The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system mo...The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.展开更多
The low accuracy using unstructured meshes to solve complicated geometry problems is a significant challenge in practical engineering.It is the key to solve this issue through enhancing the accuracy of tetrahedral ele...The low accuracy using unstructured meshes to solve complicated geometry problems is a significant challenge in practical engineering.It is the key to solve this issue through enhancing the accuracy of tetrahedral element.This work develops a simple strategy to enhance the accuracy of tetrahedral element with the Shepard interpolation function.In which the strain field is reconstructed by introducing the weighted strains of adjacent tetrahedral elements to central tetrahedral element.The stiffness of the discrete system is significantly softened with this simple operation,which leads to a great accuracy improvement.Furthermore,this simple modification makes linear tetrahedral element owns higher accuracy even compared with hexahedral element.The high precision tetrahedral element makes finite element analysis more acceptable for engineers.It provides a novel solution to finite element analysis using unstructured meshes for practical engineering problems with complicated geometry.In order to validate the accuracy and feasibility of present modified tetrahedral element(M-T4)in complicated geometry problems,several engineering examples are performed,including linear static analysis,modal analysis,frequency response analysis,transient response analysis,and response spectrum analysis.The remarkable performance of the M-T4 suggests its wide applicability to practical engineering problems.展开更多
We propose a new functional single index model, which called dynamic single-index model for functional data, or DSIM, to efficiently perform non-linear and dynamic relationships between functional predictor and functi...We propose a new functional single index model, which called dynamic single-index model for functional data, or DSIM, to efficiently perform non-linear and dynamic relationships between functional predictor and functional response. The proposed model naturally allows for some curvature not captured by the ordinary functional linear model. By using the proposed two-step estimating algorithm, we develop the estimates for both the link function and the regression coefficient function, and then provide predictions of new response trajectories. Besides the asymptotic properties for the estimates of the unknown functions, we also establish the consistency of the predictions of new response trajectories under mild conditions. Finally, we show through extensive simulation studies and a real data example that the proposed DSIM can highly outperform existed functional regression methods in most settings.展开更多
基金Supported by the China Scholarship Council,National Natural Science Foundation of China(Grant No.11402022)the Interuniversity Attraction Poles Programme of the Belgian Science Policy Office(DYSCO)+1 种基金the Fund for Scientific Research–Flanders(FWO)the Research Fund KU Leuven
文摘The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.
基金supported by the National Key R&D Program of China(No.2022YFB2503505)National Natural Science Foundation of China(No.12002124)+3 种基金National Natural Science Foundation of China(No.12302259)China Postdoctoral Science Foundation(No.2021M690965)Changsha Municipal Natural Science Foundation(No.kq2014035)Natural Science Foundation of Hunan Province(No.2022JJ40031).
文摘The low accuracy using unstructured meshes to solve complicated geometry problems is a significant challenge in practical engineering.It is the key to solve this issue through enhancing the accuracy of tetrahedral element.This work develops a simple strategy to enhance the accuracy of tetrahedral element with the Shepard interpolation function.In which the strain field is reconstructed by introducing the weighted strains of adjacent tetrahedral elements to central tetrahedral element.The stiffness of the discrete system is significantly softened with this simple operation,which leads to a great accuracy improvement.Furthermore,this simple modification makes linear tetrahedral element owns higher accuracy even compared with hexahedral element.The high precision tetrahedral element makes finite element analysis more acceptable for engineers.It provides a novel solution to finite element analysis using unstructured meshes for practical engineering problems with complicated geometry.In order to validate the accuracy and feasibility of present modified tetrahedral element(M-T4)in complicated geometry problems,several engineering examples are performed,including linear static analysis,modal analysis,frequency response analysis,transient response analysis,and response spectrum analysis.The remarkable performance of the M-T4 suggests its wide applicability to practical engineering problems.
基金supported by National Natural Science Foundation of China (Grant No. 11271080)
文摘We propose a new functional single index model, which called dynamic single-index model for functional data, or DSIM, to efficiently perform non-linear and dynamic relationships between functional predictor and functional response. The proposed model naturally allows for some curvature not captured by the ordinary functional linear model. By using the proposed two-step estimating algorithm, we develop the estimates for both the link function and the regression coefficient function, and then provide predictions of new response trajectories. Besides the asymptotic properties for the estimates of the unknown functions, we also establish the consistency of the predictions of new response trajectories under mild conditions. Finally, we show through extensive simulation studies and a real data example that the proposed DSIM can highly outperform existed functional regression methods in most settings.
