Measurement of Non-Stationary Characteristics of a Landfall Typhoon at the Jiangyin Bridge Site

sensors

Article Measurement of Non-Stationary Characteristics of a Landfall Typhoon at the Jiangyin Bridge Site

Xuhui He 1 ID , Hongxi Qin 1, Tianyou Tao 2,*, Wenshuo Liu 1,* and Hao Wang 2 ID 1 School of Civil Engineering, Central South University, Changsha 410006, China; [email protected] (X.H.); [email protected] (H.Q.) 2 School of Civil Engineering, Southeast University, Nanjing 211189, China; [email protected] * Correspondence: [email protected] (T.T.); [email protected] (W.L.)

Received: 21 August 2017; Accepted: 20 September 2017; Published: 22 September 2017

Abstract: The wind-sensitive long-span suspension bridge is a vital element in land transportation. Understanding the wind characteristics at the bridge site is thus of great significance to the wind- resistant analysis of such a flexible structure. In this study, a strong wind event from a landfall typhoon called Soudelor recorded at the Jiangyin Bridge site with the anemometer is taken as the research object. As inherent time-varying trends are frequently captured in typhoon events, the wind characteristics of Soudelor are analyzed in a non-stationary perspective. The time-varying mean is first extracted with the wavelet-based self-adaptive method. Then, the non-stationary turbulent wind characteristics, e.g.; turbulence intensity, gust factor, turbulence integral scale, and power spectral density, are investigated and compared with the results from the stationary analysis. The comparison highlights the importance of non-stationary considerations of typhoon events, and a transition from stationarity to non-stationarity for the analysis of wind effects. The analytical results could help enrich the database of non-stationary wind characteristics, and are expected to provide references for the wind-resistant analysis of engineering structures in similar areas.

Keywords: wind characteristics; tropical storm; non-stationarity; ﬁeld measurement; long-span suspension bridge

1. Introduction Nowadays, the suspension bridge has become a preferable choice to cross rivers, valleys, or even seas in the land transportation. Many remarkable long-span suspension bridges have been constructed across the world, such as the Akashi-Kaikyo Bridge in Japan, the Xihoumen Bridge in China, and the Great Belt Bridge in Denmark [1]. This kind of bridge is distinguished by its superior spanning capability due to its inherent mechanical features. However, long-span suspension bridges are flexible systems sensitive to wind actions, and the sensitivity increases with the augment of the span length [2–4]. Thus, wind actions on long-span suspension bridges attract intensive attentions in engineering communities, and high requirements are put forward to guarantee the safety and serviceability of structures facing strong wind events, especially for those severe wind disasters (e.g., typhoon/hurricane, downburst, tornado). Improving the knowledge of strong wind cases is therefore of great significance to the security of long-span suspension bridges and similar structures. In the past few decades, the characteristics of boundary layer winds have always been the research focus in structural wind engineering [3,5]. As more and more damages to property caused by typhoon events are frequently reported by public media, special attention is paid to the characteristics of this severe disaster [6–8]. A typhoon is an extreme wind event that frequently make destructive damages to engineering structures. For the wind-sensitive long-span suspension bridge, the fluctuations of typhoon winds are critical on the wind effects, emphasizing the demand to accurately analyze and accumulate the wind characteristics of typhoons.

Sensors 2017, 17, 2186; doi:10.3390/s17102186 www.mdpi.com/journal/sensors Sensors 2017, 17, 2186 2 of 14

The typical method to analyze the wind effects on a long-span suspension bridge is the Alan G. Davenport Wind Loading Chain [9,10], in which the underlying assumption is that the wind speed is stationary. In such a case, the fluctuations over a given time duration of a wind record is assumed to be a zero-mean stationary random process by subtracting a constant mean from the wind data. Accordingly, considerable results of wind characteristics obtained from field measurements have been widely adopted by specifications in different countries to guide the wind-resistant design of engineering structures [11–13]. However, strong non-stationary features are frequently captured in recent field measurements of typhoon events [14–16]. Significant time-dependent changes in the mean value, variance, frequency components, or their combinations are revealed as the inherent non-stationarities of typhoon winds [16], which are different from the stationary boundary layer wind. Hence, there will be a big barrier defending the utilization of the traditional stationary theory in the analysis of non-stationary wind records. In order to solve the faced problem, a non-stationary wind model was proposed to characterize the features of typhoon winds and other extreme wind events [14,17]. In this model, the wind speed is treated as the superposition of a time-varying mean and a stationary turbulent component from a non-stationary perspective. Then, some pioneering work on the non-stationary wind characteristics of typhoon events is conducted. For example, Xu and Chen [14] extracted the time-varying trends of non-stationary wind records with the empirical mode decomposition and defined the non-stationary wind characteristics in a statistical view. Tao et al. [18] proposed a self-adaptive method to determine the time-varying mean and provided an exhaustive analysis on the non-stationary wind characteristics of a landfall typhoon. The non-stationary wind characteristics offer the parameters to simulate a more real wind environment of typhoons to guide the wind tunnel test or computer-aided simulation. Thus, a more precise buffeting analysis of such a long-span bridge can be conducted with non-stationary parameters included. Of course, the non-stationary consideration is expected to provide a more accurate result, which is greatly related to the safety and serviceability of long-span suspension bridges. Although some research on the non-stationary wind characteristics of typhoon winds has been carried out, the accumulated data is still insufficient to establish a database of non-stationary typhoon wind characteristics that could guide structural wind-resistant analysis and design. Also, the wind characteristics are heavily dependent on the geographical location, topography, and local terrains [1,3,7]. Hence, it is of great significance to investigate and accumulate the non-stationary wind characteristics during typhoons to further enrich the database for design. In this study, a strong wind event from a landfall typhoon called Soudelor recorded by the anemometer on Jiangyin Bridge is taken for analysis. Both stationary and non-stationary gust values are characterized after the extraction of the time-varying mean with a wavelet-based method. Based on both stationary and non-stationary models, the wind characteristics, including turbulence intensity, gust factor, turbulence integral scale, and power spectral density, are then comprehensively analyzed with a comparison to the recommendations by current specifications [11,12]. The comparison highlights the importance of non-stationary considerations of typhoon events. The analytical results can help enrich the database of non-stationary wind characteristics and are expected to provide references for the wind-resistant analysis of engineering structures in similar areas.

2. Measurement and Data Source

2.1. Anemometer Utilized in Field Measurement Two anemometers are installed in the structural health monitoring systems of Jiangyin Bridge for the ﬁeld measurement. As shown in Figure1, one anemometer is installed in the middle of the main span (53.0 m above the ground), while the other is on top of the northern tower (197 m above the ground). The anemometer is an HD2003.1-type three-axis ultra-sonic anemometer made by the Delta OHM Company in Padova, Italy. The wind speed ranging from 0 m/s to 60 m/s can be accurately recorded with a resolution of 0.01 m/s, while the wind direction in the range between 0◦ and 359.9◦ can Sensors 2017, 17, 2186 3 of 14 be measured with a resolution of 0.1◦. The upper limit of the sampling frequency of the anemometer can reachSensors 50 2017 Hz., 17, For2186 the convenient storage of the massive data, the sampling frequency3 of 14 during measurements is set as 1 Hz. During the measurement, the two dimensional mode is activated for the Sensorsfrequency 2017, 17 ,during 2186 measurements is set as 1 Hz. During the measurement, the two dimensional mode3 of 14 anemometer, so only the wind speed and direction are recorded. In respect to the wind direction, due is activated for ◦the anemometer, so only the wind speed and direction are recorded. In respect to the northfrequency iswind deﬁned direction, during as 0 duemeasurementswith north a positive is defined is set direction as as 0° 1 with Hz. rotating Duringa positive the clockwise. direction measurement, rotating the clockwise. two dimensional mode is activated for the anemometer, so only the wind speed and direction are recorded. In respect to the wind direction, due north is defined as 0° with a positive direction rotating clockwise.

Figure 1. Layout of anemometers on Jiangyin Bridge. Figure 1. Layout of anemometers on Jiangyin Bridge. 2.2. Description of TyphoonFigure Soudelor 1. Layout of anemometers on Jiangyin Bridge. 2.2. Description of Typhoon Soudelor Typhoon Soudelor was the 13th tropical cyclone in 2015. It was born as a tropical storm on the Typhoon2.2.northwest Description Soudelor surface of Typhoon of was the SoudelorPacific the 13th Ocean tropical and moved cyclone towards in 2015. northwest It was on born 30th asJuly. a tropicalOn 3rd August, storm on the northwesttheTyphoon intensity surface Soudelorof of Soudelor the Paciﬁc was was the Oceanfurther 13th developedtropical and moved cyclone and towardsachieved in 2015. the northwest It samewas born level on asof 30tha supertropical July. typhoon. storm On 3rd Theon August,the the intensitynorthwestmaximum of surface Soudelorwind speedof the was near Pacific furthersea Oceansurface developed and could moved achieve and towards 65 achievedm/s. northwestOn the the morning sameon 30th of level 8thJuly. August, of On a 3rd super it madeAugust, typhoon. landfall in Taiwan and then entered the mainland of China from Fujian Province. Afterwards, it the intensity of Soudelor was further developed and achieved the same level of a super typhoon. The The maximumdowngraded wind as a speed tropical near storm sea and surface passed couldthrough achieve Jiangxi Province 65 m/s. and On Anhui the morning Province. The of 8th whole August, it maximum wind speed near sea surface could achieve 65 m/s. On the morning of 8th August, it made made landfallmoving inroute Taiwan of Typhoon and then Soudelor entered is theshown mainland in Figure of 2. China As there from is Fujianan about Province. 500 km distance Afterwards, it landfall in Taiwan and then entered the mainland of China from Fujian Province. Afterwards, it downgradedbetween as Jiangyin a tropical Bridge storm site and and passedthe nearest through moving Jiangxi route of Province Soudelor, and the Anhuistrong wind Province. data was The whole downgraded as a tropical storm and passed through Jiangxi Province and Anhui Province. The whole movingcollected route of at Typhoon the outer Soudelorvortex region. is shown in Figure2. As there is an about 500 km distance between moving route of Typhoon Soudelor is shown in Figure 2. As there is an about 500 km distance Jiangyinbetween Bridge Jiangyin site and Bridge the site nearest and movingthe nearest route moving of Soudelor, route of Soudelor, the strong the wind strong data wind was data collected was at the outercollected vortex at the region. outer vortex region.

Figure 2. Moving route of Typhoon Soudelor.

3. Mean Wind Characteristics 3.1. Measured Wind Samples ofFigure Typhoon 2. Moving Soudelor route of Typhoon Soudelor. Figure 2. Moving route of Typhoon Soudelor. 3. MeanDuring Wind theCharacteristics strong wind event, the anemometers on Jiangyin Bridge successfully recorded the 3. Meanwind Wind speeds Characteristics and directions. Among the measurements, the wind record from 00:00:00 on 10th 3.1.August Measured to 23:59:59Wind Samples on 11th of AugustTyphoon is Soudelor selected for analysis. The full wind record collected by the 3.1. Measuredanemometer Wind ANE2 Samples on top of Typhoonof the tower Soudelor is shown in Figure 3. The high oscillation of the wind direction fromDuring 30 h tothe 48 strong h is due wind to the event, wind directionthe anemometers of 360° equaling on Jiangyin to 0°. TheBridge wind successfully record in Figure recorded 3 will the Duringwindbe utilizedspeeds the strong forand the directions. following wind event, analyses.Among the the anemometers measurements, on Jiangyinthe wind Bridgerecord successfullyfrom 00:00:00 recordedon 10th the windAugust speedsIn to and order 23:59:59 directions. to validate on 11th Among the August quality the is measurements,ofselected the field for me analysis.asured the wind dataThe recordfullin Figure wind from 3,record the 00:00:00 simultaneously collected on 10th by the August to 23:59:59anemometercollected on 11th wind ANE2 August samples on top is byof selected theANE1 tower forare is analysis.selected shown infor Fi The comparison.gure full 3. The wind high The record oscillationwind collected speed of andthe by winddirection the direction anemometer in 10 min intervals of ANE1 and ANE2 are presented in Figure 4. The mean wind speed and direction ANE2from on top30 h of to the48 h tower is dueis to shown the wind in direction Figure3. of The 360° high equaling oscillation to 0°. The of the wind wind record direction in Figure from 3 will 30 h to be areutilized calculated for the according following to analyses. the vector decomposition method [3]. The variation tendencies of the 48 h is due to the wind direction of 360◦ equaling to 0◦. The wind record in Figure3 will be utilized for meanIn orderwind speedsto validate are similar, the quality and the of mean the field wind me directionsasured coincidedata in Figurewell with 3, eachthe simultaneouslyother, which the following analyses. collectedindicate wind that the samples wind data by ANE1utilized are for selectedthe following for comparison.analyses is reliable. The wind speed and direction in In10 ordermin intervals to validate of ANE1 the quality and ANE2 of the are ﬁeld presented measured in Figure data 4. in The Figure mean3, thewind simultaneously speed and direction collected windare samples calculated by ANE1 according are selectedto the vector for comparison. decomposition The method wind speed[3]. The and variation direction tendencies in 10 min of intervalsthe of ANE1mean and wind ANE2 speeds are are presented similar, and in the Figure mean4. wind The directions mean wind coincide speed well and with direction each other, are calculatedwhich accordingindicate to that the vectorthe wind decomposition data utilized for method the following [3]. The analyses variation is reliable. tendencies of the mean wind speeds are similar, and the mean wind directions coincide well with each other, which indicate that the wind data utilized for the following analyses is reliable.

Sensors 2017, 17, 2186 4 of 14 Sensors 2017, 17, 2186 4 of 14 Sensors 2017, 17, 2186 4 of 14

Figure 3. Measured wind samples during Typhoon Soudelor. FigureFigure 3. 3.Measured Measured wind wind samplessamples during during Typhoon Typhoon Soudelor. Soudelor.

-1 20 ANE1

-1 ANE1 15 ANE2 15 ANE2 10 10 5 5 Wind velocity m·s / velocity Wind 0 Wind velocity m·s / velocity Wind 00 6 12 18 24 30 36 42 48 0 6 12 18Time 24 / h 30 36 42 48 Time / h 360 360 ANE1 ANE2 ANE1 240 ANE2 240

120 120 Wind direction° /

Wind direction° / 0 00 6 12 18 24 30 36 42 48 0 6 12 18Time 24 / h 30 36 42 48 Time / h Figure 4. Comparison of the wind samples from ANE1 and ANE2. FigureFigure 4. Comparison4. Comparison of of the the windwind samples from from ANE1 ANE1 and and ANE2. ANE2. 3.2. General Wind Models 3.2. General Wind Models 3.2. GeneralIn traditional Wind Models analysis of the wind data, the wind speed is assumed to be an ergodic stationary In traditional analysis of the wind data, the wind speed is assumed to be an ergodic stationary random process consisting of a constant mean and a zero-mean turbulence, which is detailed as Inrandom traditional process analysis consisting of of the a constant wind data, mean the and wind a zero-mean speed is turbulence, assumed towhich be anis detailed ergodic as stationary random process consisting of a constant mean and=+ a zero-mean turbulence, which is detailed as Ut()=+ U ut () (1) Ut() U ut () (1) where Ut() is the wind speed; U is the Uconstant(t) = U mean+ u (overt) a time interval T, which is chosen as (1) where Ut() is the wind speed; U is the constant mean over a time interval T, which is chosen as 10 min in Chinese code [12]; and ut() is the fluctuating component. where10U min(t) isin theChinese wind code speed; [12];U andis theut() constant is the fluctuating mean over component. a time interval T, which is chosen as 10 min In the non-stationary wind model, a deterministic time-varying trend is captured in the wind in ChineseIn code the non-stationary [12]; and u(t )windis the model, fluctuating a deterministic component. time-varying trend is captured in the wind speed. Hence, the wind speed is treaded as the superposition of a time-varying mean and a residual Inspeed. the non-stationaryHence, the wind speed wind is model, treaded a as deterministic the superposition time-varying of a time-varying trend ismean captured and a residual in the wind zero-mean stationary random process, as presented in Equation (2). speed.zero-mean Hence, thestationary wind speedrandom is process, treaded as as presented the superposition in Equation of (2). a time-varying mean and a residual Ut()=+ U ** () t u () t zero-mean stationary random process, as presented=+ ** in Equation (2). (2) Ut() U () t u () t (2) Ut * () ( ) = ∗( ) + ∗( ) * where  * is the time-varying meanU reflectingt Ue thet temporalu t trend of wind speed; and ut*() is the (2) where Ut() is the time-varying mean reflecting the temporal trend of wind speed; and ut() is the fluctuating wind in the non-stationary model. Obviously, if the wind speed is a stationary process, fluctuating∗( ) wind in the non-stationary model. Obviously, if the wind speed is a stationary process,∗( ) wheretheUe time-varyingt is the time-varying mean in Equation mean (2) reflecting will be redu theced temporal to a constant trend mean, of wind which speed; is the same and asu thatt is the fluctuatingthe time-varying wind in themean non-stationary in Equation (2) model.will be redu Obviously,ced to a constant if the wind mean, speed which is is a the stationary same as that process, the time-varying mean in Equation (2) will be reduced to a constant mean, which is the same as that of Equation (1), so that Equation (2) will be the same with Equation (1). Therefore, Equation (2) is a more general form for the analysis of the wind data. It should be noted that the models presented by Sensors 2017, 17, 2186 5 of 14 ofSensors Equation2017, 17 (1),, 2186 so that Equation (2) will be the same with Equation (1). Therefore, Equation (2)5 is of 14a more general form for the analysis of the wind data. It should be noted that the models presented by Equations (1) and (2) are adapted to both the longitudinal and lateral cases, but the mean value of the lateralEquations turbulence (1) and equals (2) are zero. adapted to both the longitudinal and lateral cases, but the mean value of the lateral turbulence equals zero. 3.3. Extraction of the Time-Varying Mean 3.3. Extraction of the Time-Varying Mean When utilizing the non-stationary wind model, a critical step is to detrend the time-varying meanWhen from the utilizing wind thedata. non-stationary Many methods wind have model, been adeveloped critical step to extract is to detrend the temporal the time-varying trend for non-stationarymean from the wind wind records, data. Manyamong methods which empirical have been mode developed decomposition to extract (EMD) the temporal and wavelet trend transformfor non-stationary (WT) are wind two records, popular among and whichfrequently empirical used mode approaches. decomposition For example, (EMD) andChen wavelet and Letchfordtransform [18] (WT) estimated are two popular the time-varying and frequently mean used for approaches. downburst For wind example, by employing Chen and db4 Letchford wavelet. [18] Wangestimated et al. the [19] time-varying selected db20 mean wavelet for downburst to acquire windthe temporal by employing mean of db4 a downburst wavelet. Wang data. etXu al. and [19] Chenselected [14] db20 extracted wavelet the to time-varying acquire the temporal mean of mean a strong of a downburstwind via EMD. data. XuHowever, and Chen the [ 14selection] extracted of decompositionthe time-varying levels mean depends of a strong on windusers’ via judgment, EMD. However, which theputs selection forward of a decomposition requirement for levels a straightforwarddepends on users’ treatment judgment, of this which procedure. puts forward Su et al. a requirement[20] proposed for a ascheme straightforward to derive a treatment reasonable of time-varyingthis procedure. mean,Su etbut al. the [20 ]procedproposedure ais schemerelatively to derivecomplicated a reasonable since the time-varying estimation mean,of EPSD but and the structuralprocedure response is relatively computation complicated is sinceincluded. the estimation Tao et al. of [21] EPSD developed and structural a self-adaptive response computation WT-based approachis included. to extract Tao et al.the [ 21time-varying] developed mean a self-adaptive according WT-basedthe stationarity approach of the to signal. extract the time-varying meanWith according the wavelet-based the stationarity self-adaptive of the signal. method by Tao et al. [21], the time-varying trends of the wind Withrecords the are wavelet-based separated for self-adaptive Typhoon Soudelor method bywith Tao the et db20 al. [21 wavelet.], the time-varying In this study, trends the oftime the intervalwind records utilized are is separatedselected as for10 min Typhoon according Soudelor to the with Chinese the db20specification wavelet. [12]. In thisSome study, of the the typical time samplesinterval utilizedincluding is selectedstationary as and 10 min non-stationary according to re thecords Chinese are shown specification in Figure [12]. 5. Some As illustrated of the typical in Figuresamples 5, includingthe time-varying stationary mean and differs non-stationary much from records the constant are shown mean in for Figure the non-stationary5. As illustrated wind in records,Figure5 ,which the time-varying means the meanstationary differs assumption much from cannot the constant be utilized mean anymore. for the non-stationary For the stationary wind records,records, the which extracted means thetime-varying stationary assumptionmean is almost cannot the be same utilized as anymore.the constant For mean, the stationary indicating records, the unificationthe extracted of time-varyingEquations (1) mean and is(2) almost for stationary the same asrecords. the constant The performance mean, indicating of stationary the unification and non-stationaryof Equations (1) records and (2) verifiesfor stationary the effectiven records.ess The of performance the self-adaptive of stationary method. and Comparing non-stationary the differencesrecords verifies between the effectivenessthe time-varying of the mean self-adaptive and constant method. mean Comparingin non-stationary the differences longitudinal between and lateralthe time-varying turbulences, mean the and longitudinal constant mean wind in non-stationary speed presents longitudinal a stronger and non-stationarity lateral turbulences, than the thelongitudinal other case. wind speed presents a stronger non-stationarity than the other case.

26 22 -1 Original wind record -1 Original wind record Time-varying mean Time-varying mean 22 Constant mean 18 Constant mean

18 14

14 10 Longitudinal wind speed / m·s Longitudinal wind speed / m·s 10 6 0 100 200 300 400 500 600 0 100 200 300 400 500 600 t / s t / s 4 8 Original wind record Original wind record -1 -1 Time-varying mean Time-varying mean Constant mean Constant mean 4

0 0

Lateral wind speed / m·s -4 Lateral wind speed / m·s -4 0 100 200 300 400 500 600 0 100 200 300 400 500 600 t / s t / s (a) (b)

Figure 5. Time-varying mean wind speed versus constant mean wind speed of wind records: Figure 5. Time-varying mean wind speed versus constant mean wind speed of wind records: (a) non-stationary records; (b) stationary records. (a) non-stationary records; (b) stationary records.

Sensors 2017, 17, 2186 6 of 14 Sensors 2017, 17, 2186 6 of 14 4. Turbulent Wind Characteristics

4. Turbulent Wind Characteristics 4.1. Turbulence Intensity 4.1. TurbulenceThe turbulence Intensity intensity in the traditional stationary theory is defined as the ratio of standard deviationThe turbulenceof turbulence intensity in each in direction the traditional to the co stationarynstant mean theory wind is deﬁnedspeed in as a thegiven ratio time of standardinterval, asdeviation expressed of turbulencein Equation in each(3). The direction non-stationary to the constant turbulence mean windintensity speed is indefined a given as time Equation interval, (4), as makingexpressed it have in Equation the same (3). physical The non-stationary meaning with turbulence that of the intensity stationary is deﬁned model. as Equation (4), making it have the same physical meaning with that ofσ the stationary model. ==i Iiuvi , , (3) Uσi Ii = , i = u, v (3) U σ * * " i # IE==∗ ,, iuv (4) i ∗ σi I = EUt() , i = u, v (4) i U(t) T e T * where I and ∗Ii are stationary and non-stationary turbulence intensities, respectively; u and v where Iii and Ii are stationary and non-stationary turbulence intensities, respectively; u and v denote ∗ * the cases of longitudinal and lateral turbulences; σi and σ areσ standardσ deviations of turbulences in denote the cases of longitudinal and lateral turbulences;i i and i are standard deviations of stationary and non-stationary wind models, respectively; and E[·] represents the mean value over the turbulences in stationary and non-stationary wind models, respectively; and E[·] represents the mean time interval T, which is set as 10 min in this study. value over the time interval T, which is set as 10 min in this study. Based on the stationary and non-stationary models expressed by Equations (3) and (4), the Based on the stationary and non-stationary models expressed by Equations (3) and (4), the turbulence intensities of Typhoon Soudelor are calculated from stationary and non-stationary turbulence intensities of Typhoon Soudelor are calculated from stationary and non-stationary perspectives. The results are presented in Figure6. It is noteworthy that the non-stationary turbulence perspectives. The results are presented in Figure 6. It is noteworthy that the non-stationary turbulence intensities are smaller than stationary ones for both longitudinal and lateral cases. The difference in intensities are smaller than stationary ones for both longitudinal and lateral cases. The difference in the longitudinal case is more obvious than that in the lateral case, which means the non-stationarity of the longitudinal case is more obvious than that in the lateral case, which means the non-stationarity the longitudinal turbulence is much stronger than that of the lateral wind. of the longitudinal turbulence is much stronger than that of the lateral wind.

0.6 21

Stationary -1 Non-stationary 0.4 Wind speed 15 Chinese Code 0.2 ASCE7-10 9 Wind speed / m·s Wind speed Turbulence intensity 0.0 3 0 6 12 18 24 30 36 42 48 Time / h (a) 0.6 21 Stationary -1 Non-stationary 0.4 Wind speed 15

0.2 Chinese code 9 Wind speed / m·s

Turbulence intensity Turbulence 0.0 3 0 6 12 18 24 30 36 42 48 Time / h

(b)

Figure 6. Comparison of stationary and non-stationary turbulence intensities: (a) longitudinal case; Figure 6. Comparison of stationary and non-stationary turbulence intensities: (a) longitudinal case; (b) lateral case. (b) lateral case. The longitudinal turbulence intensity profile for categories B, C, and D exposure in ASCE7-10The longitudinal [11] is given turbulence by intensity proﬁle for categories B, C, and D exposure in ASCE7-10 [11] is given by 10 1/6 I = c (5) u z

Sensors 2017, 17, 2186 7 of 14

1/6 = 10 Icu  (5) z Sensors 2017, 17, 2186 7 of 14 where c equals to 0.15 for category D exposure. Thus, the longitudinal turbulence intensity at an altitude of 197 m is suggested as 0.091 by ASCE7-10 [11]. In Chinese code [12], a ratio between where c equals to 0.15 for category D exposure. Thus, the longitudinal turbulence intensity at an longitudinal and lateral turbulence intensities is suggested as 1:0.88, and the value for longitudinal altitude of 197 m is suggested as 0.091 by ASCE7-10 [11]. In Chinese code [12], a ratio between case is recommended as 0.10 within the altitude between 150 m and 200 m. longitudinal and lateral turbulence intensities is suggested as 1:0.88, and the value for longitudinal The recommendations of turbulence intensities in ASCE7-10 and Chinese code are also plotted case is recommended as 0.10 within the altitude between 150 m and 200 m. in Figure 6. It is shown in Figure 6 that the suggestions from both ASCE7-10 and Chinese code The recommendations of turbulence intensities in ASCE7-10 and Chinese code are also plotted in generally coincide well with the measured turbulence intensities from 0 h to 39 h for both longitudinal Figure6. It is shown in Figure6 that the suggestions from both ASCE7-10 and Chinese code generally and lateral cases of Typhoon Soudelor. However, the turbulence intensities from 39 h to 48 h are coincide well with the measured turbulence intensities from 0 h to 39 h for both longitudinal and much larger than those in the range 0–39 h. This phenomenon results from the low wind speed case lateral cases of Typhoon Soudelor. However, the turbulence intensities from 39 h to 48 h are much after the passage of typhoon winds [3]. The mean wind speed is also plotted in Figure 6 to show the larger than those in the range 0–39 h. This phenomenon results from the low wind speed case after the variation of wind speeds. The wind speed corresponds the right Y-axis of Figure 6. For longitudinal passage of typhoon winds [3]. The mean wind speed is also plotted in Figure6 to show the variation turbulence intensities during 14–20 h, they are a little larger than those in other durations from 0 h to of wind speeds. The wind speed corresponds the right Y-axis of Figure6. For longitudinal turbulence 39 h and higher than recommendations from both ASCE7-10 and Chinese code. This is mainly intensities during 14–20 h, they are a little larger than those in other durations from 0 h to 39 h and attributed to the significant convective properties of typhoon events; the turbulence intensity is thus higher than recommendations from both ASCE7-10 and Chinese code. This is mainly attributed to the not homogenous in the entire duration. significant convective properties of typhoon events; the turbulence intensity is thus not homogenous in the entire duration. 4.2. Gust Factor 4.2. GustThe Factor gust factor is an important parameter that can convert the mean wind speed to maximum gustThe value. gust In factor the stationary is an important model, parameter it is defined that as can the convert ratio of the the mean peak windmean speedwind tospeed maximum in a gust gustduration value. t Ing to the the stationary mean wind model, speed it over is defined the time as theinterval ratio ofT [11,12], the peak which mean is wind expressed speed as in Equation a gust (6). For the non-stationary gust factor, it is defined as the maximum ratio of the averaged original duration tg to the mean wind speed over the time interval T [11,12], which is expressed as Equation (6). Forwind the non-stationaryspeed to averaged gust time-varying factor, it is defined mean aswithin the maximum a given time ratio interval of the averagedT, among originalwhich both wind the speedoriginal to averaged wind speed time-varying and time-varying mean within mean a are given averaged time interval in the gustT, among duration which tg [14,21]. both the original wind speed and time-varying mean are averaged inmax[ the gustUt duration ( )] tg [14,21]. = g T GtTug(,) (6) [ ( U)] max U tg T Gu(tg, T) = (6) U  Ut() * = g GtTug(,) max"  #  (7) U(tg) * ∗  Ut()g  Gu(tg, T) = max   T (7) U∗(t ) e g T where GtT(,) and GtT* (,) are stationary and non-stationary gust factors, respectively; Ut() is ug ∗ ug g where Gu(tg, T) and Gu(tg, T) are stationary and non-stationary gust factors, respectively; U(tg) is the ∗  * meanthe mean wind speedwind speed over a over gust a duration gust durationtg; and tUeg; and(tg) Utis() theg meanis the valuemean ofvalue the time-varyingof the time-varying mean over mean theover duration the durationtg. In this tg. study,In this thestudy, gust the duration gust duration is selected is selected as 3 s according as 3 s according to ASCE7-10. to ASCE7-10. AA comparison comparison of of stationary stationary and and non-stationary non-stationary gust gust factors factors of of the the wind wind records records is is presented presented in in FigureFigure7. Similar7. Similar to to the the phenomenon phenomenon that that captured captured in thein the turbulence turbulence intensity, intensity, the the non-stationary non-stationary gustgust factor factor is is generally generally lower lower than than the the stationary stationary case.case. The variation trend trend of of the the gust gust factor factor along along the thetime time axis axis is is similar similar to to that that of the longitudinallongitudinal turbulenceturbulence intensity;intensity; thus, thus, there there may may exist exist a stronga strong relationshiprelationship between between the the gust gust factor factor and and the the longitudinal longitudinal turbulence turbulence intensity. intensity.

2.0 Stationary 1.8 Non-stationary 1.6

1.4

Gust factor 1.2

1.0 0 6 12 18 24 30 36 42 48 Time / h

FigureFigure 7. 7.Comparison Comparison of of stationary stationary and and non-stationary non-stationary gust gust factor. factor.

With an analysis of the deﬁnition of the gust factor, it is found to be strongly related to the longitudinal turbulence intensity, since the mean wind speed in a gust duration is positively correlated Sensors 2017, 17, 2186 8 of 14

Sensors 2017, 17, 2186 8 of 14 With an analysis of the definition of the gust factor, it is found to be strongly related to the longitudinal turbulence intensity, since the mean wind speed in a gust duration is positively withcorrelated the standard with the deviation standard of deviation turbulence. of turbulence The stationary. The and stationary non-stationary and non- guststationary factors gust versus factors the correspondingversus the corresponding turbulence intensitiesturbulence are intensities plotted in ar Figuree plotted8, in in which Figure the 8, turbulence in which the intensities turbulence of theintensities aforementioned of the aforementioned low wind speed low cases wind are speed not included.cases are not It is included. easy to ﬁnd It is that easy there to find is a that positive there relationshipis a positive between relationship the gust between factor andthe gust the turbulencefactor and intensity.the turbulence The presented intensity. relationships The presented of stationaryrelationships and of non-stationary stationary and cases non-statio are similarnary tocases each are other. similar to each other.

2.0 Stationary Statioanry fitted 1.8 Non-stationary Non-statioanry fitted Ishizaki [22] 1.6 Choi [23] Cao [24] Tao [21] 1.4 Gust factor

1.2

1.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Turbulence intensity

FigureFigure 8. 8.Stationary Stationary and and non-stationary non-stationary gust gust factors factors versus versus the the turbulence turbulence intensity. intensity.

Some expressions of the relationship between gust factor and the longitudinal turbulence Some expressions of the relationship between gust factor and the longitudinal turbulence intensity intensity have been proposed based on linear or nonlinear models, which can be expressed in the have been proposed based on linear or nonlinear models, which can be expressed in the general general form below, form below, k2 T G (t , T) = 1 + k I lnk T (8) GtTu(,)g =+ 11 kIu 2 ln ug1 u tg (8) t g where Ishizaki suggested k1 = 0.5, k2 = 1.0 for typhoons [22]; Choi suggested k1 = 0.62, k2 = 1.27 [23], Caowhere suggested Ishizakik 1suggested= 0.5, k2 = k 1.151 = 0.5, for k Typhoon2 = 1.0 for Maemi typhoons [24], [22]; and TaoChoi et suggested al.; suggested k1 = k0.62,1 = 0.22, k2 = k1.272 = 0.84[23], forCao a non-stationarysuggested k1 = case.0.5, k2 = 1.15 for Typhoon Maemi [24], and Tao et al.; suggested k1 = 0.22, k2 = 0.84 for aThe non-stationary relationships case. of stationary and non-stationary cases between gust factor and turbulence intensityThe arerelationships also fitted forof stationary comparison, and where non-stationary the stationary cases case betwee suggestsn gustk1 factor= 0.29, andk2 = turbulence 0.81 and 2 theintensity non-stationary are also fitted case suggestsfor comparisonk1 = 0.45,, wherek2 = the 0.96. stationary The R values case suggests of the fitting k1 = 0.29, for k stationary2 = 0.81 and and the non-stationarynon-stationary cases case are suggests 0.85 and k10.80, = 0.45, respectively. k2 = 0.96. The The fitted R2 values expressions of the together fitting withfor stationary the empirical and modelsnon-stationary are also plottedcases are in 0.85 Figure and8 .0.80, As shown respectively in Figure. The8, fitted the two expressions fitted models together can well with describe the empirical the stationarymodels are and also non-stationary plotted in Figure relationships 8. As shown between in Figure gust factor8, the andtwo turbulencefitted models intensity. can well Although describe the the Ishizakistationary model and wasnon-stationary proposed for relationships the stationary between wind model,gust factor it is similarand turbulence to the fitted intensity. non-stationary Although expressionthe Ishizaki in thismodel study was and proposed can well describe for the the stationa measuredry wind relationship model, between it is similar non-stationary to the fitted gust factornon-stationary and non-stationary expression turbulence in this study intensity. and can For well the stationary describe the relationship, measured only relationship the Tao model between in empiricalnon-stationary expressions gust factor provides and a no similarn-stationary trend but turbulence it behaves intensity. as the lower For limitthe stationary of the measured relationship, cases. only the Tao model in empirical expressions provides a similar trend but it behaves as the lower limit 4.3.of the Turbulence measured Integral cases. Scale Turbulence integral scale (TIS) is a measure of the average size of turbulent eddies [1]. In the stationary4.3. Turbulence theory, Integral TIS is mathematicallyScale defined as Equation (9) with the preliminary Taylor hypothesis. With theTurbulence physical integral meaning scale unchanged, (TIS) is a the measure non-stationary of the average TIS is definedsize of turbul froment a statistical eddies [1]. view, In asthe expressedstationary in theory, Equation TIS (10). is mathematically defined as Equation (9) with the preliminary Taylor ∞ hypothesis. With the physical meaning unchanged,U Z the non-stationary TIS is defined from a statistical Li = Ri(τ)dτ i = u, v (9) view, as expressed in Equation (10). σ2 i 0 ∞ ==U ∞ ττ LRiuviiZ ()d , (9) ∗ Uσe(2t) ∗ Li = E i 0 Ri (τ)dτ i = u, v (10) σ∗2 i 0

Sensors 2017, 17, 2186 9 of 14

 ∞ **==Ut() ττ L iiERiuv()d , (10) ()σ * 2  i 0 * τ where Li and Li are stationary and non-stationary turbulence integral scales, respectively; Ri() Sensors 2017, 17, 2186 9 of 14 * τ and Ri () are auto-covariance functions of the stationary and non-stationary fluctuations, τ respectively; and∗ is the lag time. In order to avoid the errors induced by the estimated fluctuations where Li and Li are stationary and non-stationary turbulence integral scales, respectively; Ri(τ) and of∗ covariance functions, the upper limit of the integral is suggested to take the first t where Ri (τ) are auto-covariance functions of the stationary and non-stationary fluctuations, respectively; τσ= 2 **τσ= 2 andR ii(τ )is the 0.05 lag time. and In order R ii() to avoid 0.05 the() errors induced. by the estimated fluctuations of covariance ( ) = 2 functions,Stationary the upperand non-stationary limit of the integral TIS in islongitudinal suggested toand take lateral the firstcasest where of TyphoonRi τ Soudelor0.05σi andare ∗ ∗2 calculatedRi (τ) = 0.05 accordingσi . to Equations (9) and (10). The corresponding results are presented in Figure 8. It canStationary be seen that and non-stationary non-stationary turbulence TIS in longitudinal integral scales and are lateral totally cases smaller of Typhoon than stationary Soudelor ones, are whichcalculated is mainly according attributed to Equations to the extraction (9) and (10).of th Thee time-varying corresponding mean. results Detrending are presented the non-stationary in Figure8. windIt can records be seen will that filter non-stationary some low-frequency turbulence comp integralonents, scales which are reflect totally the smaller large-scale than stationaryeddies in turbulence.ones, which is mainly attributed to the extraction of the time-varying mean. Detrending the non-stationaryThe longitudinal wind records turbulence will filter integral some scale low-frequency profile for components, categories whichB, C, reflectand D the exposure large-scale in ASCE7-10eddies in turbulence.is given by [11]

The longitudinal turbulence integral scale proﬁle forε categories B, C, and D exposure in ASCE7-10 is given by [11]: = z Llu  z ε (11) Lu = l10 (11) 10 wherewherel is equals l is equals to 198.2 to 198.2 and εandis equals ε is equals to 1/8 to for1/8 categoryfor category D exposure. D exposure. At theAt the height height of 197 of 197 m, them, thelongitudinal longitudinal turbulence turbulence integral integral scale is scale recommended is recommended as 287.68 as by ASCE7-10.287.68 by InASCE7-10. Chinese speciﬁcation,In Chinese specification,longitudinal and longitudinal lateral turbulence and lateral integral turbulence scales betweenintegral scales the height between of 150 the m height and 200 of m 150 are m suggested and 200 mas are 180 msuggested and 90 m, as respectively. 180 m and The90 m, turbulence respectively. integral The scales turbulence recommended integral byscales ASCE7-10 recommended and Chinese by ASCE7-10code are also and plotted Chinese in code Figure are9. also plotted in Figure 9.

800 Stationary 600 Non-stationary ASCE-10 Chinese code 400 TIS

200

0 0 8 16 24 32 40 48 Time / h (a) 800 Stationary 600 Non-stationary Chinese code 400 TIS

200

0 0 8 16 24 32 40 48 Time / h (b)

Figure 9. Turbulence integral scales based on stationary and non-stationary wind models: Figure 9. Turbulence integral scales based on stationary and non-stationary wind models: (a) longitudinal case; (b) lateral case. (a) longitudinal case; (b) lateral case.

As shown in Figure 9, ASCE7-10 provides a good estimate for the stationary longitudinal turbulenceAs shown integral in Figurescale of9, ASCE7-10Typhoon Soudelor. provides Th a goode mean estimate value of for measured the stationary turbulence longitudinal integral scalesturbulence is 261.8 integral m, which scale is ofwith Typhoon a 9.0% Soudelor.deviation from The meanthe suggested value of value measured by ASCE7-10. turbulence However, integral thescales recommended is 261.8 m, which values is with by aChinese 9.0% deviation code are from generally the suggested lower value than by measured ASCE7-10. TIS However, for both the recommended values by Chinese code are generally lower than measured TIS for both longitudinal and lateral cases. The mean stationary TIS of lateral turbulence is 206.8, so the ratio between longitudinal and lateral TIS is 1:0.79, which means the lateral TIS is underestimated by Chinese code. For the non-stationary TIS, the mean values of longitudinal and lateral cases are 49.4 and 44.4, respectively. Thus the ratio between the two cases is 1:0.90, which is similar to the results acquired by Tao et al. [21]. Sensors 2017, 17, 2186 10 of 14

longitudinal and lateral cases. The mean stationary TIS of lateral turbulence is 206.8, so the ratio between longitudinal and lateral TIS is 1:0.79, which means the lateral TIS is underestimated by Chinese code. For the non-stationary TIS, the mean values of longitudinal and lateral cases are 49.4 and 44.4, respectively. Thus the ratio between the two cases is 1:0.90, which is similar to the results acquired by Tao et al. [21]. This means non-stationary longitudinal and lateral turbulence integral scales are close to each other, indicating the average size of turbulent eddies is similar in the two Sensorsdirections2017, 17by, 2186the non-stationary wind model. 10 of 14

4.4. Turbulence Power Spectral Density This means non-stationary longitudinal and lateral turbulence integral scales are close to each other, indicatingTurbulence the average power size spectral of turbulent density, eddieswhich ischaracte similarrizes in the the two energy directions distribution by the of non-stationary turbulence in windfrequency model. domain, is a critical element in the precise prediction of buffeting responses of engineering structures. Based on the stationary assumption, many spectral models have been proposed via the 4.4.field Turbulence measured Power data in Spectral strong Density wind events. For example, Kaimal spectrum [25] is widely accepted for longitudinalTurbulence turbulence power spectraland employed density, in which the wind characterizes resistant-design the energy specification distribution for highway of turbulence bridges in frequencyin China [12]. domain, The expression is a critical of element Kaimal in spectrum the precise is detailed prediction as: of buffeting responses of engineering structures. Based on the stationarynS assumption,() n many spectral models have been proposed via the u = 200 f ﬁeld measured data in strong wind events.()u 25/3 For example,()+ Kaimal spectrum [25] is widely accepted(12) for longitudinal turbulence and employed in* the wind150 resistant-designf speciﬁcation for highway bridges in China [12]. The expression of Kaimal spectrum is detailed as: where Snu() is the turbulence power spectral density; n is the natural frequency of turbulence; u* is nSu(n) 200 fσ 2 the friction wind speed, which can be approximated= by u /6; and f is the Monin coordinate and 2 5/3 (12) (u∗) (1 + 50 f ) equals to nz/ U , in which z is the altitude of the wind speed. whereForSu the(n) non-stationaryis the turbulence power power spectr spectralal density, density; then is following the natural form frequency is suggested of turbulence; with the physicalu∗ is the meaning unchanged. 2 friction wind speed, which can be approximated by σu/6; and f is the Monin coordinate and equals to nz/U, in which z is the altitude of the windnS () speed.n 200 f For the non-stationary power spectralu density,= the following form is suggested with the physical  25/3 (13) meaning unchanged. ()u* ()150+ f nSeu(n) 200 fe = (13) ( )2 5/3  ue∗ 1 + 50 fe u where Snu() is the non-stationary power spectral density; * is the non-stationary friction wind ( ) *2  wherevelocitySeu andn is can the be non-stationary approximated power as ()/6 spectralσ density;; and uef∗ is is the the non-stationary non-stationary friction Mornin wind coordinate velocity ∗ 2 u and can be approximated as (σu ) /6; and fe is the non-stationary Mornin coordinate and equals to and equalsh i to nz/E U ( t ) . nz/E Ue(t) .   For the spectral analysis, a strong wind sample,sample, which includes the maximum wind speed, from 13.513.5 hh toto 14.514.5 hh inin FigureFigure3 3,, is is selected selected as as an an example example with with 1 1 h h duration. duration. TheThe originaloriginal windwind speedspeed ofof this record isis shownshown inin FigureFigure 1010.. Meanwhile, the time-varying mean is also plotted for for comparison. comparison. The mean windwind speedspeed ofof thisthis samplesample isis 17.4117.41 m/s.m/s. The The stationary stationary turbulence turbulence intensity and turbulence integralintegral scale areare 0.1830.183 andand 1509.81509.8 m,m, whilewhile thethe correspondingcorresponding non-stationarynon-stationary values are 0.1560.156 andand 228.8 m.

-1 Original record 25 Time-varying mean 20

10 Wind speed / m·s speed Wind

5 0 600 1200 1800 2400 3000 3600 Time / s Figure 10. Wind record for power spectral density analysis. Figure 10. Wind record for power spectral density analysis.

After subtracting the constant mean and time-varying mean from the original wind record separately, the stationary and non-stationary turbulences are obtained. Based on the Fourier transform, the stationary and non-stationary power spectral densities of turbulence are estimated, and the results are presented in Figure 11. Obviously, the non-stationary power spectral density is lower than the stationary case in low-frequency ranges, while the two cases keep consistent in the rest of the ranges. This phenomenon can be well explained by the ﬁltering of the time-varying mean, which physically Sensors 2017, 17, 2186 11 of 14

Sensorslower 2017than, 17 the, 2186 stationary case in low-frequency ranges, while the two cases keep consistent 11in ofthe 14 rest of the ranges. This phenomenon can be well explained by the filtering of the time-varying mean, which physically performs as the low-frequency content in wind fluctuations [1]. For a long-span performssuspension as bridge the low-frequency like Jiangyin content suspension in wind bridge, ﬂuctuations the background [1]. For a long-spanor resonant suspension buffeting bridgeresponses like Jiangyinare mainly suspension dominated bridge, by low-frequency the background mode or resonantshapes. The buffeting lowest responses frequency are of mainlyJiangyin dominated Bridge is byabout low-frequency 0.05 Hz, so the mode non-stationa shapes.rity The of lowest typhoon frequency events may of Jiangyin only influence Bridge the is aboutbackground 0.05 Hz, buffeting so the non-stationarityresponses. However, of typhoon with the events development may only inﬂuenceof long-span the backgroundsuspension buffetingbridges, the responses. structural However, lowest withfrequency the development will be much of long-span smaller suspensionand gradually bridges, approach the structural the discrepancy lowest frequency of stationary will be much and smallernon-stationary and gradually turbulence approach captured the discrepancy in this study. of stationaryThus, the captured and non-stationary differenceturbulence between stationary captured inand this non-stationary study. Thus, power the captured spectral difference densities betweenmay greatly stationary affect the and accuracy non-stationary of predicted power buffeting spectral densitiesresponses. may greatly affect the accuracy of predicted buffeting responses.

104

103 -1 s

· 2 2 10

m Measured stationary

) / Measured non-statioanry 1 n 10 ( Stationary Kaimal u

S Non-stationary Kaimal 100 Stationary Karman Non-stationary Karman Non-statioanry fitted 10-1 10-3 10-2 10-1 n / Hz

Figure 11. Comparison between measured power spectralspectral densities andand empiricalempirical models.models.

In order to verify the effectiveness of the stationary and non-stationary empirical models, the stationaryIn order and to non-stationary verify the effectiveness Kaimal spectra of the are stationary also plotted and in non-stationary Figure 10 for comparisons. empirical models, It is easy the stationaryto find that and neither non-stationary of the stationary Kaimal spectra nor non- are alsostationary plotted Kaimal in Figure spectrum 10 for comparisons. can well describe It is easy the to findmeasured that neither spectra, of including the stationary both nor stationary non-stationary and non-stationary Kaimal spectrum cases. canThey well are describe lower than the measured spectra,spectra includingin high-frequency both stationary ranges. and The non-stationary stationarycases. Kaimal They spectrum are lower is than able measured to describe spectra the in high-frequencylow-frequency feature ranges. of The stationary stationary power Kaimal spectral spectrum density, is able but to the describe non-stat theionary low-frequency Kaimal spectrum feature ofcannot stationary describe power the descending spectral density, feature but of thenon-stationary non-stationary case Kaimal in the low-frequency spectrum cannot range. describe Since thethe descendingVon Karman feature spectrum of non-stationary is widely case utilized in the low-frequencyin the building range. engineering, Since the Von its Karman stationary spectrum and isnon-stationary widely utilized forms in the are building also plotted engineering, in Figure its 11. stationary It is shown and that non-stationary the stationary forms Karman are also spectrum plotted incannot Figure well 11 describe. It is shown the measured that the stationarypower spectral Karman density. spectrum The non-stationa cannot wellry describe Karman the spectrum measured can powercapture spectral most density.of the measured The non-stationary power spectral Karman spectrumdensity, canbut capturethe low-freq most ofuency the measured feature of power the spectralnon-stationary density, case but theis still low-frequency not able to be feature presented. of the Hence, non-stationary new models case need is still to not be ableutilized to be to presented. perfectly Hence,describe new the modelsnon-stationary need to bepower utilized spectral to perfectly density. describe the non-stationary power spectral density. To copecope withwith thethe facedfaced problem,problem, Tao etet al.al. [[11]] proposedproposed aa generalgeneral modelmodel forfor non-stationarynon-stationary turbulenceturbulence viavia aa modulatingmodulating functionfunction inin frequencyfrequency domain.domain. TheThe non-stationarynon-stationary empiricalempirical modelmodel isis suggested as suggested as ∗ Su(n) = A(n) × Su(n) (14) * =× ∗ Snuu() AnSn () () (14) where Su(n) is the non-stationary power spectral density; A(n) is the frequency modulating function; and S (n)*is the empirical model via nonlinear fitting. In this study, the benchmark model utilized for whereu Sn() is the non-stationary power spectral density; A()n is the frequency modulating nonlinearu fitting is selected as: Sn() nS (n) A f function; and u is the empirical modelu = via nonlinear fitting. In this study, the benchmark 2 5/3 (15) model utilized for nonlinear fitting is selected(u∗) as: (B + C f ) where A, B, C are constants to be determined. Sensors 2017, 17, 2186 12 of 14

Based on the nonlinear ﬁtting to the measured non-stationary power spectral density, the following expression by Equation (16) can be obtained. Then, a modulating function is also calculated, and its detailed expression is presented in Equation (17).

nS (n) 1.982 f u = (16) (u∗)2 (0.118 + 2.166 f )5/3  exp(1.412 ln n + 8.928) 0 ≤ n ≤ 0.0015  A(n) = exp(0.111 ln n + 0.467) 0.0015 < n ≤ 0.015 (17)  1 n > 0.015 The obtained empirical non-stationary power spectral density is also plotted in Figure 10. It can be seen that the fitted non-stationary model can perfectly satisfy with the non-stationary power spectrum, indicating the effectiveness of the empirical model obtained after modulation. The general model by Tao et al. is also verified to be effective for non-stationary turbulence. Hence, it can be inferred that more accurate results will be acquired in the buffeting analysis of long-span suspension bridges if the general model is utilized. It should be noted that the fitted spectrum is obtained with the presented 1 h long recording. Due to the distinct convective features existing in typhoon events, the non-stationary spectrum of other records may deviate from the presented fitted spectrum. Hence, the measurements still need to be accumulated to perfect the expression of the empirical model of non-stationary turbulence in typhoon winds.

5. Conclusions In this study, the non-stationary wind characteristics of a landfall typhoon at the Jiangyin Bridge site is analyzed with a comparison of the results from stationary analysis. The following conclusions can be drawn accordingly.

• The time-varying mean differs much from the constant mean for the non-stationary wind records, which means the stationary assumption is invalid. For the longitudinal and lateral turbulences of Typhoon Soudelor, the longitudinal wind speed presents stronger non-stationarity than the other case. • The non-stationary turbulence intensities are smaller than stationary ones for both longitudinal and lateral cases. The difference in the longitudinal case is more obvious than that in the lateral case, which means the non-stationarity of the longitudinal turbulence is much stronger than that of the lateral wind. • Except low wind speed cases, the suggestions from both ASCE7-10 and Chinese code generally coincide well with the measured turbulence intensities for both longitudinal and lateral cases of Typhoon Soudelor. • The two fitted models can well describe the stationary and non-stationary relationships between gust factor and turbulence intensity. Among the presented empirical models, only the Ishizaki model is similar to the fitted non-stationary expression, and can well describe the measured relationship between non-stationary gust factor and non-stationary turbulence intensity. • Non-stationary turbulence integral scales are much smaller than stationary ones, which is mainly attributed to the extraction of the time-varying mean. Detrending the non-stationary wind records will filter some low-frequency components, which reflect the large-scale eddies in turbulence. • The non-stationary power spectral density is lower than the stationary case in low-frequency ranges, while the two cases keep consistent in the rest of the ranges. This phenomenon can be well explained by the filtering of the time-varying mean, which physically performs as the low-frequency content in wind fluctuations. Sensors 2017, 17, 2186 13 of 14

• The ﬁtted non-stationary model via modulation can perfectly satisfy the measured non-stationary power spectrum, indicating the effectiveness of the general model for non-stationary turbulence. • There is a signiﬁcant difference between stationary and non-stationary wind characteristics. In light of the typhoon cases with strong non-stationarity, a shift consideration from stationarity to non-stationarity is highlighted for the analysis of wind effects.

In general, a non-stationary model to be developed is recommended to guide the design or prediction of responses of long-span bridges in the future, since non-stationary features are frequently captured in extreme wind events and accurately simulating the buffeting responses is the main purpose of engineering practices. The challenges for this shift consideration are to include the non-stationary wind effects in the all the main components including forces, the bridge system, and responses during the simulation.

Acknowledgments: The support of National Key R & D Program of China (2017YFB1201204); Project of Science and Technology Research and Development Program of China Railway Corporation (2015G002-C); and National Natural Science Foundations of China (51508580, U1534206) are gratefully acknowledged. The third author would like to acknowledge the support of National Project Funded by the China Scholarship Council (201606090054), the Fundamental Research Funds for the Central Universities, and Funding of Jiangsu Innovation Program for Graduate Education (KYLX16_0258). The authors also would like to thank Yufeng Zhang and Zhen Sun in Jiangsu Transportation Institute for providing the measured data of Jiangyin Bridge during Typhoon Soudelor. Author Contributions: All authors discussed and agreed upon the idea and made scientific contributions. Xuhui He wrote the manuscript and proposed some suggestions for the revision. Hongxi Qin conducted the analysis of the field measured data. Tianyou Tao gave the general guidance to analyze the wind data and made an exhaustive revision of this paper. Wenshuo Liu offered essential assistance on the data analysis and provided some assistance on article revisions. Hao Wang gave some meaningful suggestion on the analysis and writing of this paper. Conflicts of Interest: The authors declare no conflict of interest.

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