Local Prediction of Chaotic Time Series Based on Polynomial Coefficient Autoregressive Model

Su, Liyun; Li, Chenlong

doi:10.1155/2015/901807

Cited by 16 publications

(5 citation statements)

References 38 publications

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“…Although the nonlinear chaos behavior is the main challenge confronting the chaotic data series prediction, the underlying data generating mechanisms can still be explored by PSR theory [19]. By means of the ability of revealing the nature of dynamic system state, the PSR theory is useful in system characterization, in nonlinear prediction, and in estimating bounds on the size of the system [20,21].…”

Section: Data Samples Reconstruction Based On Psr Theorymentioning

confidence: 99%

A New Least Squares Support Vector Machines Ensemble Model for Aero Engine Performance Parameter Chaotic Prediction

Jia

Hao

2016

Mathematical Problems in Engineering

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Aiming at the nonlinearity, chaos, and small-sample of aero engine performance parameters data, a new ensemble model, named the least squares support vector machine (LSSVM) ensemble model with phase space reconstruction (PSR) and particle swarm optimization (PSO), is presented. First, to guarantee the diversity of individual members, different single kernel LSSVMs are selected as base predictors, and they also output the primary prediction results independently. Then, all the primary prediction results are integrated to produce the most appropriate prediction results by another particular LSSVM—a multiple kernel LSSVM, which reduces the dependence of modeling accuracy on kernel function and parameters. Phase space reconstruction theory is applied to extract the chaotic characteristic of input data source and reconstruct the data sample, and particle swarm optimization algorithm is used to obtain the best LSSVM individual members. A case study is employed to verify the effectiveness of presented model with real operation data of aero engine. The results show that prediction accuracy of the proposed model improves obviously compared with other three models.

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Section: Data Samples Reconstruction Based On Psr Theorymentioning

confidence: 99%

A New Least Squares Support Vector Machines Ensemble Model for Aero Engine Performance Parameter Chaotic Prediction

Jia

Hao

2016

Mathematical Problems in Engineering

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“…Garcia et al [2] proposed the GARCH forecasting model, which improved the accuracy of the prediction model. Additionally, in reference [3], a novel local nonlinear model based on phase space reconstruction, known as the Local Polynomial Coefficient Autoregressive Prediction (LPP) model, was introduced. The LPP model effectively captures the nonlinear characteristics of chaotic time series and exhibits a simple structure with good one-step prediction performance.…”

Section: Introductionmentioning

confidence: 99%

Based on the Improved PSO-TPA-LSTM Model Chaotic Time Series Prediction

Cai,

Feng,

Wang

2023

Atmosphere

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In order to enhance the prediction accuracy and computational efficiency of chaotic sequence data, issues such as gradient explosion and the long computation time of traditional methods need to be addressed. In this paper, an improved Particle Swarm Optimization (PSO) algorithm and Long Short-Term Memory (LSTM) neural network are proposed for chaotic prediction. The temporal pattern attention mechanism (TPA) is introduced to extract the weights and key information of each input feature, ensuring the temporal nature of chaotic historical data. Additionally, the PSO algorithm is employed to optimize the hyperparameters (learning rate, number of iterations) of the LSTM network, resulting in an optimal model for chaotic data prediction. Finally, the validation is conducted using chaotic data generated from three different initial values of the Lorenz system. The root mean square error (RMSE) is reduced by 0.421, the mean absolute error (MAE) is reduced by 0.354, and the coefficient of determination (R2) is improved by 0.4. The proposed network demonstrates good adaptability to complex chaotic data, surpassing the accuracy of the LSTM and PSO-LSTM models, thereby achieving higher prediction accuracy.

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“…It is demonstrated numerically that the M-MLP outperforms a standard NN in the Lorenz twin experiment. Recently this work has been developed by the same authors to a local polynomial autoregressive model [28] which shows a good performance in onestep prediction. A detailed numerical comparison between polynomial regression (PR) and NN has also been given in [29,30].…”

Section: Introductionmentioning

confidence: 99%

Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models

Cheng¹,

Chen²,

Anastasiou³

et al. 2022

Preprint

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Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional computational fluid dynamics (CFD) application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.

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Local Prediction of Chaotic Time Series Based on Polynomial Coefficient Autoregressive Model

Cited by 16 publications

References 38 publications

A New Least Squares Support Vector Machines Ensemble Model for Aero Engine Performance Parameter Chaotic Prediction

A New Least Squares Support Vector Machines Ensemble Model for Aero Engine Performance Parameter Chaotic Prediction

Based on the Improved PSO-TPA-LSTM Model Chaotic Time Series Prediction

Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models

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