蒙特卡罗不确定性分析在受体模型来源解析中的应用

Uncertainty analysis of source apportionment by Monte Carlo methods:A case study of factor analysis with non-negative constraints

利用蒙特卡罗模拟和虚拟数据矩阵对一种受体模型(非负约束的因子分析模型)来源解析结果的不确定性进行了分析.假设多氯联苯(PCBs)产品Arolcor1016,Aroclor1248和Aroclor1260为PCBs的3个主要污染源,并设定它们在40个样品中的贡献值,由此组成一个有25种PCBs系列物和40个样品的虚拟数据矩阵,通过对每个PCBs系列物依次取变异系数(Cv)0.1,0.2,0.4和0.6,以考察输入参数的不确定性对非负约束的因子分析模型输出结果的影响,模型以随机数组为输入数据运行1000次,对输出结果进行统计分析得到均值和标准偏差等指标.通过本研究表明,当Cv在0.4之内时,模型能够较为准确地解析出主要污染源的指纹谱图和贡献率,在输入数据为正态分布的情况下,输出结果也呈正态分布,说明非负约束的因子分析模型有较好的稳健性.受体模型解析结果的不确定性主要受到输入参数误差、污染源指纹谱图的相关性等因素的影响.

Monte Carlo simulations were used to evaluate the uncertainties of a receptor model by factor analysis with non-negative constraints and an artificial data set. The Aroclors were assumed to be the main sources of the polychlorinated biphenyls （PCBs）. The Aroclors considered were Aroclor 1016, Aroclor 1248 and Aroclor 1260. The 25 PCB congeners covered the entire range of molecular weights and some congeners were unique to individual Aroclors. The postulated source contributions were developed from 40 postulated samples. The coefficients of variation （Cv） of PCB congeners used for the Monte Carlo simulations were 0.1, 0.2, 0.4 and 0.6. The simulations were repeated 1000 times with randomly selected values. The results indicated that if the Cv values were less than 0.4, the receptor model was able to reproduce the source profiles and contributions well. For normally distributed input parameters, the results were also normally distributed, indicating the robustness of the model.