An investigation of the dynamic characteristics of super high-rise buildings using real-time kinematic–global navigation satellite system technology

Abstract

This article aims to investigate the dynamic characteristics (e.g. natural frequency and damping ratio) for two super high-rise completed and uncompleted buildings. Real-time kinematic-global navigation satellite system technology is applied to observe the dynamic responses. To improve the positioning accuracy and avoid distortion of the results, a Type 1 Chebyshev high-pass digital filter is used. The natural frequencies and damping ratios of the buildings are determined using the fast Fourier transform analysis and random decrement technique combined with a logarithmic decrement method, respectively. The structural parameters are obtained. The results show that real-time kinematic-global navigation satellite system technology can provide the dynamic responses of super high-rise buildings in an efficient manner and that the dynamic characteristics from field measurements agree well with the results of the numerical simulation.

Keywords

dynamic characteristics fast Fourier transform logarithmic decrement method random decrement technique real-time kinematic-global navigation satellite system super high-rise building

Introduction

An increased number of investigations have been devoted to super high-rise buildings, which are prone to large deformation under dynamic influences such as wind and earthquakes. The deformations may result in instability and even destruction of the entire structure. The basic dynamic characteristics of super high-rise buildings include the natural frequencies, mode shapes and damping ratios. A comprehensive understanding of the actual values of the model parameters of a tall slender structure is necessary to ensure the safety and stability of the structure. This is typically achieved by evaluating the free vibration response at the design stage. However, most of the models used for simulation are idealized, thus the results may be disputed. In general, the predictions of the characteristic parameters of a structure are relatively complicated because extensive practical factors inevitably play a role in these problems, such as the properties of the structural materials, the soil properties and the foundation types. Recently, it was reported that field measurement methods can provide highly reliable information for the analysis of structural stability (Chen et al., 2014; Kijewski-Correa et al., 2006; Kwok et al., 2011; Li et al., 2014).

Note that the accurate monitoring of the dynamic responses of super high-rise buildings is very important to evaluate the stability of the structure. Until now, conventional monitoring methods have been successfully applied to structural dynamic response monitoring in various applications, and the methods include accelerometers, strain gauges and survey equipment (Tien et al., 2016; Xia and Quail, 2016; Zarikas et al., 2010). Accelerometers are widely used to monitor the dynamic response of super high-rise buildings. However, their use is limited for performing a double integral operation, that is, accelerometers cannot provide information for the accurate displacement of structures (Lee and Shinozuka, 2006; Masri et al., 2004). To monitor the displacement of structures, the emerging technology of real-time kinematic-global navigation satellite system (RTK-GNSS) was used to provide precise positional and three-dimensional information in an efficient manner (Kaloop, 2012; Li and Kuhlmann, 2010). Meo et al. (2006) identified the modal parameters of a suspension bridge using Global Positioning System (GPS) technique. Based on GPS and accelerometer measurements, Meng et al. (2007) proposed a novel peak-picking approach and applied it to extract the vibration characteristics of a suspension footbridge. Breuer et al. (2008) used GPS to study the dynamic characteristics of a TV tower affected by sun and wind. Elnabwy et al. (2013) investigated the movements of the Talkha highway steel bridge using RTK-GPS technology. Han et al. (2016) studied the dynamic responses of a long-span bridge using GPS, accelerometers and anemometers. Li and Yi (2016) investigated the effects of a typhoon on two super high-rise buildings using GPS, anemometers, accelerometers and pressure sensors. The horizontal positioning accuracy (approx. 1 cm) of RTK-GNSS is higher than the vertical positioning accuracy (approx. 2 cm), but this study is focused on the horizontal vibration of a structure. Due to the displacement of super high-rise buildings, the horizontal vibration is usually small. Therefore, it is essential to reduce the influence of background noise on RTK-GNSS using an effective filtering method. In this study, Type 1 Chebyshev high-pass digital filter was used to improve the accuracy of the dynamic displacements’ estimation.

Numerous methods for experimental modal parameter identification have been proposed. In the time domain, these methods include the logarithmic decrement method (LDM; Cooper, 1996), the Hilbert transform method (HTM; Feldman, 1985) and the stochastic subspace identification (SSI) method (Van Overschee and Moor, 1993). In the frequency domain, the methods include the frequency domain decomposition (FDD) method (Brincker et al., 2000), the half power method (HPM; Thomson, 1993), the collocation method (CM; Flaga et al., 2008) and the enhanced frequency domain decomposition method (EFDDM; Brincker et al., 2007). Furthermore, Cole (1971) put forward a time domain analysis method, which is considered a random decrement technique (RDT). The main advantage of the RDT is the determination of the stationary or nonstationary response of structures under unknown excitation. This method can also be used in conjunction with other parameter identification methods. He et al. (2011) obtained a solution for the modal parameters of an existing railway bridge using a combined method (i.e. empirical mode decomposition (EMD) and RDT). Górski (2015) investigated the dynamic characteristics of a tall industrial chimney under wind excitations based on GPS measurements and using the RDT. Huang and Gu (2016) proposed an envelope RDT and applied it to identify the damping ratios of the Shanghai World Financial Center. Morsy et al. (2016) detected the dynamic parameters of reinforced concrete and steel beams using the RDT.

In this study of the dynamic characteristics of two super high-rise buildings, the fast Fourier transform (FFT) and the RDT combined with the LDM are used to identify the natural frequencies and the damping ratios of two super high-rise buildings. To examine the influence of RTK-GNSS measurement noise on the dynamic characteristics of the buildings, a stability experiment is carried out first. Subsequently, Type 1 Chebyshev high-pass digital filter is applied to reduce the effect of background noise on the measured results. Finally, based on the obtained filtering signals, the dynamic characteristic parameters of the structures are analysed and discussed in detail.

Stability experiment

The purpose of the stability experiment is to evaluate the horizontal positioning accuracy of the instruments and ensure the reliability of the instruments during the monitoring of the dynamic characteristics of the super high-rise building. In an open and windless environment, the same instruments as in the other tests were fixed at set locations, as shown in Figure 1. Each of the rover stations automatically collected the three-dimensional coordinates of the measuring locations together with systematic errors such as satellite clock error, receiver clock error, ionospheric and tropospheric refraction error, and others; the data were transmitted to the reference station through the communication station as-revised by the rover stations to provide precise coordinate values of the measuring locations.

Figure 1.

Schematic figure for stability experiment.

In this experiment, nine instruments were used simultaneously to achieve the horizontal displacements of the monitoring locations; one of the instruments was used as the reference station and the others were the rover stations. Theoretically, the displacements of the monitoring locations should be zero. However, due to instrument errors, the value of displacement is not zero. A large amount of background noise is contained in the measured data. The root mean square (RMS) value is usually an important indicator for estimating the background noise level of the RTK-GNSS data. Therefore, we will further analyse the background noise level and its statistical properties.

We selected one of the locations as an example; the other locations were similar and are not discussed here. The background noise of the system and its statistical properties are shown in Figure 2(a) to (e). The result of the displacement, presented in Figure 2(a), confirmed a nominal accuracy of the RTK-GNSS system of 1 cm for measurements of the horizontal displacements with a sampling rate of 1 Hz. We obtained the RMS value of the background noise using MATLAB software. The RMS values of the north–south and east–west components are 0.0025 and 0.0023, respectively. It is evident that the RMS value of the background noise is small. However, the displacement of the super high-rise building is also usually small. Therefore, the presence of background noise still has a major influence on the displacement monitoring. The power spectral density (PSD) functions of the background noise are presented in Figure 2(b) and (c). The data show that the PSD values are close to the white noise spectrum with values ranging from 10⁻¹⁴ to 10⁻⁶ m² s; the largest values were limited to about 0.025 Hz. Typically, the background noise of the RTK-GNSS system can be considered as a zero-mean, stationary, white Gaussian noise and its influence can be significantly reduced by a filtering algorithm. Figure 2(d) and (e) indicates that the displacements have an approximate Gaussian distribution. This is consistent with general assumptions.

Figure 2.

(a) Horizontal displacements, (b) PSD of background noise of the north–south component, (c) PSD of background noise of the east–west component, (d) probability distribution of the north–south component and (e) probability distribution of the east–west component.

Field measurements of super high-rise buildings

Engineering background and monitoring scheme

We shall consider two super high-rise buildings. One is the Tianjin radio and television tower (Building A) (Figure 3(a)) located in the southwest of Tianjin, China. Measuring 415.2 m tall, it consists of the tower base, pedestal, body of the tower, turret and antenna. The structural form is a tube-in-tube structure. Several television and radio programmes are broadcast simultaneously from the tower. An outdoor observation deck and revolving restaurant are located at a height of 248–278 m. The second building is the Tianjin 117 Tower (Building B), which is also located in the southwest part of Tianjin, China. The building is 597 m tall and the structure’s height is 596.2 m. To date, this is the tallest concrete structure in China. The building footprint on the first floor is about 4200 m² and it gradually decreases to 2100 m² on the top floor due to the building angle of 0.88°. The structure is composed of the mega frame, core tube and mega diagonal brace. During its construction, the inner tube and outer frame were raised gradually at unequal heights, as shown in Figure 3(b).

Figure 3.

The view of two super high-rise buildings: (a) Tianjin radio and television tower and (b) Tianjin 117 tower.

The purpose of the field test was to use RTK-GNSS technology to measure the horizontal displacements of the super high-rise buildings caused by the wind and the combined influences of solar radiation and the daily air-temperature variations. In a recent study, Xia et al. (2011) investigated the vibration characteristics of a super tall structure under the influence of temperature. Su et al. (2017a; 2017b) studied the wind- and temperature-induced quasi-static responses of the 600 m-tall Canton Tower by using the field monitoring and numerical analysis. RTK-GNSS technology applied to the displacement measurements of tall slender structures have been described in detail (Li et al., 2007; Xia et al., 2014). Figure 4(a) and (b) shows the positions of the reference station and the rover station for Building A. The reference station was mounted on a sturdy tripod above a selected point on the ground and approximately 100 m away from the main tower. The four rover stations were installed at the perimeter of the outdoor observation deck (north: point C1, east: point C2, south: point C3 and west: point C4) and 265 m above the ground level. Figure 4(c) and (d) shows the positions of the reference station and the rover station for Building B. The reference station was placed approximately 150 m away from the main tower. Considering the environmental conditions of the construction site, the rover stations were located at the southeast corner (point D1), southwest corner (point D2), northwest corner (point D3) and northeast corner (point D4) of the top floor, and the monitoring height was 478 m.

Figure 4.

(a) The reference station for Building A, (b) the rover station for Building A, (c) the reference station for Building B and (d) the rover station for Building B.

RTK-GNSS displacement amplitude

The displacements of Buildings A and B were recorded using RTK-GNSS technology with a sampling rate of 1 Hz. According to the Nyquist sampling theory, a signal should be sampled at least twice as fast as the highest frequency component in the signal to reconstruct the sampled signal to its original (continuous) form without loss of information. Based on provided results for finite element (FE) models of Buildings A and B, the first natural frequencies of Buildings A and B were 0.1586 and 0.1900 Hz, respectively. For these measurements, the sampling rate of 1 Hz satisfies the experimental requirements.

Since there are many places that are similar to the measured points, points C1 and D1 are selected for further analysis. Figure 5(a) and (b) shows the displacements of the measured points C1 and D1 of Buildings A and B in two perpendicular directions (i.e. the north–south and east–west directions). Tables 1 and 2 list the results of the field-measured points. It can be observed that the maximum displacements of Buildings A and B occurred at points C4 and D4, respectively. However, the results of the field measurements contained a background noise of the RTK-GNSS system, reducing the reliability of the results. Hence, we filtered the signals, including the noise, and derived more accurate results.

Figure 5.

(a) The displacement of point C1 and (b) the displacement of point D1.

Table 1.

The displacement ranges of the measured points for Building A.

	Point C1	Point C2	Point C3	Point C4
N–S component (m)	−0.0323 to 0.0207	−0.0291 to 0.0229	−0.0227 to 0.0163	−0.0256 to 0.0364
E–W component (m)	−0.0180 to 0.0197	−0.0264 to 0.0269	−0.0226 to 0.0193	−0.0207 to 0.0229

N–S: north–south; E–W: east–west.

Table 2.

The displacement ranges of the measured points for Building B.

	Point D1	Point D2	Point D3	Point D4
N–S component (m)	−0.0203 to 0.0417	−0.0231 to 0.0359	−0.0290 to 0.0450	−0.0288 to 0.0542
E–W component (m)	−0.0202 to 0.0242	−0.0335 to 0.0233	−0.0380 to 0.0495	−0.0302 to 0.0364

N–S: north–south; E–W: east–west.

To eliminate the effect of low-frequency background noise on the real displacements, a Type 1 Chebyshev high-pass digital filter was applied. The phase response of the filter is a linear function of the frequency, and the quadratic function of the magnitude response can be expressed as (Xiao, 2016)

{| H (ω) |}^{2} = \frac{1}{1 + ε^{2} T_{n}^{2} (\frac{ω}{ω_{c}})}

(1)

where $ε$ is the coefficient related to the impulse response of the filter, $ω_{c}$ is the cut-off frequency of the filter and $T_{n} (x)$ is the Chebyshev polynomial of order n, which has the following form

T_{n} (x) = {\begin{matrix} \cos [n \cdot \cos^{- 1} (x)] & | x | ⩽ 1 \\ \cosh [n \cdot \cosh^{- 1} (x)] & | x | > 1 \end{matrix}

(2)

The system function $H (s)$ of the filter can be obtained using ${| H (ω) |}^{2}$ . Furthermore, we can derive the high-pass digital filter by performing a frequency conversion in the system function $H (s)$ . Based on the results of the stability experiment, a fifth-order Type 1 Chebyshev high-pass digital filter was used with a pass frequency range greater than 0.025 Hz and a pass ripple of 1 dB.

The filtered results of points C1 and D1 are depicted in Figure 6(a) and (b), respectively. Tables 3 and 4 list the results of the measured points after filtering. A comparison of the measured values before and after filtering indicates that the amplitude of the measured values is significantly reduced after filtering. This means that the original information of the signal can be restored to a high degree using Type 1 Chebyshev high-pass digital filter. It was also found that the maximum displacement of Building A occurred at point C1 after filtering, which implied that there was a large amount of background noise in the measured values. Therefore, the filtering process is absolutely essential.

Figure 6.

The displacements after filtering: (a) point C1 and (b) point D1.

Table 3.

The filtered displacements’ range of the measured points for Building A.

	Point C1	Point C2	Point C3	Point C4
N–S component (m)	−0.0254 to 0.0168	−0.0209 to 0.0172	−0.0184 to 0.0142	−0.0226 to 0.0244
E–W component (m)	−0.0154 to 0.0150	−0.0191 to 0.0234	−0.0183 to 0.0151	−0.0180 to 0.0192

N–S: north–south; E–W: east–west.

Table 4.

The filtered displacements’ range of the measured points for Building B.

	Point D1	Point D2	Point D3	Point D4
N–S component (m)	−0.0156 to 0.0297	−0.0177 to 0.0260	−0.0267 to 0.0339	−0.0225 to 0.0385
E–W component (m)	−0.0146 to 0.0167	−0.0250 to 0.0224	−0.0329 to 0.0364	−0.0218 to 0.0264

N–S: north–south; E–W: east–west.

Dynamic parameter identification

Natural frequency estimation using FFT

To evaluate the results of the field measurement, FE models of Buildings A and B were constructed using the FE software ANSYS 12.1 (Figure 7). We can obtain the first five orders of frequencies of Buildings A and B. The results are listed in Table 5.

Figure 7.

Finite element models of Buildings A and B.

Table 5.

Finite element results.

Frequency (Hz)	First-order	Second-order	Third-order	Fourth-order	Fifth-order
Building A	0.1586	0.2250	0.2763	0.3785	0.4581
Building B	0.1900	0.2306	0.3255	0.3729	0.5283

Based on the filtering results of points C1 and D1, a standard FFT approach is used to investigate the natural frequencies of Buildings A and B in two perpendicular directions, as shown in Figure 8(a) to (d). Due to the limited nominal measurement accuracy of RTK-GNSS technology (i.e. the measurement is only valid for the first natural frequency of Buildings A and B), higher natural frequencies cannot be detected in both directions.

Figure 8.

FFT of displacements: (a) north–south component of point C1, (b) east–west component of point C1, (c) north–south component of point D1 and (d) east–west component of point D1.

Figure 8(a) and (b) indicates that there is one peak at 0.1590 Hz that corresponds to the lowest natural frequency of Building A in the north–south component of point C1. The same conclusion can be obtained for the east–west component. The natural frequencies in all directions indicate that the structure of Building A is bisymmetrical and that the estimated value is consistent with the FE result (0.1586 Hz) from Table 5. This implies that the experimental data and calculation method are accurate and reliable. Figure 8(c) and (d) shows the natural frequencies of Building B in both directions and the north–south and east–west components are 0.1893 and 0.1907 Hz, respectively. There is a difference between the two directions, which is possibly caused by both an imperfect geometry and the inhomogeneous material properties of Building B under construction. Compared with the FE result (0.1900 Hz) from Table 5, the relative error is small and the results are reliable.

Damping ratio estimation using RDT

The damping ratio is an important dynamic structural parameter. The larger the damping ratio, the stronger the energy dissipation capacity and the damping ratio, the weaker the energy dissipation. The damping ratio is usually determined based on experience. Therefore, this research on obtaining the damping ratio by field measurement is very significant.

The RDT is a time domain signal processing method developed for constructing a characteristic signature from the ensemble average of preselected sample segments for random response signals. The characteristic signature is commonly referred to as the RD signature, which represents the free vibration of the dynamic system under an assumption of Gaussian white noise and certain initial conditions (Kua et al., 2007; Vandiver et al., 1982). The usefulness of RDT has been extended to the damage assessment of various engineering structures (Gul and Catbas, 2011; Morsy et al., 2016). At present, the RDT is widely applied by researchers in the field of civil engineering. The principle of the RDT has been presented in detail in many studies (Górski, 2015; He et al., 2011); therefore, it is not repeated here. After obtaining the RD signal, the damping ratio of the structure can be extracted using the LDM.

A range from 400 to 2000 has been used as the number of subsamples N in other studies (Tamura and Suganuma, 1996; Yang et al., 1983). In this article, a value of 1500 was chosen. Figure 9(a) to (d) presents the extracted RD signatures of points C1 and D1 at the time interval $τ = 150 s$ . The values of the damping ratio (i.e. $ξ_{1} = 0.94 %$ , $ξ_{2} = 0.85 %$ , $ξ_{3} = 1.42 %$ , $ξ_{4} = 1.59 %$ ) were obtained for Buildings A and B in two perpendicular directions. It was found that the damping ratios of Buildings A and B are about 1% and 1.5%, respectively. A damping ratio of 2% is considered appropriate based on the code for design of steel structures in China.

Figure 9.

RD signatures of Buildings A and B: (a) north–south component of point C1, (b) east–west component of point C1, (c) north–south component of point D1 and (d) east–west component of point D1.

Conclusion

In this study, the dynamic characteristic parameters of two super high-rise buildings are investigated by means of RTK-GNSS technology. Using Type 1 Chebyshev filter improved the RTK-GNSS measurement accuracy of the dynamic displacements of super high-rise buildings. The first natural frequencies of Buildings A and B were successfully extracted from FFT and the results prove reliable. Additionally, to estimate the corresponding damping ratios of Buildings A and B, the random decrement technique combined with the LDM (RDT-LDM) was used. The results indicate that the RDT-LDM is an effective tool for the analysis of the dynamic characteristics of super high-rise buildings. The first natural frequency and the corresponding damping ratio of the Tianjin radio and television tower and the Tianjin 117 tower were successfully obtained using RTK-GNSS technology. The results agree well with the numerical simulation, which verifies the reliability of the measuring method.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

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