An accurate short-term wind speed prediction algorithm based on the efficient kernel ridge pseudo inverse neural network （KRPINN） variants is proposed in this paper. The use of nonlinear kernel functions in pseudo i...An accurate short-term wind speed prediction algorithm based on the efficient kernel ridge pseudo inverse neural network （KRPINN） variants is proposed in this paper. The use of nonlinear kernel functions in pseudo inverse neural networks eliminates the trial and error approach of choosing the number of hidden layer neurons and their activation functions. The robustness of the proposed method has been validated in comparison with other models such as pseudo inverse radial basis function （PIRBF） and Legendre tanh activation function based neural network, i.e., PILNNT, whose input weights to the hidden layer weights are optimized using an adaptive firefly algorithm, i.e., FFA. However, since the individual kernel functions based KRPINN may not be able to produce accurate forecasts under chaotically varying wind speed conditions, a linear combination of individual kernel functions is used to build the multi kernel ridge pseudo inverse neural network （MK-RPINN） for providing improved forecasting accuracy, generalization, and stability of the wind speed prediction model. Several case studies have been presented to validate the accuracy of the short-term wind speed prediction models using the real world wind speed data from a wind farm in the Wyoming State of USA over time horizons varying from 10 minutes to 5 hours.展开更多
The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(...The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.展开更多
The kernel ridge regression(KRR)method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae.The widely used A^(1/3)A^(1/3),N^(1/3)N^(1/3)and Z^(1/3)...The kernel ridge regression(KRR)method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae.The widely used A^(1/3)A^(1/3),N^(1/3)N^(1/3)and Z^(1/3)Z^(1/3)formulae,and their improved versions by considering the isospin dependence are adopted as examples.The parameters in these six formulae are refitted using the Levenberg-Marquardt method,which give better results than the previous ones.The radius for each nucleus is predicted with the KRR network,which is trained with the deviations between experimental and calculated nuclear charge radii.For each formula,the resultant root-mean-square deviations of 884 nuclei with proton number Z≥8 Z≥8 and neutron number N≥8 N≥8 can be reduced to about 0.017fm after considering the modification of the KRR method.The extrapolation ability of the KRR method for the neutron-rich region is examined carefully and compared with the radial basis function method.It is found that the improved nuclear charge radius formulae by KRR method can avoid the risk of overfitting and have a good extrapolation ability.The influence of the ridge penalty term on the extrapolation ability of the KRR method is also discussed.At last,the nuclear charge radii of several recently observed K and Ca isotopes have been analyzed.展开更多
文摘An accurate short-term wind speed prediction algorithm based on the efficient kernel ridge pseudo inverse neural network （KRPINN） variants is proposed in this paper. The use of nonlinear kernel functions in pseudo inverse neural networks eliminates the trial and error approach of choosing the number of hidden layer neurons and their activation functions. The robustness of the proposed method has been validated in comparison with other models such as pseudo inverse radial basis function （PIRBF） and Legendre tanh activation function based neural network, i.e., PILNNT, whose input weights to the hidden layer weights are optimized using an adaptive firefly algorithm, i.e., FFA. However, since the individual kernel functions based KRPINN may not be able to produce accurate forecasts under chaotically varying wind speed conditions, a linear combination of individual kernel functions is used to build the multi kernel ridge pseudo inverse neural network （MK-RPINN） for providing improved forecasting accuracy, generalization, and stability of the wind speed prediction model. Several case studies have been presented to validate the accuracy of the short-term wind speed prediction models using the real world wind speed data from a wind farm in the Wyoming State of USA over time horizons varying from 10 minutes to 5 hours.
基金This work was supported by the National Natural Science Foundation of China(Nos.11875027,11975096).
文摘The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.
基金Supported by National Natural Science Foundation of China(11875027,11775112.11775026.11775099,11975096)Fundamental Research Funds for the Central Universities(2021MS046)。
文摘The kernel ridge regression(KRR)method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae.The widely used A^(1/3)A^(1/3),N^(1/3)N^(1/3)and Z^(1/3)Z^(1/3)formulae,and their improved versions by considering the isospin dependence are adopted as examples.The parameters in these six formulae are refitted using the Levenberg-Marquardt method,which give better results than the previous ones.The radius for each nucleus is predicted with the KRR network,which is trained with the deviations between experimental and calculated nuclear charge radii.For each formula,the resultant root-mean-square deviations of 884 nuclei with proton number Z≥8 Z≥8 and neutron number N≥8 N≥8 can be reduced to about 0.017fm after considering the modification of the KRR method.The extrapolation ability of the KRR method for the neutron-rich region is examined carefully and compared with the radial basis function method.It is found that the improved nuclear charge radius formulae by KRR method can avoid the risk of overfitting and have a good extrapolation ability.The influence of the ridge penalty term on the extrapolation ability of the KRR method is also discussed.At last,the nuclear charge radii of several recently observed K and Ca isotopes have been analyzed.
