Application of Wavelet Fractal Dimension Estimation in Dividing Flood Stages for Three Gorges Reservoir
Abstract Limit water level control improves water resources utilization efficiency without reducing flood control standard, while the premise is to divide the discharge series into a number of different flood stages. Db4 is selected as wavelet base, based on Mallat algorithm, put forward the model of wavelet dimension estimation method and calculated the fractal dimension of floods at the Yichang station, got the flood periods of Three Gorges reservoir. The results indicate that the method of wavelet dimension estimation can obtain the same result as traditional methods, and it has the merit of simplicity and stability. As a feasible and effective tool, the wavelet dimension estimation method is recommended in the applications of dividing flood periods.
Parameter estimation of modified gray model GM (1, N) and model application
Abstract The GM (1, N) model is an important prediction model among gray models, but the conventional GM (1, N) model shows big errors sometimes mainly due to the structural inconsistency between the gray differential equation for parameter estimation and the whitening equation for prediction. The paper derives the modified model of conventional gray differential equation based on the whitening equation, and the gray differential equation obtained in this way has the structure basically consistent with the structure of whitening equation. The paper estimates parameters with the gray differential equation of modified GM (1, N) model and gives three parameter estimation methods with different background values. The time response equation for conventional GM (1, N) model generally has no analytical solution, but the paper gives a specific solving method for the time response equation of modified model. The example proves that the modified GM (1, N) model given and the models built with the methods proposed improve the simulation and prediction accuracy significantly compared with the conventional model.
Multi-method determination of the fractal dimension of hematite aggregates
The utilisation of the fractal concept has greatly improved our ability to describe the structure of colloidal aggregates and our understanding of their formation mechanisms. We have determined the fractal dimension of KCl-induced hematite aggregates using three different approaches: (i) dynamic scaling, (ii) TEM image analysis and (iii) static light scattering (SLS). In the regime of diffusion limited aggregation ([KCl] > 100 mM), analysis of TEM images of 70 aggregates, whose longest dimension varies more than 40 fold, yields the lower limit of the fractal dimension as 1.68 ± 0.04. Direct scaling of the mean hydrodynamic size of the aggregates measured by photon correlation spectroscopy gives the upper limit of the fractal dimension as 1.87 ± 0.07. The value obtained by static light scattering as 1.83 ± 0.07. In the reaction limited regime, SLS measurements yield a fractal dimension of 2.2 ± 0.1. These results suggest the aggregates grow mainly through collision with other aggregates, rather than through the addition of primary particles.