Computational Intelligence Based Chaotic Time Series Prediction Using Evolved Neural Network

The prediction accuracy and generalization ability of neural/neurofuzzy models for chaotic time series prediction highly depends on employed network model as well as learning algorithm. In this study, several neural and neurofuzzy models with different learning algorithms are examined for prediction of several benchmark chaotic systems and time series. The prediction performance of locally linear neurofuzzy models with recently developed Locally Linear Model Tree (LoLiMoT) learning algorithm is compared with that of Radial Basis Function (RBF) neural network with Orthogonal Least Squares (OLS) learning algorithm, MultiLayer Perceptron neural network with error back-propagation learning algorithm, and Adaptive Network based Fuzzy Inference System. Particularly, cross validation techniques based on the evaluation of error indices on multiple validation sets is utilized to optimize the number of neurons and to prevent over fitting in the incremental learning algorithms. To make a fair comparison between neural and neurofuzzy models, they are compared at their best structure based on their prediction accuracy, generalization, and computational complexity. The experiments are basically designed to analyze the generalization capability and accuracy of the learning techniques when dealing with limited number of training samples from deterministic chaotic time series, but the effect of noise on the performance of the techniques is also considered. Various chaotic systems and time series including Lorenz system, Mackey-Glass chaotic equation, Henon map, AE geomagnetic activity index, and sunspot numbers are examined as case studies. The obtained results indicate the superior performance of incremental learning algorithms and their respective networks, such as, OLS for RBF network and LoLiMoT for locally linear neurofuzzy model.

Long-term prediction of chaotic time series is very difficult, for the chaos restricts predictability. In this paper a new method is studied to model and predict chaotic time series based on minimax probability machine regression (MPMR). Since the positive global Lyapunov exponents lead the errors to increase exponentially in modelling the chaotic time series, a weighted term is introduced to compensate a cost function. Using mean square error (MSE) and absolute error (AE) as a criterion, simulation results show that the proposed method is more effective and accurate for multistep prediction. It can identify the system characteristics quite well and provide a new way to make long-term predictions of the chaotic time series.

The prediction of chaotic time series can well describe the physical properties and influencing factors of a sequence of numerical data points in successive order and has played an increasingly crucial role in various scientific and engineering communities. These time series data require the prediction model to have strong dynamic feature representation ability, which often leads to excessive calculation burden. As an emerging and effective learning method, a broad learning system (BLS) can be trained quickly by incremental learning, and the system can be reconstructed without requiring a lengthy retraining process, which has been shown to facilitate superior time-saving performance. However, the historical information of time series data is often ignored, resulting in the lack of dynamic feature representation ability of the original BLS algorithm. In this article, a novel intergroup cascade BLS (ICBLS) method and its variant with optimized parameters, termed MOICBLS, are proposed, which can combine the previous knowledge with current information to determine the output results by constructing a novel intergroup cascade structure for the enhancement nodes. The new algorithms try to retain the time-saving advantage of BLS and greatly enhance the extraction ability of dynamic features of chaotic time series data. In addition, it cannot be ignored that the network structure parameters have an unquestionable impact on the performance of a BLS. In response, two conflicting goals of prediction accuracy and diversity are formulated as multiobjective optimization functions in the training phase to generate the optimized network structure parameters needed by multiple candidate models. The experimental results on two benchmark chaotic time series dataset, the Lorenz system and Rossler system, and a geomagnetic disturbance storm time chaotic time series dataset demonstrate that our proposed algorithms are effective for prediction of chaotic time series, and the prediction accuracy is better than some existing approaches.

One of the features of deterministic chaos is sensitive to initial conditions. This feature limits the prediction horizons of many chaotic systems. In this paper, we propose a new prediction technique for chaotic time series. In our method, some neighbouring points of the predicted point, for which the corresponding local Lyapunov exponent is particularly large, would be discarded during estimating the local dynamics, and thus the error accumulated by the prediction algorithm is reduced. The model is tested for the convection amplitude of Lorenz systems. The simulation results indicate that the prediction technique can improve the prediction of chaotic time series.

The prediction of chaotic time series is an important research issue. To improve the prediction accuracy, a hybrid approach called WNN-PSO is proposed, which based on the self-learning ability of wavelet neural network, whose parameters are optimized by particle swarm optimization. The WNN-PSO method has higher prediction accuracy, fast convergence, and heightens the ability of jumping the local optimums. The experiment results of the prediction for chaotic time series show the feasibility and effectiveness of the proposed method. Compared with wavelet neural network and BP neural network, the proposed method are superior to them. Finally, the WNN-PSO is applied to predict the life energy consumption of china in our lives.

The prediction of chaotic time series with neural networks is a traditional practical problem of dynamic systems. This paper is not intended for proposing a new model or a new methodology, but to s...

A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically.

Configuring radial basis function network using fractal scaling process with application to chaotic time series prediction

Chaotic systems are complex dynamical systems that play a very important role in the study of the atmosphere, aerospace engineering, finance, etc. To improve the accuracy of chaotic time series prediction, this study proposes a hybrid model CEEMDAN-LSTM which combines Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and long short-term memory (LSTM). In the model, the original time series is decomposed into several intrinsic mode functions (IMFs) and a residual component. To reduce the difficulty of predicting chaotic time series and provide a high level of predictive accuracy, the LSTM prediction model is built for all each characteristic series from CEEMDAN deposition. Finally, the final prediction results are obtained by combining all the prediction sequences. To test the effectiveness of this model we proposed, we examined the CEEMDAN-LSTM model using the Lorenz-63 system. Further compared to Autoregressive Integrated Moving Average (ARIMA ), Support Vector Regression (SVR), multilayer perceptron (MLP), and the single LSTM model, the results of the experiment show that the proposed model performs better in the prediction of chaotic time series. Besides, the hybrid model proposed in this paper has better results than the LSTM model alone. Therefore, hybrid models based on deep learning methods and signal decomposition methods have great potential in the field of chaotic time series prediction.

High rock slope engineering is typical nonlinear system, its evolution process is chaotic, dissipated and uncertain. Chaotic system can’t be forecasted for long-term and needs discuss about maximum time scale of predictability. Nonlinear theory is proposed to research maximum time scale of predictability of safety monitoring chaotic time series and construct the model APSO-RBFNN to predict the chaotic time series in maximum time scale of predictability. The largest Lyapunov exponent and maximum time scale is calculate with small data sets method. In the maximum time scale of predictability, the essay applies APSO-RBFNN to chaotic time series for risk assessment. The engineering cases studies reveal that the forecasting values are in good agreement with the measured values and this model has high accuracy and a good prospect for risk assessment of nonlinear chaotic time series of geotechnical engineering.

In this paper, an evaluation of various discriminant neural networks classifiers for text- independent speaker verification problem is presented. Each person to be verified has a personalized neural network model. A new classifier called neural tree network (NTN) is also examined for this application. The memoryless feedforward neural network architecture makes decisions based on static features. Time delay neural network (TDNNs) have proved to be an efficient way to handle the dynamic nature of speech. Furthermore, a model called recurrent time delay neural networks (RTDNNs), obtained through a local feedback connection at the first hidden layer level of TDNNs is investigated. The training is carried out by backpropagation for sequence algorithm. The database used is a subset of the TIMIT database consisting of 38 speakers from the same dialect region. The NTN is compared with the MLP, TDNN, and RTDNN. It is shown that NTN is found to perform better than the other neural networks classifiers. Also, a little bit performance improvement was achieved due to the addition of temporal information for text-independent speaker verification problem using TDNNs and RTDNNs. Finally, we described the experimental results obtained using different neural network models.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

This chapter predicts the chaotic ferroresonance time series model by the dynamic fuzzy neural network (D-FNN). Through modeling chaotic system and analysis of the results of the chaotic model, the purpose of understanding the chaotic system and control has been successfully achieved. The method does not rely on the deterministic equations and initial conditions of chaotic time series. On the basis of given training data, we use reconstruction methods for data processing and initialization. Next, we make prediction with combination of the data and the dynamic fuzzy neural network. Experiments show that this method has preferable predictive ability and accuracy. The prediction obtains satisfactory results.

Prediction and analysis of chaotic time series on the basis of support vector

In this paper, an integrated model based on efficient extreme learning machine (EELM) and differential evolution (DE) is proposed to predict chaotic time series. In the proposed model, a novel learning algorithm called EELM is presented and used to model the chaotic time series. The EELM inherits the basic idea of extreme learning machine (ELM) in training single hidden layer feedforward networks, but replaces the commonly used singular value decomposition with a reduced complete orthogonal decomposition to calculate the output weights, which can achieve a much faster learning speed than ELM. Moreover, in order to obtain a more accurate and more stable prediction performance for chaotic time series prediction, this model abandons the traditional two-stage modeling approach and adopts an integrated parameter selection strategy which employs a modified DE algorithm to optimize the phase space reconstruction parameters of chaotic time series and the model parameter of EELM simultaneously based on a hybrid validation criterion. Experimental results show that the proposed integrated prediction model can not only provide stable prediction performances with high efficiency but also achieve much more accurate prediction results than its counterparts for chaotic time series prediction.

Long-term prediction of sunspot activity is of great importance for the space activity, communication, disaster prevention and so on. Cumulative error is main shortcoming of weighted one-rank local-region forecasting model for multi-steps prediction of chaotic time series. The radial basis function neural network forecasting model based on phase reconstruction is presented for chaotic time series prediction. The model is applied to the prediction of smoothed monthly mean sunspot numbers for the 22nd and 23rd sun cycles, and compared them with the observations. The results indicate that the mean absolute errors are 5.47 and 2.82, 15 to the maximum in absolute errors, and the mean relative errors are 5.45% and 4.60%, 15.00% to the maximum in relative errors. These results show that this prediction method can be successfully used to predict the smoothed monthly mean sunspot numbers. The predicted maximal smoothed monthly mean sunspot number is 104.77 that will appear in January 2013 for 132 months of cycle 24 from January 2009 to December 2019.