Analysis of Dynamic Characteristics of the Canton Tower

Analysis of Dynamic Characteristics of the Canton Tower under Different Earthquakes H. Li1, J.K. Liu1, W.H. Chen1,2, Z.R. Lu1,*, Y. Xia3 and Y.Q. Ni3 1Department

of Applied Mechanics, Sun Yat-sen University, Guangzhou, China Jishi Construction Group Co., Ltd., Guangzhou, China 3Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China 2Guangzhou

(Received: 30 December 2013; Received revised form: 11 July 2014; Accepted: 13 October 2014)

Abstract: This paper presents the experimental modal analysis of the Canton Tower from the ambient vibration measurements under different earthquake excitation conditions. Firstly, the time history and Power Spectral Density (PSD) of the acceleration response under different earthquake excitations have been compared. Secondly, two output-only modal identification techniques are applied to the field measurements under earthquake excitations to identify the dynamic properties of the tower, namely, the Frequency Domain Decomposition (FDD) and the Subspace Stochastic Identification (SSI). At last, the Hilbert-Huang transform (HHT) method is applied to obtain the instantaneous frequencies and energy distribution under different loadings in the time-frequency domain and the results are compared with those from wavelet transform. The modal properties of the Canton Tower presented in this paper can be used as baseline for structural health monitoring and the analysis of dynamic characteristic of the high-rise structures under different earthquake excitations in future.

Key words: high-rise structure, ambient measurement, modal identification, time-frequency analysis.

1. INTRODUCTION Modal parameter identification technique through dynamic measurement is one of the most popular research areas in the civil engineering applications. In the research of civil engineering discipline, the encountered structures are complex, such as high-rise structures (Kwok et al. 2011) or large-span bridges (Ni et al. 2011). Thus, it is necessary that the modal parameter identification technique should be compatible and more effective in such complex structures. Experimental modal parameter identification of civil engineering structures includes extracting the modal parameters (natural frequencies, mode shapes and damping ratios) from measurements. These modal parameters can be used for the damage identification of structures, the finite element model updating, long-term structural health monitoring and structural vibration

control under different severe circumstances like earthquakes or typhoons. Generally, the modal parameter identifications can be conducted based on output measurement time histories using the frequency response functions in the frequency domain or impulse response functions in the time domain. In the past few decades, the modal parameter identification techniques of civil engineering structures have been developed rapidly. Because of small magnitudes of ambient vibration contaminated by noise without knowing input forces, it needs the use of special identification techniques through output-only measurements. There have been several modal parameter identification techniques based on outputonly data, such as Peak Picking (PP) from the power spectral densities (Bendat and Piersol 1993), the Frequency Domain Decomposition (FDD) algorithm

*Corresponding *Correspo nding author. E-mail address: [email protected] [email protected]. su.edu.cn.

Advances in Structural Engineering Vol. 18 No. 7 2015

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Analysis of Dynamic Characteristics of the Canton Tower under Different Earthquakes

based on Peak Picking (Brinckert et al. 2001), natural excitation technique (NExT) (James et al. 1995) and the Stochastic Subspace Identification (SSI) method (Overschee et al. 1996). A lot of studies have been carried out to evaluate the dynamic characteristics of a real building on operation conditions by using modal parameter identification techniques mentioned above. The modal parameter identification technique through ambient vibration measurement has become an attractive research topic in the area of civil engineering structures. There are many examples about ambient vibration measurements that successfully applied to large scale structures, such as the Republic Plaza in Singapore (Brownjohn et al. 1998), the Tsing Ma suspension Bridge in Hong Kong (Xu and Zhu 2000), the Guangdong International Building in Guangzhou (Li et al. 2004), the Runyang Cable-stayed Bridge tower in China (Ding and Li 2008) and four residential buildings in Hong Kong ranging in height from 130 m to 256 m (Kwok et al. 2011). However, ambient vibration measurements for high-rise structure under the earthquake excitation conditions have not been reported. The paper aims to evaluate the dynamic characteristics of the Canton Tower using the different modal parameter identification methods. The Canton Tower is a high-rise tube-in-tube structure with a total height of 600 m, which is sensitive to the wind loads and the earthquake loads. As shown in Figure 1, this tower includes the main tower and the steel spatial mast (antenna), which is 146 m high on the top of main tower. The main tower is 454 m high, which is comprised of a reinforced concrete inner tube with an ellipse crosssection of 14 m × 17 m and a steel lattice outer tube with concrete-filled-tube (CFT) columns. The outer tube uniformly spaced in a varying oval which decreases from 50 m × 80 m at the ground to the minimum of 20.65 m × 27.5 m at the height of 280 m (waist level), and then increases to 41 m × 55 m at the top of the main tower. During the construction period, a sophisticated longterm structural health monitoring (SHM) system consisting of more than 800 sensors has been designed and implemented by a consortium of The Hong Kong Polytechnic University and Sun Yat-sen University (Ni et al. 2009) for integrated in-construction and in-service monitoring of the Canton Tower. Up to the end of May 2009, the construction of the tower has been completed. Over 800 sensors of 16 types have been installed on the main tower of 454 m high, and more than 100 sensors have been finished installing on the antenna mast of 146 m high (including anemometers and accelerometers located at up to 578 m). As shown in Figure 2, the data

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Figure 1. The Canton Tower

Accelerometer direction and channel label 19.l 20.l 16.

18.l

Data acquistion Section 8, z = 446.80 m

17.

Section 7, z = 384.24 m

15. 14.l

Section 6, z = 332.15 m

13. 12.l 09.l11.l 10. 07.l 05.l

X

01.l

Section 3, z = 171.10 m

04.l

02. Y

Section 4, z = 228.50 m

06.l

03.l

Z

Section 5, z = 275.30 m 08.l

z i n o r n o h t i c a n y S

n o i s a i s t a m D s n a r t

Section 2, z = 119.30 m

Section 1, z = 30.63 m. l

Figure 2. Position of accelerometers and data acquisition system

that used in this paper collected from twenty uni-axial sensors, which were installed at the eight sections at different heights of the inner tube. In each section, horizontal vibration response at two perpendicular directions will be measured except in the 4th level and the 8th level, catering for the availability of space and


H. Li, J.K. Liu, W.H. Chen, Z.R. Lu, Y. Xia and Y.Q. Ni

access to the data acquisition units. In the 4th level and the 8th level, there are four uni-axial accelerometers, which are two for the long-axis of the inner tube and the others for the short-axis of the inner tube. The implemented SHM system has monitored the structural responses of the Canton Tower since May 2009 under different loading events, including the Koppu typhoon (September 15th, 2009), the Molave typhoon (July 18th, 2009), the Hualien earthquake (December 19th, 2009), the Shenzhen earthquake (November 19th, 2010) and the Tohoku earthquake (March 11th, 2011). It is extraordinarily useful for detecting anomalies in loading and response and assessing structural integrity, safety, serviceability, and reliability from these monitoring data. The results of modal parameters of Canton Tower under typhoon loadings have been reported by Chen et al. (2011). This paper will introduce the ambient vibration measurement and present the results of the field vibration measurements under different seismic loading conditions, including the Hualien earthquake, the Shenzhen earthquake and the Tohoku earthquake. Apart from the modal parameters identified from different methods using the dynamic measurement data under several earthquake loading events, the HilbertHuang transform technique is applied for obtaining the instantaneous frequencies and energy distribution in the time-frequency domain and the results were compared with the wavelet scalogram. The significance of this work is the study of the dynamic behaviour of structure in full scale for a better analyzes the effectiveness of identification methods. The results of this study can provide some useful information for better understanding the dynamic characteristics of a high-rise structure under different earthquake events.

2. BRIEF REVIEW OF THE THEORETICAL BACKGROUND 2.1. Modal Parameter Identification Methods 2.1.1. The frequency domain decomposition (FDD) method In order to extract the modal parameters of the structure from ambient vibration data, the Frequency Domain Decomposition (FDD) (James et al. 1995; Bendat and Piersol 1986) method was used in this paper. The FDD method is a rather simple procedure that represents an improvement of the Peak Picking (PP). Both the PP and the FDD methods are based on the evaluation of the spectral matrix in the frequency domain. But the FDD method is easier to identify each vibration mode comparing to the traditional PP method.


The first step of the FDD method is to calculate the power spectral density (PSD) matrices for each data set. The relationship between the unknown inputs x (t ) and the structural responses data y(t ) can be expressed as

G yy ( jω )  =  H ( jω )   Gxx ( jω )   H ( jω ) T

(1)

where [G xx ( jw)] is the ( r × r ) PSD matrix of the input, r is the number of inputs, [ G yy ( jw)] is the (m × m) PSD matrix of the responses, m is the number of responses, [ H ( jw)] is the (m × r ) frequency response function (FRF) matrix, the overbar and superscript T denote the complex conjugate and transpose, respectively. The FRF matrix can be written in this form

φ kγ k T φk γ k T +  H ( j ω )  = ω λ − j j ω − λ k k k =1 n

∑

(2)

where n is the number of modes, λ k is frequencies and also is the pole, φ k and γ k are the mode shape vector and the modal participation vector, respectively. Supposing the input is white noise, which means its PSD is a constant matrix ([G xx ( j ω) = [C]), then Eqn 1 becomes

G yy ( j ω )   φkγ k T   H n n  j ω − λ  φsγ sT φsγ sT  k   = ∑∑ ×C +  T  ω λ − j j ω − λ s  φ γ s  k =1 s =1  k k  +  j ω − λ k 

(3)

where superscript H denotes a complex conjugate and transpose. The output PSD [G yy( jw)] is decomposed by taking the singular value decomposition (SVD) of the matrix and can be written as

 G yy ( jω )  = [Ui ][ Si ][Ui ] H

(4)

where [U i] = [ui1, ui2, ui3, ..., uin], this matrix is a unitary matrix holding the singular vectors uij , and [Si] is a diagonal matrix holding the scalar singular values sij . In spectrum of the PSD function, a peak of this function corresponds to the structural mode. And this mode or may be a possible close mode will be dominating. So in this case, the first singular vector ui1 is an estimate of the mode shape φ = ui1 and the corresponding singular value is the auto PSD function of the corresponding singledegree-of-freedom (SDOF) system. The natural frequency and the damping can be obtained from the

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piece of the SDOF density function, which is obtained around the peak of the PSD.

ω j =

ln

( λ j )

(9)

∆t

2.1.2. The stochastic subspace identification (SSI) The Stochastic subspace identification (SSI) algorithm (Overschee et al. 1996) computes state space models from given output data and the stochastic input may be induced by traffic, wind and other stochastic processes. In the Stochastic Subspace Identification techniques, a parametric model is fitted directly to the raw times series data. A parametric model is a mathematical model with some parameters, and these parameters can be adjusted to change the way the model fits to the data. Thus, it’s important to find a set of parameters which can minimize the deviation between the predicted system response and measured system response of the model. It is well known that modal identification techniques in time domain can be formulated in a an innovation state space formulation as following

{ xt +1 } = [ A]{ xt } + wt

(5)

{ yt } = [C ]{xt } + vt

(6)

where [ A] contains the physical information, [ C] extracts the information that can be observed in the system response. { x t } is the state vector and { yt } is the measured output vector. wt and vt are the process noise and the measurement noise, respectively. Both of them are assumed to be zero-mean. The above system (5), (6) is shown in time domain. Through a complex transformation of the transfer function using the eigenvectors of [ A] they can also be represented in frequency domain by the modal decomposed transfer function H (z) H ( z ) = [ Φ ]([ I ] z −  µ j 

−1

)

[ Ψ ] + [ I ]

= exp  −ζ jω j ± iω j 

(

1 − ζ 2j ∆t 

)



2.2. Time-Frequency Analysis 2.2.1. The Hilbert-Huang transform (HHT) It is well known that the Hilbert-Huang transform (HHT) method is a two-step data-analysis method (Huang et al. 1998). The HHT is suitable for nonlinear and non-stationary data analysis. The first step of the HHT method is that a complicated time history is turned into a set of narrow band signals called intrinsic mode functions (IMFs) by the empirical mode decomposition (EMD). And the second step is performing the Hilbert transform (HT) to each IMF component (Xu et al. 2003). Once the IMFs are determined, the Hilbert transform is used to obtain the instantaneous frequencies. For the j t h IMF x(t ), its Hilbert transform can be defined as: y ( t ) =

1

π

P

x ( u)

∫ t − u du

(11)

where P indicates the Cauchy principal value. The analytic signal z (t ) of the j t h IMF is (12)

(7) where i is the imaginary unit, A (t ), and ϕ (t ) are the instantaneous amplitude and instantaneous phase, respectively. Therefore, the definition Eqns of A (t ), ϕ (t ), and ω (t ) are shown below:

A ( t ) =

x 2 ( t ) + y 2 ( t )

(13)

(8)

where ω j is the natural frequency, ζ j is damping ratio, and ∆t is the time step. Therefore

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(10)

The j th mode shape v j evaluated at sensor locations can be obtained using the following expression: ν j = [C] {Ψ j }, where {Ψ j } is the complex eigenvector of [ A] corresponding to the eigenvalue λ j . The mode shape, which is associated with the j th mode, is given by the j th column of [Φ].

z ( t ) = x ( t ) + iy ( t ) = A( t ) exp ( iϕ ( t ))

This representation of the transfer function exposes all the modal parameters. The eigenvalues of [ A] come in complex conjugate pairs and each pair represents one physical vibration mode. The second order modes are uncoupled and the j th eigenvalue of [ A] has the form

λ j

− Real  ln ( λ j )  ζ j = ω j ∆t

 y ( t )    x ( t ) 

ϕ ( t ) = arctan 

(14)



ω ( t ) =

dϕ ( t )

(15)

dt

Detailed discussions and justifications are given by Huang et al. (1998). With this definition of instantaneous frequency, its value changes from point to point in time.

2.2.2. The wavelet transform Among the spectrum of time-frequency analysis techniques, which are available for processing nonstationary data, the wavelet transform has been received much attention in recently years. The wavelet analysis depends on Fourier analysis and could provide local features in both time and frequency domains (Kurtis and Ahsan 1998). The wavelet analysis is essentially an adjustable window Fourier spectral analysis with the following general definition:

W ( a, b; X ,ψ ) = a

−1

2

∞

 t − b  dt  a  

∫ −∞

X (t )ψ *

(16)

where ψ ∗ indicates the complex conjugation of the wavelet function. a is the scale index, which controls the width of wavelet window. Although time and frequency do not appear explicitly in the transformed result, the variable |a|−1/2 gives the frequency scale. And W( a, b; X ,ψ ) is the transform that decomposes an arbitrary signal X (t ) via basis functions with compact support that are simply dilations and translations of the mother wavelet. Thus, the features can be obtained in both time and frequency domain. The normalized Morlet mother wavelet function that is used in this paper is defined as

ψ (t ) = π −1 4 ei 2π f t e− t

2

0

2

where the subscript i is the imaginary unit.

(17)

3. AMBIENT VIBRATION MEASUREMENT 3.1. Brief Description of the Three Earthquakes The first ambient vibration measurement of the Canton Tower was during the Hualien earthquake in 19th December, 2009. It was the 6.8 magnitude undersea earthquake which was off the coast of Hualien, Taiwan at a relatively shallow depth of 30 km. And the distance from Hualien to the Canton Tower is about 860 km. In 19th November, 2010, the implemented SHM system has monitored the structural responses of the Canton Tower when the Shenzhen earthquake occurred. The Shenzhen earthquake was a 2.8 magnitude earthquake which occurred in the common boundary of Shenzhen and Hong Kong. It is about 100 km away from the Canton Tower. The 9.0 magnitude undersea mega thrust earthquake occurred on 11th March, 2011 in the north-western Pacific Ocean at a relatively shallow depth of 32 km with epicenter approximately 72 km east of the Oshika Peninsula of Tohoku. The earthquake was lasting approximately six minutes. The distance between the Tohoku and the Canton Tower is approximately 3100 km.

3.2. The Acceleration Response and Data Analysis A set of ambient measurement data acquired has been available through the benchmark website (http://www.cse.polyu.edu.hk/benchmark/) to all interested participants worldwide. And the details of the ambient vibration test refer to Xia et al. (2009). The data that is used in this paper was obtained from twenty different accelerometers, which are located in 8 different height cross-sections (i.e. 30.63 m, 119.30 m, 171.10 m, 228.50 m, 275.30 m, 332.15 m, 384.24 m and 446.80 m). Table 1 shows the maximum acceleration responses monitored by the SHM system at different levels under different seismic loading conditions. It reveals that there is no direct relation between the magnitude of

Table 1. The maximum acceleration responses monitored at different levels during different earthquake Hualien earthquake Height (m) 30.63 119.30 171.10 228.50 275.30 332.15 384.24 446.80

Shenzhen earthquake

Tohoku earthquake

The short-axis The long-axis The short-axis The long-axis The short-axis The long-axis (m/s2) (m/s2) (m/s2) (m/s2) (m/s2) (m/s2) 0.00335 0.00822 0.00601 0.00485 0.00699 0.01037 0.00665 0.00884

0.00488 0.01056 0.00977 0.00736 0.00963 0.01089 0.00635 0.01023


0.00793 0.00609 0.00495 0.00644 0.00621 0.00688 0.00256 0.00534

0.00533 0.00714 0.00560 0.00566 0.00560 0.00544 0.00484 0.00395

0.00194 0.00299 0.00362 0.00366 0.00463 0.00579 0.00734 0.00902

0.00128 0.00235 0.00188 0.00242 0.00297 0.00461 0.00444 0.00590

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earthquake and the acceleration responses of structure during earthquake period. Figures 3, 4 and 5 show the twenty seconds time histories of acceleration responses at the height of 171.1 m, 332.2 m and 446.8 m respectively during the different earthquakes. It could be seen that the peak value of acceleration response under the Hualien earthquake, which is around 0.006 m/s 2, are the maximum among first two figures, As the magnitude and duration of the Shenzhen earthquake was much smaller and shorter than the Hualien’s, respectively, the peak value is about 0.004-0.002 m/s2 under the Shenzhen earthquake; and under the Tohoku earthquake, the peak values are very different at different height of the Canton Tower, which the main frequency is about 0.4 Hz. Figures 6, 7 and 8 show the results of power spectral density (PSD) of acceleration response at different height during the different earthquakes. From the PSD diagrams, we can find that the frequency components in responses of the Canton Tower were relatively high frequency vibration during these three earthquakes and they are different to those frequency components before and after the earthquakes. Meanwhile, under different earthquake loading environments, there are different dominant frequencies in each PSD diagrams. Figure 6 shows that the first two principle frequencies, which are around 0.8 Hz and 1 Hz, are dominant in the response data under the Hualien earthquake condition. However,

under the Shenzhen earthquake, the dominant frequency components lie in 1–3 Hz. In Figure 8, the dominant frequency components during the Tohoku earthquake are 0.4 Hz and 1 Hz and after the earthquake, the dominant frequency component in the responses is around 0.1 Hz, which is the fundamental natural frequency of the tower. Comparing the results above, one can find that under different earthquake loadings, the dominant frequency components in the structural response are different, and they are relatively higher frequencies. This response characteristic is different to that under typhoon excitations (Chen et al. 2011). The dominant frequency components under typhoon excitations are relatively low frequencies.

4. MODAL PARAMETER IDENTIFICATION Experimental modal parameter identification of civil engineering structures means the extraction of modal parameters (frequencies, damping ratios and mode shapes) from dynamic measurements. These modal parameters will be served as basis or input to the finite element model updating, detecting and locating the possible damage in structures, long-term health monitoring of structures and the safety evaluation of structures against different severe circumstances like earthquakes or wind loads. And modal identification has been widely used in civil engineering (Ni et al. 2012;

The short-axis of the inner structure direction 0.012

The long-axis of the inner structure direction

At 171.1 m height

0.006

0.006

0

0

−0.006 −0.012

−0.006 −0.012

21:07:15

) s / m ( e 0.012 s n o 0.006 p s e 0 r n o −0.006 i t a −0.012 r e l 21:07:15 e c c A

21:07:20

21:07:25

21:07:30

At 171.1 m height

0.012

21:07:35

21:07:15

21:07:20

21:07:25

21:07:30

21:07:35

2

0.012

At 332.2 m height

0.006 0

21:07:20

21:07:25

21:07:30

21:07:35

At 446.8 m height

−0.006 −0.012

21:07:15

0.006

0

0

−0.006 −0.012

−0.006 −0.012

21:07:20

21:07:25

21:07:30

21:07:20

21:07:35

21:07:25

21:07:30

21:07:35

At 446.8 m height

0.012

0.006

21:07:15

At 332.2 m height

0.012

21:07:15

21:07:20

21:07:25

21:07:30

21:07:35

Time (hh:mm:ss)

Figure 3. Twenty seconds time histories of acceleration response at different height during the Hualien earthquake

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The short-axis of the inner structure direction At 30.63 m height

0.008 0.004

0.004

0

0

−0.004

−0.004

−0.008

14:43:10

) s 0.008 / m ( e 0.004 s n o p 0 s e r n −0.004 o i t a r e −0.008 l e 14:43:10 c c A

14:43:15

14:43:20

14:43:25

14:43:30

14:43:35

At 228.5 m height

2

−0.008

14:43:10

14:43:20

14:43:25

14:43:30

14:43:35

14:43:30

14:43:35

14:43:30

14:43:35

At 228.5 m height

0.008

0

−0.004 14:43:15

14:43:20

14:43:25

14:43:30

14:43:35

At 446.8 m height

−0.008

14:43:10

0.004

0

0

−0.004

−0.004 14:43:15

14:43:20

14:43:25

14:43:15

14:43:30

14:43:35

−0.008

14:43:10

14:43:20

14:43:25

At 446.8 m height

0.008

0.004

14:43:10

14:43:15

0.004

0.008

−0.008

At 30.63 m height

0.008

14:43:15

14:43:20

14:43:25

Time (hh:mm:ss)

Figure 4. Twenty seconds time histories of acceleration response at different height during the Shenzhen earthquake

Brincker et al. 2000). A comparison of modal parameters has been made by using different field measurement data and simulated response data of Canton Tower. Table 2 shows the identification results of modal parameters, including frequency and damping ratio, under the different earthquake (Hualien, Shenzhen and Tohoku) excitation condition, which are obtained by the FDD method. It can be found that the natural frequency differs a little under various earthquake conditions. The result of Chen et al. (2000) revealed that the high-rise structure is in safe condition while modes differ under different conditions, which may be the effects caused by the environmental factors such as temperature, humidity. And the effect of environmental factor on the Canton Tower will be considered in the future research. From the Hualien earthquake to the Tohoku earthquake, the natural frequency slightly decreased. Meanwhile, there are significant differences in damping ratio under different conditions. This is because the damping mechanism for the general large-scale structures is too complicated and thus the damping ratio cannot be identified accurately. For the synchronized problem of


some data, the measured mode shapes under the different earthquakes cannot be calculated correctly. With a full-order FEM of Canton Tower, the modal frequencies are also calculated, as shown in the last row of Table 2. And as shown in Table 2, the modal frequencies in the first few modes obtained by measurement data and FEM are in good agreement. However, the discrepancy becomes large for the higher modes. And the mode shapes of first few bending and torsion modes are calculated by using the FEM and field measurement under the Hualien earthquake, as shown in Figure 9. The validation of this model is conducted by comparing the FE modal properties with the identified modal properties through field measurement. These two types of mode shapes are in good agreement basically. However, there is no accelerometer installed on the antenna. It is impossible to obtain mode shapes of the antenna through field measurement as shown in Figure 9. In Table 3, a comparison of two output-only modal identification algorithms was made by using the

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The short-axis of the inner structure direction


At 171.1 m height

0.01 0.005

0.005

0

0

−0.005

−0.005

−0.01

14:10:00

) s / m 0.01 ( e s n 0.005 o p s e 0 r n o i t −0.005 a r e −0.01 l e c 14:10:00 c A

14:10:05

14:10:10

14:10:15

At 171.1 m height

0.01

14:10:20

−0.01

14:10:25

14:10:00

14:10:05

14:10:10

14:10:15

14:10:20

14:10:25

14:10:20

14:10:25

14:10:20

14:10:25

2

At 332.2 m height

0.005 0

−0.005 14:10:05

14:10:10

14:10:15

14:10:20

−0.01

14:10:25

14:10:00

At 446.8 m height

0.01

0.005

0

0

−0.005

−0.005

14:10:00

14:10:05

14:10:10

14:10:15

14:10:05

14:10:10

14:10:20

−0.01

14:10:25

14:10:15

At 446.8 m height

0.01

0.005

−0.01

At 332.2 m height

0.01

14:10:00

14:10:05

14:10:10

14:10:15

Time (hh:mm)

Figure 5. Twenty seconds time histories of acceleration response at different height during the Tohoku earthquake

PSD before the earthquake 1.5

S-171.1 m L-171.1 m S-332.2 m L-332.2 m S-446.8 m L-446.8 m

× 10−4

1 0.5 0 0

) z H / 4 s /

0.2

PSD before the earthquake

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

3 2 1 0 ) z H / 4 s /

2

PSD during the earthquake

2

m ( y t i s n e d l a r t c e p s r e w o P

6

× 10−4

S-171.1 m L-171.1 m S-332.2 m L-332.2 m S-446.8 m L-446.8 m

4 2 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

× 10−4

2

0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Frequency (Hz)

Figure 6. Power spectral density of acceleration response at different height during the Hualien earthquake

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0.2 0.4 0.6 0.8

2

m ( y × 10−6 t i 4 s n 3 e d 2 l 1 a r 0 t c e 0 0.2 p s r e w o P −6

1

1.2 1.4 1.6 1.8

2

2.2 2.4 2.6 2.8

PSD during the earthquake

0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

3 2 1 0

0

0.2 0.4 0.6 0.8

S-30.63 L-30.63 S-228.5 L-228.5 S-446.8 L-446.8 2.2 2.4 2.6 2.8

PSD after the earthquake

1

1.2 1.4 1.6 1.8

2

3

3

S-30.63 L-30.63 S-228.5 L-228.5 S-446.8 L-446.8 2.2 2.4 2.6 2.8

3

Frequency (Hz)

S-171.1 m L-171.1 m S-332.2 m L-332.2 m S-446.8 m L-446.8 m

0.5

0

× 10 4

PSD after the earthquake 1

S-30.63 L-30.63 S-228.5 L-228.5 S-446.8 L-446.8

× 10−6 4

Figure 7. Power spectral density of acceleration response at different height during the Shenzhen earthquake

2

ambient measurement data under Hualien earthquake. It seems that the natural frequencies provided by the two independent methods agree well with each other. Although many studies showed that the SSI method is



PSD before the earthquake 1

× 10−5

0.5 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

PSD during the earthquake (first stage)

4

s /

2

m ( y t i s n e d l a r t c e p s r e w o P

3 2 1 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

PSD during the earthquake (second stage) 2 1 0.2

0.4

0.6

0.8

1

1.2

1.4

2

1.8

2

S-171.1 m L-171.1 m S-332.2 m L-332.2 m S-446.8 m L-446.8 m

× 10−3

0 0

1.8

S-171.1 m L-171.1 m S-332.2 m L-332.2 m S-446.8 m L-446.8 m

× 10−5

) z H /

1.6

1.8

2

Frequency (Hz)

PSD after the earthquake 1

S-171.1 m L-171.1 m S-332.2 m L-332.2 m S-446.8 m L-446.8 m

× 10−5

0.5 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

) ) 9 M E 0 F 0 r 2 ( . e l d a r t o - e l l a u i F X (

S-171.1 m L-171.1 m S-332.2 m L-332.2 m S-446.8 m L-446.8 m

1.6

1.8

2

Frequency (Hz)

Figure 8. Power spectral density of acceleration response at different height during the Tohoku earthquake

more advanced in modal parameters identification of bridge (Zong et al. 2005; Ren et al. 2005), it still can be found that this method has some limitations when processes long-term monitoring data in complex structures. These limitations include the slowness of its calculation speed, and the requirement of manual input to obtain better stabilization diagram under different excitation conditions. The identified natural frequencies under ambient vibration agree with the results of finite element model in the 1st and 2nd bending vibration modes in Table 3. But large errors are observed in the higher modes, especially the torsional vibration modes, between the FEM and ambient vibration measurement. This may be attributable to several reasons, including that the effective mass of the tower is less than that assumed at the design stage or the effective stiffness of the tower is higher than that determined at the design stage because of the contribution of non-structural components. It shows that modal parameters from ambient vibration measurement can be used to update the FEM of the tower, so that a better baseline model of the tower can


D D F y b s n o i t i d n o c g n i d a o l t n e r e f f i d r e d n u o i t a r g n i p m a d d n a y c n e u q e r F . 2 e l b a T

n o i t i ) e d k n a o u c q e k h t a r u a q e h u t r k a o E h r o e T ( d n U

n o ) i t i e d k n a o u c q e h t k r a a u e q n h e t r h a z E n e r h e S d ( n U

n o i t i ) e d k n a o u c q e k h t a r u a q e h n t e r i a l E a u r H e ( d n U

y c n ) e z u H q ( e r F

0 4 3 6 7 0 3 4 0 4 0 4 4 0 2 8 9 5 0 4 1 . 1 . 3 . 4 . 4 . 4 . 6 . 8 . 0 . 0 . 0 0 0 0 0 0 0 0 1 1

o i t a r 9 4 0 5 4 1 7 3 4 2 0 0 2 4 7 4 9 g ) 8 2 8 5 7 0 3 9 5 8 1 n % i . 0 . 6 . 4 . 7 . 3 . 2 . 7 . 2 . 2 . ( 4 1 1 0 0 0 0 0 0 0 0 p m a D


6 2 7 3 4 3 5 5 4 0 4 8 9 7 7 7 9 9 6 9 3 6 5 9 5 9 9 6 1 0 . 1 . 3 . 4 . 4 . 5 . 5 . 7 . 9 . 2 . 0 0 0 0 0 0 0 0 0 1

o i t a r 5 8 7 1 3 9 8 g ) 3 8 0 5 6 5 1 2 1 0 6 1 5 8 6 9 5 1 8 4 4 n i % ( 5 . 6 . 3 . 3 . 9 . 2 . 3 . 3 . 3 . 2 . p 1 2 0 0 0 0 0 0 0 0 m a D


9 7 4 0 7 1 5 6 9 0 7 0 1 7 8 7 0 1 8 9 3 7 6 9 7 9 0 7 1 0 . 1 . 3 . 4 . 4 . 5 . 5 . 8 . 9 . 2 . 0 0 0 0 0 0 0 0 0 1

o i t a r 1 9 5 3 1 4 g ) 5 7 2 2 1 6 8 9 4 8 2 n % 9 6 1 3 2 9 0 2 1 i ( 1 0 6 7 2 . . . . 6 . 8 . 5 . 4 . 3 . 3 . p 2 2 1 0 0 0 0 0 0 0 m a D


8 3 0 5 2 8 9 0 6 2 9 4 1 3 6 1 9 9 7 9 3 6 2 7 0 2 8 5 4 0 . 1 . 3 . 4 . 4 . 5 . 5 . 7 . 9 . 1 . 0 0 0 0 0 0 0 0 0 1

0

2 3 4 5 6 7 8 9 1 e 1 e e e e e e e e e e d d d d d d d d d d o o d o o o o o o o o o M M M M M M M M M M M

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z

z

Z

x

z

y

y

x

x

(a1) 1st short-axis

z

(a2) 1st long-axis

z

Z x

z y

Y

x

(b1) 2nd short-axis

x

y

z z

y

x

y

(b2) 2nd long-axis

z z

y

x

x

(c1) 1st torsion

y

(c2) 2nd torsion

Figure 9. Mode shapes obtained by full-scale FEM and ambient vibration measurement

Table 3. Comparison on natural frequencies from FDD, SSI and FEM under Hualien earthquake

Vibration direction 1st short-axis bending 1st long-axis bending 2nd short-axis bending 2nd long-axis bending 3rd short-axis bending 3rd long-axis bending 1st torsion 2nd torsion

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FDD

SSI

Full-order FEM

Frequency (Hz)

Frequency (Hz)

Frequency (Hz)

0.0928 0.1393 0.4732 0.5219 0.7890 0.9596 0.5068 1.248

0.0917 0.1356 0.4853 0.5825 0.7898 0.9651 0.5216 1.304

0.100 0.144 0.442 0.480 0.693 0.854 0.427 1.194



be obtained for future health monitoring and damage detection for the tower. Comparing to Table 3, Table 2 had two more modes e.g., mode 3, mode 4, which should still be the 2nd bending mode but with different mode shapes of antenna. However, there is no acceleration data acquired from the sensor on antenna. Thus, these two modes cannot be identified from the field measurement.

5. TIME-FREQUENCY ANALYSIS In this section, the time-frequency analysis of the structural responses is further investigated from Hilbert-Huang transform and wavelet analysis. Figures 10–15 show Hilbert spectrum and Morlet wavelet scalogram of acceleration responses at 446.8m height during the three earthquake conditions respectively. Figures 10, 12 and 14 show the Hilbert spectrums of acceleration responses at 446.8 m height, including the short-axis and the long-axis of the inner

tube during the Hualien, Shenzhen, Tohoku earthquake respectively. It reveals that the structural response differs slightly under different earthquake conditions. By contrasting Hilbert spectrum and Morlet wavelet scalogram under the same earthquake, one can find that both of them can describe the energy of the structural response. It should be pointed out that Hilbert spectrum can show the instantaneous frequency of the tower, while Morlet wavelet scalogram can show the energy distribution of structural vibration. It is because different from the wavelet scalogram, the HilbertHuang spectrum does not involve the concept of the frequency resolution and time resolution but represents the instantaneous frequency. Figures 10 and 11 show that the dominant frequency components are mainly 0.8 Hz and 1 Hz under the Hualien earthquake loading. However, Figures 12 and 13 show that there are many frequencies components between 1-3Hz in the responses under the Shenzhen

× 10−3

2 1.8

4.5

1.6

4

) 1.4 z H ( 1.2 y c n 1 e u q 0.8 e r F0.6

3.5 3 2.5 2 1.5

1.6 ) 1.4 z H ( 1.2 y c n 1 e u q 0.8 e r F0.6

1

0.4

0.2

0.5

0.2

0

50

100

150

200

250

5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

1.8

0.4 0

× 10−3

2

0

300

0

50

Time (second)

100

150

200

250

300

Time (second)

Figure 10. Hilbert spectrum of acceleration responses at 446.8 m height during the Hualien earthquake (the short-axis and the long-axis of the inner tube)

× 10 −3

2

12

1.8

11

1.6 ) 1.4 z H ( 1.2 y c n 1 e u q 0.8 e r F0.6

10 9 8 7 6

0.4

5

0.2 0

0

50

100 150 200 Time (second)

250

300

× 10−3

2

12

1.8

11

1.6 ) 1.4 z H ( 1.2 y c n 1 e u q 0.8 e r F0.6

10 9 8 7 6

0.4

5

0.2 0 0

50


250

300

Figure 11. Morlet wavelet scalogram of acceleration responses at 446.8 m height during the Hualien earthquake (the short-axis and the long-axis of the inner tube)


1097


× 10−4

2

5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5

1.8 1.6 ) 1.4 z H ( 1.2 y c n 1 e u q 0.8 e r F 0.6

0.4 0.2 0

0

50

100

150

200

250

× 10−4

2

4

1.8 1.6 ) 1.4 z H ( 1.2 y c n 1 e u q 0.8 e r F 0.6

3

2

1

0.4 0.2 0

300

0

50

100

150

200

250

300

0

Time second

Time second

Figure 12. Hilbert spectrum of acceleration responses at 446.8 m height during the Shenzhen earthquake (the short-axis and the long-axis of the inner tube)

× 10−3

3

3.5

2.5

3

) z 2 H ( y c n 1.5 e u q e r 1 F

2.5 2 1.5 1 0

−0.5 −1

0.5 0

0

50

100

150

200

250

× 10−3

3

4

5 4.5

2.5

4

) z 2 H ( y c n 1.5 e u q e r 1 F

3.5 3 2.5 2 1.5 1

0.5

0.5 0

300

0

50

Time (second)

100

150

200

250

300

0

Time (second)

Figure 13. Morlet wavelet scalogram of acceleration responses at 446.8 m height during the Shenzhen earthquake (the short-axis and the long-axis of the inner tube)

× 10−4

2

18

1.8

16

1.6

14

) 1.4 z H ( 1.2 y c n 1 e u q 0.8 e r F 0.6

1.6

6

0.4

4

0.4

0.2

2

0.2

0

0

0

10 8

0

50

100

150

200

250

300

1.2

1.8 ) 1.4 z H ( 1.2 y c n 1 e u q 0.8 e r F 0.6

12

× 10−3

2

Time (second)

1 0.8 0.6 0.4 0.2 0

50

100

150

200

250

300

0

Time (second)

Figure 14. Hilbert spectrum of acceleration responses at 446.8 m height during the Tohoku earthquake (the short-axis and the long-axis of the inner tube)

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× 10−3

2

8

1.8 1.6 ) z H ( y c n e u q e r F

7

1.4 6

1.2 1

5

0.8 4

0.6 0.4

3

0.2 0

0

50


250

300

2

× 10−3

2

) z H ( y c n e u q e r F

1.8

5.5

1.6

5

1.4

4.5

1.2

4

1

3.5

0.8

3

0.6

2.5

0.4

2

0.2

1.5

0

0

50


250

300

1

Figure 15. Morlet wavelet scalogram of acceleration responses at 446.8 m height during the Tohoku earthquake (the short-axis and the long-axis of the inner tube)

earthquake loading. And the last two Figures show that under the Tohoku earthquake the dominant frequency components of the tower’s responses are mainly between 0.3-1Hz. These results and the results of power spectral density (PSD) are in good agreement. Although Shenzhen earthquake has the smallest magnitude among the three earthquakes, it is very close to the tower comparing to the other two earthquakes and the high frequency components of the earthquake remains when seismic waves arrive to the Tower. Thus the high frequency of the tower can be excited.

6. CONCLUSIONS This study has presented the dynamic characteristics of Canton Tower subjected to three different earthquakes. Making use of the monitored data under different earthquakes from the SHM system on the Canton Tower, modal parameters of the tower are identified from FDD and SSI methods. These field measurements provided a unique opportunity to obtain the modal characteristics of the high-rise building from natural excitation. The time-frequency analysis is conducted for the measured time histories using Hilbert-Huang transform and wavelet transform. The following conclusions are drawn from the dynamic characteristic analysis of the Tower: (1) The dominant frequency components during the earthquakes are approximately 1 Hz. Under the earthquake excitation, higher modes of the tower can be excited, but the dominant frequency components in each earthquake are different, which is different to that under typhoon excitations. (2) The natural frequencies identified by the two independent methods (FDD and SSI) agree well in most of first ten modal parameters.


However, the discrepancy of the estimated damping ratios is relatively larger than that of the natural frequencies. The main reason for the difference of identified frequencies between different methods may lie in the effect of environmental factors on the dynamical behavior of the tower, which needs to be further investigated in future. (3) The identified natural frequencies under ambient vibration agree with the results of finite element model in the 1st and 2nd bending modes. Large errors of the natural frequencies are observed in the torsional vibration modes between the FEM and ambient vibration measurement. The modal parameters from ambient vibration measurement can be used to update the FEM of the tower. (4) Hilbert spectrum can show the instantaneous frequency of the Canton Tower clearly. And it can be observed that under earthquake condition, responses are concentrated mainly around 1 Hz. The main frequencies of the tower are relative to the distance between the earthquake and the tower rather than the magnitude. (5) The modal identification results from this study provide the modal properties of the Canton Tower during earthquake period, which can be in the application of the structural health monitoring and structural damage detection to the high-rise building under ambient vibration.

ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (11272361, 11172333), Doctoral Program Foundation of Ministry of Education of China (20130171110039), the Guangdong Province Science and

1099


Technology Program (2012A030200011), the Fundamental Research Funds for the Central Universities(13lgzd06), and the General Financial Grant from the China Postdoctoral Science Foundation (2013M531893). Such financial aids are gratefully acknowledged.

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Analysis of Dynamic Characteristics of the Canton Tower

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