Multifdelity surrogates(MFSs)replace computationally intensive models by synergistically combining information from diferent fdelity data with a signifcant improvement in modeling efciency.In this paper,a modifed MFS(...Multifdelity surrogates(MFSs)replace computationally intensive models by synergistically combining information from diferent fdelity data with a signifcant improvement in modeling efciency.In this paper,a modifed MFS(MMFS)model based on a radial basis function(RBF)is proposed,in which two fdelities of information can be analyzed by adaptively obtaining the scale factor.In the MMFS,an RBF was employed to establish the low-fdelity model.The correlation matrix of the high-fdelity samples and corresponding low-fdelity responses were integrated into an expansion matrix to determine the scaling function parameters.The shape parameters of the basis function were optimized by minimizing the leave-one-out cross-validation error of the high-fdelity sample points.The performance of the MMFS was compared with those of other MFS models(MFS-RBF and cooperative RBF)and single-fdelity RBF using four benchmark test functions,by which the impacts of diferent high-fdelity sample sizes on the prediction accuracy were also analyzed.The sensitivity of the MMFS model to the randomness of the design of experiments(DoE)was investigated by repeating sampling plans with 20 diferent DoEs.Stress analysis of the steel plate is presented to highlight the prediction ability of the proposed MMFS model.This research proposes a new multifdelity modeling method that can fully use two fdelity sample sets,rapidly calculate model parameters,and exhibit good prediction accuracy and robustness.展开更多
The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensi...The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.展开更多
基金Supported by National Key R&D Program of China(Grant No.2018YFB1700704).
文摘Multifdelity surrogates(MFSs)replace computationally intensive models by synergistically combining information from diferent fdelity data with a signifcant improvement in modeling efciency.In this paper,a modifed MFS(MMFS)model based on a radial basis function(RBF)is proposed,in which two fdelities of information can be analyzed by adaptively obtaining the scale factor.In the MMFS,an RBF was employed to establish the low-fdelity model.The correlation matrix of the high-fdelity samples and corresponding low-fdelity responses were integrated into an expansion matrix to determine the scaling function parameters.The shape parameters of the basis function were optimized by minimizing the leave-one-out cross-validation error of the high-fdelity sample points.The performance of the MMFS was compared with those of other MFS models(MFS-RBF and cooperative RBF)and single-fdelity RBF using four benchmark test functions,by which the impacts of diferent high-fdelity sample sizes on the prediction accuracy were also analyzed.The sensitivity of the MMFS model to the randomness of the design of experiments(DoE)was investigated by repeating sampling plans with 20 diferent DoEs.Stress analysis of the steel plate is presented to highlight the prediction ability of the proposed MMFS model.This research proposes a new multifdelity modeling method that can fully use two fdelity sample sets,rapidly calculate model parameters,and exhibit good prediction accuracy and robustness.
文摘The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.
