基于RBF代理模型的调水过程优化研究
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摘要
调蓄工程通过泵站调水过程中,需要通过合理的控制泵站启闭时间来调节水位,从而不断优化调水过程,但以往的优化方法效率低而且不易得到最优方案。为解决这一问题,本文以南水北调东线山东段南四湖下级湖为研究对象,基于径向基函数(Radial Basis Function,RBF)代理模型建立调水过程优化模型,得到了调水过程方案参数区间内的最优方案,并基于实际调水情况求得不同起调水位下的调水过程最优方案。首先根据调水过程方案参数区间自动选取80个调水过程方案样本,并利用一维二维耦合水动力模型算出每个方案的水位变化过程;其次采用RBF代理模型建立并验证调水过程方案与最高水位、最低水位的响应关系;最后基于RBF代理模型,以泵站工作总时间最短为目标,考虑水量平衡和水位约束建立优化模型,采用粒子群算法求解。研究结果表明,基于RBF代理模型的调水过程最优方案结果与耦合模型计算该方案结果的绝对水深误差不超过0.05 m,相对水深误差不超过0.99%,模型计算精度高。基于RBF代理模型的调水过程优化模型,求解得到调水过程参数区间内的最优方案,解决了传统方法在人为设定有限个方案内得到较优方案的局限性。
In the water transfer process of the regulating and storage project through the pump station,the water level needs to be adjusted through reasonable control of the opening and closing time of the pump station,so as to constantly optimize the water transfer process. However,previous optimization methods are inefficient and difficult to obtain an optimal solution. In order to solve this problem,this paper takes the Lower Nansi Lake in Shandong reach of the eastern route of South-to-North Water Transfer Project as the research object,and establishes the optimization model of water transfer process based on RBF(Radial Basis Function) surrogate model to study the optimal water transfer process of the Lower Nansi Lake. The method is used to obtain the optimal scheme within the parameter range of the water transfer process,and the optimal scheme for the water transfer process under different starting water levels is obtained based on the actual water transfer situation. Firstly,80 samples of the water transfer process are selected automatically according to the parameter interval of the water transfer process scheme,and the water level of each scheme is calculated using the 1 D-2 D coupled hydrodynamic model. Secondly,the RBF surrogate model is adopted to establish and verify the relationship between the water transfer process scheme and the response of the highest and lowest water levels. Finally, based on the RBF surrogate model, taking the shortest working time of the pump station as the objective,the optimization model was established considering water balance and water level constraints,and particle swarm optimization was adopted to solve the problem. The research results show that the absolute depth error is no more than 0.05 m and the relative depth error is no more than 0.99% compared with the calculation results of the scheme water level and the coupled model in the optimized water transfer process,and the optimization model of water transfer process based on RBF surrogate model has high accuracy. Based on this model,the optimal solution within the parameter interval of the water transfer process is obtained,which solves the limitation of the traditional method to obtain the optimal solution within a limited number of artificially set schemes.
In the water transfer process of the regulating and storage project through the pump station,the water level needs to be adjusted through reasonable control of the opening and closing time of the pump station,so as to constantly optimize the water transfer process. However,previous optimization methods are inefficient and difficult to obtain an optimal solution. In order to solve this problem,this paper takes the Lower Nansi Lake in Shandong reach of the eastern route of South-to-North Water Transfer Project as the research object,and establishes the optimization model of water transfer process based on RBF(Radial Basis Function) surrogate model to study the optimal water transfer process of the Lower Nansi Lake. The method is used to obtain the optimal scheme within the parameter range of the water transfer process,and the optimal scheme for the water transfer process under different starting water levels is obtained based on the actual water transfer situation. Firstly,80 samples of the water transfer process are selected automatically according to the parameter interval of the water transfer process scheme,and the water level of each scheme is calculated using the 1 D-2 D coupled hydrodynamic model. Secondly,the RBF surrogate model is adopted to establish and verify the relationship between the water transfer process scheme and the response of the highest and lowest water levels. Finally, based on the RBF surrogate model, taking the shortest working time of the pump station as the objective,the optimization model was established considering water balance and water level constraints,and particle swarm optimization was adopted to solve the problem. The research results show that the absolute depth error is no more than 0.05 m and the relative depth error is no more than 0.99% compared with the calculation results of the scheme water level and the coupled model in the optimized water transfer process,and the optimization model of water transfer process based on RBF surrogate model has high accuracy. Based on this model,the optimal solution within the parameter interval of the water transfer process is obtained,which solves the limitation of the traditional method to obtain the optimal solution within a limited number of artificially set schemes.
引文
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[15]陈文龙,宋利祥,邢领航,等.一维-二维耦合的防洪保护区洪水演进数学模型[J].水科学进展,2014,25(6):848-855.
[16]姜晓明,李丹勋,王兴奎.基于黎曼近似解的溃堤洪水一维-二维耦合数学模型[J].水科学进展,2012,23(2):214-221.
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[20]宋月清,林仁.水泵起动过程中泵站前池水位降落值的分析[J].水利学报,1999(5):71-76.
[21]张万台,路明利,吴秀云,等.引滦工程尔王庄暗渠泵站经济运行方案研究[J].水利学报,2004(8):94-97.
[22]邱亚松,白俊强,华俊.基于本征正交分解和代理模型的流场预测方法[J].航空学报,2013,34(6):1249-1260.
[23]李响,王晓鹏.径向基代理模型中形状参数对精度的影响[J].系统工程与电子技术,2015,37(3):688-692.
[24]胡旺,GARY G Yen,张鑫.基于Pareto熵的多目标粒子群优化算法[J].软件学报,2014,25(5):1025-1050.
[25]赖宇阳.Isight参数优化理论与实例详解[M].北京:北京航空航天大学出版社,2012.
[26]安伟刚,李为吉.改进的粒子群优化算法及其工程应用[J].机械科学与技术,2005(4):415-417.
[2]高学平,聂晓东,孙博闻,等.调水工程中相邻梯级泵站的开启时间差研究[J].水利学报,2016,47(12):1502-1509.
[3]张朝龙,余春日,江善和,等.基于混沌云模型的粒子群优化算法[J].计算机应用,2012,32(7):1951-1954.
[4]郭旭宁,雷晓辉,李云玲,等.跨流域水库群最优调供水过程耦合研究[J].水利学报,2016,47(7):949-958.
[5]丁咏梅,邵东国.水资源有计划市场配置模型及其应用[J].武汉大学学报(工学版),2010,43(4):438-442.
[6]高学平,闫晨丹,张岩,等.基于BP神经网络的调水工程调蓄水位预测模型[J].南水北调与水利科技,2018,16(1):8-13.
[7]穆雪峰,姚卫星,余雄庆,等.多学科设计优化中常用代理模型的研究[J].计算力学学报,2005(5):608-612.
[8]ELSAYED K,LACOR C.CFD modeling and multi-objective optimization of cyclone geometry using desirability function,artificial neural networks and genetic algorithms[J].Applied Mathematical Modelling,2013,37(8):5680-5704.
[9]龙腾,刘建,WANG G Gary,等.基于计算试验设计与代理模型的飞行器近似优化策略探讨[J].机械工程学报,2016,52(14):79-105.
[10]姚拴宝,郭迪龙,孙振旭,等.基于Kriging代理模型的高速列车头型多目标优化设计[J].中国科学(技术科学),2013,43(2):186-200.
[11]GAO X,TIAN Y,SUN B,et al.Multi-objective optimization design of bidirectional flow passage components using RSM and NSGA II:A case study of inlet/outlet diffusion segment in pumped storage power station[J].Renewable Energy,2018,115.
[12]高学平,李建国,孙博闻,等.利用多岛遗传算法的侧式进/出水口体型优化研究[J].水利学报,2018,49(2):186-194.
[13]BROAD D R,DANDY G C,MAIER H R.A systematic approach to determining metamodel scope for risk-based optimization and its application to water distribution system design[J].Environmental Modelling&Software,2015,69:382-395.
[14]王智勇,陈永灿,朱德军,等.一维-二维耦合的河湖系统整体水动力模型[J].水科学进展,2011,22(4):516-522.
[15]陈文龙,宋利祥,邢领航,等.一维-二维耦合的防洪保护区洪水演进数学模型[J].水科学进展,2014,25(6):848-855.
[16]姜晓明,李丹勋,王兴奎.基于黎曼近似解的溃堤洪水一维-二维耦合数学模型[J].水科学进展,2012,23(2):214-221.
[17]HYDROLOGIC ENGINEERING CENTER.HEC-RAS 2D Modeling User’s Manual Version 5.0[M].Davis,CA:US Army Corps of Engineering,2016.
[18]CASULLI V.A high-resolution wetting and drying algorithm for free-surface hydrodynamics[J].International Journal for Numerical Methods in Fluids,2009,60(4):391-408.
[19]HYDROLOGIC ENGINEERING CENTER.HEC-RAS Hydraulic Reference Manual Version 5.0[M].Davis,CA:US Army Corps of Engineering,2016.
[20]宋月清,林仁.水泵起动过程中泵站前池水位降落值的分析[J].水利学报,1999(5):71-76.
[21]张万台,路明利,吴秀云,等.引滦工程尔王庄暗渠泵站经济运行方案研究[J].水利学报,2004(8):94-97.
[22]邱亚松,白俊强,华俊.基于本征正交分解和代理模型的流场预测方法[J].航空学报,2013,34(6):1249-1260.
[23]李响,王晓鹏.径向基代理模型中形状参数对精度的影响[J].系统工程与电子技术,2015,37(3):688-692.
[24]胡旺,GARY G Yen,张鑫.基于Pareto熵的多目标粒子群优化算法[J].软件学报,2014,25(5):1025-1050.
[25]赖宇阳.Isight参数优化理论与实例详解[M].北京:北京航空航天大学出版社,2012.
[26]安伟刚,李为吉.改进的粒子群优化算法及其工程应用[J].机械科学与技术,2005(4):415-417.