共查询到18条相似文献,搜索用时 156 毫秒
1.
2.
3.
基于控制理论的气动设计方法作为一种基于梯度的优化方法,通过引入伴随系统计算目标函数的敏感性导数,大大降低设计成本.本文将基于控制理论的气动设计方法应用到透平叶栅的气动反问题中,应用Euler方程研究了二维叶栅的压力反设计问题,并讨论了该方法具体实施中的关键问题,包括采用非均匀B样条进行二维叶栅造型;应用Thompson时间相关边界条件理论进行伴随方程特征分析;研究伴随方程的数值求解方法,构造伴随方程的耗散通量.通过算例证明了该气动设计方法适用性好,速度快,可以大大节约计算成本. 相似文献
4.
透平叶栅三维粘性气动反问题的控制理论方法 总被引:2,自引:0,他引:2
将基于控制理论的形状优化设计方法应用于粘性可压流动条件下的透平叶栅三维气动反设计,详细推导了三维N-S方程伴随系统的偏微分方程组及其各类边界条件.讨论了伴随系统的解的适定性条件,并由此给出应用N-S方程进行气动优化的目标函数的选取限制.研究了伴随方程的数值求解技术,给出敏感性导数的最终计算式,结合拟牛顿算法发展了三维透平叶栅粘性反问题的气动设计方法. 相似文献
5.
6.
7.
8.
9.
近年来,物理信息神经网络(PINNs)因其仅通过少量数据就能快速获得高精度的数据驱动解而受到越来越多的关注.然而,尽管该模型在部分非线性问题中有着很好的结果,但它还是有一些不足的地方,如它的不平衡的反向传播梯度计算导致模型训练期间梯度值剧烈振荡,这容易导致预测精度不稳定.基于此,本文通过梯度统计平衡了模型训练期间损失函数中不同项之间的相互作用,提出了一种梯度优化物理信息神经网络(GOPINNs),该网络结构对梯度波动更具鲁棒性.然后以Camassa-Holm(CH)方程、导数非线性薛定谔方程为例,利用GOPINNs模拟了CH方程的peakon解和导数非线性薛定谔方程的有理波解、怪波解.数值结果表明,GOPINNs可以有效地平滑计算过程中损失函数的梯度,并获得了比原始PINNs精度更高的解.总之,本文的工作为优化神经网络的学习性能提供了新的见解,并在求解复杂的CH方程和导数非线性薛定谔方程时用时更少,节约了超过三分之一的时间,并且将预测精度提高了将近10倍. 相似文献
10.
列车运行的优化控制是降低运输成本,提高运输服务质量以及实现轨道交通可持续发展的重要方式.本文在传统优化速度跟驰模型的基础上,以能量节约为目标提出了一种改进的模拟模型,用以模拟分析城市轨道交通系统中列车运行的优化控制.所提出的模型是通过在经典的优化速度跟驰模型(见Phys.Rev.E 51 1035 Bando等,1995)中引入新的目标优化速度函数来实现在复杂限速条件下列车运行的优化控制.数值模拟则是以北京市地铁亦庄线为例,利用亦庄线实测数据开展研究.结果表明,所提出的模型能够很好地描述复杂限速条件下列车运行的动态特性,模拟测量得到的结果和亦庄线的实测数据较为符合,由此说明所提出模型的有效性.进一步,通过分析列车运行时空图,列车运行的速度变化及运行时间等,讨论了复杂环境下列车流的时空演化特性. 相似文献
11.
The well-posedness of the data assimilation problem for the Navier–Stokes-α equations on a bounded three-dimensional domain is investigated. The data assimilation procedures under consideration are the adjoint method of variational data assimilation (4D-Var) and the method of continuous data assimilation. Concerning the adjoint method the existence of optimal initial conditions with respect to an observation-dependent cost functional is proven, the optimizers are characterized by a first-order necessary condition involving the adjoint linearized Navier–Stokes-α equations and conditions for the uniqueness of the initial conditions are given. Well-posedness of the continuous data assimilation problem is proven and convergence rates in terms of observational resolution are provided. 相似文献
12.
In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings. 相似文献
13.
Eugene Kazantsev 《Journal of computational physics》2010,229(2):256-275
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows us to discuss in detail as the development of the adjoint model and assimilation results. It is shown what kind of errors can be corrected by this control and how these errors are corrected. This study is carried out in view of using this control to identify optimal numerical schemes in coastal regions of ocean models. 相似文献
14.
This paper applies the concept of optimal boundary control for solving inverse problems in shallow water acoustics. To treat the controllability problem, a continuous analytic adjoint model is derived for the Claerbout wide-angle parabolic equation (PE) using a generalized nonlocal impedance boundary condition at the water-bottom interface. While the potential of adjoint methodology has been recently demonstrated for ocean acoustic tomography, this approach combines the advantages of exact transparent boundary conditions for the wide-angle PE with the concept of adjoint-based optimal control. In contrast to meta-heuristic approaches the inversion procedure itself is directly controlled by the waveguide physics and, in a numerical implementation based on conjugate gradient optimization, many fewer iterations are required for assessment of an environment that is supported by the underlying subbottom model. Furthermore, since regularization schemes are particularly important to enhance the performance of full-field acoustic inversion, special attention is devoted to the application of penalization methods to the adjoint optimization formalism. Regularization incorporates additional information about the desired solution in order to stabilize ill-posed inverse problems and identify useful solutions, a feature that is of particular importance for inversion of field data sampled on a vertical receiver array in the presence of measurement noise and modeling uncertainty. Results with test data show that the acoustic field and the bottom properties embedded in the control parameters can be efficiently retrieved. 相似文献
15.
16.
I.Yu. Gejadze G.J.M. Copeland F.-X. Le Dimet V. Shutyaev 《Journal of computational physics》2011,230(22):7923-7943
The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The data contain errors (observation and background errors), hence there will be errors in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can often be approximated by the inverse Hessian of the cost functional. Here we focus on highly nonlinear dynamics, in which case this approximation may not be valid. The equation relating the optimal solution error and the errors of the input data is used to construct an approximation of the optimal solution error covariance. Two new methods for computing this covariance are presented: the fully nonlinear ensemble method with sampling error compensation and the ‘effective inverse Hessian’ method. The second method relies on the efficient computation of the inverse Hessian by the quasi-Newton BFGS method with preconditioning. Numerical examples are presented for the model governed by Burgers equation with a nonlinear viscous term. 相似文献
17.
《中国物理 B》2019,(10)
Traditional geoacoustic inversions are generally solved by matched-field processing in combination with metaheuristic global searching algorithms which usually need massive computations. This paper proposes a new physical framework for geoacoustic retrievals. A parabolic approximation of wave equation with non-local boundary condition is used as the forward propagation model. The expressions of the corresponding tangent linear model and the adjoint operator are derived, respectively, by variational method. The analytical expressions for the gradient of the cost function with respect to the control variables can be formulated by the adjoint operator, which in turn can be used for optimization by the gradient-based method. 相似文献
18.
The problem of optimal tracking control with zero steady-state error for linear time-delay systems with sinusoidal disturbances is considered. Based on the internal model principle, a disturbance compensator is constructed such that the system with external sinusoidal disturbances is transformed into an augmented system without disturbances. By introducing a sensitivity parameter and expanding power series around it, the optimal tracking control problem can be simplified into the problem of solving an infinite sum of linear optimal control series without time-delay and disturbance. The obtained optimal tracking control law with zero steady-state error consists of accurate linear state feedback terms and a time-delay compensating term, which is an infinite sum of an adjoint vector series. The accurate linear terms can be obtained by solving a Riccati matrix equation and a Sylvester equation, respectively. The compensation term can be approximately obtained through a recursive algorithm. A numerical simulation shows that the algorithm is effective and easily implemented, and the designed tracking controller is robust with respect to the sinusoidal disturbances. 相似文献