Broad Echo State Network with Reservoir Pruning for Nonstationary Time Series Prediction.

Wenjie Liu,Xiaoyi Wang,Jianlei Kong,Yuting Bai,Tingli Su,Xuebo Jin,Alexander Hošovský

doi:10.1155/2022/3672905

Wenjie Liu, Xiaoyi Wang + Show 5 more

Open Access

https://doi.org/10.1155/2022/3672905

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Abstract

The nonstationary time series is generated in various natural and man-made systems, of which the prediction is vital for advanced control and management. The neural networks have been explored in the time series prediction, but the problem remains in modeling the data's nonstationary and nonlinear features. Referring to the time series feature and network property, a novel network is designed with dynamic optimization of the model structure. Firstly, the echo state network (ESN) is introduced into the broad learning system (BLS). The broad echo state network (BESN) can increase the training efficiency with the incremental learning algorithm by removing the error backpropagation. Secondly, an optimization algorithm is proposed to reduce the redundant information in the training process of BESN units. The number of neurons in BESN with a fixed step size is pruned according to the contribution degree. Finally, the improved network is applied in the different datasets. The tests in the time series of natural and man-made systems prove that the proposed network performs better on the nonstationary time series prediction than the typical methods, including the ESN, BLS, and recurrent neural network.

Highlights

Time series data is observed and measured over time in human society and the natural environment. e analysis and prediction of the time series data have drawn attention because it is vital for managing and controlling various manmade and natural systems
The prediction of sales data is applied to optimize inventory and reduce social costs [1]. e stock data prediction can foresee the capital flows trend [2]. e precipitation [3], water bloom [4], and typhoon intensity are predicted for natural environment protection and disaster prevention [5]. e trend forecast of air pollutants provides strong support for the decisionmaking of relevant departments in the future [6–8]. e nonstationary and nonlinear trend has been the obvious feature of time series data in various application contexts
One dataset is the air quality monitoring data of Fangshan District in Beijing, and the other is the power load data of the United States. e two datasets represent the different systems, of which the air quality data is from the natural environment, and the power load data is from the man-made system. e data can be regarded as the typical time series in the common systems

Summary

Introduction

Time series data is observed and measured over time in human society and the natural environment. e analysis and prediction of the time series data have drawn attention because it is vital for managing and controlling various manmade and natural systems. E analysis and prediction of the time series data have drawn attention because it is vital for managing and controlling various manmade and natural systems. E nonstationary and nonlinear trend has been the obvious feature of time series data in various application contexts. It is impossible to extract and represent data trends intuitively because the change rule of the time series is stochastic and complex. It has been a research issue how to extract the data features and predict the future trend of the time series. For the mainstream of time series prediction, there are statistical methods [9–11] and machine learning methods [12–16]. Statistical prediction methods mainly include the autoregressive (AR) model, moving average (MA) model, autoregressive moving average (AR-MA) model, and differential autoregressive moving average (ARIMA) model integration, etc. ey transform nonstationary time series into stationary time series utilizing variance or integration

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Discussion

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