| The thesis is related to applications of genetic algorithms (GAs) in the fitting of models to electrochemical impedance data. GAs, a kind of modem optimization algorithm, are called after their similarity to evolutionary processes in nature. Although GAs have been widely applied in many fields including chemistry, the applications in electrochemistry, especially in the fitting of models to electrochemical impedance data, are few still. Therefore, the thesis aims at using GAs to fit models to electrochemical impedance data.There are mainly four parts in the thesis, which are described as follows.1.The comparison between traditional optimization algorithms. Six traditional optimization algorithms are compared with each other. A conclusion is drawn that if the good initial estimates of parameters are provided, Gauss-Newton method will be the best one, which has the highest operational efficiency and the best convergence.2.The analysis of GAs. The chapter makes a brief introduction to GAs. The selection of genetic operators and the definition of the operational parameters for GAs are completed. The genetic algorithms in this thesis adopt the commonly used proportional model, arithmetic crossover operation, and uniform mutation operation.3.The building of the hybrid GAs for the fitting of models to electrochemical impedance data. The chapter describes the combination modes of the hybrid GAs. A hybrid GA is described in detail, whose flow chart is also shown.4.A GA for the fitting of models to electrochemical impedance data. Because Jacobi matrixes are not always easy to build and the inverse of matrixes can be got only when Jacobi matrixes are not singular, it is very necessary to try using a modified GA alone to fit models to electrochemical impedance data. Such a GA is put forward in this chapter.The following are the conclusions drawn from this thesis.1.Generally speaking, the model/data set combinations of electrochemical impedance spectra are usually on strong nonlinear behavior. Therefore, there is probably more than one minimum on the response surface for the regression process of a model/data set combination. The good initial estimates of parameters should be provided in order that the nonlinear regression can converge to a correct minimum.2.Because evolutionary algorithms are based on randomness theory andtheir searching processes are of population searching, the range of the initial estimates of model parameters can be very wide. This is a prerequisite for the automatic production of good initial parameters. Most of the conventional nonlinear regression algorithms adopt deterministic searching patterns, and need good initial estimates of parameters. But, once entering the convergence domain, the iteration will become convergent quickly. Therefore, their efficiency is higher. If the random selection based on probability and the nonlinear regression based on determinacy combine to form a hybrid genetic algorithm, the advantages of the two kinds of algorithms can be integrated. The processing rules of the hybrid algorithm should be as simple as possible and have high universality.3.When such a hybrid algorithm is used for processing electrochemical impedance spectra data, the main problem which should be solved is that once the 6 optimum values from the evolutionary computation of an algorithm fall into a local minimum region, the algorithm should make the optimum values jump out the region. If the usual evolutionary computation is not modified, the global operation efficiency of the hybrid algorithm will be very low, and the probability that the operation by the hybrid algorithm will fail can not be considered a minimum.4.Modifying the mutation operation of a usual evolutionary algorithm is helpful to making a group of 6 Oftimum values enter the convergence domain of the Gauss-Newton iteration as quickly as possible. But, too big or too small a mutation rate is not helpful to either ensuring the diversity of the individuals of a... |
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