基于河流示踪实验的Bayes污染溯源:算法参数、影响因素及频率法对比

Applicability of Bayesian inference approach for pollution source identification of river chemical spills: A tracer experiment based analysis of algorithmic parameters, impacts and comparison with Frequentist approaches

基于贝叶斯理论,结合浓度时间序列方差假定和Adaptive Metropolis MCMC后验采样,建立了用于突发水污染应急溯源的贝叶斯推理方法.该方法结合经验知识和监测事实对源项参数的分布进行推理,直接对溯源结果的反向不确定性用概率分布形式进行表征.依据河流实地示踪剂实验案例,对Bayesian推理溯源的实际效果、后验参数相关性和影响因素等方面进行了验证和测试,结果表明源项参数和方差的后验概率密度的偏度对方差假定敏感,且得到关键参数推荐值:使用RMSE为目标函数;异方差假定中稳定化因子λ1为0,λ2为0.1~0.5;AM采样建议比例因子sd选择0.1~0.3.并对贝叶斯方法和传统基于优化的频率法在求解思路、计算过程、溯源结果等角度进行了深层次的辨析.本研究相关结果为贝叶斯推理技术在污染溯源的实际应用中提供了较为重要的参考价值.

Based on Bayes theorem and combined variance assumptions on pollutant concentration time series with Adaptive-Metropolis sampling, a modular Bayesian approach was established targeting at pollutant source identification during spills. This probability approach updated the prior knowledge on source information by combining experiments and monitoring and was able to directly characterize uncertainty due to the inversion process by probability distribution. Source inversion test results from field tracer experiments were investigated to determine the validity of this Bayesian inference approach, correlation of posterior parameter and impact factors. Results indicate that Bayesian approach was successful in identifying the source parameters and could effectively reduce the emergency decision risks. It is shown that the skewness of posterior distribution of source parameters and variation were sensitive to assumed variance. Using RMSE as objective function, test results also suggested that the default parameters for the established Bayesian source inversion method, were as follows： heteroscedasticity setting stabilization factors λ1 = 0, and λ2 = 0.1-0.5, and AM sampling proposal scale factor sd=0.1-0.3. Comparisons between the Bayesian approach and optimization approach on aspects of solution methodology, computing process and inverse results were made and differentiation were highlighted. This work provides valuable references for the practical usage of Bayesian approach in surface water pollution source identification.