An Intelligent Calculation Method of Volterra Time-Domain Kernel Based on Time-Delay Artificial Neural Network

Zhong, Kaiyang; Chen, Lerui

doi:10.1155/2020/8546963

Cited by 8 publications

(7 citation statements)

References 31 publications

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“…In the latter, a similar topographic pattern of Korhonen's self-organizing feature map (SOFM) network is proposed for the 4 × 4 and 1 × 4 neurons. The Volterra kernels are functions of layer-to-layer weights and neuron biases [17]. Hence, it's needed first to train the neural network with the datasets explained above to evaluate all weights and biases.…”

Section: Nn Modelmentioning

confidence: 99%

“…With a smaller number of neurons, lower accuracy is achieved, whereas, with a larger neuron number, overfitting occurs. In the case of a time-delay artificial neural network (TDANN), the length of the memory affects accuracy too, because with shallow memory length, the lower correlation between neurons has resulted, and with deep memory length, overfitting is obtained [17]. Wavelet decomposition was used to analyze and predict wind speed of chaotic nature [18].…”

Section: Introductionmentioning

confidence: 99%

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A Novel Method of Forecasting Chaotic and Random Wind Speed Regimes Based on Machine Learning with the Evolution and Prediction of Volterra Kernels

Majid¹

2023

Preprint

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This study aims to focus on using the Volterra series and machine learning for forecasting random and chaotic wind speed regimes, since the calm weather is mostly noticed at the local site, making the dataset selection difficult. A novel method is proposed to predict Volterra kernels up to the third order, using a forward-back propagation neural network with 12-month measurements at Fujairah site (UAE). Both daily and monthly wind speed data sets are investigated for forecasting. The three dominant hourly and daily kernels are extracted for each day and each month. Predicted future Volterra kernels are estimated from past values using both statistical analysis and individual neuro networks for each of the Volterra kernel coefficients. Due to the random nature of wind speed at the local site, a two-layer with 4 neurons per layer neuro network is used to locate the most variable and intense speed during 8-hours in the day. Forecasted wind speed is determined with errors arising from different sources such as the utilization of only 3rd-order Volterra kernels and the difficulty of machine training of the employed shallow network. Nevertheless, this work depicts a useful algorithm to forecast chaotic and random wind speed regimes. Computational time is a trade of the complexity of Volterra mathematical analysis.

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Section: Nn Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel Method of Forecasting Chaotic and Random Wind Speed Regimes Based on Machine Learning with the Evolution and Prediction of Volterra Kernels

Majid¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…When the system equation is known, it can be solved by the harmonic probing method [21], growth exponential method [39], Carleman linearisation method [40], etc. If the equation is unknown, it can be identified from the experimental data of the system using the least squares method [41], neural network method [42,43], Bayesian method [44], etc.…”

Section: Computation Of the Gfrfsmentioning

confidence: 99%

“…( 48 Result: Output PSD 𝑺 𝑌𝑌 = [𝑆 𝑌𝑌 1 , 𝑆 𝑌𝑌 2 , ⋯ , 𝑆 𝑌𝑌 𝑒 ] Volterra-PEM (Algorithm 1) and MCS (Algorithm 2) were used to compute the output PSD of the nonlinear spring-damped oscillator with Eq. (43).…”

Section: Inputmentioning

confidence: 99%

A Volterra-PEM approach for random vibration spectrum analysis of nonlinear systems

Zhao

2022

Preprint

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Based on Volterra series theory, a Volterra-pseudo excitation method (Volterra-PEM) is developed to compute the response power spectral density (PSD) for nonlinear systems under random excitation. Firstly, within the framework of Volterra series theory, an improved pseudo excitation method (PEM) is established for multi-dimensional power spectral density (MPSD) analysis of nonlinear systems. As a generalized PEM for linear random vibration analysis, the Volterra-PEM is used to analyse the response MPSD, which also has a very concise expression. Secondly, in the case of computation difficulties when multi-dimensional integrating from MPSD to PSD, the computational efficiency is improved by converting the multi-dimensional integral into a matrix operation. Finally, as numerical examples, the Volterra-PEM is used to estimate the response PSD for stationary random vibration of a nonlinear spring-damped oscillator and a non-ideal boundary beam with geometrical nonlinearity. Compared with Monte Carlo simulation (MCS), the results show that the proposed method can predict the response PSD for nonlinear systems quickly and accurately under appropriate excitation intensities.

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“…With a smaller number of neurons, lower accuracy is achieved, whereas, with a larger neuron number, overfitting occurs. In the case of a time-delay artificial neural network (TDANN), the length of the memory affects accuracy too because, with shallow memory length, a lower correlation between neurons has resulted and, with deep memory length, overfitting is obtained [22]. Wavelet decomposition was used to analyze and predict wind speed of chaotic nature [23].…”

Section: Introductionmentioning

confidence: 99%

A Novel Method of Forecasting Chaotic and Random Wind Speed Regimes Based on Machine Learning with the Evolution and Prediction of Volterra Kernels

Majid¹

2023

Energies

View full text Add to dashboard Cite

This study aims to focus on using the Volterra series and machine learning for forecasting random and chaotic wind speed regimes, since calm weather is mostly noticed at the local site, making dataset selection difficult. A novel method is proposed to predict Volterra kernels up to the third order, using a forward–back propagation neural network with 12-month measurements at Fujairah site (United Arab Emirates). Both daily and monthly wind speed datasets are investigated for forecasting. The three dominant hourly and daily kernels are extracted for each day and each month. Predicted future Volterra kernels are estimated from past values using both statistical analysis and individual neuro networks for each of the Volterra kernel coefficients. Using the evolved Volterra kernels, the hourly and daily wind speeds are forecasted with similar patterns of the measured values. Due to the random nature of wind speed at the local site, a two-layer with four neurons per layer neuro network is used to locate the most variable and intense speed during 8 h in the day. Forecasted wind speed is determined with errors arising from different sources, such as the utilization of only third-order Volterra kernels and the difficulty of machine training of the employed shallow network. Nevertheless, this work depicts a useful algorithm to forecast chaotic and random wind speed regimes. Computational time is a trade of the complexity of Volterra mathematical analysis.

show abstract

An Intelligent Calculation Method of Volterra Time-Domain Kernel Based on Time-Delay Artificial Neural Network

Cited by 8 publications

References 31 publications

A Novel Method of Forecasting Chaotic and Random Wind Speed Regimes Based on Machine Learning with the Evolution and Prediction of Volterra Kernels

A Novel Method of Forecasting Chaotic and Random Wind Speed Regimes Based on Machine Learning with the Evolution and Prediction of Volterra Kernels

A Volterra-PEM approach for random vibration spectrum analysis of nonlinear systems

A Novel Method of Forecasting Chaotic and Random Wind Speed Regimes Based on Machine Learning with the Evolution and Prediction of Volterra Kernels

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