A new approach to model reduction of nonlinear control systems using smooth orthogonal decomposition

A new approach to model order reduction of nonlinear control systems is aimed at developing persistent reduced order models (ROMs) that are robust to the changes in system's energy level. A multivariate analysis method called smooth orthogonal decomposition (SOD) is used to identify the dynamically relevant modal structures of the control system. The identified SOD subspaces are used to develop persistent ROMs. Performance of the resultant SOD‐based ROM is compared with proper orthogonal decomposition (POD)–based ROM by evaluating their robustness to the changes in system's energy level. Results show that SOD‐based ROMs are valid for a relatively wider range of the nonlinear control system's energy when compared with POD‐based models. In addition, the SOD‐based ROMs show considerably faster computations compared to the POD‐based ROMs of same order. For the considered dynamic system, SOD provides more effective reduction in dimension and complexity compared to POD.     

POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification

In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both linear and nonlinear equations are considered. We demonstrate the effectiveness of the ROM by several numerical examples, in which the ROM achieves the same accuracy of the full-order model (FOM) over a long-term simulation while greatly reducing the computational cost. The proposed ROM is then regarded as a surrogate of FOM and is applied to an inverse problem for identifying the order of the time-fractional derivative of the TFPDE model. Based on the Levenberg–Marquardt regularization iterative method with the Armijo rule, we develop a ROM-based algorithm for solving the inverse problem. For cases in which the observation data is either uncontaminated or contaminated by random noise, the proposed approach is able to achieve accurate parameter estimation efficiently.     

The effect of incident flow on a supersonic circumfluence of a blunt object

The influence of the inhomogeneity of a narrow wake with a reduced Mach number and total pressure values on the circumfluence about a blunt body (truncated cone) has been investigated. Two variants in the wake formation have been considered: behind the energy source and behind the moving body. A free boundary method was used for the flow simulation about moving bodies (a variant of the immersed boundary method). The dynamics of the moving body interaction with the head shock wave and formation of the reverse flow region have been studied. For consideration of these modes, it is shown that the presence of the wake before the front part of the body leads to a considerable decrease of wave resistance.     

Effects of age and gender on maximum voluntary range of motion of the upper body joints

The maximum voluntary range of motion (ROM) of the major joints of the upper body was studied in a seated position and compared between young and elderly subjects. A total of 41 subjects (22 young male and female subjects aged 25 to 35 years, 19 elderly male and female subjects aged 65 to 80 years) took part in the experiment. In total, 13 maximum voluntary joint motions were performed by each subject. Age was found to have a non-uniform effect on the ROM of the joints investigated in this study. Its effect on ROM was joint specific and motion specific. The highest loss in ROM was observed in the neck and trunk, especially for neck extension, lateral flexion and axial rotation as well as for trunk lateral flexion and axial rotation. No significant age differences were observed in the elbow and wrist joint ROMs. The effect of gender on joint ROM was much weaker than that of age. Only four among the 26 joint ROMs investigated in this study were significantly different between the two gender groups.     

Reduced Modeling of Unknown Trajectories

This paper deals with model order reduction of parametrical dynamical systems. We consider the specific setup where the distribution of the system’s trajectories is unknown but the following two sources of information are available: (i) some “rough” prior knowledge on the system’s realisations; (ii) a set of “incomplete” observations of the system’s trajectories. We propose a Bayesian methodological framework to build reduced-order models (ROMs) by exploiting these two sources of information. We emphasise that complementing the prior knowledge with the collected data provably enhances the knowledge of the distribution of the system’s trajectories. We then propose an implementation of the proposed methodology based on Monte-Carlo methods. In this context, we show that standard ROM learning techniques, such e.g., proper orthogonal decomposition or dynamic mode decomposition, can be revisited and recast within the probabilistic framework considered in this paper. We illustrate the performance of the proposed approach by numerical results obtained for a standard geophysical model.     

Effects of age and gender on maximum voluntary range of motion of the upper body joints

The maximum voluntary range of motion (ROM) of the major joints of the upper body was studied in a seated position and compared between young and elderly subjects. A total of 41 subjects (22 young male and female subjects aged 25 to 35 years, 19 elderly male and female subjects aged 65 to 80 years) took part in the experiment. In total, 13 maximum voluntary joint motions were performed by each subject. Age was found to have a non-uniform effect on the ROM of the joints investigated in this study. Its effect on ROM was joint specific and motion specific. The highest loss in ROM was observed in the neck and trunk, especially for neck extension, lateral flexion and axial rotation as well as for trunk lateral flexion and axial rotation. No significant age differences were observed in the elbow and wrist joint ROMs. The effect of gender on joint ROM was much weaker than that of age. Only four among the 26 joint ROMs investigated in this study were significantly different between the two gender groups.     

On the computation of two-dimensional compressible flow fields by the modified local stability scheme

The modified local stability scheme is applied to several two-dimensional problems—blunt body flow, regular reflection of a shock and lambda shock. The resolution of the flow features obtained by the modified local stability scheme is found to be better than that achieved by the other first order schemes and almost identical to that achieved by the second order schemes incorporating artificial viscosity. The scheme is easy for coding, consumes moderate amount of computer storage and time. The scheme can be advantageously used in place of second order schemes.     

A multi-point reduced-order modeling approach of transient structural dynamics with application to robust design optimization

Predicting the transient response of structures by high-fidelity simulation models within design optimization and uncertainty quantification often leads to unacceptable computational cost. This paper presents a reduced-order modeling (ROM) framework for approximating the transient response of linear elastic structures over a range of design and random parameters. The full-order response is projected onto a lower-dimensional basis spanned by modes computed from a proper orthogonal decomposition (POD) of full-order model simulation results at multiple calibration points. The basis is further enriched by gradients of the POD modes with respect to the design/random parameters. A truncation strategy is proposed to compensate for the increase in basis vectors due to the proposed enrichment strategies. The accuracy, efficiency and robustness of the proposed framework are studied with a two-dimensional model problem. The numerical results suggest that the proposed ROM approach is well suited for large parameter changes and that the number of basis vectors needs to be increased only linearly with the number of design and random parameters to maintain a particular ROM performance. The application of the proposed ROM approach to robust shape optimization demonstrates significant savings in computational cost over using full-order models. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.     

无线传感网中混合业务下的触发式流控制算法

无线传感器网络中,节点所具有的能量和通信能力等都十分有限,如何设计有效的协议及算法,利用有限的资源高效地完成诸多任务,成为无线传感器网络设计所面临的一大挑战.考虑接收容量模型,研究了无线传感器网络在节点接收容量和能量联合受限情况下,面向混合业务时的效用公平流控制问题,并针对传统对偶分解算法存在着收敛速度慢、步长不易调节、通信负荷大等缺陷,进一步提出了基于事件触发的分布式求解算法.理论分析与仿真验证均表明:使用事件触发算法时,传感节点的平均广播周期比使用对偶分解算法时大很多,大幅度降低了无线传感器网络节点间的通信量,减少了网络的通信开销.仿真结果显示:与对偶分解算法相比,分布式事件触发算法具有收敛速度快、对网络规模扩展的适应性强等优势;与传统的速率公平流控制机制相比,所提的效用公平流控制模型能够更加适应弹性与非弹性业务共存的网络场景.     

模型的快速降阶技术

为快速进行模型的降阶,结合平衡截断（Balanced Truncation,BT）方法和特征正交分解（Proper Orthogonal Decomposition,POD）方法提出一种模型降阶方法.该方法采用频域POD快照矩阵低阶逼近系统的可控、可观Gram矩阵;通过奇异值分解（Singular Value Decomposition,SVD）提取BT＋POD模态,对低能量模态截断形成降阶子空间,并将其映射到全阶系统,从而形成基于状态空间的降阶模型（Reduced Order Model,ROM）;该模型就成为全阶模型（Full Order Model,FOM）的ROM.通过对阶数n=406的LTI SISO系统和阶数n=9的2区间电力系统进行的验证表明,在保留BT方法输入输出平衡特性的基础上,该方法效率高于BT方法.