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Fast vision-based wave height measurement for dynamic characterization of tuned liquid column dampers
Measurement 89 (2016) 189–196
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Fast vision-based wave height measurement for dynamic characterization of tuned liquid column dampers Junhee Kim, Chan-Soo Park, Kyung-Won Min ⇑ Department of Architectural Engineering, Dankook University, Jukjeon-dong, Suji-gu, Yongin-si, Gyeonggi-do 448-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 24 October 2014 Received in revised form 7 April 2016 Accepted 12 April 2016 Available online 13 April 2016 Keywords: Vision sensing Wave height measurement Dynamic characterization Structural control Tuned liquid column dampers
a b s t r a c t In this study, a novel and rapid vision-based sensing strategy is developed exclusively for dynamic wave height measurement of tuned liquid column dampers (TLCDs). The image processing algorithm of the vision-based sensing method simply counts white pixels in a binary image and thus expedites the vision-based wave height measurement. In addition to the experimental achievement, a practical methodology of dynamic characterization for the TLCDs is proposed combining linearized equations for the TLCDs and experimental data measured. An experimental characterization of dynamic behaviors and damping properties of the TLCDs is undertaken utilizing the vision-based sensing developed. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Structural developments in design and construction of buildings and towers have rendered structures tall, slender, and flexible. The tall and slender structures are vulnerable to dynamic loading such as wind and earthquakes. While the structures operate within safety limits, they may suffer from lack of serviceability due to undesirable vibrations induced by the dynamic loading. Structural control is needed to reduce the dynamic responses of the structures and to maintain their functional performances. A constant flow of developing novel and effective devices incorporated in structures for attenuation of structural vibration has been seen over the past decades [1]. One of the pervasive strategies widely applied to attenuate structural vibration is the installation of a secondary mass damper on the top floor of a building, i.e., a device generating a reaction force induced from the oscillating motion of a secondary mass. The secondary mass is a small fraction of the entire mass of the primary structure and interfaced to inherent damping devices for increasing the energy dissipation capability. Depending on the oscillatory media, the secondary mass dampers are categorized into two groups: tuned mass damper (TMD) and tuned liquid damper (TLD). The TMDs are mechanical devices of a solid mass with springs and dashpots attached to the primary building [2] and the TLDs are liquid containers [3]. As the counterpart of the TMDs, ⇑ Corresponding author. E-mail address: [email protected] (K.-W. Min). http://dx.doi.org/10.1016/j.measurement.2016.04.030 0263-2241/Ó 2016 Elsevier Ltd. All rights reserved.
the TLDs have proven their advantages: for example, simplicity, low cost, easy installation and maintenance, just to name a few [4–7]. Two different configurations of the TLDs have been investigated and adopted in construction sites [8]. Tuned Liquid Mass Damper (TLMD) and Tuned Liquid Column Damper (TLCD) utilize energy dissipating liquid motions of oscillation in narrow tubes and wave braking/sloshing in free liquid surface, respectively. Referring to numerous design parameters relating the configuration of the TLCDs and resultant tuning feasibility to determine their dynamic characteristics, practical advantages of the TLCDs over the TLMDs have frequently been emphasized in the literature [4,9,10]. Prior to installation of a TLCD at a site, a factory test for verification and tuning of dynamic characteristics must be conducted with the pre-fabricated TLCD. Among the dynamic characteristics of the TLCD, optimal tuning frequency and damping ratio are considered primal, since they are directly related to control performance, i.e., vibration suppression of the primary structure. Wave height of the oscillating liquid column of the TLCD is measured during the factory test and the dynamic characteristics are then estimated from wave height data measured. To date, capacitive wavemeters immersed into liquid have been dominantly used for measurement of varying wave heights. However, a number of intrinsic disadvantages associated with the contact sensors have been constantly addressed: high price, laborious installation, and a loss of accuracy due to interference from a liquid medium, e.g., parasitic capacitance. While great advances have been made in analytical studies of dynamic behaviors of the TLCDs
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[6,10,11] and practical design formulas/guidelines [9,12,13], comparatively less research has been conducted toward novel measurement strategy and further characterization of the TLCDs based on experimentally measured data. Recently, there has been growing interest in noncontact sensing in the areas of structural monitoring and assessment [14]. The precedent works of noncontact sensing, especially vision-based remote sensing, are found in the literature [15–19]. In this study, a rapid, high precision, and cost-effective vision-based sensing system is developed exclusively for dynamic wave height measurement of the TLCDs. A practical methodology of experimental estimation of dynamic characteristics of the TLCDs is also proposed based on both dynamic equations derived and experimental data measured. Finally, a series of experimental investigations are conducted for the verification of the vision-based sensing system and for showcasing the methodology of dynamic characterization of the TLCDs.
2. Formulation of dynamic behavior of tlcds The equations of dynamic behavior of the TLCDs are derived for estimation of their dynamic characteristics based on the experimental data measured. While natural frequencies of the TLCDs can be directly determined by measurements, damping estimation requires physics-based relationships between damping and measurable quantities. Thus, a practical equation for estimating the damping ratio of the TLCDs is derived in this section.
2.1. Derivation of linearized equation of motion A simplified model of the TLCD built on the primary structure is illustrated in Fig. 1. The TLCD considered here has two vertically upright tubes connected together at the bottom orifice forming sharp-edged elbows. Identical cross sectional areas, denoted as A in Fig. 1, of the vertical and horizontal tubes are considered. The displacements of horizontal structural motion of the exciting primary structure and vertical surface motion of oscillating liquid of the TLCD are denoted as x and y, respectively. As for the dimensions of the TLCD, the horizontal and vertical column lengths are defined as Lh and Lv, respectively.
The Lagrange’s equations of motion on the basis of the Hamilton’s principle for conservative systems [20] are adopted to formulate equations of motion of the TLCD [6,21,22]. Summation of the kinetic energy of the oscillating liquid along the two vertical and one horizontal columns leads to
1 T ¼ qALv ðy_ 2 þ x_ 2 Þ þ qALh ðy_ 2 þ 2x_ y_ þ x_ 2 Þ 2
ð1Þ
where q is the density of the liquid filled in the TLCD. Considering wave height changes in the two vertical liquid columns, the potential energy is expressed as
V ¼ qAðyÞg
y y þ qAyg ¼ qAgy2 2 2
ð2Þ
The energy dissipated by the liquid flow passing through the orifice is often referred to as head loss in fluid dynamics. Combining the energy balance equation, i.e., the Lagrange’s equation, and the non-conservative force of the head loss leads to
d @ðT VÞ @ðT VÞ 1 _ y_ ¼ qAgjyj dt @ y_ @y 2
ð3Þ
where g is the head loss coefficient. The equation of motion of the TLCD is derived by inserting Eqs. (1) and (2) into Eq. (3):
€ þ c1 y_ þ k1 y ¼ m2 €x m1 y
ð4Þ
where the total mass of the liquid column is m1 ¼ qAðLh þ 2Lv Þ; the mass of the horizontal liquid column is m2 ¼ qALh ; the nonlinear _ the term related friction damping coefficient is c1 ¼ ð1=2ÞqAgjyj; to stiffness is k1 ¼ 2qAg. The nonlinear friction damping can be treated as linear viscous damping by the concept of equivalent damping. Considering a harmonic excitation of the primary structure with the frequency, x and corresponding sinusoidal displacement response of the vertical liquid motion with the amplitude, uy , i.e., y ¼ uy sin xt, the non-conservative force of nonlinear friction damping is calculated as
f nc1 ¼ c1 y_ ¼
1 qAgu2y x2 j cos xtj cos xt 2
ð5Þ
The energy dissipated in a full cycle is calculated by integrating the non-conservative damping force in the first quarter cycle and quadrupling the result:
Z ED1 ¼ 4
Z f nc1 dy ¼ 0
¼
uy
8 !2 9 < = u sin x t y 2qAgu2y x2 1 dy : ; uy
4 qAgu3y x2 3
ð6Þ
On the contrary, the non-conservative force is composed with the linear viscous damping as
f nc2 ¼ ceq y_ ¼ ceq uy x cos xt
ð7Þ
The energy dissipated by the linear viscous damping is calculated as
Z ED2 ¼
Z f nc2 dy ¼ 0
¼ ceq pu2y x
2p
x
_ ¼ f nc2 ydt
Z 0
2p
x
ceq u2y x2 cos2 xtdt ð8Þ
By equating the dissipated energy of the nonlinear friction damping to that of linear viscous damping, the equivalent viscous damping is derived as
ceq ¼ Fig. 1. A TLCD subjected to a vibrating structure.
4 qAguy x 3p
ð9Þ
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Inserting Eq. (9) into the equation of motion of the TLCD yields the linearized equation of motion
€þ m1 y
4 qAguy xy_ þ k1 y ¼ m2 €x 3p
ð10Þ
Dividing both sides of Eq. (10) by m1 leads to
€þ y
4guy x y_ þ x2y y ¼ p€x 3pLe
ð11Þ
where Le ¼ Lh þ 2Lv is the effective length of the TLCD; pffiffiffiffiffiffiffiffiffiffiffiffi 2g=Le is the natural frequency of the TLCD; p ¼ Lh =Le is the ratio of the horizontal length to total length of the liquid column.
xy ¼
2.2. Derivation of damping ratio Considering a harmonic motion of the exciting primary structure and corresponding response of the liquid motion, i.e., x ¼ x0 eixt and y ¼ y0 eixt , respectively, the linearized equation of motion of Eq. (11) yields the amplitude of the liquid motion:
y0 ¼
x0 pb2 4gu b2 ð1 b2 Þ þ i 3pLy e
ð12Þ
where b ¼ x=xy is the frequency ratio of the exciting frequency to the natural frequency of the TLCD. The amplitudes of the liquid motion in both sides of Eq. (12) can be arranged by the identity of uy ¼ jy0 j. As a result, the amplitude uy is calculated as the magnitude of the complex amplitude of liquid motion of Eq. (12):
ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 4 g b 2 2 2 4 4 ð1 b Þ þ ð1 b Þ þ 4x20 p2 b 3pLe uy ¼ pffiffiffi4gb2 2 3pLe
ð13Þ
Arranging Eq. (13) with respect to the head loss leads to
g¼
3pLe
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðuy uy b2 þ x0 pb2 Þðuy b2 uy þ x0 pb2 Þ 4u2y b2
ð14Þ
Damping ratio of the TLCD is calculated from the equivalent viscous damping of Eq. (9)
ny ¼
ceq 2guy b ¼ 3pLe ccr
ð15Þ
where the critical damping is given as ccr ¼ 2m1 xy . Eventually, the equation for the damping ratio of the TLCD by inserting Eq. (14) into Eq. (15) is derived as
ny ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðuy uy b2 þ x0 pb2 Þðuy b2 uy þ x0 pb2 Þ 2uy b
ð16Þ
As seen in Eq. (16), the damping ratio is a function of amplitude of motion of the primary structure, natural frequencies of both the primary structure and the TLCD, and geometrical configurations of the TLCD. 3. Expedited digital image processing for TLCDS In this section, a novel and rapid video processing technique tailed to measurement of wave height of the TLCD is presented to replace the conventional wave height meter, taking advantages of noncontact sensing. The technique requires solely counting of white pixels in the binary image matrix and is thus rapid enough for near instant processing. A detailed explanation on the technique will follow introduction to conventional retardant video processing technique.
191
A video of a laterally shaking TLCD where blue dye was added to accentuate the liquid was preliminarily taken by a digital camcorder. The lateral motion of the TLCD resulted in a vertically oscillating liquid column. A couple of freeze-frames grabbed from the video are given in Fig 2: Fig. 2(a) and (b) are still images at the instants when the free surface of the liquid column reaches the highest and lowest positions, respectively. As seen in figures, height and horizontal location of the liquid column are changing simultaneously. The measurement quantity, i.e., wave height, is defined by distance between upper and lower corners of the liquid column seen in Fig. 3(a) where the corners are highlighted by two L-shaped markers. As a result, detection of the two corners in digital images leads directly to wave height measurement. To locate a moving object by analyzing digital images entails two sequential image processing procedures [23]: edge detection and moving object tracking. Edges are paths of rapid change of image intensity in a digital image and outline targeted objects, i.e., the liquid column in the TLCD in this study (Fig. 3(b)). Edge detection is used to identify the edges in an image. Height of the liquid column of the TLCD is measured from the edge detected, while laterally tracking the position-changing liquid column. An image processing technique for tracking moving objects is conventionally conducted by correlation analysis. In this study, the two corners are moving objects to be tracked and reference image frame is used for the correlation analysis (Fig. 3(c)). However, the consecutive image processing techniques, i.e., edge detection followed by correlation analysis, are computationally expensive and time consuming. Thus, their implementation presents a challenge to the use of real time image processing for the measurement the liquid height in the TLCD. In this study, an expedited image processing technique tailored to the measurement of the liquid height of the TLCD is developed to skip the aforementioned retardant processes of edge detection and correlation analysis. The suggested technique examines on image portion, termed region of interest (ROI), extracted by cropping the original image. In this study, the ROI is set to be a portion of the image specifying the liquid column of the TLCD. The rectangle ROI contains a true-color image of the liquid column truncated above the lower sharp-edged elbow and is dealt as an RGB image, an m n 3 data array that defines red, green, and blue color components for m n pixels. In general, a graphic file format of the RGB image is 24-bit digital information, where the red, green, and blue components are 8 bits each. Since the liquid column of the TLCD is blue, the information of blue color is exclusively converted to a grayscale color map consisting of 8 bits per pixel. Finally, a binary image (1 bit per pixel) is acquired from the grayscale image using an appropriate threshold. Explanatory image matrices of the binary images at two different instants are given at Fig. 4. Two dimensional matrices of 1’s (white pixels) and 0’s (black pixels) represent the liquid column of the TLCD and the other parts, respectively. As seen, the height and horizontal position of the liquid column change in the two figures. Since the feature aimed to be measured in the study is the height of the liquid column regardless of its position, a simple strategy of analyzing the binary image matrices are adopted. It requires solely the counting of white pixels, i.e., the total sum of ones in the binary image matrix, which is directly proportional to the height of the liquid column. Mapping of the total sum of the white pixels to a metric system of length needs a reference, which is the number of pixels along a line of measured length. In this study, an a priori measurement of the width of the liquid column is adopted. Thus, the height of the liquid column at time step i, h(i) is calculated as
hðiÞ ¼ a
sðiÞ W
ð17Þ
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Fig. 2. Two still images of a working TLCD at two different instants.
Fig. 3. Conventional image processing technique for wave height measurement: (a) definition of wave height; (b) edges detected; (c) two reference frames of corners.
Fig. 4. Binary information of the image matrices for a moving liquid column in the ROI.
where s(i) is the total sum of white pixels in the ROI at time step i; a is the mapping factor (unit of m/pixel) determined by the aforementioned measurement; W is the number of white pixels along the width of the liquid column. It should be again noted that the algorithm to measure the liquid height of the TLCD using a video recorded does not require any time-consuming image processing technique and implementation of the algorithm is thus near instant.
4. Experimental verification In the experimental phases of this study, two experimental examples are present: first, a demonstration of the performance of the expedited vision-based wave height sensing is given with a comparison with conventional measurements. Next, the visionbased sensing strategy is directed to experimentally analyze dynamic behaviors of the TLCDs with different orifices.
4.1. Performance of vision-based wave height sensing Prior to the test, a laboratory-scaled prototype (Fig. 5) of the TLCDs was fabricated with 1 cm thick acrylic plates. The width and height of the TLCD are 650 and 400 mm, respectively. The inner dimension of vertical and horizontal column, i.e., cross sectional area of liquid flow, is 150 150 mm. The TLCD was mounted on a uniaxial shake table driven by a mechanical linear actuator where rotary motion of an AC servo motor (HC-SFS502, MITSUBISHI) is converted to linear motion. The AC servo motor is operated in the velocity control mode in which angular velocity of the rotary motion is subjected to applied analog electrical signals programmed in a function generator. A 60 s long 0.2–2.0 Hz chirp signal with a constant amplitude of peak-to-peak ±1 V was applied to the AC servo motor via the function generator. To measure motion of the shake table, a laser displacement sensor (CD4-350, OPTEX FA) was utilized. The laser displacement
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Fig. 5. Experiments of the vision-based wave height sensing for a shaking TLCD – oscillating liquid column is clearly noticeable.
sensor is a precision optoelectronic transducer to determine dynamic displacement by sensing phase differences between transmitted laser and back scattered laser from the moving surface of targeted objects. During the dynamic test, the laser displacement sensor was set 0.35 m away from an edge of the shake table and sensed the shake table’s displacement motion while aligning along the axis of moving direction of the shake table. The measured displacement time histories of the shake table are plotted in Fig. 6 (a). Displacement amplitude decaying due to the velocity control of the AC servo motor is witnessed over the duration of the applied excitation. The Fourier spectrum of the measured displacement is
Displacement (mm)
25
0
-25
0
10
20
30
40
50
60
Time (sec)
(a)
Amplitude
10
10
10
3
0
-3
0
0.5
1
1.5
2
2.5
3
Frequency (Hz)
(b) Fig. 6. Frequency shift excitation of the shake table: (a) measured displacement; (b) corresponding Fourier spectrum of the displacement.
presented in Fig. 6(b) where the 0.2–2.0 Hz frequency band of the applied excitation is confirmed. To demonstrate the cost-effectiveness and accuracy of the proposed vision-based sensing system compared to a conventional contact sensor, both sensors were utilized record the dynamic motion of the TLCD during the test. A commercially available digital camcorder (HMX-QF20, SAMSUNG) which costs 300 USD in the market was deployed. The high-definition (HD) digital camcorder is a 1920 1080 pixel full HD camcorder capturing 60 frames per sec. The video compression format supported by the camcorder is H.264, i.e., MPEG-4, which is the latest video coding format standardized by the ISO/IEC and compatible with the image processing toolbox of MATLAB. The camcorder was placed on a stationary tripod 2 meters away from the shake table. Accuracy of the visionbased wave height measurement system was cross-checked with that of a conventional wavemeter, i.e., capacitive wave height sensor (CH-601, KENEK). The wavemeter costs 3000 USD and its installation is laborious compared to the proposed system – the wave probe was immersed in the liquid column of the TLCD as well as the sensor body was clamped on top of the TLCD as seen in Fig. 5. After the dynamic test was completed, the video recorded by the camcorder was transferred to a PC via USB interface for digital image processing as proposed by this study. The number of frames, image size, video duration, and frame-rate were identified in the MATLAB image processing toolbox – the frame rate is 60 frames per sec and thus the 60 s video is composed of a total of 3840 frames; the 1920 1080 pixels of the individual frames have 24 bit RGB information. The aforementioned image processing for wave height measurement was consecutively conducted with sequences of the freeze-frames grabbed from the video and the results are depicted in Fig. 7. For comparison purposes, time histories of wave height measured by the wavemeter are superimposed. Time synchronization of the two different signals was conducted by maximizing correlation of the signals. As seen, a very close match of two measurements is observed in Fig. 7(a). A quantitative accuracy evaluation of the proposed methodology was conducted by calculating the following RMS error between the signals:
RMS Error ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi X 2 ðhðiÞ hðiÞ Þ =N video wave i
ð18Þ
where hðiÞvideo and hðiÞwave are measured wave heights at time step i, by the vision-based sensing and wavemeter, respectively; N is the
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J. Kim et al. / Measurement 89 (2016) 189–196 Table 1 Computing time of digital video processing.
40
0
-40
10
20
30
40
50
Proposed technique (s)
1 2 3
47.470 47.346 47.315
13.385 13.353 13.354
Average
47.377
13.364
Proposed technique Conventional technique
60
(a) 3 Wavemeter Vision-based sensing
2 Amplitude
Conventional technique (s)
40 0
Time (sec)
0
-40 20
1
0
No. of test
Displacement (mm)
Displacement (mm)
Wavemeter Vision-based sensing
30
40
Time (sec) Fig. 8. Comparison of responses of the TLCD mounted on the shake table (thin: vision-based sensing proposed, thick: wavemeter):
0
0.5
1
1.5
2
2.5
3
Frequency (Hz)
(b) Fig. 7. Comparison of responses of the TLCD mounted on the shake table (thin: vision-based sensing proposed, thick: wavemeter): (a) measured heights; (b) corresponding Fourier spectra of the heights.
number of discrete data measured. In this study, the RMS error was evaluated as 1.053 mm. Considering the fact that the wave height is sensed at a point of the liquid surface by the wavemeter while the vision-based sensing yields the average height of the liquid column, the small RMS error evaluated suggests excellent accuracy of the vision-based sensing proposed. The Fourier spectra of the measured wave heights are presented in Fig. 7(b). Dominant peaks at 0.854 Hz are clearly observed at the two measurements. Amplitude decay is witnessed near 2.0 Hz, suggesting the bandwidth of the applied excitation, i.e., 0.2–2.0 Hz. So far, the high precision of the expedited vision-based sensing proposed in this study has been quantitatively proven through the comparison with the conventional capacitive wavemeter. Based on the successful results, advantages of the expedited vision-based sensing over the conventional image processing technique explained in Fig. 3 were studied. Identical tests with the 60 s long shake table driven by 0.2–2.0 Hz chirp signal were repeated three times and then three 3840 frame video files were recorded – in each image frame, 1920 1080 pixels contained 24 bit RGB information. For each video file, two different video processing techniques were applied to determine wave heights. As for the conventional technique, a 250 250 pixel image frame of an Lshaped marker was used as the reference in correlation analysis to detect locations of the liquid corners. Since the two video processing techniques were implemented with the MATLAB image processing toolbox in an identical personal computer processed by Intel Core2 Q9400 (2.66 GHz), a comparison of computing time was carried out and the results are tabulated in Table 1. As seen in the table, it consistently takes nearly the same amount of time to compute the wave height in each technique. It is concluded that the expedited technique proposed in this study is 3.55 times faster than the conventional technique. One of the three results is given in Fig. 8 – for a more precise examination, time histories in a range
of 20–40 s are plotted. A good agreement between two wave height measurements is confirmed; thus, it can be concluded that performance of the proposed technique matches that of the conventional technique, despite a significant drop in time consumption.
4.2. Dynamic characterization of TLCDS On the basis of the previous confirmation of the accuracy of the vision-based wave height sensing, dynamic characteristics of the TLCDs were estimated from experimentally measured data solely by the vision-based sensing. To investigate wide ranges of dynamic characteristics of the TLCDs, three different orifices with varying blocking ratios were placed in the laboratory scaled prototype (Fig. 5). The blocking ratio of an orifice is defined as the ratio of closed to cross-sectional areas. In this study, blocking ratios of 25%, 50%, and 75% were selected as seen in Fig. 9. First, damped natural frequencies of the TLCDs with different orifices were estimated from the vision-based wave height measurements during shake table tests with the previous chirp excitation of Fig. 5, while consecutively installing one of the orifices in the TLCD. Time histories of wave heights measured are plotted in Fig. 10(a). As the blocking ratios increase, the vertical oscillations of the liquid column of the TLCDs are suppressed especially in time interval of 18–29 s. The trend witnessed is also confirmed in the Fourier spectra seen in Fig. 10(b) – the magnitude drops of the peaks near resonance frequencies depending on the blocking ratios are noticeable. Since the energy dissipation, i.e., damping, of the TLCDs is mainly induced by narrowing liquid flow and disturbance near the orifices, the damping is proportional to the blocking ratio. The dominant peak at 0.854 Hz observed with the 25% blocking ratio orifice becomes blunt in the experiments for the 50% and 75% blocking ratio orifices. Flattening and multiple peaks, i.e., ripples, of frequency components of liquid motion suggest the aforementioned complex phenomena relating the energy dissipation and similar experimental findings are reported in the literature [24,25]. Regardless of the blunt peaks, migration of the damped
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Fig. 9. (a) Three different orifices of 25%, 50%, and 75% blocking ratios and (b) perspective view of their installations in the TLCD.
40
10
0
-40
0
10
20
30
40
50
2
Damping ratio (%)
Displacement (mm)
= 25% = 50% = 75%
60
Time (sec)
10
1
0.4
0.8
1
1.2
1.4
1.6
Fig. 11. Damping ratios of the TLCDs with orifices of 25%, 50%, and 75% blocking ratios.
3 = 25% = 50% = 75%
Amplitude
0.6
Frequency ratio ( )
(a)
2
1
0
= 25% = 50% = 75%
0
0.5
1
1.5
2
2.5
3
Frequency (Hz)
(b) Fig. 10. Dynamic characteristics of the TLCD with 25%, 50%, and 75% blocking ratio orifices: (a) measured heights; (b) corresponding Fourier spectra of the heights.
natural frequencies of TLCDs depending on damping ratio is also observed in Fig. 10(b). Next, dynamic characteristics of damping ratios of the TLCDs with different orifices were quantitatively studied using the practical equation, i.e., Eq. (16), derived in Section 2.2. Since in the equation, damping ratio is a function of the amplitude of harmonic oscillation of the liquid column, a series of harmonic excitation tests were undertaken changing the frequencies of the harmonic excitation of the shake table. 17 consecutive harmonic excitation tests in the frequency range of 0.4–1.3 Hz with an increment of 0.05 Hz were conducted with the TLCDs. Excitation force applied to the liquid of the TLCDs during the tests is the reaction force against the shake table in harmonic motion. The excitation force is the product of acceleration of the shake table and mass of the liquid filling the horizontal column of the TLCDs. In the experimental phases, the harmonic excitation motions of the shake table were set to generate a constant acceleration amplitude of peak-to-peak ±0.2 m/s2. Thus, constant excitation forces were assumed for the 17 consecutive harmonic excitation tests regardless of frequencies of the harmonic motion.
The wave height of the liquid column and displacement of the shake table were measured by the vision-based sensing and laser displacement sensor, respectively. To measure the wave height of harmonic steady state response, 20 s tests were run. Damping ratio calculation, by inserting the measured wave height and shake table displacement into uy and x0 in Eq. (16), respectively, followed a total of 51 (=17 3) dynamic tests for the TLCDs with three different orifices and the results are summarized in Fig. 11. In the figure, x axis ranging from 0.47 to 1.53 with increments of 0.06 is the frequency ratio of the excitation frequencies of harmonic motion to the natural frequency of the TLCD, i.e., 0.854 Hz. Two notable aspects of the damping estimates can be found: (1) proportionality of damping ratio to blocking ratio and (2) frequency dependent equivalent damping. This is intuitive because damping is proportional to head loss experienced by the liquid column moving through the narrowed orifice and attenuation of the oscillation of the liquid column under harmonic dynamic tests with constant excitation forces is also proportional to the head loss. 5. Conclusions Dynamic characterization of the TLCDs is a primal factory task prior to their installation at a site and is mainly undertaken by measurement of wave height during the test. In this study, a rapid, high precision, and cost-effective vision-based sensing system is developed exclusively for dynamic wave height measurement of the TLCDs. The robust image processing algorithm developed enables fast and accurate measurement of the wave height simply by counting binary digits in image pixels representing liquid columns of the TLCDs without requiring conventional retardant image processing techniques. In addition to the novel wave height sensing developed in this study, a practical methodology of experimental estimation of dynamic characteristics of the TLCDs is also proposed: under the
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assumption of harmonic excitation, a linear solution of the liquid motion of the TLCDs is derived and then utilized for damping estimation with experimental data measured. In laboratory tests with a prototype of the TLCDs, accuracy of the proposed vision-based sensing is confirmed through comparison with conventional contact measurement and dynamic characterization is successfully conducted including estimation of damped natural frequencies and damping ratio. Ongoing and future work is aimed at developing a more sophisticated vision-based wave height sensing system for the TLCDs and other types of TLDs. For example, a combined approach of heterogeneous sensor data fusion by multi-rate Kalman filtering [26,27]. In addition, twofold efforts are underway to close a gap between basic researches and engineering practice: (1) development of design procedure and (2) direct consideration on the nonlinear behavior of the TLCDs. Since the amplitude-dependent behaviors of the TLCDs, especially damping, dynamic characterization of the TLCDs are still needed be sophisticated to further develop a practical design guide. The authors are interested in pursuing developing the practical ways of damping estimation for the TLCDs. Leveraging the fast and simple vision-based system developed in the study, a combined approach of experiments and computer simulations, e.g., pseudo-dynamic testing of the TLCDs [28], will be strategically pursued. Acknowledgement The present research was supported by the research funds of Dankook University in 2015. The authors gratefully acknowledge the financial support. References [1] A. Kareem, T. Kijewski, Mitigation of motions of tall buildings with specific examples of recent applications, Wind Struct. 2 (3) (1999) 201–251. [2] K.C.S. Kwok, B. Samali, Performance of tuned mass dampers under wind loads, Eng. Struct. 17 (9) (1995) 655–667. [3] Y. Fujino et al., Tuned liquid damper (TLD) for suppressing horizontal motion of structures, J. Eng. Mech., ASCE 118 (10) (1992) 2017–2030. [4] K.W. Min et al., Performance evaluation of tuned liquid column dampers for response control of a 76-story benchmark building, Eng. Struct. 27 (7) (2005) 1101–1112. [5] Y.L. Xu, B. Samali, K.C.S. Kwok, Control of along-wind response of structures by mass and liquid dampers, ASCE J. Eng. Mech. 118 (1992) 20–39. [6] H. Gao, K.C.S. Kwok, B. Samali, Optimization of tuned liquid column dampers, Eng. Struct. 19 (1997) 476–486.
[7] T. Balendra, C.M. Wang, G. Rakesh, Vibration control of various types of buildings using TLCD, J. Wind Eng. Ind. Aerodyn. 83 (1999) 197–208. [8] K.W. Min, J. Kim, Y.W. Kim, Design and test of tuned liquid mass dampers for attenuating wind responses of a full scale building, Smart Mater. Struct. 23 (2014) 045020. [9] J.-C. Wu et al., Design guidelines for tuned liquid column damper for structures responding to wind, Eng. Struct. 27 (2005) 1893–1905. [10] S.K. Yalla, A. Kareem, Optimum absorber parameters for tuned liquid column dampers, J. Struct. Eng., ASCE 126 (2000) 906–915. [11] J.-C. Wu, C.-H. Chang, Y.-Y. Lin, Optimal designs for non-uniform tuned liquid column dampers in horizontal motion, J. Sound Vib. 326 (1–2) (2009) 104– 122. [12] C.C. Chang, W.L. Qu, Unified dynamic absorber design formulas for windinduced vibration control of tall buildings, Struct. Des. Tall Build. 7 (1998) 147–166. [13] K.W. Min, J. Kim, H.R. Lee, A design procedure of two-way liquid dampers for attenuation of wind-induced responses of tall buildings, J. Wind Eng. Ind. Aerodyn. 129 (2014) 22–30. [14] H. Sohn, Noncontact laser sensing technology for structural health monitoring and nondestructive testing, in: SPIE, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems. San Diego, CA, 2014. [15] H.-N. Ho et al., A synchronized multipoint vision-based system for displacement measurement of civil infrastructures, Sci. World J. 2012 (2012) 519146. [16] J.J. Lee, M. Shinozuka, A vision-based system for remote sensing of bridge displacement, NDT E Int. 39 (2006) 425–431. [17] P. Olaszek, Investigation of the dynamic characteristic of bridge structures using a computer vision method, Measurement 25 (1999) 227–236. [18] H.-S. Choi et al., Structural dynamic displacement vision system using digital image processing, NDT E Int. 44 (7) (2011) 597–608. [19] A.M. Wahbeh, J.P. Caffrey, S.F. Masri, A vision-based approach for the direct measurement of displacements in vibrating systems, Smart Mater. Struct. 12 (2003) 785–794. [20] L. Meirovitch, Principles and Techniques of Vibrations, Prentice-Hall, Upper Saddle River, NJ, 1997. [21] J.C. Wu, Experimental calibration and head loss prediction of tuned liquid column damper, Tamkang J. Sci. Eng. 8 (4) (2005) 319–325. [22] C.C. Chang, C.T. Hsu, Control performance of liquid column vibration absorbers, Eng. Struct. 20 (1998) 580–586. [23] J. Lewis, Fast normalized cross-correlation, Vision Interface 10 (1) (1995) 120– 123. [24] S.K. Yalla, A. Kareem, Semiactive tuned liquid column dampers: experimental study, J. Struct. Eng., ASCE 129 (2003) 960–971. [25] S. Colwell, B. Basu, Experimental and theoretical investigations of equivalent viscous damping of structures with TLCD for different fluids, J. Struct. Eng., ASCE 134 (2008) 154–163. [26] J. Kim, K. Kim, H. Sohn, Autonomous dynamic displacement estimation from data fusion of acceleration and intermittent displacement measurements, Mech. Syst. Signal Process. 42 (2014) 194–205. [27] C.C. Chang, X.H. Xiao, An integrated visual–inertial technique for structural displacement and velocity measurement, Smart Struct. Syst. 6 (9) (2010) 1025–1039. [28] K.-W. Min, S.-J. Jang, J. Kim, A standalone vision sensing system for pseudodynamic testing of tuned liquid column dampers, J. Sens. 2016 (in press).
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Measurement journal homepage: www.elsevier.com/locate/measurement
Fast vision-based wave height measurement for dynamic characterization of tuned liquid column dampers Junhee Kim, Chan-Soo Park, Kyung-Won Min ⇑ Department of Architectural Engineering, Dankook University, Jukjeon-dong, Suji-gu, Yongin-si, Gyeonggi-do 448-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 24 October 2014 Received in revised form 7 April 2016 Accepted 12 April 2016 Available online 13 April 2016 Keywords: Vision sensing Wave height measurement Dynamic characterization Structural control Tuned liquid column dampers
a b s t r a c t In this study, a novel and rapid vision-based sensing strategy is developed exclusively for dynamic wave height measurement of tuned liquid column dampers (TLCDs). The image processing algorithm of the vision-based sensing method simply counts white pixels in a binary image and thus expedites the vision-based wave height measurement. In addition to the experimental achievement, a practical methodology of dynamic characterization for the TLCDs is proposed combining linearized equations for the TLCDs and experimental data measured. An experimental characterization of dynamic behaviors and damping properties of the TLCDs is undertaken utilizing the vision-based sensing developed. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Structural developments in design and construction of buildings and towers have rendered structures tall, slender, and flexible. The tall and slender structures are vulnerable to dynamic loading such as wind and earthquakes. While the structures operate within safety limits, they may suffer from lack of serviceability due to undesirable vibrations induced by the dynamic loading. Structural control is needed to reduce the dynamic responses of the structures and to maintain their functional performances. A constant flow of developing novel and effective devices incorporated in structures for attenuation of structural vibration has been seen over the past decades [1]. One of the pervasive strategies widely applied to attenuate structural vibration is the installation of a secondary mass damper on the top floor of a building, i.e., a device generating a reaction force induced from the oscillating motion of a secondary mass. The secondary mass is a small fraction of the entire mass of the primary structure and interfaced to inherent damping devices for increasing the energy dissipation capability. Depending on the oscillatory media, the secondary mass dampers are categorized into two groups: tuned mass damper (TMD) and tuned liquid damper (TLD). The TMDs are mechanical devices of a solid mass with springs and dashpots attached to the primary building [2] and the TLDs are liquid containers [3]. As the counterpart of the TMDs, ⇑ Corresponding author. E-mail address: [email protected] (K.-W. Min). http://dx.doi.org/10.1016/j.measurement.2016.04.030 0263-2241/Ó 2016 Elsevier Ltd. All rights reserved.
the TLDs have proven their advantages: for example, simplicity, low cost, easy installation and maintenance, just to name a few [4–7]. Two different configurations of the TLDs have been investigated and adopted in construction sites [8]. Tuned Liquid Mass Damper (TLMD) and Tuned Liquid Column Damper (TLCD) utilize energy dissipating liquid motions of oscillation in narrow tubes and wave braking/sloshing in free liquid surface, respectively. Referring to numerous design parameters relating the configuration of the TLCDs and resultant tuning feasibility to determine their dynamic characteristics, practical advantages of the TLCDs over the TLMDs have frequently been emphasized in the literature [4,9,10]. Prior to installation of a TLCD at a site, a factory test for verification and tuning of dynamic characteristics must be conducted with the pre-fabricated TLCD. Among the dynamic characteristics of the TLCD, optimal tuning frequency and damping ratio are considered primal, since they are directly related to control performance, i.e., vibration suppression of the primary structure. Wave height of the oscillating liquid column of the TLCD is measured during the factory test and the dynamic characteristics are then estimated from wave height data measured. To date, capacitive wavemeters immersed into liquid have been dominantly used for measurement of varying wave heights. However, a number of intrinsic disadvantages associated with the contact sensors have been constantly addressed: high price, laborious installation, and a loss of accuracy due to interference from a liquid medium, e.g., parasitic capacitance. While great advances have been made in analytical studies of dynamic behaviors of the TLCDs
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[6,10,11] and practical design formulas/guidelines [9,12,13], comparatively less research has been conducted toward novel measurement strategy and further characterization of the TLCDs based on experimentally measured data. Recently, there has been growing interest in noncontact sensing in the areas of structural monitoring and assessment [14]. The precedent works of noncontact sensing, especially vision-based remote sensing, are found in the literature [15–19]. In this study, a rapid, high precision, and cost-effective vision-based sensing system is developed exclusively for dynamic wave height measurement of the TLCDs. A practical methodology of experimental estimation of dynamic characteristics of the TLCDs is also proposed based on both dynamic equations derived and experimental data measured. Finally, a series of experimental investigations are conducted for the verification of the vision-based sensing system and for showcasing the methodology of dynamic characterization of the TLCDs.
2. Formulation of dynamic behavior of tlcds The equations of dynamic behavior of the TLCDs are derived for estimation of their dynamic characteristics based on the experimental data measured. While natural frequencies of the TLCDs can be directly determined by measurements, damping estimation requires physics-based relationships between damping and measurable quantities. Thus, a practical equation for estimating the damping ratio of the TLCDs is derived in this section.
2.1. Derivation of linearized equation of motion A simplified model of the TLCD built on the primary structure is illustrated in Fig. 1. The TLCD considered here has two vertically upright tubes connected together at the bottom orifice forming sharp-edged elbows. Identical cross sectional areas, denoted as A in Fig. 1, of the vertical and horizontal tubes are considered. The displacements of horizontal structural motion of the exciting primary structure and vertical surface motion of oscillating liquid of the TLCD are denoted as x and y, respectively. As for the dimensions of the TLCD, the horizontal and vertical column lengths are defined as Lh and Lv, respectively.
The Lagrange’s equations of motion on the basis of the Hamilton’s principle for conservative systems [20] are adopted to formulate equations of motion of the TLCD [6,21,22]. Summation of the kinetic energy of the oscillating liquid along the two vertical and one horizontal columns leads to
1 T ¼ qALv ðy_ 2 þ x_ 2 Þ þ qALh ðy_ 2 þ 2x_ y_ þ x_ 2 Þ 2
ð1Þ
where q is the density of the liquid filled in the TLCD. Considering wave height changes in the two vertical liquid columns, the potential energy is expressed as
V ¼ qAðyÞg
y y þ qAyg ¼ qAgy2 2 2
ð2Þ
The energy dissipated by the liquid flow passing through the orifice is often referred to as head loss in fluid dynamics. Combining the energy balance equation, i.e., the Lagrange’s equation, and the non-conservative force of the head loss leads to
d @ðT VÞ @ðT VÞ 1 _ y_ ¼ qAgjyj dt @ y_ @y 2
ð3Þ
where g is the head loss coefficient. The equation of motion of the TLCD is derived by inserting Eqs. (1) and (2) into Eq. (3):
€ þ c1 y_ þ k1 y ¼ m2 €x m1 y
ð4Þ
where the total mass of the liquid column is m1 ¼ qAðLh þ 2Lv Þ; the mass of the horizontal liquid column is m2 ¼ qALh ; the nonlinear _ the term related friction damping coefficient is c1 ¼ ð1=2ÞqAgjyj; to stiffness is k1 ¼ 2qAg. The nonlinear friction damping can be treated as linear viscous damping by the concept of equivalent damping. Considering a harmonic excitation of the primary structure with the frequency, x and corresponding sinusoidal displacement response of the vertical liquid motion with the amplitude, uy , i.e., y ¼ uy sin xt, the non-conservative force of nonlinear friction damping is calculated as
f nc1 ¼ c1 y_ ¼
1 qAgu2y x2 j cos xtj cos xt 2
ð5Þ
The energy dissipated in a full cycle is calculated by integrating the non-conservative damping force in the first quarter cycle and quadrupling the result:
Z ED1 ¼ 4
Z f nc1 dy ¼ 0
¼
uy
8 !2 9 < = u sin x t y 2qAgu2y x2 1 dy : ; uy
4 qAgu3y x2 3
ð6Þ
On the contrary, the non-conservative force is composed with the linear viscous damping as
f nc2 ¼ ceq y_ ¼ ceq uy x cos xt
ð7Þ
The energy dissipated by the linear viscous damping is calculated as
Z ED2 ¼
Z f nc2 dy ¼ 0
¼ ceq pu2y x
2p
x
_ ¼ f nc2 ydt
Z 0
2p
x
ceq u2y x2 cos2 xtdt ð8Þ
By equating the dissipated energy of the nonlinear friction damping to that of linear viscous damping, the equivalent viscous damping is derived as
ceq ¼ Fig. 1. A TLCD subjected to a vibrating structure.
4 qAguy x 3p
ð9Þ
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Inserting Eq. (9) into the equation of motion of the TLCD yields the linearized equation of motion
€þ m1 y
4 qAguy xy_ þ k1 y ¼ m2 €x 3p
ð10Þ
Dividing both sides of Eq. (10) by m1 leads to
€þ y
4guy x y_ þ x2y y ¼ p€x 3pLe
ð11Þ
where Le ¼ Lh þ 2Lv is the effective length of the TLCD; pffiffiffiffiffiffiffiffiffiffiffiffi 2g=Le is the natural frequency of the TLCD; p ¼ Lh =Le is the ratio of the horizontal length to total length of the liquid column.
xy ¼
2.2. Derivation of damping ratio Considering a harmonic motion of the exciting primary structure and corresponding response of the liquid motion, i.e., x ¼ x0 eixt and y ¼ y0 eixt , respectively, the linearized equation of motion of Eq. (11) yields the amplitude of the liquid motion:
y0 ¼
x0 pb2 4gu b2 ð1 b2 Þ þ i 3pLy e
ð12Þ
where b ¼ x=xy is the frequency ratio of the exciting frequency to the natural frequency of the TLCD. The amplitudes of the liquid motion in both sides of Eq. (12) can be arranged by the identity of uy ¼ jy0 j. As a result, the amplitude uy is calculated as the magnitude of the complex amplitude of liquid motion of Eq. (12):
ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 4 g b 2 2 2 4 4 ð1 b Þ þ ð1 b Þ þ 4x20 p2 b 3pLe uy ¼ pffiffiffi4gb2 2 3pLe
ð13Þ
Arranging Eq. (13) with respect to the head loss leads to
g¼
3pLe
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðuy uy b2 þ x0 pb2 Þðuy b2 uy þ x0 pb2 Þ 4u2y b2
ð14Þ
Damping ratio of the TLCD is calculated from the equivalent viscous damping of Eq. (9)
ny ¼
ceq 2guy b ¼ 3pLe ccr
ð15Þ
where the critical damping is given as ccr ¼ 2m1 xy . Eventually, the equation for the damping ratio of the TLCD by inserting Eq. (14) into Eq. (15) is derived as
ny ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðuy uy b2 þ x0 pb2 Þðuy b2 uy þ x0 pb2 Þ 2uy b
ð16Þ
As seen in Eq. (16), the damping ratio is a function of amplitude of motion of the primary structure, natural frequencies of both the primary structure and the TLCD, and geometrical configurations of the TLCD. 3. Expedited digital image processing for TLCDS In this section, a novel and rapid video processing technique tailed to measurement of wave height of the TLCD is presented to replace the conventional wave height meter, taking advantages of noncontact sensing. The technique requires solely counting of white pixels in the binary image matrix and is thus rapid enough for near instant processing. A detailed explanation on the technique will follow introduction to conventional retardant video processing technique.
191
A video of a laterally shaking TLCD where blue dye was added to accentuate the liquid was preliminarily taken by a digital camcorder. The lateral motion of the TLCD resulted in a vertically oscillating liquid column. A couple of freeze-frames grabbed from the video are given in Fig 2: Fig. 2(a) and (b) are still images at the instants when the free surface of the liquid column reaches the highest and lowest positions, respectively. As seen in figures, height and horizontal location of the liquid column are changing simultaneously. The measurement quantity, i.e., wave height, is defined by distance between upper and lower corners of the liquid column seen in Fig. 3(a) where the corners are highlighted by two L-shaped markers. As a result, detection of the two corners in digital images leads directly to wave height measurement. To locate a moving object by analyzing digital images entails two sequential image processing procedures [23]: edge detection and moving object tracking. Edges are paths of rapid change of image intensity in a digital image and outline targeted objects, i.e., the liquid column in the TLCD in this study (Fig. 3(b)). Edge detection is used to identify the edges in an image. Height of the liquid column of the TLCD is measured from the edge detected, while laterally tracking the position-changing liquid column. An image processing technique for tracking moving objects is conventionally conducted by correlation analysis. In this study, the two corners are moving objects to be tracked and reference image frame is used for the correlation analysis (Fig. 3(c)). However, the consecutive image processing techniques, i.e., edge detection followed by correlation analysis, are computationally expensive and time consuming. Thus, their implementation presents a challenge to the use of real time image processing for the measurement the liquid height in the TLCD. In this study, an expedited image processing technique tailored to the measurement of the liquid height of the TLCD is developed to skip the aforementioned retardant processes of edge detection and correlation analysis. The suggested technique examines on image portion, termed region of interest (ROI), extracted by cropping the original image. In this study, the ROI is set to be a portion of the image specifying the liquid column of the TLCD. The rectangle ROI contains a true-color image of the liquid column truncated above the lower sharp-edged elbow and is dealt as an RGB image, an m n 3 data array that defines red, green, and blue color components for m n pixels. In general, a graphic file format of the RGB image is 24-bit digital information, where the red, green, and blue components are 8 bits each. Since the liquid column of the TLCD is blue, the information of blue color is exclusively converted to a grayscale color map consisting of 8 bits per pixel. Finally, a binary image (1 bit per pixel) is acquired from the grayscale image using an appropriate threshold. Explanatory image matrices of the binary images at two different instants are given at Fig. 4. Two dimensional matrices of 1’s (white pixels) and 0’s (black pixels) represent the liquid column of the TLCD and the other parts, respectively. As seen, the height and horizontal position of the liquid column change in the two figures. Since the feature aimed to be measured in the study is the height of the liquid column regardless of its position, a simple strategy of analyzing the binary image matrices are adopted. It requires solely the counting of white pixels, i.e., the total sum of ones in the binary image matrix, which is directly proportional to the height of the liquid column. Mapping of the total sum of the white pixels to a metric system of length needs a reference, which is the number of pixels along a line of measured length. In this study, an a priori measurement of the width of the liquid column is adopted. Thus, the height of the liquid column at time step i, h(i) is calculated as
hðiÞ ¼ a
sðiÞ W
ð17Þ
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Fig. 2. Two still images of a working TLCD at two different instants.
Fig. 3. Conventional image processing technique for wave height measurement: (a) definition of wave height; (b) edges detected; (c) two reference frames of corners.
Fig. 4. Binary information of the image matrices for a moving liquid column in the ROI.
where s(i) is the total sum of white pixels in the ROI at time step i; a is the mapping factor (unit of m/pixel) determined by the aforementioned measurement; W is the number of white pixels along the width of the liquid column. It should be again noted that the algorithm to measure the liquid height of the TLCD using a video recorded does not require any time-consuming image processing technique and implementation of the algorithm is thus near instant.
4. Experimental verification In the experimental phases of this study, two experimental examples are present: first, a demonstration of the performance of the expedited vision-based wave height sensing is given with a comparison with conventional measurements. Next, the visionbased sensing strategy is directed to experimentally analyze dynamic behaviors of the TLCDs with different orifices.
4.1. Performance of vision-based wave height sensing Prior to the test, a laboratory-scaled prototype (Fig. 5) of the TLCDs was fabricated with 1 cm thick acrylic plates. The width and height of the TLCD are 650 and 400 mm, respectively. The inner dimension of vertical and horizontal column, i.e., cross sectional area of liquid flow, is 150 150 mm. The TLCD was mounted on a uniaxial shake table driven by a mechanical linear actuator where rotary motion of an AC servo motor (HC-SFS502, MITSUBISHI) is converted to linear motion. The AC servo motor is operated in the velocity control mode in which angular velocity of the rotary motion is subjected to applied analog electrical signals programmed in a function generator. A 60 s long 0.2–2.0 Hz chirp signal with a constant amplitude of peak-to-peak ±1 V was applied to the AC servo motor via the function generator. To measure motion of the shake table, a laser displacement sensor (CD4-350, OPTEX FA) was utilized. The laser displacement
J. Kim et al. / Measurement 89 (2016) 189–196
193
Fig. 5. Experiments of the vision-based wave height sensing for a shaking TLCD – oscillating liquid column is clearly noticeable.
sensor is a precision optoelectronic transducer to determine dynamic displacement by sensing phase differences between transmitted laser and back scattered laser from the moving surface of targeted objects. During the dynamic test, the laser displacement sensor was set 0.35 m away from an edge of the shake table and sensed the shake table’s displacement motion while aligning along the axis of moving direction of the shake table. The measured displacement time histories of the shake table are plotted in Fig. 6 (a). Displacement amplitude decaying due to the velocity control of the AC servo motor is witnessed over the duration of the applied excitation. The Fourier spectrum of the measured displacement is
Displacement (mm)
25
0
-25
0
10
20
30
40
50
60
Time (sec)
(a)
Amplitude
10
10
10
3
0
-3
0
0.5
1
1.5
2
2.5
3
Frequency (Hz)
(b) Fig. 6. Frequency shift excitation of the shake table: (a) measured displacement; (b) corresponding Fourier spectrum of the displacement.
presented in Fig. 6(b) where the 0.2–2.0 Hz frequency band of the applied excitation is confirmed. To demonstrate the cost-effectiveness and accuracy of the proposed vision-based sensing system compared to a conventional contact sensor, both sensors were utilized record the dynamic motion of the TLCD during the test. A commercially available digital camcorder (HMX-QF20, SAMSUNG) which costs 300 USD in the market was deployed. The high-definition (HD) digital camcorder is a 1920 1080 pixel full HD camcorder capturing 60 frames per sec. The video compression format supported by the camcorder is H.264, i.e., MPEG-4, which is the latest video coding format standardized by the ISO/IEC and compatible with the image processing toolbox of MATLAB. The camcorder was placed on a stationary tripod 2 meters away from the shake table. Accuracy of the visionbased wave height measurement system was cross-checked with that of a conventional wavemeter, i.e., capacitive wave height sensor (CH-601, KENEK). The wavemeter costs 3000 USD and its installation is laborious compared to the proposed system – the wave probe was immersed in the liquid column of the TLCD as well as the sensor body was clamped on top of the TLCD as seen in Fig. 5. After the dynamic test was completed, the video recorded by the camcorder was transferred to a PC via USB interface for digital image processing as proposed by this study. The number of frames, image size, video duration, and frame-rate were identified in the MATLAB image processing toolbox – the frame rate is 60 frames per sec and thus the 60 s video is composed of a total of 3840 frames; the 1920 1080 pixels of the individual frames have 24 bit RGB information. The aforementioned image processing for wave height measurement was consecutively conducted with sequences of the freeze-frames grabbed from the video and the results are depicted in Fig. 7. For comparison purposes, time histories of wave height measured by the wavemeter are superimposed. Time synchronization of the two different signals was conducted by maximizing correlation of the signals. As seen, a very close match of two measurements is observed in Fig. 7(a). A quantitative accuracy evaluation of the proposed methodology was conducted by calculating the following RMS error between the signals:
RMS Error ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi X 2 ðhðiÞ hðiÞ Þ =N video wave i
ð18Þ
where hðiÞvideo and hðiÞwave are measured wave heights at time step i, by the vision-based sensing and wavemeter, respectively; N is the
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J. Kim et al. / Measurement 89 (2016) 189–196 Table 1 Computing time of digital video processing.
40
0
-40
10
20
30
40
50
Proposed technique (s)
1 2 3
47.470 47.346 47.315
13.385 13.353 13.354
Average
47.377
13.364
Proposed technique Conventional technique
60
(a) 3 Wavemeter Vision-based sensing
2 Amplitude
Conventional technique (s)
40 0
Time (sec)
0
-40 20
1
0
No. of test
Displacement (mm)
Displacement (mm)
Wavemeter Vision-based sensing
30
40
Time (sec) Fig. 8. Comparison of responses of the TLCD mounted on the shake table (thin: vision-based sensing proposed, thick: wavemeter):
0
0.5
1
1.5
2
2.5
3
Frequency (Hz)
(b) Fig. 7. Comparison of responses of the TLCD mounted on the shake table (thin: vision-based sensing proposed, thick: wavemeter): (a) measured heights; (b) corresponding Fourier spectra of the heights.
number of discrete data measured. In this study, the RMS error was evaluated as 1.053 mm. Considering the fact that the wave height is sensed at a point of the liquid surface by the wavemeter while the vision-based sensing yields the average height of the liquid column, the small RMS error evaluated suggests excellent accuracy of the vision-based sensing proposed. The Fourier spectra of the measured wave heights are presented in Fig. 7(b). Dominant peaks at 0.854 Hz are clearly observed at the two measurements. Amplitude decay is witnessed near 2.0 Hz, suggesting the bandwidth of the applied excitation, i.e., 0.2–2.0 Hz. So far, the high precision of the expedited vision-based sensing proposed in this study has been quantitatively proven through the comparison with the conventional capacitive wavemeter. Based on the successful results, advantages of the expedited vision-based sensing over the conventional image processing technique explained in Fig. 3 were studied. Identical tests with the 60 s long shake table driven by 0.2–2.0 Hz chirp signal were repeated three times and then three 3840 frame video files were recorded – in each image frame, 1920 1080 pixels contained 24 bit RGB information. For each video file, two different video processing techniques were applied to determine wave heights. As for the conventional technique, a 250 250 pixel image frame of an Lshaped marker was used as the reference in correlation analysis to detect locations of the liquid corners. Since the two video processing techniques were implemented with the MATLAB image processing toolbox in an identical personal computer processed by Intel Core2 Q9400 (2.66 GHz), a comparison of computing time was carried out and the results are tabulated in Table 1. As seen in the table, it consistently takes nearly the same amount of time to compute the wave height in each technique. It is concluded that the expedited technique proposed in this study is 3.55 times faster than the conventional technique. One of the three results is given in Fig. 8 – for a more precise examination, time histories in a range
of 20–40 s are plotted. A good agreement between two wave height measurements is confirmed; thus, it can be concluded that performance of the proposed technique matches that of the conventional technique, despite a significant drop in time consumption.
4.2. Dynamic characterization of TLCDS On the basis of the previous confirmation of the accuracy of the vision-based wave height sensing, dynamic characteristics of the TLCDs were estimated from experimentally measured data solely by the vision-based sensing. To investigate wide ranges of dynamic characteristics of the TLCDs, three different orifices with varying blocking ratios were placed in the laboratory scaled prototype (Fig. 5). The blocking ratio of an orifice is defined as the ratio of closed to cross-sectional areas. In this study, blocking ratios of 25%, 50%, and 75% were selected as seen in Fig. 9. First, damped natural frequencies of the TLCDs with different orifices were estimated from the vision-based wave height measurements during shake table tests with the previous chirp excitation of Fig. 5, while consecutively installing one of the orifices in the TLCD. Time histories of wave heights measured are plotted in Fig. 10(a). As the blocking ratios increase, the vertical oscillations of the liquid column of the TLCDs are suppressed especially in time interval of 18–29 s. The trend witnessed is also confirmed in the Fourier spectra seen in Fig. 10(b) – the magnitude drops of the peaks near resonance frequencies depending on the blocking ratios are noticeable. Since the energy dissipation, i.e., damping, of the TLCDs is mainly induced by narrowing liquid flow and disturbance near the orifices, the damping is proportional to the blocking ratio. The dominant peak at 0.854 Hz observed with the 25% blocking ratio orifice becomes blunt in the experiments for the 50% and 75% blocking ratio orifices. Flattening and multiple peaks, i.e., ripples, of frequency components of liquid motion suggest the aforementioned complex phenomena relating the energy dissipation and similar experimental findings are reported in the literature [24,25]. Regardless of the blunt peaks, migration of the damped
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Fig. 9. (a) Three different orifices of 25%, 50%, and 75% blocking ratios and (b) perspective view of their installations in the TLCD.
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(b) Fig. 10. Dynamic characteristics of the TLCD with 25%, 50%, and 75% blocking ratio orifices: (a) measured heights; (b) corresponding Fourier spectra of the heights.
natural frequencies of TLCDs depending on damping ratio is also observed in Fig. 10(b). Next, dynamic characteristics of damping ratios of the TLCDs with different orifices were quantitatively studied using the practical equation, i.e., Eq. (16), derived in Section 2.2. Since in the equation, damping ratio is a function of the amplitude of harmonic oscillation of the liquid column, a series of harmonic excitation tests were undertaken changing the frequencies of the harmonic excitation of the shake table. 17 consecutive harmonic excitation tests in the frequency range of 0.4–1.3 Hz with an increment of 0.05 Hz were conducted with the TLCDs. Excitation force applied to the liquid of the TLCDs during the tests is the reaction force against the shake table in harmonic motion. The excitation force is the product of acceleration of the shake table and mass of the liquid filling the horizontal column of the TLCDs. In the experimental phases, the harmonic excitation motions of the shake table were set to generate a constant acceleration amplitude of peak-to-peak ±0.2 m/s2. Thus, constant excitation forces were assumed for the 17 consecutive harmonic excitation tests regardless of frequencies of the harmonic motion.
The wave height of the liquid column and displacement of the shake table were measured by the vision-based sensing and laser displacement sensor, respectively. To measure the wave height of harmonic steady state response, 20 s tests were run. Damping ratio calculation, by inserting the measured wave height and shake table displacement into uy and x0 in Eq. (16), respectively, followed a total of 51 (=17 3) dynamic tests for the TLCDs with three different orifices and the results are summarized in Fig. 11. In the figure, x axis ranging from 0.47 to 1.53 with increments of 0.06 is the frequency ratio of the excitation frequencies of harmonic motion to the natural frequency of the TLCD, i.e., 0.854 Hz. Two notable aspects of the damping estimates can be found: (1) proportionality of damping ratio to blocking ratio and (2) frequency dependent equivalent damping. This is intuitive because damping is proportional to head loss experienced by the liquid column moving through the narrowed orifice and attenuation of the oscillation of the liquid column under harmonic dynamic tests with constant excitation forces is also proportional to the head loss. 5. Conclusions Dynamic characterization of the TLCDs is a primal factory task prior to their installation at a site and is mainly undertaken by measurement of wave height during the test. In this study, a rapid, high precision, and cost-effective vision-based sensing system is developed exclusively for dynamic wave height measurement of the TLCDs. The robust image processing algorithm developed enables fast and accurate measurement of the wave height simply by counting binary digits in image pixels representing liquid columns of the TLCDs without requiring conventional retardant image processing techniques. In addition to the novel wave height sensing developed in this study, a practical methodology of experimental estimation of dynamic characteristics of the TLCDs is also proposed: under the
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assumption of harmonic excitation, a linear solution of the liquid motion of the TLCDs is derived and then utilized for damping estimation with experimental data measured. In laboratory tests with a prototype of the TLCDs, accuracy of the proposed vision-based sensing is confirmed through comparison with conventional contact measurement and dynamic characterization is successfully conducted including estimation of damped natural frequencies and damping ratio. Ongoing and future work is aimed at developing a more sophisticated vision-based wave height sensing system for the TLCDs and other types of TLDs. For example, a combined approach of heterogeneous sensor data fusion by multi-rate Kalman filtering [26,27]. In addition, twofold efforts are underway to close a gap between basic researches and engineering practice: (1) development of design procedure and (2) direct consideration on the nonlinear behavior of the TLCDs. Since the amplitude-dependent behaviors of the TLCDs, especially damping, dynamic characterization of the TLCDs are still needed be sophisticated to further develop a practical design guide. The authors are interested in pursuing developing the practical ways of damping estimation for the TLCDs. Leveraging the fast and simple vision-based system developed in the study, a combined approach of experiments and computer simulations, e.g., pseudo-dynamic testing of the TLCDs [28], will be strategically pursued. Acknowledgement The present research was supported by the research funds of Dankook University in 2015. The authors gratefully acknowledge the financial support. References [1] A. Kareem, T. Kijewski, Mitigation of motions of tall buildings with specific examples of recent applications, Wind Struct. 2 (3) (1999) 201–251. [2] K.C.S. Kwok, B. Samali, Performance of tuned mass dampers under wind loads, Eng. Struct. 17 (9) (1995) 655–667. [3] Y. Fujino et al., Tuned liquid damper (TLD) for suppressing horizontal motion of structures, J. Eng. Mech., ASCE 118 (10) (1992) 2017–2030. [4] K.W. Min et al., Performance evaluation of tuned liquid column dampers for response control of a 76-story benchmark building, Eng. Struct. 27 (7) (2005) 1101–1112. [5] Y.L. Xu, B. Samali, K.C.S. Kwok, Control of along-wind response of structures by mass and liquid dampers, ASCE J. Eng. Mech. 118 (1992) 20–39. [6] H. Gao, K.C.S. Kwok, B. Samali, Optimization of tuned liquid column dampers, Eng. Struct. 19 (1997) 476–486.
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