基于贝叶斯推断的时变流场下污染源反演

Source Inversion in Time-Variant Flow Field Based on Bayesian Inference

摘要:

对5个不同位置的污染源分别做污染物扩散数值模拟，将其计算结果作为测量浓度；利用伴随方程计算时变流场下传感器的模拟浓度。通过测量浓度和模拟浓度构造似然函数，基于贝叶斯推断计算了在时变流场下污染源参数的后验概率。结果表明：污染源参数反演的误差取决于测量浓度与模拟浓度之间的误差。当污染源与传感器的距离较远时，污染源参数的后验概率呈较宽的分布，反演结果具有较大的不确定性；当污染源与传感器距离较近时，反演结果的不确定性得到了显著的降低。此外，还讨论了反演污染源参数时，利用污染物扩散不同阶段的测量数据对反演效果的影响。发现利用扩散初始阶段的测量浓度反演源位置，可以得到比利用稳定阶段数据时更小的反演误差和后验概率标准差，但效果没有得到显著提升。

关键词:污染物扩散;污染源反演;伴随方程;贝叶斯推断

Abstract:

In this paper， a numerical simulation of pollutant diffusion was conducted at five different locations and the results were taken as the measurement. The adjoint equation was used to calculate the simulated concentration of the sensors in time-variant flow field. The likelihood function was constructed by measurement and simulated concentration and the posterior probability of source parameters in time-varying flow field was calculated based on Bayesian inference. The results show that the errors of inversion of source parameters depend on the error between the measurement and the simulated concentration. When the distance between the source and the sensors is greater， the posterior probability of source parameters shows a wider distribution， indicating the larger uncertainty of the inversion result. When the source is closer to the sensors， the uncertainty of the inversion result is significantly reduced. In addition， the influence of measured data at different stages of pollutant diffusion in the process of inversion was also discussed. The inversion errors and the standard deviation of posterior probability are found to be smaller by using the measurement in the initial stage of diffusion than by using the data in the stable stage， but the improvement is not obvious.

Key words:pollutant dispersion;pollution source inversion;adjoint equation;Bayesian inference