• 关键词：水质模型  参数估值  贝叶斯优化  高斯过程  采集函数

• 基金项目：云南省科技厅科技计划重点研发项目（No.2018BC001）

• 任婷玉
• 北京大学环境科学与工程学院, 水沙科学教育部重点实验室, 北京 100871

• 梁中耀
• 北京大学环境科学与工程学院, 水沙科学教育部重点实验室, 北京 100871

• 刘永
• 北京大学环境科学与工程学院, 水沙科学教育部重点实验室, 北京 100871

• 邹锐
• 1. 北京大学环境科学与工程学院, 水沙科学教育部重点实验室, 北京 100871;2. 北京英特利为环境科技有限公司, 锐思计算智能实验室(RCIL), 北京 100085;3. 南京智水环境科技有限公司, 南京 210012

• 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.

• Abstract：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.

• Key words：water quality model  parameters estimation  Bayesian optimization  Gaussian process  acquisition function

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