Time-frequency analysis in deep learning framework: theory, computation and applications

深度学习框架中的时频分析：理论、计算和应用

• 批准号: RGPIN-2021-03657
• 负责人: Zhu, Hongmei
• 金额: $ 1.53万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=742662
• 关键词: Time; frequency; analysis; deep; learning

Abnormal brain activities or structural vibrations that have a sudden onset and occur at a distinct frequency range, may provide early warnings of abnormal conditions or structural failure. Time-frequency analysis (TFA) is comprised of various mathematical transforms that describe how frequency content evolves with time. Local features are often first extracted from the time-frequency representation of time-varying signals and then feed to the machine learning algorithms for classification and pattern recognition. Thus, integrating TFA into a realtime monitoring and diagnosis system, we can make early detection to prevent expensive and fatal damages. Despite of its usefulness, two main issues severely impede the effectiveness of the TFA based monitoring and diagnoses. First, the computational effort of TFA is often substantial. This is particularly problematic for processing ultra large data set and/or realtime data. Second, many standard TFA techniques use a fixed set of bases/frames to decompose a signal. In practice, many of important applications will generate highly random and timevarying signals. Using the same set of bases/frames to analyze the entire signal may not be effective. In recent years, with the easy access to powerful computing resources, better performance can be obtained using deep learning neural networks in image recognition, manufacturing], disease diagnosis, and speech processing. The main advantages of deep learning network is that it does not require expert knowledge but often produces higher accuracy than the classic methods. But mathematical understanding of deep learning networks is still not yet clear. The main objective of this research program is to theoretically investigate the time-frequency analysis in the deep learning framework and explore whether such a combination can overcome the limitations of existing classic time-frequency analysis. We aim to answer the following questions: 1) Does the deep learning framework of a time-frequency analysis alter the original signal? 2) Can it help to determine an optimal time-frequency representation of a signal dynamically? 3) If so, what are the essential mathematical properties of dynamic timefrequency analysis using deep learning architecture 4) Can we implement fast algorithms to compute such a representation? This research proposal is interdisciplinary and practical. It integrates mathematics, deep learning, computing, and application development. The trainees in the program will work closely with scientists in data science, health care and industries and make significant original contributions relevant to important real world problems. The success of this program will advance time-frequency analysis field, create sophisticated  time-frequency analysis tailored for specific types of signals and lead to the R&D development of computer-assisted monitoring and detection software for various applications.

突然发生并在不同频率范围内发生的异常大脑活动或结构振动可能会提供异常情况或结构故障的早期预警。时频分析 (TFA) 由各种数学变换组成，描述频率内容如何随时间变化。通常首先从时变信号的时频表示中提取局部特征，然后将其输入机器学习算法以进行分类和模式识别。因此，将 TFA 集成到实时监测和诊断系统中，我们可以进行早期检测，以防止昂贵且致命的损害。 尽管它很有用，但有两个主要问题严重阻碍了基于 TFA 的监测和诊断的有效性。首先，TFA 的计算量通常很大。这对于处理超大数据集和/或实时数据来说尤其成问题。其次，许多标准 TFA 技术使用一组固定的基数/帧来分解信号。在实践中，许多重要的应用都会生成高度随机和时变的信号。使用同一组碱基/帧来分析整个信号可能并不有效。近年来，随着强大的计算资源的便捷获取，深度学习神经网络在图像识别、制造、疾病诊断和语音处理等方面可以获得更好的性能。深度学习网络的主要优点是它不需要专家知识，但往往比经典方法产生更高的准确性。但深度学习网络的数学理解仍不清楚。本研究项目的主要目标是从理论上研究深度学习框架中的时频分析，并探讨这样的组合是否可以克服现有经典时频分析的局限性。我们的目标是回答以下问题：1）时频分析的深度学习框架是否会改变原始信号？ 2）它可以帮助动态确定信号的最佳时频表示吗？ 3) 如果是这样，使用深度学习架构进行动态时频分析的基本数学特性是什么？ 4) 我们可以实现快速算法来计算这种表示吗？这项研究计划是跨学科的和实用的。它集成了数学、深度学习、计算和应用程序开发。该项目的学员将与数据科学、医疗保健和工业领域的科学家密切合作，并就现实世界的重要问题做出重大的原创贡献。该计划的成功将推动时频分析领域的发展，为特定类型的信号创建复杂的时频分析，并促进针对各种应用的计算机辅助监测和检测软件的研发。