基于贝叶斯优化的三维水动力-水质模型参数估值方法
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摘要
随着水质目标管理要求的提升,基于复杂的三维水动力-水质模型的决策成为流域精准治理的必需.水质模型通常具有复杂的结构,包含大量的方程和参数,而参数取值的准确性会影响模型对水体系统表征的可靠性,进而影响根据模型结果进行水环境管理的效果,因此,有必要探究适用于复杂水质模型的高效参数估值方法.传统的自动参数估值方法应用于复杂的水质模型时会面临计算瓶颈,而贝叶斯优化适用于高运算成本模型的优化问题.本研究提出基于贝叶斯优化的复杂水质模型参数估值方法,主要包括:①重要影响参数识别;②重要参数敏感性排序与筛选;③采用贝叶斯优化对筛选出的参数进行估值;④方法的适用性评估.同时,将该方法应用于云南异龙湖的三维水动力-水质模型的参数估值中,发现进行参数估值后模型lg(NSE)均大于0.65,表明模型达到了满意的级别.研究表明,当贝叶斯优化算法的采集函数为EI时,仅需要141次迭代lg(NSE)即可达到0.766,该方法对复杂水质模型的参数估值具有一定的借鉴意义.
Reliable decision-making based on complex three-dimensional hydrodynamic and water quality modeling becomes essential under the circumstances of increasingly demand for water management requirement. However, due to the complicated modeling structure, enormous parameters and governing equations, it is extremely difficult if not impossible to obtain reasonable parameters to represent the underlying mechanisms in lake systems, which is the prerequisite of robust decision-making support. It is hence critical to explore highly effective parameter estimation techniques for complex water quality models. Traditional automatic parameter estimation techniques are usually computationally intensive, while Bayesian optimization algorithm has been shown to be able to tackle optimization problems for computational expensive models in a timely manner. In this study, we proposed a Bayesian optimization-based parameter estimation strategy, which includes ① critical parameters identification; ② critical parameters sensitivity analysis, sorting and filtering; ③parameter estimation using Bayesian optimization; and ④ method applicability evolution. We have successfully applied this strategy in parameter estimation for a three-dimensional hydrodynamic and water quality model of Lake Yilong in Southwestern China. The lg(NSE) for models using parameters identified by this strategy was all above 0.65, indicating a satisfactory representation of the lake system. Our results show that lg(NSE) could reach 0.766 after only 141 iterations when using EI as the acquisition function for the Bayesian optimization algorithm, indicating that the method proposed in this study has the potential to be applied in real world water quality modeling practices.
Reliable decision-making based on complex three-dimensional hydrodynamic and water quality modeling becomes essential under the circumstances of increasingly demand for water management requirement. However, due to the complicated modeling structure, enormous parameters and governing equations, it is extremely difficult if not impossible to obtain reasonable parameters to represent the underlying mechanisms in lake systems, which is the prerequisite of robust decision-making support. It is hence critical to explore highly effective parameter estimation techniques for complex water quality models. Traditional automatic parameter estimation techniques are usually computationally intensive, while Bayesian optimization algorithm has been shown to be able to tackle optimization problems for computational expensive models in a timely manner. In this study, we proposed a Bayesian optimization-based parameter estimation strategy, which includes ① critical parameters identification; ② critical parameters sensitivity analysis, sorting and filtering; ③parameter estimation using Bayesian optimization; and ④ method applicability evolution. We have successfully applied this strategy in parameter estimation for a three-dimensional hydrodynamic and water quality model of Lake Yilong in Southwestern China. The lg(NSE) for models using parameters identified by this strategy was all above 0.65, indicating a satisfactory representation of the lake system. Our results show that lg(NSE) could reach 0.766 after only 141 iterations when using EI as the acquisition function for the Bayesian optimization algorithm, indicating that the method proposed in this study has the potential to be applied in real world water quality modeling practices.
引文
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Bennett N D,Croke B F W,Guariso G,et al.2013.Characterising performance of environmental models[J].Environmental Modelling & Software,40:1-20
Borgomeo E,Farmer C L,Hall J W.2015.Numerical rivers:A synthetic streamflow generator for water resources vulnerability assessments[J].Water Resources Research,51(7):5382-5405
陈卫平,涂宏志,彭驰等.2017.环境模型中敏感性分析方法评述[J].环境科学,38(11):4889-4896
崔佳旭,杨博.2018.贝叶斯优化方法和应用综述[J].软件学报,29(10):3068-3090
Candelieri A,Perego R,Archetti F.2018.Bayesian optimization of pump operations in water distribution systems[J].Journal of Global Optimization,71(1):213-235
Chaudhary A,Hantush M M.2017.Bayesian Monte Carlo and maximum likelihood approach for uncertainty estimation and risk management:Application to lake oxygen recovery model[J].Water Research,108:301-311
Chinyama A,Ochieng G M,Nhapi I,et al.2014.A simple framework for selection of water quality models[J].Reviews in Environmental Science and Bio-Technology,13(1):109-119
Cibin R,Sudheer K P,Chaubey I.2010.Sensitivity and identifiability of stream flow generation parameters of the SWAT model[J].Hydrological Processes,24(9):1133-1148
Cornejo-Bueno L,Garrido-Merchan E C,Hernandez-Lobato D,et al.2018.Bayesian optimization of a hybrid system for robust ocean wave features prediction[J].Neurocomputing,275:818-828
邓帅.2019.基于改进贝叶斯优化算法的CNN超参数优化方法[J].计算机应用研究,36(7):1-2
Ghahramani Z.2015.Probabilistic machine learning and artificial intelligence[J].Nature,521(7553):452-459
Harmel R D,Smith P K,Migliaccio K W,et al.2014.Evaluating,interpreting,and communicating performance of hydrologic/water quality models considering intended use:A review and recommendations[J].Environmental Modelling & Software,57:40-51
姜龙,李一平,章双双等.2018.大型浅水湖泊藻类模型参数敏感性分析[J].湖泊科学,30(3):693-700
Jia H,Xu T,Liang S,et al.2018.Bayesian framework of parameter sensitivity,uncertainty,and identifiability analysis in complex water quality models[J].Environmental Modelling & Software,104:13-26
Jiang L,Li Y,Zhao X,et al.2018.Parameter uncertainty and sensitivity analysis of water quality model in Lake Taihu,China[J].Ecological Modelling,375:1-12
Jones D R.2001.A taxonomy of global optimization methods based on response surfaces[J].Journal of Global Optimization,21(4):345-383
Kavetski D,Fenicia F,Reichert P,et al.2018.Signature-domain calibration of hydrological models using approximate bayesian computation:Theory and comparison to existing applications[J].Water Resources Research,54(6):4059-4083
Kushner H J.1963.A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise[J].Journal of Fluids Engineering,86(1):97-106
Liang S,Jia H,Xu C,et al.2016.A Bayesian approach for evaluation of the effect of water quality model parameter uncertainty on TMDLs:A case study of Miyun Reservoir[J].Science of the Total Environment,560:44-54
Marchant R,Ramos F.2012.Bayesian Optimisation for Intelligent Environmental Monitoring[C].IEEE/RSJ International Conference on Intelligent Robots and Systems.Vilamoura,Algarve:2242-2249
Martinezcantin R.2014.BayesOpt:A bayesian optimization library for nonlinear optimization,experimental design and bandits[J].Journal of Machine Learning Research,15:3735-3739
Mckay M D,Beckman R J,Conover W J.2000.A comparison of three methods for selecting values of input variables in the analysis of output from a computer code M.D.Mckay[J].Technometrics,21(2):266-294
Mockus J,Tiesis V,Zilinskas A.1978.The Application of Bayesian Methods for Seeking the Extremum[M].Amsterdam:North-Holland
Morelli B,Hawkins T R,Niblick B,et al.2018.Critical review of eutrophication models for life cycle assessment[J].Environmental Science & Technology,52(17):9562-9578
Nash J E,Sutcliffe J V.1970.River flow forecasting through conceptual models part I — A discussion of principles[J].Journal of Hydrology,10(3):282-290
Nossent J,Elsen P,Bauwens W.2011.Sobol′ sensitivity analysis of a complex environmental model[J].Environmental Modelling & Software,26(12):1515-1525
Ostojski M S,Gebala J,Orlinska-Wozniak P,et al.2016.Implementation of robust statistics in the calibration,verification and validation step of model evaluation to better reflect processes concerning total phosphorus load occurring in the catchment[J].Ecological Modelling,332:83-93
Pastres R,Chan K,Solidoro C,et al.1999.Global sensitivity analysis of a shallow-water 3D eutrophication model[J].Computer Physics Communications,117(1/2):62-74
Rasmussen C E,Williams C K I.2005.Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)[M].Cambridge,MA:The MIT Press
Rigosi A,Marce R,Escot C,et al.2011.A calibration strategy for dynamic succession models including several phytoplankton groups[J].Environmental Modelling & Software,26(6):697-710
Ritter A,Muňoz-Carpena R.2013.Performance evaluation of hydrological models:Statistical significance for reducing subjectivity in goodness-of-fit assessments[J].Journal of Hydrology 480(4):33-45
Shahriari B,Swersky K,Wang Z,et al.2016.Taking the human out of the loop:a review of bayesian optimization[J].Proceedings of the IEEE,104(1):148-175
Snoek J,Larochelle H,Adams R P.2012.Practical bayesian optimization of machine learning algorithms[J].Advances in Neural Information Processing Systems,2:2951-2959
Song X,Zhang J,Zhan C,et al.2015.Global sensitivity analysis in hydrological modeling:Review of concepts,methods,theoretical framework,and applications[J].Journal of Hydrology,523:739-757
Stedinger J R,Vogel R M,Lee S U,et al.2008.Appraisal of the generalized likelihood uncertainty estimation (GLUE) method[J].Water Resources Research,44(12):1-10
宋晓猛,张建云,占车生,等.2015.水文模型参数敏感性分析方法评述[J].水利水电科技进展,35(6):105-112
Tang Y,Reed P,Wagener T,et al.2007.Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation[J].Hydrology and Earth System Sciences,11(2):793-817
Vanderbilt K,Porter J H,Lu S S,et al.2017.A prototype system for multilingual data discovery of International Long-Term Ecological Research (ILTER) Network data[J].Ecological Informatics,40:93-101
Wellen C,Kamran-Disfani A R,Arhonditsis G B.2015.Evaluation of the current state of distributed watershed nutrient water quality modeling[J].Environmental Science & Technology,49(6):3278-3290
王冰,刘晓威,王灵志,等.2016.基于IWIND-LR模型的河流突发性溢油事故模拟与应急响应分析[J].安全与环境工程,23(4):148-153
Yang J.2011.Convergence and uncertainty analyses in Monte-Carlo based sensitivity analysis[J].Environmental Modelling & Software,26(4):444-457
Yang J,Jakeman A,Fang G,et al.2018.Uncertainty analysis of a semi-distributed hydrologic model based on a Gaussian Process emulator[J].Environmental Modelling & Software,101:289-300
Yi X,Zou R,Guo H.2016.Global sensitivity analysis of a three-dimensional nutrients-algae dynamic model for a large shallow lake[J].Ecological Modelling,327:74-84
伊璇,郭怀成.2017.三维水动力水质模型不确定性研究[M].北京:科学出版社
张月霞,谢骏.2018.IWIND-LR模型在抚仙湖水位模拟中的应用[J].环境科学导刊,37(3):46-51
张质明,王晓燕,李明涛.2014.基于全局敏感性分析方法的WASP模型不确定性分析[J].中国环境科学,34(5):1336-1346
邹锐,苏晗,余艳红,等.2018.基于水质目标的异龙湖流域精准治污决策研究[J].北京大学学报(自然科学版),54(2):426-434
Zou R,Lung W S,Wu J.2007.An adaptive neural network embedded genetic algorithm approach for inverse water quality modeling[J].Water Resources Research,43(8):1-13
Zou R,Lung W S,Wu J.2009.Multiple-pattern parameter identification and uncertainty analysis approach for water quality modeling[J].Ecological Modelling,220(5):621-629
Zou R,Lung W S.2004.Robust water quality model calibration using an alternating fitness genetic algorithm[J].Journal of Water Resources Planning & Management,130(6):471-479
Zou R,Zhang X,Liu Y,et al.2014.Uncertainty-based analysis on water quality response to water diversions for Lake Chenghai:A multiple-pattern inverse modeling approach[J].Journal of Hydrology,514:1-14
Zwart J A,Hanson Z J,Vanderwall J,et al.2018.Spatially explicit,regional-scale simulation of lake carbon fluxes[J].Global Biogeochemical Cycles,32(9):1276-1293
Bae S,Seo D.2018.Analysis and modeling of algal blooms in the Nakdong River,Korea[J].Ecological Modelling,372:53-63
Bennett N D,Croke B F W,Guariso G,et al.2013.Characterising performance of environmental models[J].Environmental Modelling & Software,40:1-20
Borgomeo E,Farmer C L,Hall J W.2015.Numerical rivers:A synthetic streamflow generator for water resources vulnerability assessments[J].Water Resources Research,51(7):5382-5405
陈卫平,涂宏志,彭驰等.2017.环境模型中敏感性分析方法评述[J].环境科学,38(11):4889-4896
崔佳旭,杨博.2018.贝叶斯优化方法和应用综述[J].软件学报,29(10):3068-3090
Candelieri A,Perego R,Archetti F.2018.Bayesian optimization of pump operations in water distribution systems[J].Journal of Global Optimization,71(1):213-235
Chaudhary A,Hantush M M.2017.Bayesian Monte Carlo and maximum likelihood approach for uncertainty estimation and risk management:Application to lake oxygen recovery model[J].Water Research,108:301-311
Chinyama A,Ochieng G M,Nhapi I,et al.2014.A simple framework for selection of water quality models[J].Reviews in Environmental Science and Bio-Technology,13(1):109-119
Cibin R,Sudheer K P,Chaubey I.2010.Sensitivity and identifiability of stream flow generation parameters of the SWAT model[J].Hydrological Processes,24(9):1133-1148
Cornejo-Bueno L,Garrido-Merchan E C,Hernandez-Lobato D,et al.2018.Bayesian optimization of a hybrid system for robust ocean wave features prediction[J].Neurocomputing,275:818-828
邓帅.2019.基于改进贝叶斯优化算法的CNN超参数优化方法[J].计算机应用研究,36(7):1-2
Ghahramani Z.2015.Probabilistic machine learning and artificial intelligence[J].Nature,521(7553):452-459
Harmel R D,Smith P K,Migliaccio K W,et al.2014.Evaluating,interpreting,and communicating performance of hydrologic/water quality models considering intended use:A review and recommendations[J].Environmental Modelling & Software,57:40-51
姜龙,李一平,章双双等.2018.大型浅水湖泊藻类模型参数敏感性分析[J].湖泊科学,30(3):693-700
Jia H,Xu T,Liang S,et al.2018.Bayesian framework of parameter sensitivity,uncertainty,and identifiability analysis in complex water quality models[J].Environmental Modelling & Software,104:13-26
Jiang L,Li Y,Zhao X,et al.2018.Parameter uncertainty and sensitivity analysis of water quality model in Lake Taihu,China[J].Ecological Modelling,375:1-12
Jones D R.2001.A taxonomy of global optimization methods based on response surfaces[J].Journal of Global Optimization,21(4):345-383
Kavetski D,Fenicia F,Reichert P,et al.2018.Signature-domain calibration of hydrological models using approximate bayesian computation:Theory and comparison to existing applications[J].Water Resources Research,54(6):4059-4083
Kushner H J.1963.A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise[J].Journal of Fluids Engineering,86(1):97-106
Liang S,Jia H,Xu C,et al.2016.A Bayesian approach for evaluation of the effect of water quality model parameter uncertainty on TMDLs:A case study of Miyun Reservoir[J].Science of the Total Environment,560:44-54
Marchant R,Ramos F.2012.Bayesian Optimisation for Intelligent Environmental Monitoring[C].IEEE/RSJ International Conference on Intelligent Robots and Systems.Vilamoura,Algarve:2242-2249
Martinezcantin R.2014.BayesOpt:A bayesian optimization library for nonlinear optimization,experimental design and bandits[J].Journal of Machine Learning Research,15:3735-3739
Mckay M D,Beckman R J,Conover W J.2000.A comparison of three methods for selecting values of input variables in the analysis of output from a computer code M.D.Mckay[J].Technometrics,21(2):266-294
Mockus J,Tiesis V,Zilinskas A.1978.The Application of Bayesian Methods for Seeking the Extremum[M].Amsterdam:North-Holland
Morelli B,Hawkins T R,Niblick B,et al.2018.Critical review of eutrophication models for life cycle assessment[J].Environmental Science & Technology,52(17):9562-9578
Nash J E,Sutcliffe J V.1970.River flow forecasting through conceptual models part I — A discussion of principles[J].Journal of Hydrology,10(3):282-290
Nossent J,Elsen P,Bauwens W.2011.Sobol′ sensitivity analysis of a complex environmental model[J].Environmental Modelling & Software,26(12):1515-1525
Ostojski M S,Gebala J,Orlinska-Wozniak P,et al.2016.Implementation of robust statistics in the calibration,verification and validation step of model evaluation to better reflect processes concerning total phosphorus load occurring in the catchment[J].Ecological Modelling,332:83-93
Pastres R,Chan K,Solidoro C,et al.1999.Global sensitivity analysis of a shallow-water 3D eutrophication model[J].Computer Physics Communications,117(1/2):62-74
Rasmussen C E,Williams C K I.2005.Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)[M].Cambridge,MA:The MIT Press
Rigosi A,Marce R,Escot C,et al.2011.A calibration strategy for dynamic succession models including several phytoplankton groups[J].Environmental Modelling & Software,26(6):697-710
Ritter A,Muňoz-Carpena R.2013.Performance evaluation of hydrological models:Statistical significance for reducing subjectivity in goodness-of-fit assessments[J].Journal of Hydrology 480(4):33-45
Shahriari B,Swersky K,Wang Z,et al.2016.Taking the human out of the loop:a review of bayesian optimization[J].Proceedings of the IEEE,104(1):148-175
Snoek J,Larochelle H,Adams R P.2012.Practical bayesian optimization of machine learning algorithms[J].Advances in Neural Information Processing Systems,2:2951-2959
Song X,Zhang J,Zhan C,et al.2015.Global sensitivity analysis in hydrological modeling:Review of concepts,methods,theoretical framework,and applications[J].Journal of Hydrology,523:739-757
Stedinger J R,Vogel R M,Lee S U,et al.2008.Appraisal of the generalized likelihood uncertainty estimation (GLUE) method[J].Water Resources Research,44(12):1-10
宋晓猛,张建云,占车生,等.2015.水文模型参数敏感性分析方法评述[J].水利水电科技进展,35(6):105-112
Tang Y,Reed P,Wagener T,et al.2007.Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation[J].Hydrology and Earth System Sciences,11(2):793-817
Vanderbilt K,Porter J H,Lu S S,et al.2017.A prototype system for multilingual data discovery of International Long-Term Ecological Research (ILTER) Network data[J].Ecological Informatics,40:93-101
Wellen C,Kamran-Disfani A R,Arhonditsis G B.2015.Evaluation of the current state of distributed watershed nutrient water quality modeling[J].Environmental Science & Technology,49(6):3278-3290
王冰,刘晓威,王灵志,等.2016.基于IWIND-LR模型的河流突发性溢油事故模拟与应急响应分析[J].安全与环境工程,23(4):148-153
Yang J.2011.Convergence and uncertainty analyses in Monte-Carlo based sensitivity analysis[J].Environmental Modelling & Software,26(4):444-457
Yang J,Jakeman A,Fang G,et al.2018.Uncertainty analysis of a semi-distributed hydrologic model based on a Gaussian Process emulator[J].Environmental Modelling & Software,101:289-300
Yi X,Zou R,Guo H.2016.Global sensitivity analysis of a three-dimensional nutrients-algae dynamic model for a large shallow lake[J].Ecological Modelling,327:74-84
伊璇,郭怀成.2017.三维水动力水质模型不确定性研究[M].北京:科学出版社
张月霞,谢骏.2018.IWIND-LR模型在抚仙湖水位模拟中的应用[J].环境科学导刊,37(3):46-51
张质明,王晓燕,李明涛.2014.基于全局敏感性分析方法的WASP模型不确定性分析[J].中国环境科学,34(5):1336-1346
邹锐,苏晗,余艳红,等.2018.基于水质目标的异龙湖流域精准治污决策研究[J].北京大学学报(自然科学版),54(2):426-434
Zou R,Lung W S,Wu J.2007.An adaptive neural network embedded genetic algorithm approach for inverse water quality modeling[J].Water Resources Research,43(8):1-13
Zou R,Lung W S,Wu J.2009.Multiple-pattern parameter identification and uncertainty analysis approach for water quality modeling[J].Ecological Modelling,220(5):621-629
Zou R,Lung W S.2004.Robust water quality model calibration using an alternating fitness genetic algorithm[J].Journal of Water Resources Planning & Management,130(6):471-479
Zou R,Zhang X,Liu Y,et al.2014.Uncertainty-based analysis on water quality response to water diversions for Lake Chenghai:A multiple-pattern inverse modeling approach[J].Journal of Hydrology,514:1-14
Zwart J A,Hanson Z J,Vanderwall J,et al.2018.Spatially explicit,regional-scale simulation of lake carbon fluxes[J].Global Biogeochemical Cycles,32(9):1276-1293
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