Stable Output Feedback in Reservoir Computing Using Ridge Regression

wyffels, Francis; Schrauwen, Benjamin; Stroobandt, Dirk

doi:10.1007/978-3-540-87536-9_83

Cited by 47 publications

(32 citation statements)

References 8 publications

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“…In recent years, a number of applications of ESN in streamflow forecasting [7][8][9] for hydropower plant and load forecasting [10][11][12] for power system have been revealed in the literature. The results indicate that ESN not only benefits from some feedbacks like other RNNs that enable them to model any complex dynamic behavior, but also gains a sparsely interconnected reservoir of neurons leading to a very fast and simple training procedure, unlike the complicated and time consuming training process of other RNNs without reservoir.…”

Section: Introductionmentioning

confidence: 99%

“…Although this method could achieve better forecast results, the regularization parameter was hard to determine and the cross-validation process was time-consuming. Wyffels et al [9] utilized the ridge regression algorithm to obtain the optimal output weights, however, it is hard to determine the ridge parameter. The Bayesian theory that is usually used as parameter regularization algorithm to optimize the parameters of forward neural network (FNN), has begun to be employed to optimize the output weights of ENN.…”

Section: Introductionmentioning

confidence: 99%

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Echo State Network with Bayesian Regularization for Forecasting Short-Term Power Production of Small Hydropower Plants

et al. 2015

Energies

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Abstract:As a novel recurrent neural network (RNN), an echo state network (ESN) that utilizes a reservoir with many randomly connected internal units and only trains the readout, avoids increased complexity of training procedures faced by traditional RNN. The ESN can cope with complex nonlinear systems because of its dynamical properties and has been applied in hydrological forecasting and load forecasting. Due to the linear regression algorithm usually adopted by generic ESN to train the output weights, an ill-conditioned solution might occur, degrading the generalization ability of the ESN. In this study, the ESN with Bayesian regularization (BESN) is proposed for short-term power production forecasting of small hydropower (SHP) plants. According to the Bayesian theory, the weights distribution in space is considered and the optimal output weights are obtained by maximizing the posterior probabilistic distribution. The evidence procedure is employed to gain optimal hyperparameters for the BESN model. The recorded data obtained from the SHP plants in two different counties, located in Yunnan Province, China, are utilized to validate the proposed model. For comparison, the feed-forward neural networks with Levenberg-Marquardt algorithm (LM-FNN) and the generic ESN are also employed. The results indicate that BESN outperforms both LM-FNN and ESN.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Echo State Network with Bayesian Regularization for Forecasting Short-Term Power Production of Small Hydropower Plants

et al. 2015

Energies

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“…The stability of the generated y[n] output signal is essential for the identification task and can be achieved by using noise injection during training [21] or finding the optimal regularization parameter λ in ridge regression [43]. To test the hypothesis of stability, two experiments were devised using the test data: the first experiment consisted of adding a single large and increasing perturbation during 6 seconds, whereas the second was done by adding Gaussian noise to y[n] at each timestep.…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore, stabilization of the system with output feedback is a concern to be handled. That can be achieved by state noise injection [21] or regularizing the readout output [43].…”

Section: Esn Modelmentioning

confidence: 99%

“…It has been shown that RC networks can model self-generating attractor patterns such as the digit 8 in Cartesian coordinates [43]; and central pattern generators with modulable amplitude, and shift [42,27]. The feedback connections for this type of task are mandatory, as it requires a long-term (non-fading) memory sufficient to sustain either an oscillation or a constant value.…”

Section: Introductionmentioning

confidence: 99%

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Echo State Networks for data-driven downhole pressure estimation in gas-lift oil wells

Antonelo¹,

Camponogara²,

Foss

2017

Neural Networks

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Process measurements are of vital importance for monitoring and control of industrial plants. When we consider offshore oil production platforms, wells that require gas-lift technology to yield oil production from low pressure oil reservoirs can become unstable under some conditions. This undesirable phenomenon is usually called slugging flow, and can be identified by an oscillatory behavior of the downhole pressure measurement. Given the importance of this measurement and the unreliability of the related sensor, this work aims at designing data-driven soft-sensors for downhole pressure estimation in two contexts: one for speeding up first-principle model simulation of a vertical riser model; and another for estimating the downhole pressure using real-world data from an oil well from Petrobras based only on topside platform measurements. Both tasks are tackled by employing Echo State Networks (ESN) as an efficient technique for training Recurrent Neural Networks. We show that a single ESN is capable of robustly modeling both the slugging flow behavior and a steady state based only on a square wave input signal representing the production choke opening in the vertical riser. Besides, we compare the performance of a standard network to the performance of a multiple timescale hierarchical architecture in the second task and show that the latter architecture performs better in modeling both large irregular transients and more commonly occurring small oscillations.

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Photonic Reservoir Computer with Output Feedback

Antonik

2018

Springer Theses

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Stable Output Feedback in Reservoir Computing Using Ridge Regression

Cited by 47 publications

References 8 publications

Echo State Network with Bayesian Regularization for Forecasting Short-Term Power Production of Small Hydropower Plants

Echo State Network with Bayesian Regularization for Forecasting Short-Term Power Production of Small Hydropower Plants

Echo State Networks for data-driven downhole pressure estimation in gas-lift oil wells

Photonic Reservoir Computer with Output Feedback

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