基于极大熵原理的改进型地累积指数研究

Improvement of Geo-Accumulation Index Based on Maximum Entropy Principle

摘要: 由于采样误差、测量误差以及沉积物时空分布的不均匀性等因素的影响，在实际的环境调查中，沉积物的重金属浓度往往具有一定的不确定性，而传统的地累积指数难以处理这类问题。为解决这一问题，本研究首先基于极大熵原理，建立了改进的地累积指数模型。而后以洞庭湖的沉积物重金属污染评价为例，对两种模型的评价效果进行了比较。结果显示改进的地累积指数模型能够更好地处理实测值以区间形式表示的重金属污染评价问题，而且相对于传统的地累积指数模型，改进的地累积指数模型在等级识别和污染程度排序方面均更有优势。最后，本研究通过数学证明，揭示了两种模型的联系与区别：改进的地累积指数是传统地累积指数向不确定性分析的拓展和深化，而传统地累积指数本质上是改进的地累积指数在不确定区间宽度趋于0时的特例。

Abstract: For the sampling error, the measuring error, the inhomogeneity of minerals, and the other uncertain factors, in the practical environmental investigation, the concentrations of heavy metals in the sediments are often represented informs of intervals instead of accurate values. However, the conventional geo-accumulation index (CGI) cannot deal with these uncertainties in heavy metal pollution evaluation. To solve this problem, an improved geo-accumulation index (IGI) model is established based on the maximum entropy principle. The heavy metal pollution in the sediment in the Dongting Lake is evaluated as an illustration to compare the effects of these two models. The result shows that IGI has a better capacity in dealing with the heavy metals, the concentrations of which are represented informs of intervals, and an obvious advantage in the hierarchical recognition and the pollution degree schedule. At last, the mathematical relationship between these two models is revealed. IGI is the generalization of CGI into uncertainty analysis, while CGI can be regarded as a special case when the width of the uncertainty interval in IGI approximates to zero.