Research On The Pollutant Concentration Model Based On Gray System Theory

The worsening pollution situation of water affects our daily life and the economic development. Governance and management of the water pollution become generally concerned about as environmental issues. Study of the pollutants'diffusion law and concentration distribution in the water body of rivers can provide theoretical basis for calculation of the water body's pollutant carrying capacity,formulation the planning and management of pollution control programs.Mathematical models of the water quality are the description of the pollutants'spatial and temporal diffusion process, and they are powerful tools for study of the pollutants'diffusion law and concentration distribution in the water body. However, at present, most of the water quality models are mechanism models which base on the deductive modeling method, they always demand for high technical requirements and lots of computing workload. So the gray system modeling method was introduced into this paper, and the inductive modeling technique was used to set up a pollutant concentration model from observed data of pollutant concentration sequence. The contents of this paper mainly include the following parts: 1)The pollutants'transport and diffusion process in the river was studied,The common grey models,methods and steps of gray forecast were introduced;2)Models which are used for gray forecast and their solving methods were improved , that's mainly includes using the least squares method to solute GM(1,1),GM(2,1),the grey verhulst model and the improvement of GM(2,1);3)Aimed at the characteristic of observed data sequence, the forecasting of data sequence with mutation and the modeling method of non-equidistant data sequence are researched;4)A tracer experiment in the river was designed, which collects data for the parameter calibration and validation of the model;5)The non-equidistance sequence modeling method which has been presented in this paper was used in the simulation and forecast of pollutant concentration in actual rivers, continuous time response function expressions of the pollutant concentration were obtained, not only that, but by backstepping the pollutant concentration model ,the initial pollutant concentration and the general attenuation coefficient can be got, which provides an effective method for other models'parameter calibration.