# Ultrasonic Lateral Displacement Sensor for Health Monitoring in Seismically Isolated Buildings

^{*}

## Abstract

**:**

## 1. Introduction

**Figure 1.**(

**a**) Seismically isolated building; (

**b**) Enlarged view of the seismically isolated layer and installation of ultrasonic lateral displacement sensor.

## 2. Experimental Setup

#### 2.1. Ultrasound Intensity Distribution of Air-Coupled Ultrasound Transducer

**Figure 2.**(

**a**) Experimental setup for measuring ultrasound intensity distribution of air-coupled ultrasound transducer; (

**b**) Front view of the receiver.

#### 2.2. Measurement Principal for Lateral Displacement Sensing

**Figure 3.**Experimental setup for measuring relative lateral displacement sensing using two transmitters.

#### 2.3. Measuring Lateral Displacement over a Wide Measurement Range

## 3. Results and Discussion

#### 3.1. Ultrasound Intensity Distribution of Air-Coupled Ultrasound Transducer

#### 3.2. Measurement Principal for Lateral Displacement Sensing

_{1}and I

_{2}show the ultrasound intensity transmitted by transmitters 1 and 2, respectively, x

_{0}is the relative lateral displacement of the receiver from the origin, σ

_{0}is the standard deviation of the ultrasound intensity distribution which is common to both transmitters, μ

_{1}and μ

_{2}are the original positions of the transmitters in x direction, and d is the interval between transmitters 1 and 2. Note that in the experiment detailed in this paper, the ultrasound transducers are alternately turned on and off, so each ultrasound beam is generated as an independent event. From Equations (2–4), the relative lateral displacement x

_{0}is derived:

_{0}is expressed as a logarithm of the ratio of I

_{1}to I

_{2}, which are obtained from the two transmitters. If the calibration for the displacement measurement is carried out, we can obtain the values of A and B as known constants beforehand in Equations (6) and (7). Even if the shapes of the data curves obtained from transmitters 1 and 2 are not identical to each other, the difference in the standard deviations and their absolute values are included by the constants A and B as long as the Gaussian fitting is applied to I

_{1}and I

_{2}. Therefore, the lateral displacement x

_{0}is successfully derived by measuring the logarithm of the ratio of I

_{1}to I

_{2}. If a wider range of lateral displacement measurement is required, the arrangement of continuous pairs of ultrasound transducers will make it possible. Figure 6b shows the actual data plots representing the ultrasound intensity distributions according to the position of the receiver. The open circles and closed circles show the ultrasound intensities obtained from transmitters 1 and 2, respectively. The solid line shows the fitted curve that is explained after the following procedure.

**Figure 6.**(

**a**) Schematic of two ultrasound intensity distributions; (

**b**) Ultrasound intensity distributions were measured by the receiver according to its lateral displacement.

_{0}is obtained. In Figure 7b, the fitted curve is also drawn by using Equations (5), (6) and (8). Figure 7b shows the estimated lateral displacement compared with the reference displacement. The open circles show the estimated lateral displacement. The solid line shows the reference displacement. Although the estimated lateral displacement basically agrees with the reference, it fluctuates considerably and its maximum value is 1.36 mm. As mentioned above, we have tried to obtain more accurate ultrasound intensity distributions by utilizing a mask on the receiver. However, as shown in Figure 4, the ultrasound intensity distribution still remains imperfect, which causes fluctuations in the calculated lateral displacement. Therefore, it is considered that a further correction method is essential for obtaining more precise lateral displacement measurements for health monitoring of seismically isolated buildings.

**Figure 7.**Estimation of lateral displacement. (

**a**) Lateral displacement and the logarithm of the ratio of the ultrasound intensities obtained from the two transmitters; (

**b**) Estimated lateral displacement.

_{t1}and I

_{t2}are normally approximated values that are described on the fitted curve as shown in Figure 6b, e

_{1}and e

_{2}are compensation coefficients for the obtained ultrasound intensities I

_{1}and I

_{2}, respectively. Compensation coefficients are expressed as functions of the logarithm of the ratio of I

_{1}to I

_{2}in Equations (9) and (10). Figure 8 shows the values of I

_{t1}/I

_{1}and I

_{t2}/I

_{2}by changing the logarithm of the ratio of I

_{1}to I

_{2}to derive the compensation coefficients e

_{1}and e

_{2}. For these coefficients, polynomial approximation is applied because the values of I

_{t1}/I

_{1}and I

_{t2}/I

_{2}fluctuate greatly as shown in Figure 8. The compensation coefficients are represented as follows:

_{1}to I

_{2}. As shown in Figure 8 and Equations (11) and (12), the compensation coefficients were successfully obtained. Figure 9a shows the corrected ultrasound intensity distribution with the application of Equations (11) and (12). Open circles show corrected values. The solid line shows the fitted curve previously shown in Figure 6b. The fitted curve and the corrected values overlap fairly well. Figure 9b shows the corrected lateral displacement. Open circles show the corrected lateral displacement. The solid line shows the reference displacement. From the Figures, it is clear that the corrected lateral displacement agrees well with the reference. The fluctuation between corrected values and the reference is within 0.20 mm at maximum. Because the fluctuation rate for the 30 mm range corresponds to 0.67%, it is verified that this system has sufficient accuracy for a small displacement region. For the actual measurement activity, a manual stage needs to be arranged under the transmitters or the receiver for the system calibration. After the calibration, the stage should be fixed as a base keeping its position at the origin.

**Figure 10.**The dynamic response experiment in 0.6 Hz movement. (

**a**) Estimated lateral displacement; (

**b**) Corrected lateral displacement.

#### 3.3. Measuring Lateral Displacement over a Wide Range

**Figure 11.**Measuring lateral displacement over a wide range. (

**a**) The ultrasound intensity distribution obtained from five transmitters; (

**b**) The corrected lateral displacement.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Ariga, T.; Kanno, Y.; Takewaki, I. Resonant behaviour of base-isolated high-rise buildings under long-period ground motions. Struct. Des. Tall Spec. Build.
**2006**, 15, 325–338. [Google Scholar] [CrossRef] - Kurata, N.; Kobori, T.; Takahashi, M.; Niwa, N.; Midorikawa, H. Actual seismic response controlled building with semi-active damper system. Earthq. Eng. Struct. Dyn.
**1999**, 28, 1427–1447. [Google Scholar] [CrossRef] - Islam, A.B.M.S.; Jameel, M.; Jumaat, M.Z. Seismic isolation in buildings to be a practical reality: behavior of structural and installation technique. J. Eng. Technol. Res.
**2011**, 3, 99–117. [Google Scholar] - Ramirez, O.M.; Constantinou, M.C.; Whittaker, A.S.; Kircher, C.A.; Chrysostomou, C.Z. Elastic and inelastic seismic response of buildings with damping system. Earthq. Spectra
**2002**, 18, 531–547. [Google Scholar] [CrossRef] - Heaton, T.H.; Hall, J.F.; Wald, D.J.; Halling, M.W. Response of high-rise and base-isolated buildings to a hypothetical M
_{w}7.0 blind thrust earthquake. Science**1995**, 267, 206–211. [Google Scholar] [CrossRef] [PubMed] - Ventura, C.E.; Finn, W.D.L.; Lord, J.-F.; Fujita, N. Dynamic characteristics of a base isolated building from ambient vibration measurements and low level earthquake shaking. Soil Dyn. Earthq. Eng.
**2003**, 23, 313–322. [Google Scholar] [CrossRef] - Kani, N.; Takayama, M.; Wada, A. Performance of seismically isolated buildings in Japan—observation records and vibration perception by people in buildings with seismic isolation. In Proceedings of the 8th U.S. National Conference on Earthquake Engineering, San Francisco, CA, USA, 18–22 April 2006.
- Moroni, M.O.; Sarrazin, M.; Boroschek, R. Experiments on a Base-Isolated Building in Santiago, Chile. Eng. Struct.
**1998**, 20, 720–725. [Google Scholar] [CrossRef] - Chang, P.C.; Flatau, A.; Liu, S.C. Review paper: health monitoring of civil infrastructure. Struct. Health Monit.
**2003**, 2, 257–267. [Google Scholar] [CrossRef] - Miyashita, T.; Nagai, M. Vibration-based structural health monitoring for bridges using laser Doppler vibrometers and MEMS-based technologies. Int. J. Steel Struct.
**2008**, 8, 325–331. [Google Scholar] - Nishitani, A.; Matsui, C.; Hara, Y.; Xiang, P.; Nitta, Y.; Hatada, T.; Katamura, R.; Matsuya, I.; Tanii, T. Drift displacement data based estimation of cumulative plastic deformation ratios for buildings. Smart Struct. Syst.
**2015**, 15, 881–896. [Google Scholar] [CrossRef] - Nagayama, T.; Abe, M.; Fujino, Y.; Asce, M.; Ikeda, K. Structural identification of a nonproportionally damped system and its application to a full-scale suspension bridge. J. Struct. Eng.
**2005**, 131, 1536–1545. [Google Scholar] [CrossRef] - Nitta, Y.; Nishitani, A.; Spencer, B.F., Jr. Semiactive control strategy for smart base isolation utilizing absolute acceleration information. Struct. Control Health Monit.
**2005**, 13, 649–659. [Google Scholar] [CrossRef] - Park, J.W.; Sim, S.H.; Jung, H.J.; Spencer, B.F., Jr. Development of a wireless displacement measurement system using acceleration responses. Sensors
**2013**, 13, 8377–8392. [Google Scholar] [CrossRef] [PubMed][Green Version] - Park, H.S.; Park, K.; Kim, Y.; Choi, S.W. Deformation monitoring of a building structure using a motion capture system. IEEE/ASME Trans. Mechatron.
**2014**, PP, 1–9. [Google Scholar] [CrossRef] - Matsuya, I.; Tomishi, R.; Sato, M.; Kanekawa, K.; Nitta, Y.; Takahashi, M.; Miura, S.; Suzuki, Y.; Hatada, T.; Katamura, R.; et al. Development of lateral-displacement sensor for real-time detection of structural damage. IEEJ Trans. Electr. Electron. Eng.
**2011**, 6, 266–272. [Google Scholar] [CrossRef] - Matsuya, I.; Katamura, R.; Sato, M.; Iba, M.; Kondo, H.; Kanekawa, K.; Takahashi, M.; Hatada, T.; Nitta, Y.; Tanii, T.; et al. Measuring relative-story displacement and local inclination angle using multiple position-sensitive detectors. Sensors
**2010**, 10, 9687–9697. [Google Scholar] [CrossRef] [PubMed][Green Version] - Chan, T.H.T. Vertical displacement measurements for bridges using optical fiber sensors and CCD cameras—a preliminary study. Struct. Health Monit.
**2009**, 8, 243–249. [Google Scholar] [CrossRef] - Sukumana, D.D.; Ihara, I. Application of an air-coupled ultrasound to non-contact surface roughness evaluation. Jpn. J. Appl. Phys.
**2005**, 44, 4417–4420. [Google Scholar] [CrossRef] - Matsuya, I.; Matsumoto, F.; Ihara, I. Experimental study on lateral displacement measurement using air-coupled ultrasound transducers. Mechan. Eng. J.
**2015**, 2. [Google Scholar] [CrossRef]

© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Matsuya, I.; Matsumoto, F.; Ihara, I.
Ultrasonic Lateral Displacement Sensor for Health Monitoring in Seismically Isolated Buildings. *Sensors* **2015**, *15*, 17000-17012.
https://doi.org/10.3390/s150717000

**AMA Style**

Matsuya I, Matsumoto F, Ihara I.
Ultrasonic Lateral Displacement Sensor for Health Monitoring in Seismically Isolated Buildings. *Sensors*. 2015; 15(7):17000-17012.
https://doi.org/10.3390/s150717000

**Chicago/Turabian Style**

Matsuya, Iwao, Fumiya Matsumoto, and Ikuo Ihara.
2015. "Ultrasonic Lateral Displacement Sensor for Health Monitoring in Seismically Isolated Buildings" *Sensors* 15, no. 7: 17000-17012.
https://doi.org/10.3390/s150717000