Image Registration with Guaranteed Displacement Regularity

The goal of image registration is twofold. One goal is to enforce a certain similarity of two images by geometrically transforming one of the images. The second goal is to keep this transformation meaningful or regular. There exists a large amount of approaches aiming for regularity. Most of those are based on certain regularization techniques, others use so-called regridding options. Here, we present a mathematically sound formulation that explicitly controls the deformation in terms of the determinant of the Jacobian of the transformation. In contrast to similar work, we use pointwise inequality constraints, i.e., the volume is controlled voxel by voxel and not by integral measures. This approach guaranties grid regularity and prevent folding. As it turns out, the discretization of the volume constraint inequality is not straightforward. Therefore, we present a new type of discretization enabling the detection of twists in a pixel or a voxel. Such detection is crucial since a twists indicates that a transformation is physically meaningless. To solve the large-scale inequality constrained optimization problem, we present a numerical approach based on an interior point method. We finally present some numerical examples that demonstrate the advantage of including inequality constraints explicitly. This work was supported by NSF grant CCF-0427094 and NIH grant NIH R01 HL068904.     

边箱形梁剪力滞效应的能量变分法研究

利用能量变分法[1,4]对边箱形截面的剪力滞效应进行分析.通过变分法推得微分方程组并对其求解所得进行分析讨论.最后结合示例进行计算,并与有限元分析软件计算结果进行比较分析.     

设置跨内横隔板的箱形梁畸变效应分析

为了分析跨内横隔板布置对箱形梁畸变效应的影响,提出一种适用于跨内有横隔板的箱形梁畸变效应解析法。应用基于最小势能原理的能量变分法建立畸变控制微分方程并导出以克雷洛夫函数表达的初参数解。将跨内横隔板对畸变变形的约束作用通过未知畸变矩代替,并根据变形协调关系及初参数解确定未知畸变矩大小,从而获得有跨内横隔板的箱形梁畸变效应解析解。用该文解析法和ANSYS有限元法分别计算悬臂箱梁试验模型和简支箱梁算例的畸变效应,并分析跨中横隔板布置及截面参数变化对简支箱梁畸变效应的影响规律。研究结果表明：该文解析解与模型试验实测值及ANSYS有限元数值解均吻合良好;仅在跨中布置1道横隔板虽然可以减小畸变变形及畸变横向弯矩,但使畸变翘曲双力矩显著增大;随着悬臂板宽度的增大,腹板与顶板交接处的畸变翘曲应力迅速减小;腹板厚度变化对腹板与底板交接处的畸变翘曲应力也有显著影响。     

Computational structural and material stability analysis in finite electro‐elasto‐statics of electro‐active materials

Dielectric materials like electro‐active polymers (EAPs) exhibit coupled electro‐mechanical behavior at large strains. They respond by a deformation to an applied electrical field and are used in advanced industrial environments as sensors and actuators, for example, in robotics, biomimetics and smart structures. In field‐activated or electronic EAPs, the electric activation is driven by Coulomb‐type electrostatic forces, resulting in Maxwell stresses. These materials are able to provide finite actuation strains, which can even be improved by optimizing their composite microstructure. However, EAPs suffer from different types of instabilities. This concerns global structural instabilities, such as buckling and wrinkling of EAP devices, as well as local material instabilities, such as limit‐points and bifurcation‐points in the constitutive response, which induce snap‐through and fine scale localization of local states. In this work, we outline variational‐based definitions for structural and material stability, and design algorithms for accompanying stability checks in typical finite element computations. The formulation starts from stability criteria for a canonical energy minimization principle of electro‐elasto‐statics, and then shifts them over to representations related to an enthalpy‐based saddle point principle that is considered as the most convenient setting for numerical implementation. Here, global structural stability is analyzed based on a perturbation of the total electro‐mechanical energy, and related to statements of positive definiteness of incremental finite element tangent arrays. We base the local material stability on an incremental quasi‐convexity condition of the electro‐mechanical energy, inducing the positive definiteness of both the incremental electro‐mechanical moduli as well as a generalized acoustic tensor. It is shown that the incremental arrays to be analyzed in the stability criteria appear within the enthalpy‐based setting in a distinct diagonal form, with pure mechanical and pure electrical partitions. Applications of accompanying stability analyses in finite element computations are demonstrated by means of representative model problems. Copyright © 2015 John Wiley & Sons, Ltd.     

混凝土箱梁考虑翼板厚度变化的剪力滞效应

针对翼板沿截面宽度方向变厚度的混凝土箱梁,利用势能变分原理,建立了可以考虑翼板厚度变化的剪滞效应分析通用方法;针对简支梁和悬臂梁等基本结构体系,系统研究了改变翼板厚度变化对正剪力滞效应、负剪力滞效应和剪力滞变形的影响规律.结果表明,翼板厚度变化对箱梁的截面应力和变形均产生影响.考虑翼板厚度变化对计算结果的影响可达15％.     

Formulation and numerical exploitation of mixed variational principles for coupled problems of Cahn–Hilliard‐type and standard diffusion in elastic solids

This work develops variational principles for the coupled problem of standard and extended Cahn–Hilliard‐type species diffusion in solids undergoing finite elastic deformations. It shows that the coupled problem of diffusion in deforming solids, accounting for phenomena like swelling, diffusion‐induced stress generation and possible phase segregation caused by the diffusing species, is related to an intrinsic mixed variational principle. It determines the rates of deformation and concentration along with the chemical potential, where the latter plays the role of a mixed variable. The principle characterizes a canonically compact model structure, where the three governing equations involved, that is, the mechanical equilibrium condition, the mass balance for the species content and a microforce balance that determines the chemical potential, appear as the Euler equation of a variational statement. The existence of the variational principle underlines an inherent symmetry of the coupled deformation–diffusion problem. This can be exploited in the numerical implementation by the construction of time‐discrete and space‐discrete incremental potentials, which fully determine the update problems of typical time stepping procedures. The mixed variational principles provide the most fundamental approach to the monolithic finite element solution of the coupled deformation–diffusion problem based on low‐order basis functions. They induce in a natural format the choice of symmetric solvers for Newton‐type iterative updates, providing a speedup and reduction of data storage when compared with non‐symmetric implementations. This is a strong argument for the use of the developed variational principles in the computational design of deformation–diffusion problems. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple periodic solutions with prescribed minimal period to second-order Hamiltonian systems

A new variational method based on Ekeland’s principle is introduced for the existence, localization and multiplicity of periodic solutions of a prescribed minimal period to second-order Hamiltonian systems. The oscillatory property at zero or infinity of only one component of the gradient of the potential function is sufficient for the existence of infinitely many solutions. Also, oscillating properties of several components of the gradient of the potential function yield sequences of solutions with some of the components tending in norm to zero and others to infinity.     

基于VMD和多尺度熵的变压器内绝缘局部放电信号特征提取及分类

为了有效提取局部放电信号的特征,提出了一种基于变分模态分解(VMD)和多尺度熵(MSE)的特征向量提取方法,并采用BP神经网络分类器对放电类型进行识别。特征向量的提取过程是首先利用VMD分解算法对局部放电信号进行分解,得到数个有限带宽的固有模态分量;然后分别计算分解得到的模态分量的MSE,将其组合得到初始特征向量;最后利用主成分分析法对初始特征向量进行降维处理。用该方法对实验室条件下4种放电信号和不同放电程度的电晕放电进行特征提取及识别。结果表明,该方法能有效提取放电信号的特征,以其作为特征向量可以正确识别不同的放电类型和同种放电类型下的不同放电程度。     

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.     

用于鲁棒协同推荐的元信息增强变分贝叶斯矩阵分解模型

托攻击是协同过滤推荐系统面临的重大安全威胁. 研究可抵御托攻击的鲁棒协同推荐技术已成为目前的重要课题. 本文在引入用户嫌疑性评估策略的基础上, 通过将用户嫌疑性及项类属等元信息与贝叶斯概率矩阵分解模型相融合, 提出了用于鲁棒协同推荐的元信息增强变分贝叶斯矩阵分解模型(Metadata-enhanced variational Bayesian matrix factorization, MVBMF), 并设计了相应的模型增量学习策略. 实验表明, 与现有推荐模型相比, 这种模型具备更强的攻击耐受力, 能够有效提高推荐系统的鲁棒性.