To sum up, on one hand, this dissertation has been helpful to develop a set of environmental system modeling based on complexity theory and essentially deepen to recognize the objective rules. On the other hand, the results of the typical case study, such as Three-Gorge Reservoir and Dongting Lake, proved that the models based on complexity theory could more accurately and effectively account for the complex behaviors of water environment. And these offered theoretical and technical bases for environmental management and planning, and thus would more effectively boost the sustainable development of environmental system.
引文
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