多元可逆深度概率学习及齿轮退化分析研究

齿轮退化状态的准确评估对于设备安全运行具有重要意义。常规的齿轮退化状态评估方法的效果受特征提取、预处理等因素的影响。基于生成模型的状态评估方法利用原始观测进行评估,能够降低人为因素的影响。但传统生成模型如变分自编码器(VAE)存在边缘估计不准确的缺点。本文提出了多元可逆深度概率学习(MIDPL),通过叠加可以被优化的可逆变换实现从既定初始分布到未知观测分布的转换,将分布特性复杂的多观测序列转换至既定初始分布进行边缘概率计算继而实现状态评估。本文通过齿轮退化实验验证了MIDPL的有效性,与VAE相比,MIDPL在点蚀和断齿数据集下的评估误差分别降低了30.92%和69.25%,MIDPL能够实现更为稳定和准确的齿轮退化过程评估。     

关于某些特殊分块矩阵的群逆

分块矩阵的广义逆不仅在数学理论上有广泛研究而且在自动控制、系统理论、概率统计、数学规划等领域有着广泛的实际研究背景.该文对形如[A B/C 0]分块矩阵的群逆的表达式问题进行了研究.设P是复数域上的幂等阵.令矩阵A,B,C取自集合{P,PP*,PP*P },则可以得到27个形如[A B/C 0]的分块矩阵.给出了这27个分块矩阵群逆的存在性与表示形式.     

Dedekind模

给出了整环上的有限生成挠自由Dedekind R-模M与Dedekind（M）-模M以及环（M）之间的等价关系.进而得到了在Dedekind模下的一些等价刻画.     

奇异系统的输出稳定化通过一般状态反馈的可解性

讨论了奇异系统的输出稳定化问题,得到了在初始值为容许且不保证闭环正则的情 形下,通过一般状态反馈求解此问题的充要条件及计算步骤.     

Semi‐global stabilization of discrete‐time systems subject to non‐right invertible constraints

This paper investigates time‐invariant linear systems subject to input and state constraints. We study discrete‐time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non‐right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time‐invariant linear systems with non‐right invertible constraints, necessary and sufficient conditions are developed under which semi‐global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well. Copyright © 2009 John Wiley & Sons, Ltd.     

拟（h,k）存贮有限自动机的可逆性

主要研究拟（h,k）阶存贮有限自动机的延迟k步与k＋1步弱可逆性,以及它的弱逆,得到了拟（h,k）阶存贮有限自动机的延迟k步与k＋1步弱可逆的充分必要条件,并且通过所得结果可以比较简便地构造出延迟k步与k＋1步弱可逆拟（h,k）阶存贮有限自动机的延迟k步与k＋1步弱逆。     

拟(h,k)存贮有限自动机的可逆性

主要研究拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱可逆性,以及它的弱逆,得到了拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱可逆的充分必要条件,并且通过所得结果可以比较简便地构造出延迟k步与k+1步弱可逆拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱逆.     

Design of 3-D Noncausal Filters with Small Roundoff Noise and No Overflow Oscillations

The contribution of this paper consists of two individual parts. First, an invertible mapping technique is presented for 3-D digital system design, and it is applied to approximate 3-D noncausal filters in the spatial domain. Secondly, an algorithm is proposed for obtaining a structure for 3-D IIR filters with small roundoff noise and no overflow oscillations. The design of noncausal filters can be carried out by three steps: 1), a given noncausal impulse response is transformed into the first octant using the proposed 3-D invertible mapping technique; 2), the transformed impulse response in the first octant is approximated by balanced model reduction of 3-D separable denominator systems;3), the resultant 3-D IIR filter is transformed back to the original coordinates.     

广义分布参数系统的初值问题

本文定义了广义左逆、广义Ｆｏｕｒｉｅｒ变换，矩产方根等概念，论述了由带奇异系数矩耦合偏微分方程描述的广义分布参数系统，由广义Ｆｕｒｉｅｒ变换定理讨论了广义分布参数系统的初值问题，得到了该系统的解及其相容的初值条件。