齿轮箱故障边缘智能诊断方法及应用研究

针对齿轮箱运行状态监测数据量大而数据价值密度低导致的数据传输和存储困难、受到带宽影响导致的故障辨识实时性差以及大而深的深度学习模型难以有效部署至边缘端硬件等问题,本文提出了一种基于乘法-卷积网络(MCN)的齿轮箱故障边缘智能诊断方法。首先,综合考虑信号滤波在特征表征以及深度学习在特征提取的优势,设计了一种轻量化的MCN模型,同时在嵌入式微处理器搭建了一套端侧边缘智能处理原型与系统。该系统可以直接部署于齿轮箱边缘,通过云服务器训练和更新MCN模型参数并部署至边缘端,于边缘端完成数据采集、处理和故障状态辨识等功能,将大量传感器数据直接消耗在边缘端。实验结果显示MCN具有99.75%的平均识别精度,且部署MCN的齿轮箱故障边缘智能诊断系统可以在0.696 s内准确识别出故障状态。

调频连续波SAR MCM成像算法

针对调频连续波SAR实时成像问题,提出了一种新的"乘法-卷积-乘法"(MCM)成像算法。在详细分析调频连续波SAR信号特征的基础上,算法采用MCM方法完成距离向处理,仅需FFT和乘法运算即可实现去斜率信号的时间尺度变换,从而实现距离徙动的精确校正。采用步进变换实现方位向压缩,不需要几何校正即可获得高质量的压缩效果。算法运算效率高,适合实时成像处理。给出了算法的推导过程和实现步骤,通过仿真试验证明了算法的正确性和有效性。

Fast alternating direction method of multipliers for total-variation-based image restoration

A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.

黎曼ζ-函数之一:KS-变换——献给杨乐先生八十华诞

我们定义了KS-变换和自然数乘法结构相关的Fourier变换,建立了实数乘法半群[1,∞)={x:x∈R,x≥1}和复半平面Ω={s=σ+it:σ,t∈R,σ≥1/2}之间的由KS-变换诱导的对偶关系,证明了KS-变换是希尔伯特空间L^2([1,∞))和哈代空间H^2(Ω)之间的等距算子,而且该算子保持了相关的函数空间之间由实数的乘法卷积和复数点点相乘诱导出的代数结构的同构.作为应用,我们给出了黎曼假设成立的有关算子指标的等价命题,从而算子理论为研究黎曼ζ-函数和自然数的乘法结构提供了新思路.