摘要:变分模态分解方法（VMD）是一种最近几年被提出，由国内外多个专家进行研究开发的一种对信号进行处理的算法。这种算法运用了一种新的理论为框架，这种框架和之前的经验模态分解(EMD)算法所用的那种不相同。而且他们两种算法的原理也不同，所以产生的效果和应用方面都有很大差别。VMD方法通过不断地进行循环过程，对变分模型进行多次的求解，直到获取到其最合适的解，来确定要求的分量的中心频率和带宽，最后得到分离后的分量。在对信号进行处理的过程中通过算法分离得到的信号个数k，可以在算法进行之前就先预设好，如果这个值选取的合理，那么模态混叠现象就能够很大程度上的减少。在实际运用中VMD方法在去除信号中的噪声方面有着的较为理想的去除效果。本文首先阐述了信号处理的几个基本概念，包括了解析信号和瞬时频率以及维纳滤波的相关概念。然后详细介绍了VMD方法的基本原理和它的算法的具体的流程。在这之后，了解学习了关于MATLAB的使用方法和一些基本的语法。最后运用VMD方法对不同的混合信号进行分离并得出分离后的仿真波形，针对不通信号分离后的仿真结果验证这种算法的性能，证明它能够完成对混合信号的分离。

本文主要研究的是变分模态分解方法的主要原理以及这种算法在完成各种不同的混合信号的分解中的效果。

关键词：变分模态分解；信号处理；混合信号分离；仿真分析

Abstract:Variational Mode Decomposition (VMD) is a recent years been proposed an algorithm for signal processing performed by a plurality of one kind of research and development of domestic and foreign experts.This algorithm uses a new theory as a framework, which is not the same as the one used in the EMD algorithm.And they have different principles of two algorithms, effects and applications so produced are very different.The VMD method solves the variational model several times by continuously cycling the process until the most appropriate solution is obtained to determine the center frequency and bandwidth of the required component, and finally the separated component is obtained.VMD method in the removal of the noise in the signal has a more ideal removal effect,At the same time want to separate the algorithm by the number of signals K can be done before the algorithm is first set,If the value of the selection of reasonable, then the modal aliasing phenomenon can be greatly reduced.This paper first elaborates several basic concepts of signal processing, including analytic signal, instantaneous frequency, VMD basic principle,And then details the basic principles of the VMD method and the specific process of its algorithm, and learn to understand the VMD algorithm.After that, we learned about the use of MATLAB and some basic grammar.The Finally, the VMD method is used to separate the different mixed signals and obtain the separated simulation waveform,The performance of this algorithm is verified by the simulation results after the separation of the signal.To prove that it can complete the separation of the mixed signal.

In this paper, we mainly study the main principle of variational modal decomposition method and the effect of this algorithm in the decomposition of various mixed signals.

Keywords: variational mode decomposition;signal processing;mixed signal separation;Simulation analysis

目录

第一章绪论 1

1.1研究背景 1

1.2VMD算法的研究现状 1

1.2.1国内研究现状 2

1.2.2国外研究现状 2

1.3信号处理的发展过程