2016/10/12 by Jieren Xu, Haizhao Yang, Xu, Jieren +3
Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Machine Fault Diagnosis Techniques #Numerical Analysis (math.NA) #Statistics Theory (math.ST) #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.1610.03819
openalex publication_date 2016/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes αk(t)sk(2πNkϕk(t)) from their superposition ∑k=1K αk(t)sk(2πNkϕk(t)). First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., αk(t) and Nkϕk(t). Second, a novel approach based on diffeomorphisms and nonparametric regression is proposed to estimate wave shape functions sk(t). These two methods lead to a framework for the generalized mode decomposition problem under a weak well-separation condition. Numerical examples of synthetic and real data are provided to demonstrate the fruitful applications of these methods.