A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency ...A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a high computational cost, slower response, and need for more memory resources. One possible strategy to overcome this problem is to dynamically adjust the time-step with respect to the system’s stiffness. Therefore, small time-steps can be applied when needed, and larger time-steps can be used when allowable. This paper presents a new algorithm for adjusting the dynamic time-step based on a BDF discretization method. The parameters used to dynamically adjust the size of the time-step can be optimally specified to result in a minimum computation time and reasonable accuracy for a particular case of ODEs. The proposed algorithm was applied to solve the system of ODEs obtained from an activated sludge model (ASM) for biological wastewater treatment processes. The algorithm was tested for various solver parameters, and the optimum set of three adjustable parameters that represented minimum computation time was identified. In addition, the accuracy of the algorithm was evaluated for various sets of solver parameters.展开更多
针对先验误差评估时间自适应方法ATAM(Apriori Time Adaptive Method)计算效率提高程度的评估问题,根据文献[1]提出的评估方法,本文选用具有解析解的Bernoulli-Euler梁算例对多个节点的情况进行了验证.结果证实该评估方法对多个节点的...针对先验误差评估时间自适应方法ATAM(Apriori Time Adaptive Method)计算效率提高程度的评估问题,根据文献[1]提出的评估方法,本文选用具有解析解的Bernoulli-Euler梁算例对多个节点的情况进行了验证.结果证实该评估方法对多个节点的情况同样准确有效,从而解决了实际工程数值模拟计算中需要同时对多节点变量评估计算效率提高程度的问题.展开更多
Blind adaptive multiuser detector has become a research hotspot in recent years due to a number of advantages, but many blind adaptive algorithms involve low convergence rate. This paper presents a novel stochastic bl...Blind adaptive multiuser detector has become a research hotspot in recent years due to a number of advantages, but many blind adaptive algorithms involve low convergence rate. This paper presents a novel stochastic blind adaptive multiuser detector without requiring training sequences, which needs only two system parameters: the signature sequence of the desired user i, s i and the variance of the additive white Gaussian noise (AWGN),σ 2. Simulation results show that by reasonably choosing time varying step size, the proposed detector can not only improve the convergence rate, but also reduce the limiting NSE (Normalized Squared Error) values, so it can effectively increase the performance of the system.展开更多
文摘A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a high computational cost, slower response, and need for more memory resources. One possible strategy to overcome this problem is to dynamically adjust the time-step with respect to the system’s stiffness. Therefore, small time-steps can be applied when needed, and larger time-steps can be used when allowable. This paper presents a new algorithm for adjusting the dynamic time-step based on a BDF discretization method. The parameters used to dynamically adjust the size of the time-step can be optimally specified to result in a minimum computation time and reasonable accuracy for a particular case of ODEs. The proposed algorithm was applied to solve the system of ODEs obtained from an activated sludge model (ASM) for biological wastewater treatment processes. The algorithm was tested for various solver parameters, and the optimum set of three adjustable parameters that represented minimum computation time was identified. In addition, the accuracy of the algorithm was evaluated for various sets of solver parameters.
文摘针对先验误差评估时间自适应方法ATAM(Apriori Time Adaptive Method)计算效率提高程度的评估问题,根据文献[1]提出的评估方法,本文选用具有解析解的Bernoulli-Euler梁算例对多个节点的情况进行了验证.结果证实该评估方法对多个节点的情况同样准确有效,从而解决了实际工程数值模拟计算中需要同时对多节点变量评估计算效率提高程度的问题.
文摘Blind adaptive multiuser detector has become a research hotspot in recent years due to a number of advantages, but many blind adaptive algorithms involve low convergence rate. This paper presents a novel stochastic blind adaptive multiuser detector without requiring training sequences, which needs only two system parameters: the signature sequence of the desired user i, s i and the variance of the additive white Gaussian noise (AWGN),σ 2. Simulation results show that by reasonably choosing time varying step size, the proposed detector can not only improve the convergence rate, but also reduce the limiting NSE (Normalized Squared Error) values, so it can effectively increase the performance of the system.
