As the solution of the two equations for determining the existing fifth order Stokes wave derived by Skjelbreia is complex and tedious, the two equations are simplified into one equation for determining d / L, i. e., ...As the solution of the two equations for determining the existing fifth order Stokes wave derived by Skjelbreia is complex and tedious, the two equations are simplified into one equation for determining d / L, i. e., f(H, T, d / L) = 0. According to this simplified method, three cases of the solution for the Skjelbreia equations have been found: one accurate solution; more than one accurate solution and no accurate solution (but there exists the optimum approximate solution in the area of satisfying Skjelbreia equations). As to the case of more than one accurate solution, the reasonable solution can be judged from the method of variational principle, by means elf which an optimum solution improved from the solution of Skjelbreia equations in the area of satisfying the original mathematical equations of non-vortex and nonlinear wave theory, i. e., the optimum fifth order Stokes wave, is given.展开更多
Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motiva...Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.展开更多
基于简化标记和单元(Simplified marker and cell,SMAC)方法,发展一种在任意曲线坐标系中求解三维非定常不可压湍流Reynolds时均方程的隐式数值方法。控制方程包括以逆变速度为变量的动量方程、压力Poisson方程和k-ε湍流模型方程,控制...基于简化标记和单元(Simplified marker and cell,SMAC)方法,发展一种在任意曲线坐标系中求解三维非定常不可压湍流Reynolds时均方程的隐式数值方法。控制方程包括以逆变速度为变量的动量方程、压力Poisson方程和k-ε湍流模型方程,控制方程的离散在三维标记和单元(Marker and cell,MAC)交错网格系统中进行。为提高方程数值计算的稳定性,动量方程、k方程和ε方程对流项离散均采用Chakravarthy-Osher总变差衰减(Total variation diminishing,TVD)格式。动量方程、k方程和ε方程离散后的代数方程组采用循环三对角阵算法(Cyclic tridiagonal matrix algorithm,CTDMA)方法进行求解,Poisson方程离散后的代数方程组采用Tschebyscheff超线性松弛(successive linear over relaxation,SLOR)方法交替方向迭代求解。用该方法自编程序对简化后的射流放水阀内非定常流场进行数值模拟,计算结果和试验结果吻合。展开更多
Probability-based seismic performance assessment of in-service bridges has gained much attention in the scientific community during the past decades. The nonlinear static pushover analysis is critical for describing t...Probability-based seismic performance assessment of in-service bridges has gained much attention in the scientific community during the past decades. The nonlinear static pushover analysis is critical for describing the seismic behaviour of bridges subjected to moderate to high seismicity due to its simplicity. However, in existing analysis methods,the generation of pushover curve needs tremendous amount of computational costs and requires skills, which may halter its application in practice, implying the importance of developing practice-oriented analysis method with improved efficiency. Moreover, the bridge pier performance has been modelled as deterministic, indicating that the variation associated with the pier material and mechanical properties remains unaddressed. The correlation in the performance of different piers also exists due to the common design provisions and construction conditions but has neither been taken into account. This paper develops a simplified pushover analysis procedure for the seismic assessment of simply supported RC bridges. With the proposed method, the pushover curve of the bridge can be obtained explicitly without complex finite element modelling. A random factor is introduced to reflect the uncertainty in relation to the pushover curve. The correlation in the pier performance is considered by employing the Gaussian copula function to construct the joint probability distribution. Illustrative examples are presented to demonstrate theapplicability of the method and to investigate the impact of variation and correlation in bridge pier behaviour on the seismic performance assessment.展开更多
文摘As the solution of the two equations for determining the existing fifth order Stokes wave derived by Skjelbreia is complex and tedious, the two equations are simplified into one equation for determining d / L, i. e., f(H, T, d / L) = 0. According to this simplified method, three cases of the solution for the Skjelbreia equations have been found: one accurate solution; more than one accurate solution and no accurate solution (but there exists the optimum approximate solution in the area of satisfying Skjelbreia equations). As to the case of more than one accurate solution, the reasonable solution can be judged from the method of variational principle, by means elf which an optimum solution improved from the solution of Skjelbreia equations in the area of satisfying the original mathematical equations of non-vortex and nonlinear wave theory, i. e., the optimum fifth order Stokes wave, is given.
文摘Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.
文摘基于简化标记和单元(Simplified marker and cell,SMAC)方法,发展一种在任意曲线坐标系中求解三维非定常不可压湍流Reynolds时均方程的隐式数值方法。控制方程包括以逆变速度为变量的动量方程、压力Poisson方程和k-ε湍流模型方程,控制方程的离散在三维标记和单元(Marker and cell,MAC)交错网格系统中进行。为提高方程数值计算的稳定性,动量方程、k方程和ε方程对流项离散均采用Chakravarthy-Osher总变差衰减(Total variation diminishing,TVD)格式。动量方程、k方程和ε方程离散后的代数方程组采用循环三对角阵算法(Cyclic tridiagonal matrix algorithm,CTDMA)方法进行求解,Poisson方程离散后的代数方程组采用Tschebyscheff超线性松弛(successive linear over relaxation,SLOR)方法交替方向迭代求解。用该方法自编程序对简化后的射流放水阀内非定常流场进行数值模拟,计算结果和试验结果吻合。
基金supported by the National Natural Science Foundation of China(Grant Nos.51578315,51778337)the National Key Research and Development Program of China(Grant No.2016YFC0701404)the Faculty of Engineering and IT PhD Research Scholarship(SC 1911)from The University of Sydney
文摘Probability-based seismic performance assessment of in-service bridges has gained much attention in the scientific community during the past decades. The nonlinear static pushover analysis is critical for describing the seismic behaviour of bridges subjected to moderate to high seismicity due to its simplicity. However, in existing analysis methods,the generation of pushover curve needs tremendous amount of computational costs and requires skills, which may halter its application in practice, implying the importance of developing practice-oriented analysis method with improved efficiency. Moreover, the bridge pier performance has been modelled as deterministic, indicating that the variation associated with the pier material and mechanical properties remains unaddressed. The correlation in the performance of different piers also exists due to the common design provisions and construction conditions but has neither been taken into account. This paper develops a simplified pushover analysis procedure for the seismic assessment of simply supported RC bridges. With the proposed method, the pushover curve of the bridge can be obtained explicitly without complex finite element modelling. A random factor is introduced to reflect the uncertainty in relation to the pushover curve. The correlation in the pier performance is considered by employing the Gaussian copula function to construct the joint probability distribution. Illustrative examples are presented to demonstrate theapplicability of the method and to investigate the impact of variation and correlation in bridge pier behaviour on the seismic performance assessment.
