a high-speed camera measurement set-up for deflection...

A high-speed camera measurement set-up for deflectionshape analysis

J. Javh 1, M. Brumat 1, J. Slavic 1, M. Boltezar 1

1 University of Ljubljana, Laboratory for Dynamics of Machines and Structures,Askerceva 6, 1000 Ljubljana, Sloveniae-mail: [email protected]

AbstractThis research discusses the experimental techniques required to increase the minimal identifiable displace-ments and the spectrum range of optical measurement approaches. A pseudo-random excitation, tailoredto the camera frame rate and recording time, is used to eliminate the windowing effect. The influence ofmotion estimation parameters, camera settings and the visual pattern is discussed. Because of the cameraslimited sampling speed, frequency zooming is used to measure the response at frequencies above the Nyquistfrequency by allowing aliasing. Multiple measurements of consecutive sections of excited frequency rangesare combined to produce greater displacements and form a data set spanning over the Nyquist frequency upto the sampling frequency. At a distance of 3 m deflection shapes of a 840x510 mm plate were measuredat more than 7000 locations with a noise floor of 0.0003 pixel / approx. 0.3 µm using an 8-bit B&W highspeed camera at 2000 fps and a resolution of 816x850 pixels.

1 Introduction

The classic accelerometer based approach to the deflection shape analysis requires long-lasting measure-ments, when lots of measurement points are required. Further, mass loading problems can arise whenmeasuring lightweight structures. Contactless optical measurement techniques are increasingly being usedinstead. Laser Doppler vibrometers and their scanning versions (SLDV) are well established optical mea-surement approaches in structural dynamics [1]. Another optical measurement approach is the Electronicspeckle pattern interferometry (ESPI) [2], which results in a simultaneous full-field measurement. Stress canbe measured via thermoelasticity using high-speed thermocameras to produce stress modal analysis [3]. Inlast years the displacement measurements based on the high-speed cameras are becoming a standard tool foranalyzing the structural dynamics. Such measurements result in displacement series at hundreds of locations,simultaneously. Typically the digital image correlation (DIC) [4] method is used to estimate the displace-ment; however, a gradient based optical-flow method [5] is used herein instead, enabling the measurementof displacement amplitudes below 0.001 pixel. Despite the good performance of the gradient based optical-flow approach, the structural displacements at higher frequencies are easily at (or below) 1 µm and thereforeproblematic to measure.

The aim of this article is to provide an insight and a guideline for structural dynamics measurements us-ing optical flow on high-speed footage. Such measurements are typically limited with lower acquisitioncapabilities and a displacement resolution not far greater then the motion set to measure. To increase themeasurement capabilities, the possibility of measuring above the Nyquist frequency is explored, along witha tailored excitation used to produce greater displacements. Additional considerations for measuring withsuch a set-up are presented.

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2 Optical flow

There are various algorithms for displacement identification from image sequences [5]. The most commonimage-processing technique used to determine full-field displacements in structural engineering is digitalimage correlation (DIC) [4]. DIC determines displacements based on the location of the highest correlationbetween subsets of the two sequential images.

Another method are the phase based optical flow techniques [5]. Phase-based techniques determine thedisplacements from the spatial phase of the image subsets [6].

The algorithm used here is a developed simplified form of a gradient based optical flow (similar to the Lucas-Kanade method [7] or the Horn-Schunck method [8]). It was chosen, because it offers the most direct routefrom the optical information to the displacement, by relating the image intensity values I(x, y, t), where xand y are the pixel locations and t is time, to displacements ∆s over the intensity gradient∇I:

| ∇I | ∆s = I(xj , yk, t)− I(xj , yk, t+ ∆t) (1)

Displacement is visually only observable in the direction of the intensity gradient [9]. Optical flow meth-ods determine the 2D displacement based on the information of a larger subset containing various gradientdirections (Figure 1 (a)), but since the aim of this paper is to measure one dimensional / out-of-plane displace-ments only, a pattern of lines producing a uniform direction of gradient was used (Figure 1 (b)). The patternshould be high contrasting to produce the greatest intensity gradient and therefore the greatest displacementsensitivity, this is the case for all optical flow methods (DIC, Phase based, gradient based,...)

(a) (b)

Figure 1: Pattern and the intensity gradient direction.

3 Frequency zoom

High-speed cameras are so-called because they can acquire still images at high speeds; e.g. 1000 framesper second. Typically they can store a couple of gigabytes of data, usually sufficing for a couple of secondsfilming, depending on the frame size settings. More expensive cameras are capable of filming at higherspeeds (up to 2 million frames per second at a reduced resolution) and can store larger amounts of stills (upto hundreds of gigabytes of data). The dynamic response of structures often spans above the capabilities oftypical high-speed cameras. This paper looks at the possibilities of exceeding those limitations.

The camera frame-rate is analogous to the sampling frequency fs in classical data acquisition and is usuallylower for high-speed cameras than it is for the classical ADCs. The sampling frequency sets the upperfrequency limit to what can be measured. The upper frequency limit is set at the Nyquist frequency fNq [10],which is equal to half the sampling frequency fNq = fs/2. Frequency content above the Nyquist frequencyaliases itself over the Nyquist frequency and overlaps the lower frequency content causing the true contentto get distorted (Figure 2).

1044 PROCEEDINGS OF ISMA2016 INCLUDING USD2016

X( f )

f

aliasedoverlap

-fs fs

signal

-f /2s f /2s

Figure 2: Aliasing

The length of the measured signal T determines the frequency resolution ∆f of the discrete Fourier Trans-form:

∆f =1

T(2)

∆f is also the lower limit of the measured frequency range.

When faced with a problem of an insufficient sampling speed, as can be the case when using high-speedcameras, measurements of the frequencies above the Nyquist frequency can be performed using frequencyzoom [11] by exploiting aliasing. Care should be taken when doing so. Frequency zoom works by aliasingthe frequency content from a frequency above the Nyquist frequency to a frequency below the Nyquistfrequency, therefore it should be assured that no frequency content is present where the aliasing is to occur(Figure 3)).

f

aliased

-fs fs

signal

-f /2s f /2s

X( f )

Figure 3: Frequency zoom

The name frequency zooming is due to a smaller sampling speed a longer acquisition can be achieved fora fixed buffer size, therefore producing a greater frequency resolution, in effect producing a zoom in thespectrum.

4 Tailored excitation

A pseudo-random excitation tailored to the camera sampling was used to excite the structure. Pseudo-randomexcitation is produced from the chosen excitation frequencies [12]. These frequencies should coincide withthe frequencies to be measured by (in this case) the camera. Due to discrete sampling the measured fre-quencies are discrete as well [13]. The frequency resolution is proportional to the acquisition window timetherefore the length of acquisition time and the length of the generated signal should match. The generatedsignal should be generated at a higher sampling rate than that of the camera to produce a more continuoussignal. In this research the pseudo random noise generation was used where the chosen excitation frequen-cies are varied with a random phase. The obtained spectrum is then transformed to the time domain usingthe inverse discrete Fourier transform to retrieve the excitation signal. Such form of excitation produces nospectral leakage [12] and can be used to excite a selected frequency range as seen in Figure 4, showing thespectrum of a chosen point on the plate measured with the high-speed camera.

DYNAMIC TESTING: METHODS AND INSTRUMENTATION 1045

0 200 400 600 800 1000f [Hz]

10 5

10 4

10 3

10 2

10 1

100

X [p

ixel]

Figure 4: The displacement spectrum of point (41,40) on the plate measured with the high-speed camera

As seen in Figure 4, the measured vibration is barely above the noise floor, despite the noise floor being0.0003 pixel or ≈ 0.3 µm. To produce a higher structural response multiple measurements were performed.Each time a short segment of the spectrum was excited in order to concentrate the excitation energy withinthe segment and producing a higher response. The segments were arranged up to the sampling frequencyfs = 2000 Hz in bins of 100 Hz. Since no leakage is present these measurements can be superpositioned toform a complete spectrum.

An alternative excitation signal can be the Schroeder sweep [14], as it can translate more power from theamplifier to vibrations before clipping is reached.

5 Camera set-up

Several camera set-up parameters have to be taken into account before measurement can be successfullyaccomplished.

Shutter speed. The shutter speed (also exposure time) is the duration of time in which the image is ac-quired. The maximal shutter time is equal to ts max = 1/fs. This is the cameras preferred setting, because along exposure requires less illumination. The shutter speed has an influence on the measured spectrum sinceit works as a filter smoothing out the time series lowering the amplitudes of higher frequencies. The shutterfilterring effect is shown in Figure 5 for different shutter lengths. The maximal shutter length will produce adrop at the Nyquist frequency. Since the aim of this paper is to measure above that, a shorter shutter speed isrequired.

0.00.20.40.60.81.0

Gain

0 fNq fs

100 %50 %40 %

Figure 5: The effect of the shutter length on the measured spectrum


Foreshortening. To measure the out-of-plane displacements, the camera has to be set an angle to theplate (Figure 7). Filming at an angle will produce foreshortening (distortion of plate dimensions due toa perspective) causing the distant edge to appear shorter than the one closer to the camera, as seen in ameasurement frame (Figure 6). Foreshortening causes an uneven displacement resolution over the measuredobject. It can be mitigated by placing the camera at a greater distance to the filmed object and using a zoomlens, but at a price of a poorer illumination.

Figure 6: A still frame from the high-speed footage

high-speedcamera Light

source

shaker

plate withpattern

Figure 7: The used measurement set-up

Lighting. The lighting should be chosen so that it will not produce flicker caused by the alternating currentfrom the power grid. A good option are LEDs (Light Emitting Diodes). LEDs are becoming cheaper, theyhave a good efficiency and produce stable light if powered correctly. The lighting should be positioned ina way that uniformly lights the filmed object without producing direct reflections, because the location ofthe reflection is related to the angle of the filmed surface and will change accordingly producing apparentidentified displacements.

The object should be well lit, so that the whole intensity range of the camera sensor is used, this way themotion is more evident and the noise floor appropriately smaller. The lighting should be adjusted with thehelp of an intensity histogram showing the measured intensity range. Intensity values should not exceed themaximal value, as this causes clipping and consequently errors in the displacement identification.

6 Results

A measurement of a damped 840 mm × 510 mm × 0.8 mm plate was performed using the presented set-up.The camera used was an 8-bit high-speed camera, filming at a frame-rate of 2000 frames per second with


a resolution of 816×850 pixel. The measured displacement amplitude noise level is at ≈ 0.0003 pixel or≈ 0.3 µm .

Figure 8 shows all the different excited frequency ranges for point (41,40). The axis are excluded for trans-parency, but they are the same as in Figure 4. The excited ranges (coloured yellow) were combined to forma full frequency range up to the sampling frequency of 2000 Hz (Figure 9).

Figure 10 shows some of the deflection shapes tagged in Figure 9 as (a-f). Unfortunately frequency contentabove 1100 Hz drops bellow the noise level and thereafter the deflection shapes are no longer recognisable(Figure 10 (f)).

10-100 Hz 100-200 Hz 200-300 Hz 300-400 Hz 400-500 Hz

500-600 Hz 600-700 Hz 700-800 Hz 800-900 Hz 900-1000 Hz

1000-1100 Hz 1100-1200 Hz 1200-1300 Hz 1300-1400 Hz 1400-1500 Hz

1500-1600 Hz 1600-1700 Hz 1700-1800 Hz 1800-1900 Hz 1900-2000 Hz

Figure 8: The displacement spectra of the chosen point for all measurements

0 500 1000 1500 2000f [Hz]

10 5

10 4

10 3

10 2

10 1

100

X [p

ixel]

(a) (b) (c) (d) (e) (f)

Figure 9: The combined displacement spectrum for the chosen point and the noise level (yellow)


0 20 40 60 800

204060

(a) f = 47. 3 Hz

0.0e+00

6.1e-02 0 20 40 60 800

204060

(b) f = 138. 6 Hz

0.0e+00

7.5e-02 0 20 40 60 800

204060

(c) f = 538. 4 Hz

0.0e+00

8.2e-03

0 20 40 60 800

204060

(d) f = 891. 5 Hz

0.0e+00

5.6e-03 0 20 40 60 800

204060

(e) f = 1096. 9 Hz

0.0e+00

3.1e-03 0 20 40 60 800

204060

(f) f = 1682. 5 Hz

0.0e+00

1.1e-03

Figure 10: Some of the measured deflection shapes tagged in Figure 9

7 Conclusion

The motion of a vibrating structure is commonly near the limit of the measuring range of visual basedmethods. Greater considerations need to be taken to produce descent results. A high contrasting patternshould be applied to the measured object to intensify the optical flow. The camera and measurement set-upare equally important. This research demonstrates measurements above the Nyquist frequency by allowingaliasing. To do so a tailored excitation producing a limited frequency range was used. This excitation wasalso tailored to concentrate all the power to a limited frequency range, producing greater displacements.By combining measurements, a large spectrum of the tested plate dynamics was measured at a high spatialresolution producing a true full-field measurement.

References

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[3] R. Marsili, M. Moretti, G. L. Rossi, Thermoelastic Modal Stress Analysis, in Proc. of 26th InternationalModal Analysis Conference (IMAC XXVI), Orlando USA (2008)

[4] W. H. Peters, W. F. Ranson, Digital imaging techniques in experimental stress analysis, Optical Engi-neering, Vol. 21, No. 3, (1982), pp. 427-432.

[5] J. L. Barron, D. J. Fleet,S. S. Beauchemin, Performance of optical flow techniques, International journalof computer vision, Vol. 12, No. 1, (1994), pp. 43-77.

[6] N. Wadhwa, M. Rubinstein, F. Durand, W. T. Freeman, Phase-Based Video Motion Processing, ACMTransactions on Graphics, Vol. 32, No. 4, (2013)

[7] B. D. Lucas, T. Kanade, An iterative image registration technique with an application to stereo vision,IJCAI, (1981), 674-679.


[8] B. K. Horn, B. G. Schunck, Determining optical flow, In 1981 Technical Symposium East. InternationalSociety for Optics and Photonics, (1981), pp. 319-331.

[9] E. Hildreth, The measurement of visual motion, PhD thesis, MIT (1983).

[10] H. Nyquist, Certain topics in telegraph transmission theory, (1928)

[11] D. H. Ewins, Modal Testing: Theory and Practise, Research studies press (1984)

[12] A. Brandt, Noise and vibration analysis: signal analysis and experimental procedures, John Wiley &Sons (2011)

[13] Maia, Silva, He, Lieven, Lin, Skingle, To, Urgueira. Theoretical and experimental modal analysis,Research studies press (1997)

[14] M. Schroeder, Synthesis of low-peak-factor signals and binary sequences with low autocorrelation(Corresp.), Information Theory, IEEE (1970), pp. 85-89.


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