In this paper, the on-orbit identification of modal parameters for a spacecraft is investigated. Firstly, the coupled dynamic equation of the system is established with the Lagrange method and the stochastic state-spa...In this paper, the on-orbit identification of modal parameters for a spacecraft is investigated. Firstly, the coupled dynamic equation of the system is established with the Lagrange method and the stochastic state-space model of the system is obtained. Then, the covariance-driven stochastic subspace identification（SSI-COV） algorithm is adopted to identify the modal parameters of the system. In this algorithm, it just needs the covariance of output data of the system under ambient excitation to construct a Toeplitz matrix, thus the system matrices are obtained by the singular value decomposition on the Toeplitz matrix and the modal parameters of the system can be found from the system matrices. Finally,numerical simulations are carried out to demonstrate the validity of the SSI-COV algorithm. Simulation results indicate that the SSI-COV algorithm is effective in identifying the modal parameters of the spacecraft only using the output data of the system under ambient excitation.展开更多
In this paper,the authors give a characterization of finite Blaschke products with degree n.The main results are:(1)An n-dimensional complex vector can be the first n Taylor coefficients of a finite Blaschke product w...In this paper,the authors give a characterization of finite Blaschke products with degree n.The main results are:(1)An n-dimensional complex vector can be the first n Taylor coefficients of a finite Blaschke product with degree no more than n-1 if and only if the vector induces a lower triangular Toeplitz matrix with norm 1;(2)an n-dimensional complex vector can be the first n Taylor coefficients of an inner function if and only if the vector induces a lower triangular Toeplitz matrix with norm no more than 1.M¨obius transformations acting on contraction matrices play an important role in the proofs.展开更多
We investigate the large deviations properties for centered stationary AR(1)and MA(1)processes with independent Gaussian innovations,by giving the explicit bivariate rate functions for the sequence of two-dimensional ...We investigate the large deviations properties for centered stationary AR(1)and MA(1)processes with independent Gaussian innovations,by giving the explicit bivariate rate functions for the sequence of two-dimensional random vectors.Via the Contraction Principle,we provide the explicit rate functions for the sample mean and the sample second moment.In the AR(1)case,we also give the explicit rate function for the sequence of two-dimensional random vectors(W_(n))n≥2=(n^(-1(∑_(k=1)^(n)X_(k),∑_(k=1)^(n)X_(k)^(2))))_(n∈N)n≥2,but we obtain an analytic rate function that gives different values for the upper and lower bounds,depending on the evaluated set and its intersection with the respective set of exposed points.A careful analysis of the properties of a certain family of Toeplitz matrices is necessary.The large deviations properties of three particular sequences of one-dimensional random variables will follow after we show how to apply a weaker version of the Contraction Principle for our setting,providing new proofs for two already known results on the explicit deviation function for the sample second moment and Yule-Walker estimators.We exhibit the properties of the large deviations of the first-order empirical autocovariance,its explicit deviation function and this is also a new result.展开更多
基金supported by the National Natural Science Foundation of China(Grants 11132001,11272202,11472171)the Key Scientific Project of Shanghai Municipal Education Commission(Grant 14ZZ021)+1 种基金the Natural Science Foundation of Shanghai(Grant 14ZR1421000)the Special Fund for Talent Development of Minhang District of Shanghai
文摘In this paper, the on-orbit identification of modal parameters for a spacecraft is investigated. Firstly, the coupled dynamic equation of the system is established with the Lagrange method and the stochastic state-space model of the system is obtained. Then, the covariance-driven stochastic subspace identification（SSI-COV） algorithm is adopted to identify the modal parameters of the system. In this algorithm, it just needs the covariance of output data of the system under ambient excitation to construct a Toeplitz matrix, thus the system matrices are obtained by the singular value decomposition on the Toeplitz matrix and the modal parameters of the system can be found from the system matrices. Finally,numerical simulations are carried out to demonstrate the validity of the SSI-COV algorithm. Simulation results indicate that the SSI-COV algorithm is effective in identifying the modal parameters of the spacecraft only using the output data of the system under ambient excitation.
文摘In this paper,the authors give a characterization of finite Blaschke products with degree n.The main results are:(1)An n-dimensional complex vector can be the first n Taylor coefficients of a finite Blaschke product with degree no more than n-1 if and only if the vector induces a lower triangular Toeplitz matrix with norm 1;(2)an n-dimensional complex vector can be the first n Taylor coefficients of an inner function if and only if the vector induces a lower triangular Toeplitz matrix with norm no more than 1.M¨obius transformations acting on contraction matrices play an important role in the proofs.
基金M.J.Karling was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior(CAPES)-Brazil(Grant No.1736629)Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq)-Brazil(Grant No.170168/2018-2)+1 种基金A.O.Lopes’research was partially supported by CNPq-Brazil(Grant No.304048/2016-0)S.R.C.Lopes’research was partially supported by CNPq-Brazil(Grant No.303453/2018-4).
文摘We investigate the large deviations properties for centered stationary AR(1)and MA(1)processes with independent Gaussian innovations,by giving the explicit bivariate rate functions for the sequence of two-dimensional random vectors.Via the Contraction Principle,we provide the explicit rate functions for the sample mean and the sample second moment.In the AR(1)case,we also give the explicit rate function for the sequence of two-dimensional random vectors(W_(n))n≥2=(n^(-1(∑_(k=1)^(n)X_(k),∑_(k=1)^(n)X_(k)^(2))))_(n∈N)n≥2,but we obtain an analytic rate function that gives different values for the upper and lower bounds,depending on the evaluated set and its intersection with the respective set of exposed points.A careful analysis of the properties of a certain family of Toeplitz matrices is necessary.The large deviations properties of three particular sequences of one-dimensional random variables will follow after we show how to apply a weaker version of the Contraction Principle for our setting,providing new proofs for two already known results on the explicit deviation function for the sample second moment and Yule-Walker estimators.We exhibit the properties of the large deviations of the first-order empirical autocovariance,its explicit deviation function and this is also a new result.
