scholarly journals A Color-Coded Complex Mode Indicator Function for Selecting a Final Mode Set

2018 ◽  
pp. 263-270
Author(s):  
Randy L. Mayes ◽  
Daniel P. Rohe
Keyword(s):  
Indicator Function ◽  
Complex Mode ◽  
Final Mode

Identification of Coupled Mode Shapes Based on Complex Mode Indicator Function

2015 ◽  
Vol 732 ◽  
pp. 183-186
Author(s):  
Róbert Huňady ◽  
Martin Hagara ◽  
Martin Schrötter
Keyword(s):  
Modal Analysis ◽  
Correlation Method ◽  
Indicator Function ◽  
Experimental Modal Analysis ◽  
Image Correlation ◽  
Mode Shapes ◽  
Complex Mode ◽  
Coupled Mode ◽  
Value Decomposition ◽  
Function Matrix

Paper deals with the identification of coupled mode shapes by experimental modal analysis. Main attention is focused on the using of Complex Mode Indicator Function that is based on singular value decomposition of frequency response function matrix and allows to separate coupled and also closed modes. In the paper there is described experimental modal analysis at which digital image correlation method is used to measure responses of a circular plate. The measurement was evaluated in program Modan 3D that is being developed by the authors.

The Development of an Enhanced Mode Indicator Function Parameter Estimation Algorithm

1997 ◽  
Author(s):  
William A. Fladung ◽  
Allyn W. Phillips ◽  
David L. Brown
Keyword(s):  
Parameter Estimation ◽  
Estimation Procedure ◽  
Indicator Function ◽  
Degree Of Freedom ◽  
Function Parameter ◽  
Single Degree Of Freedom ◽  
Complex Mode ◽  
Single Degree ◽  
Parameter Estimation Procedure ◽  
Multiple Reference

Abstract The renewed interest in Multiple Reference Impact Testing has triggered the development of an Enhanced Complex Mode Indicator Function (EMIF) parameter estimation procedure. The EMIF method is a multiple degree of freedom extension of the Complex Mode Indicator Function (CMIF) method which is a simple but popular multiple reference parameter estimation procedure. The CMIF procedure uses a Enhanced Frequency Response Function (EFRF) which for many multiple reference systems looks like a single degree of freedom system over a narrow frequency band around a selected system eigenvalue. A single degree of freedom algorithm is used to obtain the system eigenvalue at the enhanced frequency. The EMIF method has been developed to handle those cases where the Single degree of freedom method is not valid.

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

scholarly journals Laplacian networks: bounding indicator function smoothness for neural networks robustness

2021 ◽  
Vol 10 ◽  
Author(s):  
Carlos Lassance ◽  
Vincent Gripon ◽  
Antonio Ortega
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Supervised Learning ◽  
Indicator Function ◽  
Training Data ◽  
Theoretical Justification ◽  
The Past ◽  
Noisy Examples

For the past few years, deep learning (DL) robustness (i.e. the ability to maintain the same decision when inputs are subject to perturbations) has become a question of paramount importance, in particular in settings where misclassification can have dramatic consequences. To address this question, authors have proposed different approaches, such as adding regularizers or training using noisy examples. In this paper we introduce a regularizer based on the Laplacian of similarity graphs obtained from the representation of training data at each layer of the DL architecture. This regularizer penalizes large changes (across consecutive layers in the architecture) in the distance between examples of different classes, and as such enforces smooth variations of the class boundaries. We provide theoretical justification for this regularizer and demonstrate its effectiveness to improve robustness on classical supervised learning vision datasets for various types of perturbations. We also show it can be combined with existing methods to increase overall robustness.

scholarly journals Simulation of Waveguide Crossings and Corners With Complex Mode-Matching Method

2012 ◽  
Vol 30 (12) ◽  
pp. 1795-1801 ◽  
Author(s):  
Rui Wang ◽  
Lin Han ◽  
Jianwei Mu ◽  
Weiping Huang
Keyword(s):  
Mode Matching ◽  
Matching Method ◽  
Mode Matching Method ◽  
Complex Mode
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