This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
针对正交时频空(Orthogonal Time Frequency Space,OTFS)通信系统信号检测复杂度高的问题,提出一种改进的高斯近似消息传递(Gaussian Approximate Message Passing,GA-MP)检测算法。依据最大后验概率检测准则,对发送信号及隐变量进行逐...针对正交时频空(Orthogonal Time Frequency Space,OTFS)通信系统信号检测复杂度高的问题,提出一种改进的高斯近似消息传递(Gaussian Approximate Message Passing,GA-MP)检测算法。依据最大后验概率检测准则,对发送信号及隐变量进行逐符号高斯近似,基于置信传播算法与联合因子图进行消息传递,用边缘后验概率替代GA-MP中的外部信息以减少运算量,结合阻尼因子提升收敛速度,同时引入概率阈值减少后续更新的节点数,从而使运算复杂度得到有效降低。实验结果表明,改进后的GA-MP算法在保证误码率性能的前提下具有更低的复杂度。展开更多
软基水闸底板脱空是水闸在长期服役期间受水流侵蚀等环境因素影响所产生的一种危害极大且难以察觉的病害。由于其病害部位于水下,传统方法难以检测,该研究提出一种基于高斯过程回归(Gaussian process regression,GPR)代理模型和遗传-自...软基水闸底板脱空是水闸在长期服役期间受水流侵蚀等环境因素影响所产生的一种危害极大且难以察觉的病害。由于其病害部位于水下,传统方法难以检测,该研究提出一种基于高斯过程回归(Gaussian process regression,GPR)代理模型和遗传-自适应惯性权重粒子群(genetic algorithm-adaptive particle swarm optimization,GA-APSO)混合优化算法的水闸底板脱空动力学反演方法,用于检测软基水闸底板脱空。首先,构建表征软基水闸底板脱空参数和水闸结构模态参数之间非线性关系的GPR代理模型;其次,基于GPR代理模型与水闸实测模态参数建立脱空反演的最优化数学模型,将反演问题转化为目标函数最优化求解问题;最后,为提高算法寻优计算的精度,提出一种GA-APSO混合优化算法对目标函数进行脱空反演计算,并提出一种更合理判断反演脱空区域面积和实际脱空区域面积相对误差的指标—面积不重合度。为验证所提方法性能,以一室内软基水闸物理模型为例,对两种不同脱空工况开展研究分析,结果表明,反演脱空区域面积和模型实际设置脱空区域面积的相对误差分别为8.47%和10.77%,相对误差值较小,证明所提方法能有效反演出水闸底板脱空情况,可成为软基水闸底板脱空反演检测的一种新方法。展开更多
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
文摘针对正交时频空(Orthogonal Time Frequency Space,OTFS)通信系统信号检测复杂度高的问题,提出一种改进的高斯近似消息传递(Gaussian Approximate Message Passing,GA-MP)检测算法。依据最大后验概率检测准则,对发送信号及隐变量进行逐符号高斯近似,基于置信传播算法与联合因子图进行消息传递,用边缘后验概率替代GA-MP中的外部信息以减少运算量,结合阻尼因子提升收敛速度,同时引入概率阈值减少后续更新的节点数,从而使运算复杂度得到有效降低。实验结果表明,改进后的GA-MP算法在保证误码率性能的前提下具有更低的复杂度。
