Research On Pollution Source Inversion Based On Fractional Order Anomalous Diffusion Equation

The pollution of the environment come into sight and become the focus of the public. The accurate verification of sea water quality model in ecology is an urgent problem. The shortage of pollution source’s background information, uncertainty of pollution source location, less understanding of sea biochemical process and other external conditions are factors that hinder the successful solution of the sea water quality model. The pollution source inversion of the river has become a research object of many scholars.The diffusion phenomenon of river pollution source is anomalous diffusion phenomenon, which is a kind of non Markovian and nonlocality movement. The movement process is involved the time and space correlation, we can describe it by fractional order anomalous diffusion equation. A global optimization algorithm--niche ant colony algorithm based on sharing fitness value(NACA) can be used in mathematical optimization model. We apply niche ant colony algorithm based on sharing fitness value(NACA) to discuss the parameter inversion of the fractional order anomalous diffusion equation.Firstly, we apply the basic ant colony algorithm(ACA) and niche ant colony algorithm based on sharing fitness value(NACA) to multi-modal function optimization to get the local and global optimal solutions in this thesis. In global optimization, optimization results of niche ant colony algorithm based on fitness sharing is compared with the optimization results of the standard binary encoded genetic algorithm(SGA), then we can get a conclusion that the former algorithm has advantages of high precision, fast convergence speed and easy to realize. Secondly, we apply niche ant colony algorithm based on fitness shari ng to inversion the diffusion coefficient and convection coefficient, source and fractional number of the fractional order anomalous diffusion equation.Then we successfully invert single, two and three parameters with high precision, then we validate the strong anti-noise properties of the method. Finally, based on inversion of three parameters in fractional order anomalous diffusion equation, we analyze the sensitivity of the equation, including the global transition probabilities, pheromone evaporation coefficient, and the number of iterations. We find that the accuracy of inversion is affected by the global transition probabilities and pheromone evaporation coefficient mainly, the number of iterations less.