The present work describes the application of the method of fundamental solutions (MFS) along with the analog equation method (AEM) and radial basis function (RBF) approximation for solving the 2D isotropic and ...The present work describes the application of the method of fundamental solutions (MFS) along with the analog equation method (AEM) and radial basis function (RBF) approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson's equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition (SVD) technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric (MQ) are fully analyzed to provide useful reference.展开更多
Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps: first, d...Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps: first, decomposing cutting torque components from the original signals by wavelet packet decomposition (WPD); second, extracting wavelet coefficients of different wear states (i.e., slight, normal, or severe wear) with signal features adapting to Welch spectrum. Finally, monitoring and recognition of the feature vectors of cutting torque signal are performed by using the K-means cluster and radial basis function neural network (RBFNN). The experiments on different tool wears of the multivariable features reveal that the results of monitoring and recognition are significant and effective.展开更多
The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equ...The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters' values. It makes the equation's solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.展开更多
The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult.Currently,some hydrologists employ the complete ensemble empirical mode decompos...The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult.Currently,some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)method,a new time-frequency analysis method based on the empirical mode decomposition(EMD)algorithm,to decompose non-stationary raw data in order to obtain relatively stationary components for further study.However,the endpoint effect in CEEMDAN is often neglected,which can lead to decomposition errors that reduce the accuracy of the research results.In this study,we processed an original runoff sequence using the radial basis function neural network(RBFNN)technique to obtain the extension sequence before utilizing CEEMDAN decomposition.Then,we compared the decomposition results of the original sequence,RBFNN extension sequence,and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method.The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect.At both ends of the components,the extension sequence more accurately reflected the true fluctuation characteristics and variation trends.These advances are of great significance to the subsequent study of hydrology.Therefore,the CEEMDAN method,combined with an appropriate extension of the original runoff series,can more precisely determine multi-time scale characteristics,and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting.展开更多
In view of the usefulness of Empirical Mode Decomposition (EMD), Artificial Neural Networks ( ANN), and Most Relevant Matching Extension (MRME) methods in dealing with nonlinear signals, we pro- pose a new way o...In view of the usefulness of Empirical Mode Decomposition (EMD), Artificial Neural Networks ( ANN), and Most Relevant Matching Extension (MRME) methods in dealing with nonlinear signals, we pro- pose a new way of combining these methods to deal with signal prediction. We found the results of combining EMD with either ANN or MRME to have higher prediction precision for a time series than the result of using EMD alone.展开更多
针对传统方法难以准确预测复杂工况下的燃油流量,进而影响排放计算精度的问题,提出一种基于神经网络基函数分解的NBEATS-MARS(neural basis expansion analysis for time series with multi-variable adaptive rapid state-transition)...针对传统方法难以准确预测复杂工况下的燃油流量,进而影响排放计算精度的问题,提出一种基于神经网络基函数分解的NBEATS-MARS(neural basis expansion analysis for time series with multi-variable adaptive rapid state-transition)模型。该模型采用多栈分解结构,设计多类型基函数系统,通过基函数分解实现可解释的高精度预测。实验表明:NBEATS-MARS模型方均根误差为59.49,对称平均绝对百分比误差为5.75%,中位数误差仅为0.29%;在爬升巡航下降阶段表现最佳,方均根误差为32.75,对称平均绝对百分比误差为1.87%。基于此构建了综合航空排放计算方法,通过将预测的燃油流量数据作为核心输入,结合发动机排气温度等健康状态参数,实现了二氧化碳、氮氧化物、黑碳和有机碳等多种航空排放物的精确量化。燃油流量预测误差的降低使排放计算不确定性显著减小,巡航阶段排放量计算精度提升至±2%以内。该方法通过提高上游燃油流量预测精度,有效改善了下游航空排放评估的准确性和空间分辨率。展开更多
摘要The present work describes the application of the method of fundamental solutions (MFS) along with the analog equation method (AEM) and radial basis function (RBF) approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson's equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition (SVD) technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric (MQ) are fully analyzed to provide useful reference.
摘要Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps: first, decomposing cutting torque components from the original signals by wavelet packet decomposition (WPD); second, extracting wavelet coefficients of different wear states (i.e., slight, normal, or severe wear) with signal features adapting to Welch spectrum. Finally, monitoring and recognition of the feature vectors of cutting torque signal are performed by using the K-means cluster and radial basis function neural network (RBFNN). The experiments on different tool wears of the multivariable features reveal that the results of monitoring and recognition are significant and effective.
基金Supported by National Natural Science Foundation of China(Grants 61100129)Open Program of Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences(IIP2014-7)
摘要The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters' values. It makes the equation's solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.
基金supported by the National Key R&D Program of China(Grant No.2018YFC0406501)Outstanding Young Talent Research Fund of Zhengzhou Uni-versity(Grant No.1521323002)+2 种基金Program for Innovative Talents(in Science and Technology)at University of Henan Province(Grant No.18HASTIT014)State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University(Grant No.HESS-1717)Foundation for University Youth Key Teacher of Henan Province(Grant No.2017GGJS006).
摘要The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult.Currently,some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)method,a new time-frequency analysis method based on the empirical mode decomposition(EMD)algorithm,to decompose non-stationary raw data in order to obtain relatively stationary components for further study.However,the endpoint effect in CEEMDAN is often neglected,which can lead to decomposition errors that reduce the accuracy of the research results.In this study,we processed an original runoff sequence using the radial basis function neural network(RBFNN)technique to obtain the extension sequence before utilizing CEEMDAN decomposition.Then,we compared the decomposition results of the original sequence,RBFNN extension sequence,and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method.The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect.At both ends of the components,the extension sequence more accurately reflected the true fluctuation characteristics and variation trends.These advances are of great significance to the subsequent study of hydrology.Therefore,the CEEMDAN method,combined with an appropriate extension of the original runoff series,can more precisely determine multi-time scale characteristics,and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting.
基金supporteal by the Notional Natural Scince Foundation of Hebei Province(D201000921)
摘要In view of the usefulness of Empirical Mode Decomposition (EMD), Artificial Neural Networks ( ANN), and Most Relevant Matching Extension (MRME) methods in dealing with nonlinear signals, we pro- pose a new way of combining these methods to deal with signal prediction. We found the results of combining EMD with either ANN or MRME to have higher prediction precision for a time series than the result of using EMD alone.
摘要针对传统方法难以准确预测复杂工况下的燃油流量,进而影响排放计算精度的问题,提出一种基于神经网络基函数分解的NBEATS-MARS(neural basis expansion analysis for time series with multi-variable adaptive rapid state-transition)模型。该模型采用多栈分解结构,设计多类型基函数系统,通过基函数分解实现可解释的高精度预测。实验表明:NBEATS-MARS模型方均根误差为59.49,对称平均绝对百分比误差为5.75%,中位数误差仅为0.29%;在爬升巡航下降阶段表现最佳,方均根误差为32.75,对称平均绝对百分比误差为1.87%。基于此构建了综合航空排放计算方法,通过将预测的燃油流量数据作为核心输入,结合发动机排气温度等健康状态参数,实现了二氧化碳、氮氧化物、黑碳和有机碳等多种航空排放物的精确量化。燃油流量预测误差的降低使排放计算不确定性显著减小,巡航阶段排放量计算精度提升至±2%以内。该方法通过提高上游燃油流量预测精度,有效改善了下游航空排放评估的准确性和空间分辨率。