A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole ...A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincare map of the system is constructed. Using the Poincare map and the Gram Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.展开更多
Polynomial chaos expansions(PCEs)have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of t...Polynomial chaos expansions(PCEs)have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs.PCEs for models with independent inputs have been extensively explored in the literature.Recently,different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications.Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs.However,the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions,respectively.In this paper,we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions.The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output.The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency.Four numerical examples are implemented to validate the proposed algorithm.The source code is made publicly available for reproducibility.展开更多
针对高原湖泊面积监测问题,采用2017年4月和2018年4月的SPOT6遥感影像,结合DEM数据,首先对数据进行图像镶嵌、正射校正和Gram-Schmidt Pan Sharpening算法融合等处理;再利用归一化差异水体指数提取湖泊整体;然后通过高斯低通滤波器突出...针对高原湖泊面积监测问题,采用2017年4月和2018年4月的SPOT6遥感影像,结合DEM数据,首先对数据进行图像镶嵌、正射校正和Gram-Schmidt Pan Sharpening算法融合等处理;再利用归一化差异水体指数提取湖泊整体;然后通过高斯低通滤波器突出水体特征,结合目视解译,选取合适的阈值精确划分水体边界;最后统计得到玛旁雍错湖泊的面积。结果表明,截至2018年4月,玛旁雍错湖泊总面积由412万km2减少到411.4万km2,平均退缩率为0.1%。通过分析普兰气象站的气象数据发现,玛旁雍错湖泊的萎缩与当年降水量变化和气温变化有关,降水量减少、气温升高导致湖泊萎缩,说明气象变化对玛旁雍错湖泊面积变化具有一定的影响。展开更多
经典估计信源个数的Akaike信息论准则(Akaike information criterion,AIC)和最小描述长度(Minimum description length,MDL)方法需要特征分解,运算量较大且需要较多快拍数,为了便于工程实现,在传统的针对数据域Gram-Schmidt(GS)正交投...经典估计信源个数的Akaike信息论准则(Akaike information criterion,AIC)和最小描述长度(Minimum description length,MDL)方法需要特征分解,运算量较大且需要较多快拍数,为了便于工程实现,在传统的针对数据域Gram-Schmidt(GS)正交投影算法估计信源个数的基础上,提出了一种对协方差矩阵进行GS正交化来估计信源个数新方法,并推导出这种算法的自适应门限。仿真结果表明,该算法和AIC及MDL算法相比,虽然估计性能有所下降,但性能下降幅度不大,且其运算量小、所需快拍数少;与传统GS算法相比,运算量增加不大,但估计性能有较大提高。展开更多
This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-eliminat...This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.展开更多
From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric...From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes： the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10972059)the Natural Science Foundation of the Guangxi Zhuang Autonmous Region of China (Grant Nos. 0640002 and 2010GXNSFA013110)+1 种基金the Guangxi Youth Science Foundation of China (Grant No. 0832014)the Project of Excellent Innovating Team of Guangxi University
文摘A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincare map of the system is constructed. Using the Poincare map and the Gram Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.
基金This work was supported in part by the U.S.National Science Foundation(NSF grants CMMI-1824681,DMS-1952781,and BCS-2121616).
文摘Polynomial chaos expansions(PCEs)have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs.PCEs for models with independent inputs have been extensively explored in the literature.Recently,different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications.Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs.However,the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions,respectively.In this paper,we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions.The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output.The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency.Four numerical examples are implemented to validate the proposed algorithm.The source code is made publicly available for reproducibility.
文摘针对高原湖泊面积监测问题,采用2017年4月和2018年4月的SPOT6遥感影像,结合DEM数据,首先对数据进行图像镶嵌、正射校正和Gram-Schmidt Pan Sharpening算法融合等处理;再利用归一化差异水体指数提取湖泊整体;然后通过高斯低通滤波器突出水体特征,结合目视解译,选取合适的阈值精确划分水体边界;最后统计得到玛旁雍错湖泊的面积。结果表明,截至2018年4月,玛旁雍错湖泊总面积由412万km2减少到411.4万km2,平均退缩率为0.1%。通过分析普兰气象站的气象数据发现,玛旁雍错湖泊的萎缩与当年降水量变化和气温变化有关,降水量减少、气温升高导致湖泊萎缩,说明气象变化对玛旁雍错湖泊面积变化具有一定的影响。
文摘经典估计信源个数的Akaike信息论准则(Akaike information criterion,AIC)和最小描述长度(Minimum description length,MDL)方法需要特征分解,运算量较大且需要较多快拍数,为了便于工程实现,在传统的针对数据域Gram-Schmidt(GS)正交投影算法估计信源个数的基础上,提出了一种对协方差矩阵进行GS正交化来估计信源个数新方法,并推导出这种算法的自适应门限。仿真结果表明,该算法和AIC及MDL算法相比,虽然估计性能有所下降,但性能下降幅度不大,且其运算量小、所需快拍数少;与传统GS算法相比,运算量增加不大,但估计性能有较大提高。
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.
基金supported by ACI NIM(171)from the French Ministry of Education and Scientific Research
文摘From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes： the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.
