Chaotic Time Series Prediction And Application Based On Extreme Learning Machine

Changes in the real world tend to be nonlinear and instability.The great majority of time series are chaotic.Chaotic time series which is the main research of nonlinear science,has been widely applied in daily life.Those numerical sequence which are appearing over time,such as temperature,share price and population.Those time series are closely related to human activities.Therefore,to study chaotic time series in depth has become one of the main effective tool to realize the movement rule of the real world.Collecting,sorting these chaotic time series,to applicate science approach forecasting the future evolution trend of system.Its effective to make scientific decisions,avoid unnecessary losses and maximizing revenue.Extreme learning machine is a feedforward network algorithm which has only one hidden layer.ELM has a lot of advantages,such as simple structure,understand principle and efficient learning,etc.It has achieved fruitful achievement in the field of prediction.Aiming to predict the chaotic time series,this paper mainly studies the optimization method of extreme learning machine algorithm,proposing an optimized extreme learning machine prediction model based on the traditional extreme learning with phase space reconstruction.Starting from the probability distribution of the output target of the extreme learning machine,the distribution of abnormal points and the distribution of normal points are separated,and the output distribution is designed as a robust mixed distribution.To solve the unknown parameters in the extreme learning machine using Bayesian inference and variational inference,avoid the tedious and huge computation of integrating the distributed likelihood function of the output.Considering the relationship between the abnormal point and normal point,choose the uniform distribution based the most value of the sample as the distribution of abnormal point.The BP neural network which has a similar feedforward structure like extreme learning machine and support vector regression machine are introduced to verify the prediction effect of the proposed model for chaotic time series.The Lorenz chaotic time series and the actual data sunspot number are used for the experiment.Finally,to avoid the disadvantages of traditional signal detection method such as suppression of useful signals,large amount of computation and lower sensitivity,apply the optimized extreme learning machine prediction model to signal detection.The results shows:(1)The optimal delay time of Lorenz and sunspot are 7 and 12 by autocorrelation method.The optimal embedding dimensions of Lorenz and sunspot are 6and 9 by Cao method.(2)It can be seen from MSE,MAE and MAPE that the optimized extreme learning machine proposed in this paper performs better than BP neural network and support vector regression machine in the prediction of Lorenz chaotic time series and actual sunspot data.Five points are randomly selected from each of the two data sets.It can be intuitively see the superiority of the optimized extreme learning machine in the prediction ability by comparing the absolute errors of the five points.(3)From the test evaluation index,accuracy,sensitivity and accuracy,the optimized extreme learning machine detection model performs better in single/double periodic pulse signals at the same SNR,compared with the single-layer neural network detection model and the linear regression detection model.The detection effect is obvious when the SNR is high.