The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019
Comparison study of typhoon characteristics based on stationary and non-stationary models
*Wen Xie1) , Peng Huang2) and Ming Gu3)
1), 2),3) State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China 2) [email protected]
ABSTRACT
A comparison study of the wind characteristics of typhoon Jongdari based on stationary and non-stationary mode was presented. The original data was collected at the height of 40m in seaside (Shanghai Province, China) where typhoon passed through directly. First, the run-test method and discrete wavelet transform way were employed to evaluate the stationarity and extract the time-varying mean wind speed, respectively. Then the gust factor, turbulence intensity and turbulence integral scale were compared accordingly. The results demonstrate that the wind characteristics described by the non-stationary model are more centralized and more stable. In addition, the power spectral density and the evolutionary power spectral density were calculated and compared. the Von Karman spectra fits well with the measured spectra.
1. INTRODUCTION
Accurately understanding and establishing the wind characteristics of typhoon have always been a hot research. With the improvement of sensors acquisition capability and stability (e.g., structural health monitoring system), more reliable measurement data are providing(Xu et al. 2017).In general, the wind characteristics were studied based on stationary assumption (Davenport 1961) which has adopted by various codes (ASCE/SEI 7–10. 2010, AIJ-RLB-2004. 2014, GB50009-2012. 2012). During this hypothesis, the statistical characteristics of wind speed were considered as constant and it is convenient to apply to wind-resistant design (Solari et al. 2015, Fenerci et al. 2018, Lin et al. 2018, He et al. 2019, Li et al. 2019).However, recent measurement wind records indicate that the boundary-layer wind speed induced by typhoons might not be stationary(Tao et al. 2017), which means it may be inappropriate to describe the wind speed as the ergodic random process. As such, the analysis of
1) Graduate Student 2),3) Professor
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019 nonstationary typhoon wind characteristics is also gradually concerned (Huang et al. 2015, Hong 2016, Kim et al. 2018, Wang et al. 2019). This article was concentrated on the comparison study of the near-ground wind characteristics during typhoon Jongdari (No.1812) landing. As the result of the influence induced by different factors (e.g. terrain, wind attack angle and measurement situation), although some articles (Tao et al. 2016, Tao et al. 2017)have studied wind characteristics using both two models, the measured results are still insufficient to establish a database of non-stationary characteristics for wind designing. There were two differences between this paper and forementioned. The original data captured the overall process that typhoon passed through directly. The terrain around measurement site was flat which is the typical landform on the southeast coast of China. The remainder of this article is organized as follows: Section 2 describes the detail of measurement site and wind data. Section 3 introduces the theories of stationary and nonstationary models briefly. The run-test method and discrete wavelet transform way were employed to evaluate the stationarity and separate the time-varying mean wind speed, respectively. Section 4 and section 5 investigate and compare the wind characteristics in two models, including the gust factor, turbulence intensity, turbulence integral scale, power spectral density (PSD) and evolutionary power spectral density (EPSD). Section 6 presents the main findings and conclusions.
2. FIELD MEASUREMENT AND WIND DATA
2.1. Field measurement The meteorological tower is 40 m in height and situated on a flat area close to the Yangtze River's estuary near Shanghai Pudong International Airport. The surrounding terrain can be regarded as terrain B according to the China design code (GB50009- 2012. 2012) and the exposures around the facility are of inhomogeneous roughness situations. The type of the anemometer is R.M. Young 81000, and it has a sampling frequency of 4 Hz, which can directly measure the three-dimensional wind speed, horizontal wind direction, and vertical wind direction. The north wind is defined as a wind direction angle of 0°, and the wind angle increases clockwise. For more detail about this measurement site see Huang (Huang et al. 2012) .
2.2. wind data The typhoon Jongdari was a strong, long-lived and erratic tropical cyclone that impacted Japan and East China in late July and early August 2018. Typhoon Jongdari was born on the northwest Pacific Ocean on July 25, 2018. On July 26, as Jongdari started to interact with an upper-level cold-core low to the north which significantly enhanced poleward outflow, it intensified to a typhoon in the afternoon despite increasingly unfavorable vertical wind shear. At around 01:00 JST on July 29 (16:00 UTC July 28), Typhoon Jongdari made landfall over Ise, Mie Prefecture with ten-minute maximum sustained winds at 120 km/h (75 mph) and the central pressure at 975 hPa (28.79 inHg). The storm weakened rapidly inland and made its second landfall over Buzen, Fukuoka Prefecture. At around 10:30 CST (02:30 UTC) on August 3, Jongdari made landfall over Jinshan District, Shanghai. It rapidly weakened after landfall and dissipated on the next day. The wind data recorded during Jongdari effected the
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019 measurement site around 18:00 CST on August 2 to 18:00 CST on August 3.The typhoon rote and the measurement site are shown in Fig. 1 and Fig. 2.
Fig. 1 typhoon rote (from the Japan Meteorological Agency website)
Fig. 2 measurement site
16
8
original measured data windspeed (m/s) data after reconstructing
0 150 300 450 600 time (s) Fig. 3 comparison of original measured data and data after reconstructing
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019
It should be noted that the accuracy, integrity and reliability of data are critical to the analysis result. Some data loss occurred in the original wind record inevitably, which might induce by sensor failures. So the compressive sensing method (Comerford et al. 2016), which is shown to estimate successfully the essential features of the stochastic process power spectrum, was employed to reconstruct the original signal. A sample is given in Fig. 3, Comparing with the original data, the data after reconstructing is more reasonable without data mutation.
3. THEORY BACKGROUND
3.1. stationary and non-stationary models For the traditional stationary wind model, the wind speed Ut() was regarded as a constant mean U plus a zero-mean turbulence component ut(), detailed as U()() t U u t (1) Based on the stationary random process hypothesis, the wind characteristics (e.g. gust factor, turbulence intensity, turbulence integral scale and power spectral density) can be calculated by using U and ut(). For the non-stationary wind model, the wind speed was regarded as a deterministic time-varying mean Ut*() plus a zero-mean turbulence component ut*() (Chen et al. 2004), detailed as U()()*() t U* t u t (2) Where the fluctuation ut*() of typhoon is regarded to be stationary. For simplicity，all the parameters in non-stationary model are distinguished with others in stationary model by asterisk.
3.2. Stationary test Several methods are applied to evaluate the stationarity of data series. Such as the run test method (Levitan 1988) and the reverse arrangement method(McCullough et al. 2013). Due to the simplicity of the run test method which is non-parametric and detect the existence of underlying trends of a signal in the view of hypothesis testing, it was adopted in this paper. For the detail see Levitan (Levitan 1988). The sample duration and the desired level of significance were taken as 10min and 5%, respectively. The stationary test result is shown in Fig. 4, the proportion of nonstationary segments is 55%. It shows that the data has strong nonstationary characteristics.
3.3. Extract the time-varying wind speed As mentioned before, extract the time-varying wind speed is critical to non- stationary analysis. A variety of techniques, including the moving average (MA)(Lombardo et al. 2014), empirical model decomposition (EMD) (Xu et al. 2004, Cheng et al. 2017) and discrete wavelet transform (DWT) (Chen et al. 2005, McCullough et al. 2013, Su et al. 2015) are using to extract the time-varying component by researchers. But MA has limited resolution and may lead to unsmoothed mean, it could not capture the rapidly varying mean (Chen and Letchford 2005). Comparing with MA, EMD and DWT perform better. Also known that EMD face the problem of boundary
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019 effect and mode fixing and the choose of decomposition level in DWT are still critical to the estimation (Huang et al. 2015). Because DWT is capable to decompose both univariate and multivariate data, it will be used for deriving the mean component, detailed as J U()()() t DjJ t A t (3) j1
Where J is the decomposition levels, Dtj () an AtJ () are the detail component at level j and the approximation component, respectively. For more detail see Ye(Ye et al. 2017). Here Daubechies’ wavelets of order 10 (Db 10) was chosen and the wavelet-based self-adaptive method by Tao (Tao et al. 2017) was employed to calculate the reasonable decomposition level. In addition, the stationarity of the residual after extract the time-varying mean wind data was calculated. As presented in Fig. 5, the proportion of stationary segments is 96%. The result shows that the residual can be regard as stationary random process which also reflect that it is suitable to define the non-stationary wind speed equal to a deterministic time-varying mean plus a zero-mean stationary component.
stationary 4 nonstationary
2
0 | Z | Z | 2
4
0 36 72 108 144 segement number Fig. 4 stationary test result before extracting the time-varying wind speed
stationary 4 nonstationary
2
0 | Z | Z | 2
4
0 36 72 108 144 segement number Fig. 5 stationary test result after extracting the time-varying wind speed
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4. MEAN WIND CHARACTERISTICS
After removing the singular points and reconstructing the original data, the mean wind speed and wind angle were calculated. Each 10-min wind speed Ut() recorded by anemometer was partitioned into three components (longitudinal ut(), lateral vt() and vertical wt()). It can be found in Fig. 6 that the maximum of the 10 min mean wind speeds is 18.5 m/s and the horizontal wind directions is shifted approximately from 5° to 78° during Jongdari landing.
20 360
) mean speed 300
mean wind angle m/s ( 15 240
180
10 120
60
mean speed speed mean mean wind angle (°) angle wind mean 5 0 18:00:00 22:00:00 02:00:00 06:00:00 10:00:00 14:00:00 18:00:00 Fig. 6 10August-min 2meanAugust wind 2 speedAugust and 3 horizontalAugust 3 meanAugust wind 3 angleAugust 3 August 3
5. TURBULENCE WIND CHARACTERISTICS
5.1. Gust factor The gust factor reflects the ratio of the gust wind speed to the average wind speed. In stationary model, It is usually defined as the ratio of the maximum mean wind speed in the gust duration (generally tg =3 s) to the longitudinal mean wind speed in the analysis time interval (T =10 min). In the nonstationary model the constant mean wind speed was replaced with the mean time-varying wind speed.
Gu( t g , T ) 1 max[ u ( t g )] / U ( T ) Gv( t g , T ) max[ v ( t g )] / U ( T ) (4) Gw( t g , T ) max[ w ( t g )] / U ( T ) *** Gu(,) t g T 1 max[ u ()/ t g U ()] t g *** Gv( t g , T ) max[ v ( t g ) / U ( t g )] (5) *** Gw( t g , T ) max[ w ( t g ) / U ( t g )] * Where Gig(,) t T and Gig(,) t T are the stationary gust factor and non-stationary * gust factor at the direction i (i u,, v w), respectively.Ut()g is the average of time- varying mean speed over a gust duration tg .
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As illustrated in Fig. 7, the non-stationary gust factor is generally lower than the stationary gust factor, especially in longitudinal and lateral. The mean gust factor of two models in three direction are G 1.28,G 0.18 ,G 0.09 and G* 1.24 ，G* 0.15 ， u v v u v G* 0.09 . v
1.8 stationary model non-stationary model
1.4 longitudinal 1.0 (a) 0.6
0.3 lateral
0.0 (b) 0.2
0.1 vertical
0.0 0 36 72 108 144 (c) segment number Fig. 7 comparison of gust factor
5.2. Turbulence intensity Turbulence intensity reflects the intensity of fluctuating wind and it is an important parameter in the determination the wind load of the structure. For the stationary model, turbulence intensity is defined as the ratio of the standard deviation i of fluctuating wind to mean wind speed U for a given duration (T =10 min), which is expressed as
Iii / U ( i u , v , w ) (6) For the non-stationary model, the mean wind speed U in was replaced with mean time-varying wind speed U * , detailed as *** Iii / U ( i u , v , w ) (7) * Where i is the standard deviation of residual turbulent component. Fig. 8 depicts that the comparison of turbulence intensity. It is similar to the comparison of gust factor the nonstationary results are more stable. When the typhoon leaving from
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019 measurement site (wind speed decreasing), the turbulence intensity shows obvious fluctuation. For detail, the mean values are given: IIIu:: v w =0.162:0.114:0.079 =1:0.71:0.49 and III***::=0.146:0.104:0.080=1:0.71:0.55. u v w
0.50 stationary model non-stationary model
0.25 longitudinal 0.00 (a) 0.30
0.15 lateral
0.00 (b) 0.20
0.10 vertical
0.00 0 36 72 108 144 (c) segment number Fig. 8 comparison of turbulence intensity
The turbulence intensity and gust factor both characterize the instantaneous intensity of the fluent wind. According to Fig. 7, Fig. 8 and the definition of them, these two turbulence parameters are not independent. Ishizaki (Ishizaki 1983) derived the empirical relationship between gust factor and turbulence intensity based on typhoon data and theory. The expression is as follows: b G1 a Iu ln( T0 / T ) (8) Where Ishizaki suggested a=0.5, b =1.0, Choi (Choi 1978) suggested a=0.62, b=1.27, Cao (Cao et al. 2009) suggested a=0.5, b=1.15 and Tao (Tao et al. 2017) fitted with both two models (for stationary model a=0.22, b=0.84; for nonstationary model a=0.26, b=0.91).T0 = averaging time of the mean wind speed. T = averaging time of the maximum peak gust. From Fig. 9, the models suggested by Ishizaki and Choi cannot describe the relation between gust factor and turbulence intensity well. As mentioned before: each typhoon characteristics influenced by some critical parameters, although the model suggested by Tao can fit well when gust factor and turbulence intensity are both small, with the increase with turbulence intensity, the model deviates from measured data. The fitted parameters in this paper are a=0.31, b =0.98 and a=0.34, b
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019
=1.06 in stationary and nonstationary models, respectively. Note that the parameters in two models are similar to each other which shows the relation of gust factor and turbulence intensity is consistent and the ratio about turbulence intensity in three directions of two models also demonstrates this phenomenon.
1.6 stationary model Choi non-stationary model stationary fitted Cao non-stationary fitted Tao stationary 1.4 Tao non-stationary
Ishizaki
u G
1.06 1.2 G = 1+0.34× Iu × ln(T0/T)
0.98 G = 1+0.31× Iu × ln(T0/T) 1.0 0.050 0.125 0.200 0.275 I u Fig. 9 stationary and nonstationary gust factor with turbulence intensity
5.3. Turbulence integral scale Turbulence integral scale represents the influence range of fluctuating wind on structure, and it is an important index to reflect the characteristics of wind field. There are kinds of methods to determine turbulence integral scale: The autocorrelation function integral method (Flay et al. 1988), the wavelength method (Webb et al. 1955), the autocorrelation exponent law method (G. Davenport 1961) and the auto-regression mode method (Reed et al. 1984). Due to the difficulty to measure multiple points in the same time in filed measurement, most researchers calculate the turbulence integral scale based on Taylor’s hypothesis: L( U / 2 ) R ( x ) dx ( i u , v , w ) (9) i i ii 0
Where Rxii () is the autocorrelation function of fluctuating wind speed. With the physical meaning unchanged, the non-stationary turbulence integral scale is defined from a statistical view, detailed as: L*E ( U * ( t ) / ( * ) 2 R * ( x ) dx ( i u , v , w ) (10) i i ii 0
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Where Rx* () is the autocorrelation function of fluctuations in non-stationary ii model. In case of large errors caused by Taylor hypothesis when the autocovariance is small, The autocorrelation function was integrated until the correlation dropped to 0.05(Flay and Stevenson 1988).The comparsion of turbulence integral scale are presented in Fig. 10. By removing the time-varying wind speed, the turbulence integral scale in nonstationary model is smaller than it in stationary model, espacially in the nonstationary segments. The mean values of turbulence integral scale are LLLu:: v w = 155m:132m:18m = 1:0.85:0.12 and LLL***::= 76m:42m:20m = 1:0.55:0.26. u v w
600 stationary model non-stationary model
300
longitudinal 0 (a)
740
370 lateral
0 (b) 70
35 vertical
0 0 36 72 108 144 (c) segment number Fig. 10 comparison of turbulence integral scale
5.4. power spectral density (PSD) and evolutionary power spectral density (EPSD) The turbulent power spectrum characterizes the distribution of turbulent energy in the frequency domain and can describe the characteristics of the turbulent wind more accurately. For the stationary model, the general form is given in Richards(Richards et al. 2000).According to Kolmgorov's principle, many scholars have proposed empirical expressions of fluctuating wind power spectrum function. The Von-Karman spectrum (Von Karman 1948) and Kaimal spectrum (proposed by Kaimal (Kaimal et al. 1972) and modified by Simu (Simiu et al. 1996)) are most applied in several previous measurements and wind tunnel tests.The expression of Von-Karman spectrum is detailed as: longitudinal:
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nSu () n 4 f 2 2 5/6 (11) u (1 70.8f ) lateral, vertical: 2 nSi () n 4ff (1 755.2 ) 2 2 11/6 ,i v, w (12) i (1 283.2f )
Where Sni () is normalized power spectral density, n is frequency (Hz).
f=/ nLi U is monin cooridinate. U is mean velocity in height z . The experssion of Kaimal spectrum is detailed as: longitudinal: nS() n 200 f u (13) (uf )2 (1 50 ) 5/3 lateral: nS() n 15 f v (14) (uf )2 (1 9.5 ) 5/3 vertical (Panofsky et al. 1960): nS() n 6 f w (15) (uf )22 (1 4 ) Where f=/ nz U is moonin similarity cooradinate. u is the friction wind speed, 22 which can be approximated by (u ) ( u ) / 6 . For non-stationary model, researchers using two main ways to reveal the time- frequency characteristics of wind record. One is the direct extension from the current stationary wind spectrum(Tao et al. 2017, Yu et al. 2019), which means replace the monin cooridinate with f***=/ nL U in eq.(11) and eq.(12), also replace the i and with f*= nz / U * and (u* ) 2 ( * ) 2 / 6 in eq.(13)-(15), u respectively. The other way is describing based on EPSD which developed by Priestly and his associates (Priestley 1965, Zhou et al. 2015, Wang et al. 2018). The EPSD was compared with PSD in this paper. Numerous efforts in calculating EPSD have already been made recently. There are a variety of ways, such as: Multifilter technique(Kameda 1975), the discrete wavelet transform (DWT) approach (Spanos et al. 2005) and time- varying AR model (TVAR) (Dahlhaus 1997). But there are some critical parameters (e.g. the wavelet parameters for DWT and the model coefficient in TVAR) need to be chosen carefully (most were chosen by experience), or might cause wrong estimation. Hence, the traditional way presented by Priestley was still widely applied (YouLin et al. 2014, Huang et al. 2015), which was expressed as: t Sˆ(,)()()() t W X X * (16) n T t nt n tT t Xt( n ) g ( ) U ( t )exp i n ( t ) , t 1,2,3,..., T (17) tT
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019 ˆ Where St(,)n is the evolutionary spectral density of Ut() for n . For more detail see Priestly (Priestley 1965).The filter function gu() and the weight function
WuT () were selected as: 1/ (2hh ), g() (18) 0, h 1/TT , 12 WT () (19) 0, 12T Optimal choices of the above quantities will ensure a good compromise between resolvability and variability in both the time domain and the frequency domain. So the parameter h and T in filter and weight function were chosen based on minimizing the relative mean-square error (RMSE)(Priestley 1966). Although there are some papers studied similar simplified model based some special assumption (Chen and Letchford 2005, Huang et al. 2013), such as the wind fluctuation follows the uniformly modulated process (Huang et al. 2015) which also noted that the assumption might not suitable for middle- and low-rise buildings(Huang et al. 2013) .In considering of the extensive applicability, those content were not concluded in this article. Two 10-min segments (No.63 stationary segment and No.38 nonstationary segment) were chosen to depict the results. From Fig. 11 and Fig. 13, the PSD of stationary and nonstationary model are similar in the large-eddy region and the high- frequency region, but discrete in the inertial subregion (due to the extracting of time- varying wind speed, the energy of low-frequency component decrease), especially in nonstationary segment. This is same to others researches (Tao et al. 2016, Ye et al. 2017). Comparing to Kaimal spectrum, the Von-Karman spectrum fits the measured spectrum well in three directions. Note that the mean EPSD (averaged in the time domain) was also given in Fig. 11 and Fig. 13 for convenient comparison. The distributions of the mean EPSD and measured spectrum are concentrated in the universal equilibrium range, but quite different in the energy containing range which is different with Wang (Wang et al. 2016). Since the energy distribution of turbulence is engineers’ primary concern, the EPSD of two segments were also illustrated in Fig. 12 and Fig. 14. The EPSD displays certain differences with time domain. The longitudinal and lateral EPSD of one same segment are similar, might owing to the decomposition of wind. The energy of typhoon Jongdari is concentrated in 0 Hz ~ 0.5 Hz and the peak power spectral density occurred at different time without uniform distribution characteristic. As shown in Fig. 11 to Fig. 14, the division of PSD and EPSD also suggest that the directing extend from stationary model to nonstationary model is not reasonable (Huang et al. 2015), especially there is an obvious non-stationarity in original wind data.
6. CONCLUSIONS
In order to investigate the wind characteristics of typhoon Jongdari based on stationary and nonstationary models. The gust factor, turbulence intensity, turbulence integral
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019 scale, PSD and EPSD are calculated with the measured wind data after data filtering and reconstruction. The main conclusions drawn from this study are summarized as follows: 1. The compressive sensing method can reconstruct the original signal well. This provided a real base for data analysis. 2. Most measured data, which recorded during typhoon landing, have obvious non-stationarity. The DWT can separate the time-varying wind speed efficiently and the residual fluctuating components can be regard as stationary process. 3. The wind characteristics (include gust factor, turbulence intensity, turbulence integral scale) of non-stationary model are smaller and more stable than stationary model. Especially shown in longitudinal and lateral. This suggested that the energy in vertical is low. 4. Due to the different condition of different typhoon, the relation between gust factor and turbulence intensity cannot be describe well with a certain model. The fitted parameters also given in this paper. It shows the relation of gust factor and turbulence intensity is similar in two models. 5. The measured PSD is same in two models except in the large-eddy region, because of the definition of direct extension from stationary model to nonstationary model. Comparing to Kaimal spectrum the Von-Karman spectrum fitted the measured spectrum well in all components. 6. For convenient, the mean EPSD is provided to comparison with stationary and nonstationary models. The EPSD has the advantage to reveal the wind energy distribution in both time and frequency domain. According to the observation of this article, The longitudinal and lateral EPSD of one same segment are similar during typhoon Jongdari.
The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019
102 102
101 101
-1
-1
·s
·s
2
2
) / m
) / m
n
n
(
( v
u 0 0 S S 10 10
10-1 10-1
10-2 10-1 100 10-2 10-1 100 (a) n / Hz (b) n / Hz
101
-1 ·s
2 100
) / m
n
( w
S nonstationary measured data stationary measured data 10-1 nonstationary Karman nonstationary Kaiml stationary Karman measured data stationary Kaiml constant mean wind speed mean EPSD time-varring wind speed 10-2 -2 -1 0 10 10 10 (d) (c) n / Hz Fig. 11 comparison of PSD and mean EPSD in stationary segment (No.63)
90 39 (a) longitudinal (b) lateral 15 (c) vertical
S
S S 60 * * * v 26 w u
10 (
( ( m
m m
2
2 2
/s /s /s
) 30 ) 13 ) 5
600 600 600 0 0 0.0 450 0.00 450 0.0 450 0.5 0.5 300 300 0.5 300 f (Hz) 1.0 f (Hz)1.0 f (Hz)1.0 150 T (s) 150 T (s) 150 T (s) 1.5 1.5 1.5 0 0 0 2.0 2.0 2.0 Fig. 12 EPSD in stationary segment (No.63)
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102 102
101 101
-1
-1
·s
·s
2
2 ) / m
100 ) / m 100
n
n
(
(
v
u
S S
10-1 10-1
10-2 10-2 10-2 10-1 100 10-2 10-1 100 (a) n / Hz (b) n / Hz 101
100
-1
·s
2
) / m
n
( w
S nonstationary measured data stationary measured data 10-1 nonstationary Karman nonstationary Kaiml stationary Karman measured data stationary Kaiml constant mean wind speed mean EPSD time-varring wind speed 10-2 -2 -1 0 10 10 10 (d) (c) n / Hz Fig. 13 comparison of PSD and EPSD in nonstationary segment (No.38)
20 15 25 (a) longitudinal (b) lateral (c) vertical 20 15
S
S S
* 10
* * v
w u
(
15 ( ( m m 10 m 2 2 2
/s /s /s 10 5 ) ) ) 5 5 600 600 600 0 0 0.0 450 0.00 450 0.0 450 0.5 0.5 300 0.5 300 300 f (Hz) 1.0 f (Hz)1.0 f (Hz)1.0 150 T (s) 150 T (s) 150 T (s) 1.5 1.5 1.5 0 0 0 2.0 2.0 2.0 Fig. 14 EPSD in nonstationary segment (No.38)
REFERENCES
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The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019
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The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019
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The 2019 World Congress on Advances in Structural Engineering and Mechanics (ASEM19) Jeju Island, Korea, September 17 - 21, 2019
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