Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is con...Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.展开更多
A further development of exclusively inverse frequency domain method for leak detection in pipelines is presented and validated.The location and leakage can be determined by analyzing the difference of transient water...A further development of exclusively inverse frequency domain method for leak detection in pipelines is presented and validated.The location and leakage can be determined by analyzing the difference of transient water head response between the simulated and measured data in frequency domain.The transient signals are generated by portion sharp closure of a valve from the small constant opening and it needs only a few meters of water.The discrete boundary conditions and observation data are both transformed in frequency domain by Laplace transform.Example in numerical simulation is studied for demonstration of this approach.The application of the method to an experimental pipeline confirms the analysis and illustrates successful detection of the single pipeline leak.The precalibration approach is presented to minimize the effect of data and model error and it splits the method into two parts.One uses data from a known state to fit the parameters of the model and the other uses data from the current state for the fitting of leak parameters using the now calibrated model.Some important practical parameters such as wave speed,friction in steady and unsteady state and the adaptability of the method are discussed.It was found that the nonlinearity errors associated with valve boundary condition could be prevented by consideration of the induced flow perturbation curve shape.展开更多
基金CHEN Min's work is supported by Grant No. 70221001 and No. 70331001 from NNSFC and Grant No. KZCX2-SW-118 from CAS.
文摘Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51109230, 50679085)the Special Funds of IWHR (Grant No. 0912)
文摘A further development of exclusively inverse frequency domain method for leak detection in pipelines is presented and validated.The location and leakage can be determined by analyzing the difference of transient water head response between the simulated and measured data in frequency domain.The transient signals are generated by portion sharp closure of a valve from the small constant opening and it needs only a few meters of water.The discrete boundary conditions and observation data are both transformed in frequency domain by Laplace transform.Example in numerical simulation is studied for demonstration of this approach.The application of the method to an experimental pipeline confirms the analysis and illustrates successful detection of the single pipeline leak.The precalibration approach is presented to minimize the effect of data and model error and it splits the method into two parts.One uses data from a known state to fit the parameters of the model and the other uses data from the current state for the fitting of leak parameters using the now calibrated model.Some important practical parameters such as wave speed,friction in steady and unsteady state and the adaptability of the method are discussed.It was found that the nonlinearity errors associated with valve boundary condition could be prevented by consideration of the induced flow perturbation curve shape.
