Quadratic properties of least-squares solutions of linear matrix equations with statistical applications

Assume that a quadratic matrix-valued function \(\psi (X) = Q - X^{\prime }PX\) is given and let \(\mathcal{S} = \left\{ X\in {\mathbb R}^{n \times m} \, | \, \mathrm{trace}[\,(AX - B)^{\prime }(AX - B)\,] = \min \right\} \) be the set of all least-squares solutions of the linear matrix equation \(AX = B\). In this paper, we first establish explicit formulas for calculating the maximum and minimum ranks and inertias of \(\psi (X)\) subject to \(X \in {\mathcal S}\), and then derive from the formulas the analytic solutions of the two optimization problems \(\psi (X) =\max \) and \(\psi (X)= \min \) subject to \(X \in \mathcal{S}\) in the Löwner partial ordering. As applications, we present a variety of results on equalities and inequalities of the ordinary least squares estimators of unknown parameter vectors in general linear models.     

软夹硬力学不均匀焊接接头疲劳裂纹闭合行为的实验研究

力学性能不均匀是焊接接头的三大待征之一，本文采用柔度法研究了不同硬夹层宽度的软夹硬力学不均匀焊接接头疲劳裂纹的闭俣行为。研究结果表明，裂纹尖端附近软区的局部屈服在疲劳载荷卸载过程中促使裂纹闭合。随着硬夹层宽度的减小，这一影响越来越明显。     

采用MRAC的气－液联合多通道协调加载控制系统的研究

气压系统与液压系统的特性存在着较大的差异，本文研究了该系统的自适应控制方法。根据气－液控制系统的技术特点，作者提出了采用参考模型自适应控制的策略，并解决了控制器设计、实现中的一系列技术问题。经过试验，证明本文的研究是成功的。     

硬岩中地下爆炸的自由场位移衰减规律

本文从两个方面叙述总结了硬岩中,地下爆炸引起的自由场的径向质点位移随爆心距的变化规律。其一是分析地下爆炸应力波经验规律结合方程式求解得到的地运动位移,有下规律:DM/W?=2.01(（1/100）(R/W?))?(DM为地运动位移峰值,W为爆炸当量,R为爆炸距,其二是用地运动位移传感器直接测到的地运动位移,可用DM/W?=2.1(（1/100）(R/W?))?表示地运动位移的变化规律。由这两种方法得到的位移结果的一致性较好。文中并对所得位移经验公式与国外报导的位移公式作了对比分析。     

时滞对结构振动半主动控制效果的影响

应用磁流变阻尼器对结构振动进行控制，采用最优控制原理设计了控制器，给出在地震激励下结构半主动控制的仿真计算。研究了时滞对结构振动半主动控制效果的影响。数值结果表明：本文设计的半主动控制策略可有效地减小结构的振动响应，时滞对磁流变半主动控制效果随着时滞的增大而变差，但时滞不会导致该反馈控制系统的失稳。     

计算机模拟升降法试验的研究

介绍了计算机模拟感度试验的原理，运用计算机模拟方法研究了升降法试验的初始参数选择对感度分布参数估计精度的影响，取得了对升降法有利的试验条件。     

Formation, structure, and evolution of boiling nucleus and interfacial tension between bulk liquid phase and nucleus

In this paper, the concept of the molecular free path is introduced to derive a criterion distinguishing active molecules from inactive molecules in liquid phase. A concept of the critical aggregation concentration (CAC) of active molecules is proposed to describe the physical configuration before the formation of a nucleus during vapor–liquid phase transition. All active molecules exist as monomers when the concentration of active molecules is lower than CAC, while the active molecules will generate aggregation once the concentration of the active molecules reaches CAC. However, these aggregates with aggregation number, N, smaller than five can steadily exist in bulk phase. The other excess active molecules can only produce infinite aggregation and form a critical nucleus of vapor–liquid phase transition. Without any outer perturbation the state point of CAC corresponds to the critical superheated or supercooled state. Meanwhile, a model of two-region structure of a nucleus is proposed to describe nucleus evolution. The interfacial tension between bulk liquid phase and nucleus is dependent of the density gradient in the transition region and varies with the structure change of the transition region. With the interfacial tension calculated using this model, the predicted nucleation rate is very close to the experimental measurement. Furthermore, this model and associated analysis provides solid theoretical evidences to clarify the definition of nucleation rate and understand nucleation phenomenon with the insight into the physical nature.     

Characteristic-value analysis for plastic dynamic buckling of columns under elastoplastic compression waves

The characteristic-value analysis of plastic dynamic buckling is presented for columns under the action of elastoplastic compression wave caused by an axial-step load. Two critical conditions constituting a dynamic instability criterion are derived on the basis of transformation and conservation of energy. The governing equations, the boundary conditions and the continuity conditions derived by the use of the first critical condition are the same as those given by the adjacent-equilibrium criterion and are insufficient for determining two characteristic parameters involved in the governing equations. A supplementary restraint equation for buckling deformations at the plastic-wave front and the elastic-wave front is derived by the use of the second critical condition. Then, a couple of characteristic equations for two characteristic parameters are derived on the condition that the governing equations have non-trivial solutions satisfying the boundary conditions, the continuity conditions and the supplementary restraint equation. The critical-load parameters, dynamic characteristic parameter (exponent parameter of inertia term) and dynamic buckling modes are calculated from the solutions of the characteristic equations.     

DYNAMICS ANALYSIS OF STOCHASTIC SPATIAL FLEXIBLE MULTIBODY SYSTEM 1)

轻质、高精度的柔性多体系统被广泛应用于实际工程领域中.由于实际设计公差、制造误差及环境温度等多种不确定因素的存在,使得柔性多体系统的结构参数(物理参数和几何参数)表现出随机性.具有随机结构参数的动力学模型能够客观地反映出真实系统的动力学行为,且结构参数的不确定性对空间柔性多体系统动力学响应的影响是不容忽视的.针对具有多个随机参数的空间柔性多体系统,提出了一种基于广义alpha算法的非侵入式随机柔性多体系统动力学计算方法.采用绝对节点坐标公式(absolute node coordinate formulation, ANCF)来描述柔性体, 推导建立多体系统动力学模型.利用混沌多项式展开(polynomial chaos expansion, PCE)法构建系统随机动力学方程的代理模型,然后将随机响应面法(stochastic response surface method, SRSM)嵌入广义-alpha方法中,分别采用改进抽样的回归方法(regression method of improved sampling, RMIS)和单项求容积法则(Monte Carlo simulation, MCR)来确定样本点.将数值计算结果与蒙特卡洛模拟(Monte Carlo simulation, MCS)结果进行对比, 验证了所提算法的有效性.在相同的定积分精度的条件下,根据单项求容积法则确定的样本点的计算结果稳定性更强, 且其计算效率更高.