ATD: Algorithm, Analysis, and Prediction for Nonlinear and Non-Stationary Signals via Data-Driven Iterative Filtering Methods

你有没有想过如何区分在一个房间里同时录制的两段对话，或者如何识别心电图读数中的不规则模式？在信号处理中，这些任务被称为解混，这是非常具有挑战性的，特别是当信号以时变方式混合（非平稳）或当它们不是简单地加在一起（非线性）时。标准方法，如基于经典傅立叶分析或小波的算法，可以有效地处理线性和平稳信号，但对于非线性或非平稳信号则不尽如人意。开发能够处理此类信号的算法成为一项及时的任务，近年来激发了一波研究浪潮。本课题提出了一种新的自适应局部迭代滤波方法。ALIF可以将一个非平稳的非线性信号分解成有限多个分量，每个分量称为一个内禀模态函数（IMF），它反映了某一频率下的局部特性。ALIF是一种可以根据输入信号自适应的非线性过程，可以自动分离不同的局部特征（频率）。ALIF还将与一种称为因子分解机（FM）的机器学习方法一起使用，以开发一种新的信号预测策略。预计ALIF及其预测算法可用于各种应用，如化学和生物威胁检测，地球物理学中的电离层无线电功率闪烁，社交媒体中的数据分类和预测以及金融数据分析。非线性和非平稳信号在实际应用中无处不在，由于非线性和/或时变性质，基于傅里叶/小波变换的标准算法往往不能有效地处理它们。为了捕获这些信号中的特征，特别是隐藏的特征，分析方法必须具有局域性、自适应性和稳定性。本项目的重点有两个部分：1)设计数据自适应算法，涉及时频分析的迭代滤波等技术；2)结合神经网络，采用自适应迭代滤波技术对非线性非平稳信号进行预测。在第一部分中，设计了一种自适应局部迭代滤波（ALIF），在不事先知道其瞬时频率信息的情况下对非线性非平稳信号进行分解。伴随ALIF而来的是一种基于动力系统概念的计算分解信号瞬时频率的新方法。该项目的第二部分是特征预测策略，使用ALIF和来自神经网络的因子分解机，从噪声信号中学习和预测有用的特征。在这两个部分中，数学性质，如所提出算法的收敛性和稳定性，是研究的中心，以及各种应用，包括化学和生物威胁检测，地球物理学中的电离层无线电功率闪烁和金融数据分析。研究课题内容广泛，可作为适合本科、研究生教育和博士后培养的课题。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Have you ever wondered how to separate two conversations recorded at the same time in one room or how to identify irregular patterns in a electrocardiogram reading? In signal processing, those tasks are called de-mixing, which is very challenging, especially when the signals are mixed in a time-varying manner (non-stationary), or when they are not simply added together (nonlinear). The standard methods, such as the algorithms based on classical Fourier analysis or wavelets, can work effectively for linear and stationary signals, but are not as satisfactory for nonlinear or non-stationary signals. Developing algorithms that can handle such signals becomes a timely task that inspires a wave of research in recent years. A new method, named adaptive local iterative filtering (ALIF) is proposed in this project. ALIF can decompose a non-stationary and nonlinear signal into finitely many components, each of which is called an intrinsic mode function (IMF) that reflects the local property at a certain frequency. ALIF is a nonlinear process that can be adaptive according to the input signals, and can separate different local features (frequencies) automatically. ALIF will also be used together with a machine learning method called factorization machine (FM) to develop a novel signal prediction strategy. It is expected that the ALIF and its prediction algorithms can be used in various applications such as chemical and biological threat detections, ionospheric radio power scintillation in geophysics, data classification and prediction in social media, and financial data analysis.Nonlinear and non-stationary signals are ubiquitous in real world applications, and they often cannot be handled effectively by the standard algorithms based on Fourier/wavelet transforms, due to the non-linearity and/or their time-varying nature. To capture features, especially the hidden ones, in these signals, it is necessary for the analysis methods to be local, adaptive and stable. The focus of this project has two parts: 1) designing data adaptive algorithms that involve techniques such as iterative filtering for the time frequency analysis; and 2) developing prediction strategies using adaptive iterative filtering techniques in conjunction with the neural networks on nonlinear and non-stationary signals. In the first part, an adaptive local iterative filtering (ALIF) is designed to decompose nonlinear and non-stationary signals, without knowing its instantaneous frequency information in advance. Accompanied with ALIF is a new way, based on dynamical system concepts, to calculate the instantaneous frequencies for decomposed signals. The second part of the project is on a feature prediction strategy, using ALIF together with the factorization machine from neural networks, to learn and predict useful features from noisy signals. In both parts, the mathematical properties, such as convergence and stability of the proposed algorithms, are at the center of studies along with various applications including chemical and biological threat detection, ionospheric radio power scintillation in geophysics, and financial data analysis. The research topic contains a wide range of problems that can be used as projects suitable for undergraduate and graduate education, and postdoctoral scholar training.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.