Adjoint Hamiltonian Monte Carlo algorithm for the estimation of elastic modulus through the inversion of elastic wave propagation data

Efficient inversion of noisy seismic waveform data produced due to elastic wave propagation for the estimation of a high-dimensional elastic modulus vector is achieved. Estimation is carried out in a Bayesian framework using Hamiltonian Monte Carlo (HMC) that enables efficient statistical estimation over high-dimensional parameters. The truncated Karhunen-Loève (K-L) expansion is introduced to reduce the dimensionality of the elastic modulus vector. Expensive computations of the gradient of the state vector with respect to the parameter vector at every step are also eliminated through the adjoint method, which is developed from a general one-step discretization of the governing second-order ordinary differential equations (ODEs). An Adjoint HMC algorithm that employs a truncated K-L expansion of the elastic modulus vector is presented. The efficacy of the algorithm is investigated with respect to two representative problems with varying geometric complexity. Adjoint HMC offers a significant speed up in gradient calculation time over the direct differentiation counterpart as the number of terms in the K-L expansion increases. The algorithm is able to estimate the true elastic modulus within the credible intervals for both cases.     

Inverse Design Strategies for 3D Surfaces Formed by Mechanically Guided Assembly

Deterministic transformations of 2D patterns of materials into well-controlled 3D mesostructures serve as the basis for manufacturing methods that can bypass limitations of conventional 3D micro/nanofabrication. Here, guided mechanical buckling processes provide access to a rich range of complex 3D mesostructures in high-performance materials, from inorganic and organic semiconductors, metals and dielectrics, to ceramics and even 2D materials (e.g., graphene, MoS₂). Previous studies demonstrate that iterative computational procedures can define design parameters for certain targeted 3D configurations, but without the ability to address complex shapes. A technical need is in efficient, generalized inverse design algorithms that directly yield sets of optimized parameters. Here, such schemes are introduced, where the distributions of thicknesses across arrays of separated or interconnected ribbons provide scalable routes to 3D surfaces with a broad range of targeted shapes. Specifically, discretizing desired shapes into 2D ribbon components allows for analytic solutions to the inverse design of centrally symmetric and even general surfaces, in an approximate manner. Combined theoretical, numerical, and experimental studies of ≈20 different 3D structures with characteristic sizes (e.g., ribbon width) ranging from ≈200 µm to ≈2 cm and with geometries that resemble hemispheres, fire balloons, flowers, concave lenses, saddle surfaces, waterdrops, and rodents, illustrate the essential ideas.     

Antiferromagnetic Inverse Spinel Oxide LiCoVO4 with Spin-Polarized Channels for Water Oxidation

Exploring highly efficient catalysts for the oxygen evolution reaction (OER) is essential for water electrolysis. Cost-effective transition-metal oxides with reasonable activity are raising attention. Recently, OER reactants' and products' differing spin configurations have been thought to cause slow reaction kinetics. Catalysts with magnetically polarized channels could selectively remove electrons with opposite magnetic moment and conserve overall spin during OER, enhancing triplet state oxygen molecule evolution. Herein, antiferromagnetic inverse spinel oxide LiCoVO₄ is found to contain d⁷ Co²⁺ ions that can be stabilized under active octahedral sites, possessing high spin states S = 3/2 (t_2g⁵e_g²). With high spin configuration, each Co²⁺ ion has an ideal magnetic moment of 3 µ_B, allowing the edge-shared Co²⁺ octahedra in spinel to be magnetically polarized. Density functional theory simulation results show that the layered antiferromagnetic LiCoVO₄ studied contains magnetically polarized channels. The average magnetic moment (µ_ave) per transition-metal atom in the spin conduction channel is around 2.66 µ_B. Such channels are able to enhance the selective removal of spin-oriented electrons from the reactants during the OER, which facilitates the accumulation of appropriate magnetic moments for triplet oxygen molecule evolution. In addition, the LiCoVO₄ reported has been identified as an oxide catalyst with excellent OER activity.     

Biomechanical demands of percussive techniques in the context of early stone toolmaking

Recent discoveries in archaeology and palaeoanthropology highlight that stone tool knapping could have emerged first within the genera Australopithecus or Kenyanthropus rather than Homo. To explore the implications of this hypothesis determining the physical demands and motor control needed for performing the percussive movements during the oldest stone toolmaking technology (i.e. Lomekwian) would help. We analysed the joint angle patterns and muscle activity of a knapping expert using three stone tool replication techniques: unipolar flaking on the passive hammer (PH), bipolar (BP) flaking on the anvil, and multidirectional and multifacial flaking with free hand (FH). PH presents high levels of activity for Biceps brachii and wrist extensors and flexors. By contrast, BP and FH are characterized by high solicitation of forearm pronation. The synergy analyses depict a high muscular and kinematic coordination. Whereas the muscle pattern is very close between the techniques, the kinematic pattern is more variable, especially for PH. FH displays better muscle coordination and conversely lesser joint angle coordination. These observations suggest that the transition from anvil and hammer to freehand knapping techniques in early hominins would have been made possible by the acquisition of a behavioural repertoire producing an evolutionary advantage that gradually would have been beneficial for stone tool production.     

一种针对含非线性子结构多点耦合运输包装系统的解耦方法

目的 考虑到运输包装系统耦合形式复杂,包装材料及包装结构具有非线性特性,不容易测量局部物理参数,需要对传统逆向子结构方法进行优化,使之能够求解非线性多点耦合系统中子结构的动态响应特性。方法 使用描述函数法将非线性的运输包装系统线性化,测量其在若干特定振动幅值下的频率响应函数;之后,应用逆向子结构方法和参数识别方法,计算包装件的模态参数;最后,拟合包装件模态参数与振动幅值之间的关系,构建函数来描述包装件的动态响应特性。结果 在集总参数模型中,解耦预测值与实际值吻合;在有限元模型中,对响应峰值的预测误差小于5%,对响应跳跃现象所在频率的预测误差小于3%。结论 该研究将传统逆向子结构方法的应用范围拓展到了非线性多点耦合系统,对复杂运输包装系统动力学模型的构建和防振包装的设计具有指导意义。     

强干扰环境下声源可视化重建方法的研究进展

准确识别噪声源是机电产品噪声控制的关键,其中,近场声全息和波束形成是两种常用的声源可视化重建方法,分别适用于近场低频和远场高频声源重建的情况。传统的声全息和波束形成方法基于自由场假设,即适用于目标声源辐射声与干扰噪声之间的信噪比大于10 dB的情况。然而很多机电产品的噪声测试只能在工作现场进行,不满足自由场条件。为此,从声学传播方程和信号处理两个方面出发,回顾了强干扰环境下声源可视化重建方法的研究发展历程,评点了每种方法的特点和适用范围。重点介绍了强干扰环境下的近场声全息方法,包括声场分离法和逆块传递函数法。另外,还介绍了混响环境下的声源重建方法以及基于信号处理的信号噪声分离方法。最后,讨论了强干扰环境下声源重建有待解决的问题及其发展趋势。     

分裂四元数矩阵方程$AXB+CYD=E$的最小二乘$\eta$-埃尔米特解问题

分裂四元数矩阵方程求约束解问题在数学研究和物理应用中有重要的科学意义,针对分裂四元数矩阵的范数定义所造成的最小二乘解求解困难问题,研究了分裂四元数矩阵方程$AXB +CY D = E$的最小二乘$\eta$-埃尔米特解。首先定义分裂四元数反对合变换和$\eta$-埃尔米特矩阵,其次引入分裂四元数矩阵的Frobenius范数,通过基于分裂四元数矩阵的复表示,解决最小二乘解的求解困难问题。最后利用矩阵的Moore-Penrose广义逆以及Kronecker积,推导出分裂四元数矩阵方程的最小二乘$\eta$-埃尔米特解以及唯一极小范数解的表达式。数值实验验证了该方法的可行性。     

Lagrange函数族及其存在条件的再研究

再研究由第一积分组成Lagrange函数族的结构及其存在条件,指出同一个函数族有多种表示方式,并给出新形式的函数族的存在条件.     

牵引式下肢康复机器人机构参数优化及轨迹规划

为满足下肢运动功能障碍患者在不同阶段的康复训练需求,针对现有下肢康复机器人训练方式单一的问题,提出了一种可实现卧姿、坐姿训练模式的牵引式下肢康复机器人。首先,根据人体下肢运动机理和仿生原理,设计了一种五自由度混联机构构型。然后,建立了机器人的运动学模型,分别计算了其运动学正、逆解。接着,以人体下肢末端与机器人末端的工作空间重合度为目标函数,采用遗传算法对机器人的机构参数进行了优化,并求得人机系统矢状面内人体下肢的有效工作空间比为0.71。最后,规划了CPM（continuous passive motion,连续被动运动）、圆周运动和螺旋运动等3种康复训练运动轨迹,并根据优化后的机构参数搭建了机器人样机,通过运动捕捉实验验证了机器人结构设计与优化结果的合理性以及轨迹规划的正确性,表明该机器人能够满足下肢运动功能障碍患者的康复需求。