基于混沌进化的水库调度和洪灾评估的理论与方法
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摘要
洪水是水资源系统的重要组成部分,具有致灾、兴利的双重属性。我国洪水灾害和水资源短缺是一对尖锐的矛盾,如何合理解决这一矛盾,变害为利,是一个既具有理论意义,又具有很大实用价值的课题。同时,研究洪水灾害的资源转化模式是洪水资源管理的主要内容之一。为此,本文针对洪水资源自身的特点,从兴利(发电调度)、预防(防洪调度)、洪水分类、洪灾等级评估四个研究对象出发,提出了几种基于混沌搜索的种群进化算法(混沌粒子群,混沌差分进化),取得了一些具有理论意义和实用价值的成果。主要研究工作及创新成果如下：
(1)针对梯级水电系统优化调度问题,提出一种新颖的混沌粒子群算法(CPSO),对比了三种分布在对称区间上的一维混沌映射的效率。该算法在粒子群算法求出的最优解附近进行混沌搜索,提高了混沌粒子群算法的全局优化能力,能有效避免算法容易陷入局部最优以及解决logistic映射不能在负值区间进行搜索的问题。此外,采用分段线性插值函数将所有的约束转化为对上游水位的限制,从而实现了对目标函数的求解。通过三峡梯级水电系统的实例,比较了不同的算法的效果和计算速度。
(2)为求解水库防洪优化调度问题,以下泄流量过程为决策变量,结合死亡罚函数,提出了一种基于改进logistic映射的混沌粒子群算法；按照最大消峰原则,建立了以下泄流量的标准差最小为目标的防洪调度模型。以三峡水库两场典型洪水为例,比较了所提出的算法和模型与现在有的算法和模型的效果。此外,研究了不同洪水预报精度下,水库遭遇超标洪水时,下泄流量超过安全标准的风险率。
(3)洪水灾害是一种常见的自然灾害。洪水分类的目的是建立管理洪水和预防洪灾的灾难评估模型。根据混沌优化理论,提出了一种求解洪水分类模糊聚类迭代模型的混沌差分进化算法。该算法运用改进的logistic混沌映射和罚函数,可以更好地处理目标函数,并选择了两个实际的洪水样本测试提出的算法的性能。通过仿真结果和对比可以发现：与基本的差分进化算法和其它文献中的提出的优化方法相比,混沌差分进化算法更加可靠、稳定。
(4)针对洪水灾情等级评估问题,建立了投影寻踪多项式函数模型,并提出一种基于分段线性映射的混沌差分进化算法求解投影指标函数,同时采用罚函数法处理约束条件,求出了最佳投影方向。通过灾情等级表各指标边界值的投影求出多项式函数的系数,获得一个用于评估洪灾等级的多项式函数,进而实现了连续型洪灾等级的有效划分。两个实例计算的结果以及与其它模型和算法的对比表明,该方案简单实用,并且具有广泛的应用性。
As a important component part of water resource system, flood possesses dual attribute of hazard and profit. It is a penetrating contradiction of flood disaster and water resources shortage, and is a theoretical and practical issue how to solve this contradiction reasonably. Furthermore, the transformation mode of flood disaster and resource is one of major content of flood resource management. Hence, in view of the characteristics of flood resource, this article presents several population evolution algorithms based on chaotic searcher for dealing with four objects including profit (power generation scheduling), prevention(flood control), flood classification and flood disaster grade evaluation, and obtains some theoretical and practical results. The research work and innovation achievements can be described as follows:
(1) Aiming at the problem of cascaded hydropower system optimal dispatchling, we propose a novel chaotic particle swarm optimization (CPSO) algorithm and compares the efficiency of three one-dimensional chaotic maps within symmetrical region. This approach, which process chaotic search nearby the optimal solution computed by PSO algorit hm, improves the global optimization capability of CPSO algorithm in order to solve the problem that particle swarm optimization (PSO) algorithm is easy to trap in local optima and logistic map can't search in the negative region effectively. Moreover, a piecewise linear interpolation function is employed to transform all constraints into restrict upriver water level for solving the objective function. Numerical results and comparisons demonstrate the effect and speed of different algorithms on the Three Gorges cascaded hydroelectric system
(2) In order to solve the problem of reservoir flood control, a chaotic particle swarm optimization (CPSO) algorithm based on the improved logistic map is presented, which uses the discharge flow process as the decision variables combined with the death penalty function. According to the principle of maximum eliminating flood peak, the flood control operation model has been eatablished with the goal of minimum the discharge flow. The case of two typical floods on Gorges reservoir compares the effect of proposed model and algorithm with existing models and algorithms. Moreover, the risk rate that discharge flow overtakes the safety standard under the different accuracy of flood forecasting is investigated while the reservoir encounters the over-level flood.
(3) Flood disaster is a kind of frequent natural hazards. The objective of flood classification is to establish hazard assessment model for managing flood and preventing disaster. Base on the chaotic optimization theory, a chaotic differential evolution algorithm (CDE) is proposed to solve a fuzzy clustering iterative model for flood disaster classification. By using improved logistic chaotic map and penalty function, the objective function can be solved more perfectly and ave taken into account two practical flood disaster cases so as to test the effect of novel hybrid method. Simulation results and comparisons show that the chaotic differential evolution algorithm is competitive and stable in performance with simple differential evolution and other optimization approaches presented in literatures.
(4) In allusion to the problem of evaluating flood disaster grade, we establish the projection pursuit polynomial function model, and propose a chaotic differential evolution (CDE) algorithm using piecewise linear chaotic map for optimizing the projection index function, and adopt penalty function method of dealing with constraints to detect optimal projection direction. The coefficients of polynomial function are solved by projecting the index boundary values of flood disaster grade table so as to implement the division of continuous flood disaster grade. The calculation results of two example show this scheme is effective and easy to implement in comparison with other models and algorithms, which can be applied to many scientific field.
(1)针对梯级水电系统优化调度问题,提出一种新颖的混沌粒子群算法(CPSO),对比了三种分布在对称区间上的一维混沌映射的效率。该算法在粒子群算法求出的最优解附近进行混沌搜索,提高了混沌粒子群算法的全局优化能力,能有效避免算法容易陷入局部最优以及解决logistic映射不能在负值区间进行搜索的问题。此外,采用分段线性插值函数将所有的约束转化为对上游水位的限制,从而实现了对目标函数的求解。通过三峡梯级水电系统的实例,比较了不同的算法的效果和计算速度。
(2)为求解水库防洪优化调度问题,以下泄流量过程为决策变量,结合死亡罚函数,提出了一种基于改进logistic映射的混沌粒子群算法；按照最大消峰原则,建立了以下泄流量的标准差最小为目标的防洪调度模型。以三峡水库两场典型洪水为例,比较了所提出的算法和模型与现在有的算法和模型的效果。此外,研究了不同洪水预报精度下,水库遭遇超标洪水时,下泄流量超过安全标准的风险率。
(3)洪水灾害是一种常见的自然灾害。洪水分类的目的是建立管理洪水和预防洪灾的灾难评估模型。根据混沌优化理论,提出了一种求解洪水分类模糊聚类迭代模型的混沌差分进化算法。该算法运用改进的logistic混沌映射和罚函数,可以更好地处理目标函数,并选择了两个实际的洪水样本测试提出的算法的性能。通过仿真结果和对比可以发现：与基本的差分进化算法和其它文献中的提出的优化方法相比,混沌差分进化算法更加可靠、稳定。
(4)针对洪水灾情等级评估问题,建立了投影寻踪多项式函数模型,并提出一种基于分段线性映射的混沌差分进化算法求解投影指标函数,同时采用罚函数法处理约束条件,求出了最佳投影方向。通过灾情等级表各指标边界值的投影求出多项式函数的系数,获得一个用于评估洪灾等级的多项式函数,进而实现了连续型洪灾等级的有效划分。两个实例计算的结果以及与其它模型和算法的对比表明,该方案简单实用,并且具有广泛的应用性。
As a important component part of water resource system, flood possesses dual attribute of hazard and profit. It is a penetrating contradiction of flood disaster and water resources shortage, and is a theoretical and practical issue how to solve this contradiction reasonably. Furthermore, the transformation mode of flood disaster and resource is one of major content of flood resource management. Hence, in view of the characteristics of flood resource, this article presents several population evolution algorithms based on chaotic searcher for dealing with four objects including profit (power generation scheduling), prevention(flood control), flood classification and flood disaster grade evaluation, and obtains some theoretical and practical results. The research work and innovation achievements can be described as follows:
(1) Aiming at the problem of cascaded hydropower system optimal dispatchling, we propose a novel chaotic particle swarm optimization (CPSO) algorithm and compares the efficiency of three one-dimensional chaotic maps within symmetrical region. This approach, which process chaotic search nearby the optimal solution computed by PSO algorit hm, improves the global optimization capability of CPSO algorithm in order to solve the problem that particle swarm optimization (PSO) algorithm is easy to trap in local optima and logistic map can't search in the negative region effectively. Moreover, a piecewise linear interpolation function is employed to transform all constraints into restrict upriver water level for solving the objective function. Numerical results and comparisons demonstrate the effect and speed of different algorithms on the Three Gorges cascaded hydroelectric system
(2) In order to solve the problem of reservoir flood control, a chaotic particle swarm optimization (CPSO) algorithm based on the improved logistic map is presented, which uses the discharge flow process as the decision variables combined with the death penalty function. According to the principle of maximum eliminating flood peak, the flood control operation model has been eatablished with the goal of minimum the discharge flow. The case of two typical floods on Gorges reservoir compares the effect of proposed model and algorithm with existing models and algorithms. Moreover, the risk rate that discharge flow overtakes the safety standard under the different accuracy of flood forecasting is investigated while the reservoir encounters the over-level flood.
(3) Flood disaster is a kind of frequent natural hazards. The objective of flood classification is to establish hazard assessment model for managing flood and preventing disaster. Base on the chaotic optimization theory, a chaotic differential evolution algorithm (CDE) is proposed to solve a fuzzy clustering iterative model for flood disaster classification. By using improved logistic chaotic map and penalty function, the objective function can be solved more perfectly and ave taken into account two practical flood disaster cases so as to test the effect of novel hybrid method. Simulation results and comparisons show that the chaotic differential evolution algorithm is competitive and stable in performance with simple differential evolution and other optimization approaches presented in literatures.
(4) In allusion to the problem of evaluating flood disaster grade, we establish the projection pursuit polynomial function model, and propose a chaotic differential evolution (CDE) algorithm using piecewise linear chaotic map for optimizing the projection index function, and adopt penalty function method of dealing with constraints to detect optimal projection direction. The coefficients of polynomial function are solved by projecting the index boundary values of flood disaster grade table so as to implement the division of continuous flood disaster grade. The calculation results of two example show this scheme is effective and easy to implement in comparison with other models and algorithms, which can be applied to many scientific field.
引文
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