Prediction To Chaotic Time Series Based On Genetic Algorithm

Chaos phenomenon is extremely universal in our daily life. Normal phenomenasuch as the continuously change of temperature and the seasonal explode of sunspotare all chaos phenomenon. It’s rather difficult for us to construct a model that is goodenough to predict what would be next based on the data of partial chaos series that wehave, but once we construct a model of that kind, it’d be very useful for us to live abetter life. So, it’s the mission of this research to construct a model which is goodenough to predict future data of the sequence based on the sequence that we have.BP Algorithm is used to perform the prediction of Chaotic Time Series, but themodel that BP Algorithm construct may not be wonderful in predicting Chaotic TimeSeries because it’s BP Algorithm’s character to reach locally optimal solution muchmore easily than to reach globally one. So, in the essay, we use the Genetic Algorithm,which is more efficient in finding globally optimal solution, to optimize theBP-Algorithm, expecting to get a better model in predicting Chaotic Time Series. Andthe essay implement the GA-BP Algorithm and apply it to construct the predictingmodel, then evaluate the effectiveness of the model and raise some aspect to beoptimized.When the progress of phase space reconstruction is performed,2variables,called m and tau, which are short from embedding dimension and time delay, areextremely important. We use self correlation function to get the value of tau, then usea method called False Nearest Neighbor to calculate the embedding dimension ofchaotic sequence, thus we can reconstruct a m-dimensional sequence which is the realseries of chaotic motion. Using the real sequence, we can start out prediction with BPAlgorithm optimized by Genetic Algorithm. prediction base on BP Algorithm is oneof the method to preict chaotic seriese, but sometimes it’s not working very well. GA,short from Genetic Algorithm, is the imitation of evolution in the nature, so wenaturally think about optimizing BP Algorithm with GA. We initialize a model topredict the next data of chaotic series and then evaluate this model. If the difference istoo great, we should begin to modify our model according to the algorithm and theresult of the train, otherwise, the current model is the best model that we are lookingfor. With the model we constuct during the experiment, we can begin our prediction.BP Algorithm optimized by GA is not suitable for every chaotic series, but thereis no doubt that we can predict well if the model that we construct through ourtraining progress is good enough.