Use of a quantile regression based echo state network ensemble for construction of prediction Intervals of gas flow in a blast furnace

Lv, Zheng; Zhao, Jun; Liu, Ying; Wang, Wei

doi:10.1016/j.conengprac.2015.10.003

Cited by 37 publications

(7 citation statements)

References 18 publications

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“…Because RMSE, MAE and MAPE all reflect the deviation between the actual value and the predicted value, so smaller index value of them stands for better model predictive performance. RMSE index is used as fitness function in equation (13).…”

Section: Algorithm Implementationmentioning

confidence: 99%

“…In [12], Rabin et al used a linear learning method based on the nonlinear monotone function to build a multi-reservoirs echo state network model, which has better prediction performance than single reservoir. Lv et al [13] proposed an ESN ensemble modeling method based on quantile regression (QR), which builds one reservoir for each group samples after using the QR method to divide the original data set into many subsets and then output an integrate result. For the problem of prognostics and health management (PHM), Zhong et al [9] proposed an echo state network model with two reservoirs, of which one reservoir is used to build model of the sensor data sequence and the other is used to build model of the state parameter data sequence.…”

Section: Introductionmentioning

confidence: 99%

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Network Traffic Prediction Using Variational Mode Decomposition and Multi- Reservoirs Echo State Network

Han

Jing

et al. 2019

IEEE Access

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The network traffic prediction is significant for the network load pre-warning and network congestion control. But the nonlinearity and nonstationarity of the actual network traffic data would reduce the prediction accuracy. In this paper, an optimized network traffic prediction method using variational mode decomposition (VMD) and multi-reservoirs echo state network (ESN) is presented. VMD method has advantages of reducing the signal transmission errors, removing the mode aliasing, and decreasing the degree of endpoint effects. However, VMD needs to preset the number of modes and the iterative factor, which are mainly decided by subjective experiences. In order to solve this, an optimized VMD method is proposed, and then a multi-reservoirs echo state network based prediction model is constructed. The main works are as follows: First, VMD is used to decompose the original network traffic data into several subsets; then, multiple subreservoirs are built after the phase space reconstruction (PSR) of each data subset; finally, the training set is used to train the prediction model. Moreover, in the training process, an improved fruit fly optimization algorithm (IFOA) is proposed combined with the levy's flight function and the cloud generator, which is used to optimize some model parameters. Compared with several prediction models, the proposed VMD-IFOA-ESN has better predictive stability and convergence performance. Three WIDE backbone network traffic data sets with different time intervals verify the effectiveness of the proposed prediction model. INDEX TERMSEcho state network, fruit fly optimization algorithm, multiple reservoirs, network traffic prediction, time series analysis, variational modal decomposition.

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Section: Algorithm Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Network Traffic Prediction Using Variational Mode Decomposition and Multi- Reservoirs Echo State Network

Han

Jing

et al. 2019

IEEE Access

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“…where S is the transpose of S, λ is a regularization parameter, I is an identity matrix and Y is a (T − θ) × k matrix with the actual outputs, that is {x(t)} t=(θ+1),...,T . Additionally, in order to obtain prediction intervals, in [53], an ESN ensemble is proposed using Quantile Regression (QR) [54] to calculate the output layer weights of each network. This technique is supported by the fact that quantiles associated with a random variable Y, of order τ, are position measures that indicate the value of Y to reach a desired cumulative probability τ, that is,…”

Section: The Matrix Is Updated Asmentioning

confidence: 99%

Wind Power Forecasting Based on Echo State Networks and Long Short-Term Memory

et al. 2018

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Wind power generation has presented an important development around the world. However, its integration into electrical systems presents numerous challenges due to the variable nature of the wind. Therefore, to maintain an economical and reliable electricity supply, it is necessary to accurately predict wind generation. The Wind Power Prediction Tool (WPPT) has been proposed to solve this task using the power curve associated with a wind farm. Recurrent Neural Networks (RNNs) model complex non-linear relationships without requiring explicit mathematical expressions that relate the variables involved. In particular, two types of RNN, Long Short-Term Memory (LSTM) and Echo State Network (ESN), have shown good results in time series forecasting. In this work, we present an LSTM+ESN architecture that combines the characteristics of both networks. An architecture similar to an ESN is proposed, but using LSTM blocks as units in the hidden layer. The training process of this network has two key stages: (i) the hidden layer is trained with a descending gradient method online using one epoch; (ii) the output layer is adjusted with a regularized regression. In particular, the case is proposed where Step (i) is used as a target for the input signal, in order to extract characteristics automatically as the autoencoder approach; and in the second stage (ii), a quantile regression is used in order to obtain a robust estimate of the expected target. The experimental results show that LSTM+ESN using the autoencoder and quantile regression outperforms the WPPT model in all global metrics used.

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“…The goal of the optimization is to achieve the PIs of the best quality through optimizing the connection weights with respect to the objective function (12). Because the objective function of the proposed method is complex and nondifferentiable, gradient descent based techniques are not suitable for this problem.…”

Section: Weight Adjustments By Psomentioning

confidence: 99%

“…The prediction interval (PI) is a well-known tool for quantifying the uncertainty of prediction. The PI provides not only a range within which the target values are highly likely to lie but also an indication of their accuracy [11,12].…”

Section: Introductionmentioning

confidence: 99%

Prediction Interval Construction for Byproduct Gas Flow Forecasting Using Optimized Twin Extreme Learning Machine

Sun

Wang

2017

Mathematical Problems in Engineering

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Prediction of byproduct gas flow is of great significance to gas system scheduling in iron and steel plants. To quantify the associated prediction uncertainty, a two-step approach based on optimized twin extreme learning machine (ELM) is proposed to construct prediction intervals (PIs). In the first step, the connection weights of the twin ELM are pretrained using a pair of symmetric weighted objective functions. In the second step, output weights of the twin ELM are further optimized by particle swarm optimization (PSO). The objective function is designed to comprehensively evaluate PIs based on their coverage probability, width, and deviation. The capability of the proposed method is validated using four benchmark datasets and two real-world byproduct gas datasets. The results demonstrate that the proposed approach constructs higher quality prediction intervals than the other three conventional methods.

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Use of a quantile regression based echo state network ensemble for construction of prediction Intervals of gas flow in a blast furnace

Cited by 37 publications

References 18 publications

Network Traffic Prediction Using Variational Mode Decomposition and Multi- Reservoirs Echo State Network

Network Traffic Prediction Using Variational Mode Decomposition and Multi- Reservoirs Echo State Network

Wind Power Forecasting Based on Echo State Networks and Long Short-Term Memory

Prediction Interval Construction for Byproduct Gas Flow Forecasting Using Optimized Twin Extreme Learning Machine

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