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Research Papers

Virtual Vibration Measurement Using KLT Motion Tracking Algorithm

[+] Author and Article Information
Joseph Morlier1

 Université de Toulouse, ISAE, DMSM, 10 Avenue Edouard Belin, BP 54032, 31055 Toulouse Cedex 4, Francejoseph.morlier@isae.fr

Guilhem Michon

 Université de Toulouse, ISAE, DMSM, 10 Avenue Edouard Belin, BP 54032, 31055 Toulouse Cedex 4, France

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(1), 011003 (Dec 01, 2009) (8 pages) doi:10.1115/1.4000070 History: Received October 28, 2008; Revised July 16, 2009; Published December 01, 2009; Online December 01, 2009

This paper presents a practical framework and its applications of motion tracking algorithms applied to structural dynamics. Tracking points (“features”) across multiple images are a fundamental operation in many computer vision applications. The aim of this work is to show the capability of computer vision (CV) for estimating the dynamic characteristics of two mechanical systems using a noncontact, markerless, and simultaneous single input multiple output analysis. Kanade–Lucas–Tomasi trackers are used as virtual sensors on mechanical systems’ video from a high speed camera. First we introduce the paradigm of virtual sensors in the field of modal analysis using video processing. To validate our method, a simple experiment is proposed: an Oberst beam test with harmonic excitation (mode 1). Then with the example of a helicopter blade, frequency response functions’ (FRFs) reconstruction is carried out by introducing several signal processing enhancements (filtering and smoothing). The CV experimental results (frequencies and mode shapes) are compared with the classical modal approach and the finite element model (FEM) showing high correlation. The main interest of this method is that displacements are simply measured using only video at fps respecting the Nyquist frequency.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Optical flow principle. Pixel motion from image I to image J is estimated solving the pixel correspondence problem: given a pixel in I, look for nearby pixels of the same color in J. Two key assumptions are needed: color constancy (a point in I looks the same in J) and small motion (points do not move very far).

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Figure 2

Virtual sensor paradigm using KLT tracker. The chosen key points are used as a virtual sensor to measure the relative displacement frame after frame (sampling frequency is inverse of fps). In our experiment simple plane problems are analyzed in measuring bending displacement (Y in pixel). The true displacement (in meters) is obtained from the conversion of a known size part of the structure in pixels.

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Figure 3

Oberst beam experimental setup for the free-free beam excited at its center. The half-period of the first mode is visualized from several successive frames. Virtual sensors are visualized with a small green dot; displacement is measured in the Y direction (green arrows).

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Figure 4

Validation of the algorithm using two virtual sensors on the left (blue line) and right mass (red dot line). The displacement (Y) is measured as a function of time. These displacements have a harmonic form according to the excitation frequency in this experiment close to the resonant frequency, which appears at 3.8 Hz (period of 0.26 s).

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Figure 5

Frequency contents of the virtual sensors, which highlight the expected harmonic mode of the beam at 3.8 Hz

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Figure 6

Helicopter blade example: KLT trackers are used to follow nine targets in bending (Y displacement). The targets are numbered from 1 to 9, and the blade is excited at its center.

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Figure 7

Stability diagram: variation of the displacement in the X direction is a very small function of the frame number (proportional to time vector). So each target varies only in the Y direction excepted for KLT 8 (in blue). The virtual sensors are well “attached” to the virtual structure: The points belong well to a ROI in the image space.

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Figure 8

Experimental displacements measured on virtual sensors 1–9 sampled at fps. The zoom on the enhanced displacement signals shows the effect of the moving average function on the temporal signal. This preprocessing aims at obtaining smooth FRFs for better modal parameter estimation.

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Figure 9

KLT trackers show classically damped sinusoids containing two main frequencies. Tracker 1 (in blue) at the free end of the blade exhibits higher displacement than Tracker 9 just near the clamped end (in green).

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Figure 10

Half-period is visualized from several successive frames. Virtual sensors are visualized with a small green dot; displacement is measured in the Y direction (green dots).

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Figure 11

Filtered FRFs form nine measurement points and identification of the second resonance at 15 Hz using the SDOF RFP method

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Figure 12

Two first mode shapes extracted using KLT on experimental data in black continuous line: The global content of these modes is very close to the two first modes computed using CATIA (red dotted line). Mode 1 is on top of the figure, and mode 2 at the bottom. The mode shapes are normalized in order to be compared with the FE modal analysis.

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