Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian rand...Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model （CAR） of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a con- ditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.展开更多
It is shown that if M is an R-quasi-continuous left R-module and R satisfies ACC on left ideals of the form l(m), m ∈ M, then M is a direct sum of uniform sub-modules.
In this paper we carry out a study of modules over a 3 × 3 formal triangular matrix ringГ=（T 0 0 M U 0 N×UM N V）where T, U, V are rings, M, N are U-T, V-U bimodules, respectively. Using the alternative ...In this paper we carry out a study of modules over a 3 × 3 formal triangular matrix ringГ=（T 0 0 M U 0 N×UM N V）where T, U, V are rings, M, N are U-T, V-U bimodules, respectively. Using the alternative description of left Г-module as quintuple （A, B, C; f, g） with A ∈ mod T, B ∈ mod U and C ∈ mod V, f ： M ×T A →B ∈ mod U, g ： N ×U B → C ∈ mod V, we shall characterize uniform, hollow and finitely embedded modules over F, respectively. Also the radical as well as the socle of r （A ＋ B ＋ C） is determined.展开更多
A new time-domain modal identification method of linear time-invariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model.The method can identify physica...A new time-domain modal identification method of linear time-invariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model.The method can identify physical parameters of the system from response data.In order to identify the parameters of the system,the structural dynamic equation is first transformed into the continuous time AR model,and subsequently written into the forms of observation equation and state equation which is just a stochastic differential equation.Secondly,under the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short time period,the uniformly modulated function is identified piecewise.Then,we present the exact maximum likelihood estimators of parameters by virtue of the Girsanov theorem.Finally,the modal parameters are identified by eigenanalysis.Numerical results show that the method we introduce here not only has high precision and robustness,but also has very high computing efficiency.Therefore,it is suitable for real-time modal identification.展开更多
Based on the continuous time AR model,this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random excitation.The structural dynamic equation is fi...Based on the continuous time AR model,this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random excitation.The structural dynamic equation is first transformed into the observation equation and the state equation(namely,stochastic differential equation).Based on the property of the strong solution of the stochastic differential equation,the uniformly modulated function is identified piecewise.Then by virtue of the Girsanov theorem,we present the exact maximum likelihood estimators of parameters.Finally,the modal parameters are identified by eigen analysis.Numerical results show that the method not only has high precision and robustness but also has very high computing efficiency.展开更多
Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges.The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of ...Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges.The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of a super long-span suspension bridge was investigated in this paper.Firstly,four non-stationary wind velocity models are established by combing the time-varying average wind velocity with an exponential function and the fluctuating wind velocity with four modulation functions,respectively.These non-stationary wind velocity models have obvious non-stationary characteristics and then are validated by the classical power spectrum densities.Finally,three displacement responses of the bridge deck under four different independent variables ofβin the exponential function and four modulation functions were compared,respectively.Results show that the turbulence intensities using two non-uniform modulation functions(NMF)are larger than those using uniform modulation functions(uMF).Moreover,the root mean square(RMS)values of three displacement responses increase with the decrease ofβ.Besides,the RMS values of three displacement under two NMFs are larger than those under two uMFs,and their RMS values under the second uMF are the smallest.展开更多
基金supported by the National Natural Science Foundation of China (No. 50278017)
文摘Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model （CAR） of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a con- ditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.
文摘It is shown that if M is an R-quasi-continuous left R-module and R satisfies ACC on left ideals of the form l(m), m ∈ M, then M is a direct sum of uniform sub-modules.
基金the National Natural Science Foundation of China （No. 10371107）.
文摘In this paper we carry out a study of modules over a 3 × 3 formal triangular matrix ringГ=（T 0 0 M U 0 N×UM N V）where T, U, V are rings, M, N are U-T, V-U bimodules, respectively. Using the alternative description of left Г-module as quintuple （A, B, C; f, g） with A ∈ mod T, B ∈ mod U and C ∈ mod V, f ： M ×T A →B ∈ mod U, g ： N ×U B → C ∈ mod V, we shall characterize uniform, hollow and finitely embedded modules over F, respectively. Also the radical as well as the socle of r （A ＋ B ＋ C） is determined.
基金Supported by the Major Project of National Natural Science Foundation of China(Grant No.50278017)
文摘A new time-domain modal identification method of linear time-invariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model.The method can identify physical parameters of the system from response data.In order to identify the parameters of the system,the structural dynamic equation is first transformed into the continuous time AR model,and subsequently written into the forms of observation equation and state equation which is just a stochastic differential equation.Secondly,under the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short time period,the uniformly modulated function is identified piecewise.Then,we present the exact maximum likelihood estimators of parameters by virtue of the Girsanov theorem.Finally,the modal parameters are identified by eigenanalysis.Numerical results show that the method we introduce here not only has high precision and robustness,but also has very high computing efficiency.Therefore,it is suitable for real-time modal identification.
文摘Based on the continuous time AR model,this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random excitation.The structural dynamic equation is first transformed into the observation equation and the state equation(namely,stochastic differential equation).Based on the property of the strong solution of the stochastic differential equation,the uniformly modulated function is identified piecewise.Then by virtue of the Girsanov theorem,we present the exact maximum likelihood estimators of parameters.Finally,the modal parameters are identified by eigen analysis.Numerical results show that the method not only has high precision and robustness but also has very high computing efficiency.
基金the National Natural Science Foundation of China(Nos.52278311,52178503,U2005216,and 51908374)the Guangdong Basic and Applied Basic Research Foundation(No.2023A1515030148)+2 种基金the Shenzhen Science and Technology Innovation Program(Nos.JCYJ20220531101609020,KQTD20200820113004005,and GJHZ20220913143006012)the Foundation of State Key Laboratory for Disaster Reduction in Civil Engineering,Tongji University(No.SLDRCE19-B-10)the National Key Laboratory of Green and Long-Life Road Engineering in Extreme Environment.
文摘Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges.The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of a super long-span suspension bridge was investigated in this paper.Firstly,four non-stationary wind velocity models are established by combing the time-varying average wind velocity with an exponential function and the fluctuating wind velocity with four modulation functions,respectively.These non-stationary wind velocity models have obvious non-stationary characteristics and then are validated by the classical power spectrum densities.Finally,three displacement responses of the bridge deck under four different independent variables ofβin the exponential function and four modulation functions were compared,respectively.Results show that the turbulence intensities using two non-uniform modulation functions(NMF)are larger than those using uniform modulation functions(uMF).Moreover,the root mean square(RMS)values of three displacement responses increase with the decrease ofβ.Besides,the RMS values of three displacement under two NMFs are larger than those under two uMFs,and their RMS values under the second uMF are the smallest.
