sensors

Article Field Monitoring and Analysis of the Vibration of Stay Cables under Typhoon Conditions

Jian Guo * and Xujiang Zhu Institute of Engineering, University of Technology, Hangzhou 310023, ; [email protected] * Correspondence: [email protected]; Tel.: +86-137-3801-7518

 Received: 15 July 2020; Accepted: 9 August 2020; Published: 12 August 2020 

Abstract: Structural health monitoring systems provide many advantages for full-scale measurements in bridge monitoring. In this study, a strong landing typhoon event recorded at the Jintang Bridge (Zhejiang Province, China) in 2019 was selected to study the nonstationary wind and cable vibration characteristics. To study the characteristics of the recorded typhoon, the time-varying mean wind was extracted based on the adaptive method of the wavelet-matrix transform. The nonstationary characteristics of Typhoon Lekima, including the turbulence intensity, gust factor, and fluctuating wind power spectral density, were analyzed and compared with the stationary model characteristics of a typhoon, and the typical characteristics and parameters were obtained. In addition, the measured vibration response of the cables was analyzed. The vibration characteristics of the cables and the energy distribution of the wind speed wavelet packet were investigated. The vibrations at different positions were compared. A power spectrum analysis and a wavelet packet energy analysis of the cable were performed. The results of this study can be used as a basis for wind-resistant design and performance evaluation of under similar operational conditions.

Keywords: sea-crossing bridge; field measurement; stay cable; wavelet-matrix transform; wavelet packet; wind characteristics; nonstationary

1. Introduction With the demand for economic development, China has built many long-span bridges, seven of which are among the ten longest main-span, cable-stayed bridges in the world [1]. However, with the increase in bridge span, the structure has become flexible, the basic natural vibration period has reached >10 s, and the damping has decreased, making such bridges more sensitive to wind-induced vibration [2]. Especially for a cable-stayed bridge, the stay cables are vulnerable components, and the buffeting effects of the stay cables are more serious. Consequently, the wind load has become the most important control factor affecting structural safety [3]. Therefore, field monitoring of the wind environment [4–6] and structure dynamic response [7] has become an important topic. Recording wind environment measurements and performing a buffeting statistical analysis of the measured data constitute the most effective way to understand the wind characteristics of a region. Previous studies of the wind characteristics of typhoons have focused on a stationary wind model hypothesis. Early investigations were conducted by Davenport [8], Kaimal et al. [9], Panofsky and Singer [10], Harris [11], and Shiotani and Iwatani [12]. These researchers have done considerable work in the field of wind characteristics measurement and have developed their own wind field models, and their results have been widely used in wind engineering specifications in various countries [13–15]. Because typhoons have obvious nonstationary characteristics that differ from those of stationary wind models, researchers have turned their attention to the study of nonstationary random wind fields under extreme weather conditions [16–19]. Based on the above premise, various nonstationary characteristics methods have been devised and their feasibility has been demonstrated. Proposed methodologies

Sensors 2020, 20, 4520; doi:10.3390/s20164520 www.mdpi.com/journal/sensors Sensors 2020, 20, 4520 2 of 20 based on empirical mode decomposition and the discrete wavelet transform have also been closely followed and further investigated in many more recent studies, including those by Xu and Chen [20], Tao et al. [21], and Huang and Chen [22], which mostly address the nonstationary characteristics of typhoons in field measurements. However, for natural wind with strong randomness, it is very difficult to formulate universal standards and use them in the wind-resistant design of various engineering structures. The most common problem is that the design is too conservative to ensure the safety of the structures or that the lack of research on wind characteristics leads to insufficient wind-resistant design and structural safety problems. Therefore, it is necessary to conduct measured research in targeted cases. In this paper, we propose that the wavelet-matrix transform (WMT) be directly applied to the nonstationary characteristics of typhoons [23,24]. Because any complex function can be described by a dense equidistant sampling data series, the discrete WMT is still general. Compared with the nonstationary characteristics analysis method mentioned above, WMT entails analyzing the essence of the wavelet transform from another aspect. It can be used to directly understand the decomposition and reconstruction of the orthogonal wavelets from the time domain, and the calculation of wavelet orthogonal decomposition through a matrix analysis is faster and easier to understand. In this study, Typhoon Lekima, which landed on the Jintang Bridge in 2019, was taken as the background object. Based on the measured data of Typhoon Lekima collected by the structural health monitoring system (SHMS), a nonstationary wind speed model suitable for the nonstationary wind speed data and the corresponding time-varying mean wind speed and fluctuating wind speed extraction method were established. Comparison with the wind resistance specifications of Chinese bridges provides a basis for the wind resistance safety assessment of the bridge based on the SHMS and provides a reference for other large structures in similar marine environments, especially for other sea-crossing bridges in Zhejiang Province.

2. Case Study The Jintang Bridge in China is a long cable-stayed bridge carrying a dual four-lane highway on the upper level of the bridge deck. The overall length and the main span of the bridge are 21.029 km and 620 m, respectively. The height of its two towers is 204 m, as measured from the base level to the tower saddle. The width of the bridge deck is 30.1 m. The bridge was opened to traffic in 2009. It is also located in a typhoon-prone area in the northwest of the Pacific Ocean. Typhoon Lekima formed as a tropical depression at the east of Luzon, Philippines, on 4 August 2019. It directly landed at Wenling City, Zhejiang Province, at 01:45 a.m. (UTC+8) on 10 August 2019, with a maximum wind force near the center of 52 m/s, and it arrived at Shanghai at 00:00 a.m. on 11 August 2019. Finally, it crossed Jiangsu Province on 10 August 2019 and moved to Shandong and its adjacent waters, from where Lekima transformed into an extratropical cyclone. From 03:00 p.m. to 05:00 p.m. on 10 August 2019, it passed the site of the Jintang Bridge. Figure1 shows the route of Typhoon Lekima and the location of the Jintang Bridge. At present, the Jintang Bridge is equipped with an overall SHMS, which is used to evaluate the health status of the bridge by monitoring the wind environment, temperature distribution, traffic distribution, bridge vibration response, and other bridge working environments. However, the existing cable vibration monitoring sensor of the Jintang Bridge is a unidirectional acceleration sensor, which can only monitor the vibration in the plane of the cables, while the actual vibration is an in-plane and out-of-plane common vibration. Therefore, to fully understand the wind-induced vibration response of the stay cables, a two-way acceleration sensor and a displacement sensor were added to the existing SHMS (see Figure2). Four sensors were installed on the longest stay cable near the side. One sensor can monitor the in-plane and out-of-plane vibration of the stay cable. Figure3 shows the field installation of the sensor, and Table1 lists the technical standard of the wireless acceleration node TZT3805. The sampling frequency of the anemometer was 32 Hz. In this study, the wind speed data collected by the anemometer on the Jintang Bridge and the data collected by the sensor on the stay cable Sensors 2020, 20, 4520 3 of 20 Sensors 2020, 20, x FOR PEER REVIEW 3 of 20 Sensors 2020, 20, x FOR PEER REVIEW 3 of 20 wereby the taken sensor as theon the research stay cable objects. were The taken wind as speed the research samples duringobjects. theThe landing wind speed period samples of the typhoon during were selected for analyzing the wind characteristics and the vibration characteristics of the stay cable. theby the landing sensor period on the of stay the cabletyphoon were were taken selected as the research for analy objects.zing the The wind wind characteristics speed samples and during the Data from Typhoon Lekima were selected from 00:00 a.m. to 06:00 a.m. on 10 August. As can be seen vibrationthe landing characteristics period of theof the typhoon stay cable. were Data selected from forTyphoon analy zLekimaing the were wind selected characteristics from 00:00 and a.m. the from Figure4, the wind speed time history of the strong wind samples has clear time-varying and tovibration 06:00 a.m. characteristics on 10 August. of theAs canstay be cable. seen Data from from Figure Typhoon 4, the wind Lekima speed were time selected history from of the 00:00 strong a.m. local mutation characteristics. windto 06:00 samples a.m. on has 10 clear August. time -Asvarying can be and seen local from mutation Figure 4characteristics., the wind speed time history of the strong wind samples has clear time-varying and local mutation characteristics.

Figure 1. Moving track of Typhoon Lekima. Figure 1. Moving track of Typhoon Lekima.

Figure 2. Sensor layout on the Jintang Bridge (in units of meters).

FigureFigure 2. 2.Sensor Sensor layoutlayout onon thethe JintangJintang BridgeBridge (in(in unitsunits ofof meters).meters).

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Sensors 2020, 20, 4520 4 of 20 Sensors 2020, 20, x FOR PEER REVIEW 4 of 20

Figure 3. Sensor field installation on the Jintang Bridge.

Table 1. Wireless acceleration node TZT3805.

Project Figure 3. Sensor fieldfield installation onTechnical the Jintang Standard Bridge. Number of channels Single and double Table 1. Wireless acceleration node TZT3805. Sampling frequency Table 1. Wireless acceleration node200 TZT3805Hz, adjustable. FrequencyProject responseProject TechnicalTechnical78 Hz Standard Standard DC NumberNumberRange of channels of channels SingleSingle and and2 doubleg double CommunicationSamplingSampling frequency frequencymode 200200 Hz, Hz, adjustable adjustable4G FrequencySamplingFrequency response method response Timing, interval, trigger, 7878 Hz Hz DC DCcontinuous acquisition Data storageRange Cloud 2 g server CommunicationRange mode 4G2 g Work time Solar energy or 220 V AC, long-term monitoring CommunicationSampling m methodode Timing, interval, trigger,4G continuous acquisition SamplingWork temperatureData method storage Timing, interval, Cloud−trigger,10 °C server to continuous +80 °C acquisition RelativeData storage humidityWork time Solar energy or 220Cloud V20% AC, –server long-term85% monitoring IP protectionWork temperature level 10 ◦C toIR67+80 ◦C Work time Solar energy or− 220 V AC, long-term monitoring IR protectionRelative level humidity 20%–85%IK10 Work temperatureIP protection level−10 ° IR67C to +80 °C

RelativeIR humidity protection level20% IK10–85% IP protection level IR67 IR protection level IK10

Figure 4. Cont.

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FigureFigure 4. 4.Measured Measured wind wind samples samples during during Typhoon Typhoon Lekima. Lekima.

3.3. Wavelet-Matrix Wavelet-Matrix Transform Transform 3.1. Daubechies Wavelet and Mallat Matrix 3.1. Daubechies Wavelet and Mallat Matrix Wavelet analysis can be used to decompose nonstationary processes in the time–frequency domain. Wavelet analysis can be used to decompose nonstationary processes in the time–frequency Except for the explicit formula of the Harr wavelet, other wavelet functions have no explicit expression. domain. Except for the explicit formula of the Harr wavelet, other wavelet functions have no explicit Let f (t) be a signal in the time domain ( , ). We call ψ(t) the mother wavelet. Wavelets are expression. Let ft() be a signal in the −∞ time∞ domain (,)−  . We call ()t the mother wavelet. generated from the mother wavelet by translation and dilation as follows: Wavelets are generated from the mother wavelet by translation and dilation as follows: 1 t b ψ ( ) = 1ψ( tb− ) a,bt =  − (1)(1) ab, ()()t √a a a a wherewherea isa is a dilationa dilation parameter parameter and andb isb is a translationa translation parameter. parameter. The The wavelet wavelet transform transform of of the the signal signal f (tft)()is definedis defined as as Z∞  ψ W f W(a, b(,)()() a) =b=f f(t t) a,b(t t)dt dt (2) f · a, b (2) − −∞ TheThe definition definition of of a a wavelet wavelet is is far far from from this this simple, simple, as as only only a a wavelet wavelet family family with with orthogonal orthogonal characteristicscharacteristics can can decompose decompose the function the functionf (t); thatft() is,; t ithat can is, be it decomposed can be decomposed into a series into of orthogonal a series of waveletorthogonal combinations, wavelet combinations, and the result and is unique. the result Only is in unique. this way Only can in the this wavelet way can be reconstructed the wavelet be backreconstructed to the original back function. to the original function. WeWe consider consider the the Daubechies Daubechies (DB4) (DB4) wavelet wavelet matrix matrix as as an an example. example. It It has has four four supporting supporting points. points. WeWe show show the the scale scale matrix matrix and and wavelet wavelet matrix matrix of of DB4. DB4. Through Through multiscale multiscale decomposition, decomposition, we we can can performperform a multiresolution a multiresolution analysis analysis of the wavelet of the matrix. wavelet Wavelet matrix. matrix Wavelet analysis matrix entails analysis decomposing entails eachdecomposing layer one byeach one layer according one by to one the according scale and to wavelet the scale coe ffiandcients wavelet and displayingcoefficients theand amplitude displaying ofthe the amplitude wavelet and of the scale wavelet of each and layer scale step of each by step.layer Instep this by process,step. In this the process, number the of signalnumber points of signal in [ ] eachpoints layer in shouldeach layer be halved. should Accordingbe halved. toAccording the above to method, the above the method, matrix A the8, 8matrixcan be A constructed[8,8] can be as follows: constructed as follows:   h h h h 0 0 0 0 First phase scale waveform  0 1 h2 h3 h h 0 0 0 0  0 1 2 3  First phase scale waveform  0 0 h00 h 01 h2 h3 h0 h 0  0Second 0 Second phase scalephase waveform scale waveform  0 1 2 3   0 0 00 0 h 0h 0 h hh  hThird h phaseThird scalephase waveform scale waveform  0 1 02 13  2 3  0 0 0 0 0 0 hh01Fourth phase scale waveform  A0[8,8] 0=  0 0 0 0 h0 h1  Fourth phase scale waveform A[8, 8] =  g0 g 1 g 2 g 3 0 0 0 0 First phase wavelet waveform  g0 g1 g2 g3 0 0 0 0  First phaseSecond wavelet phase wavelet waveform waveform  0 0g0 g 1 g 2 g 3  0 0    0 0 g00 g 01 g 02 g 03 g00 g 0 1 g 2Second g 3 Third phase phase wavelet wavelet waveform waveform   Fourth phase wavelet waveform  0 0 0 0 0 0 gg01  0 0 0 0 g0 g1 g2 g3  Third phase wavelet waveform   Here,0 the 0first 0four 0 row 0’s elements 0 g0 areg1 scaleFourth coefficients, phase wavelet and the waveform last four row’s elements are waveletHere, coefficients. the first four For row’s example, elements the are first scale row coe’sffi cients, elements and consists the last of four four row’s scale elements coefficients are (,,,h h h and h ) and four zeros on the right, which is the scale coefficient in the first phase; the wavelet0 1 coe 2 fficients.3 For example, the first row’s elements consists of four scale coefficients (h0, h1, h2,

second row’s elements is a shift of the first row of data (,,,h0 h 1 h 2 and h3 ) to the right by two

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and h3) and four zeros on the right, which is the scale coefficient in the first phase; the second row’s elements is a shift of the first row of data (h0, h1, h2, and h3) to the right by two columns, and the rest are all zeros, which is the scale coefficient in the second phase; and so on. When Row 4 shifts Row 3’s data to the right by two columns, data truncation occurs, and there are two columns of data that are out of the range of the eighth-order square matrix. As a result, there are only two nonzero data values in Row 4. The law of wavelet coefficients is similar to that of scale coefficients. In the fifth row’s elements, there are four wavelet coefficients (g0, g1, g2, and g3) and four zeros on the right, which is the wavelet coefficient in the first phase. The wavelet coefficients in the second, third, and fourth phases are similar, shifting two columns to the right. The DB4 wavelet scale coefficient and the wavelet coefficient are given by Zhang [25]. The four coefficients of scale are

1 + √3 3 + √3 3 √3 1 √3 h0 = ; h1 = ; h2 = − ; h3 = − (3) 4 √2 4 √2 4 √2 4 √2

2 + 2 + 2 + 2 = and h0 h1 h2 h3 1. This meets the condition of unitary. The corresponding four wavelet coefficients are

g = h ; g = h ; g = h ; g = h (4) 0 3 1 − 2 2 1 3 − 0 and g0 + g1 + g2 + g3 = 0, which satisfies the condition that the wavelet integral is zero. The original signal can be decomposed into Y[8] by multiplying the A[8, 8] F[8] matrix, including · the scale amplitude C[4] = c , c , c , c and the wavelet amplitude D[4] = d , d , d , d . { 0 1 2 3 { 0 1 2 3          h0 h1 h2 h3 0 0 0 0   f0   y0   c0           0 0 h h h h 0 0   f   y   c   0 1 2 3   1   1   1           0 0 0 0 h0 h1 h2 h3   f2   y2   c2           0 0 0 0 0 0 h h   f   y   c   0 1   3  =  3  =  3          (5)  g0 g1 g2 g3 0 0 0 0 · f4   y4   d0           0 0 g g g g 0 0   f   y   d   0 1 2 3   5   5   1           0 0 0 0 g0 g1 g2 g3   f6   y6   d2          0 0 0 0 0 0 g0 g1 f7 y7 d3

If we want to reconstruct the original function according to the scale and wavelet coefficients, we can use Equation (5), but the key is whether the matrix A is orthogonal. The verification is as follows:

A F = Y (6) · AT Y = F (7) · 1 As shown in the matrix, A is not an orthogonal matrix and needs to be modified as follows:   0.25 0.433      0.433 0.75     1      T  1  A A =   (8) ·  1       1     1     1 

If we move the two columns of data truncated during the shift of Rows 4 and 8 to the first and second columns of the corresponding rows circularly, then, equivalent to the original data, the eighth Sensors 2020, 20, 4520 7 of 20

and ninth data entries are not 0, but f8 = f0; f9 = f1 and g2 and g3 move to Columns 1 and 2 in Row 4, which is similar to moving g2 and g3 to Columns 1 and 2 of Row 8. Such circularly shifted matrices are called B matrices. B matrices are orthogonal matrices:    h0 h1 h2 h3 0 0 0 0     0 0 h h h h 0 0   0 1 2 3     0 0 0 0 h0 h1 h2 h3     h h 0 0 0 0 h h  B =  2 3 0 1    (9)  g0 g1 g2 g3 0 0 0 0     0 0 g g g g 0 0   0 1 2 3     0 0 0 0 g0 g1 g2 g3    g2 g3 0 0 0 0 g0 g1

BT B = E[8, 8] (10) · The improved DB4 wavelet matrix is represented by a square matrix B, and its inner part is divided into two matrices: the upper H is called the “scale matrix” and the lower G is called the “wavelet matrix.” They are all rectangular matrices: ! H[4, 8] B[8, 8] = (11) G[4, 8]

Decomposing the original data F[8] to obtain the “scale time spectrum C1[8]” and the “wavelet time spectrum D1[8]” gives          h0 h1 h2 h3 0 0 0 0   f0   y0   c0           0 0 h h h h 0 0   f   y   c   0 1 2 3   1   1   1           0 0 0 0 h0 h1 h2 h3   f2   y2   c2           h h 0 0 0 0 h h   f   y   c   2 3 0 1   3  =  3  =  3  = Y         (12)  g0 g1 g2 g3 0 0 0 0 · f4   y4   d0           0 0 g g g g 0 0   f   y   d   0 1 2 3   5   5   1           0 0 0 0 g0 g1 g2 g3   f6   y6   d2          g2 g3 0 0 0 0 g0 g1 f7 y7 d3

B F = Y (13) · 3.2. Multiscale Decomposition of the Wavelet Matrix The wavelet matrix is used to explain the process of multiscale decomposition. Suppose that the original data to be analyzed consist of 128 points and that their corresponding DB4 wavelet matrix is also a 128th-order square matrix B[128, 128]. B includes the scale matrix H[64, 128] and wavelet matrix G[64, 128], in which the H matrix is located in the upper half of the B matrix, and the G matrix is located in the lower half of the B matrix. The square brackets represent the number of rows and columns, as shown in ! H[64, 128] B[128, 128] = (14) G[64, 128] ! ! T C1  T T  C1 T T F = B = H G = H C1 + G D1 = F1 + X1 (15) · D1 · D1

Inserting the relationships of C1 and D1 into this latter equation gives   F = HTH + GTG F = HTHF + GTGF = F + X (16) · 1 1 Sensors 2020, 20, 4520 8 of 20

In this formula, HTH is called the “low-frequency filter matrix” and GTG is called the “high-frequency filter matrix.” Taking the eighth-order DB4 orthogonal matrix as an example, because the B matrix is an orthogonal square matrix, we have

BTB = BBT = E[128, 128] (17)

To calculate the next scale, we decompose the original data into a scale amplitude and a wavelet amplitude: ! H1[32, 64] B1[64, 64] = (18) G1[32, 64]

There are 64 points in total. From the wavelet amplitude, we can get the high-frequency wave X1; because it is the highest frequency, there is no need for division. To decompose the lower frequency wave F2, we start from the scale amplitude C1, so we need to introduce the 64th-order DB4 wavelet matrix in Equation (18). Note that the DB4 wavelet matrices of various scales are orthogonal matrices: ) BT B = E[128, 128] · (19) B T B = E [64, 64] 1 · 1 1 where E is the unit matrix of order 128 and E1 is the unit matrix of order 64. We regard the scale amplitude C1[64] as the original data, and we decompose and reconstruct it as follows:

(BTB ) C = (HTH + GTG ) C = FC + XC (20) 1 1 · 1 1 1 1 1 · 1 2 2 C[ ] C[ ] In addition, note that F2 64 and X2 64 are the only data at a Scale 2 level, with only 64 points. After performing a further double expansion, the low-frequency wave F2[128] and high-frequency wave X2[128] under Scale 1 are obtained as   HT FC + XC = F + X (21) · 2 2 2 2 Similarly, the wavelet decomposition of Scale 3 can be derived, and its function can be expressed as follows: F = HT(HT[HTH ]H )H F = (H H H)T(H H H) F (22) 3 1 2 2 1 · 2 1 2 1 · X = HT(HT[GTG ]H )H F = (G H H)T(G H H) F (23) 3 1 2 2 1 · 2 1 2 1 · In this paper, the form of the DB4 wavelet matrix is expressed clearly by the method of the wavelet matrix. Luckily, in the analysis of discrete wavelets, DB6, DB8, ...... , DB20 and other DB 2N (N is a positive integer) can form an orthogonal B matrix according to the method, and realize the multiscale decomposition of the signals.

3.3. Extraction of the Nonstationary Wind Model In the stationary wind speed model, when calculating the influence of wind load on the structure, it is usually assumed that the wind load consists of two parts: static action caused by mean wind and dynamic action caused by fluctuating wind. Respectively, these can expressed as

U(t) = U + u(t) (24)

V(t) = V + v(t) (25)

W(t) = W + w(t) (26) Sensors 2020, 20, 4520 9 of 20 where U, V, and W represent the mean wind speed in the longitudinal, lateral, and vertical directions, respectively; and u(t), v(t), and w(t) are the corresponding zero-mean fluctuating wind. In the nonstationary wind speed model, the wind model can be expressed as

U(t) = U∗ + u∗(t) (27)

V(t) = V∗ + v∗(t) (28)

W(t) = W∗ + w∗(t) (29) where U∗, V∗, and W∗ represent the time-varying mean wind speed in the longitudinal, lateral, and vertical directions, respectively; and u∗(t), v∗(t), and w∗(t) are the corresponding zero-mean fluctuatingSensorsSensors 20 202020, 20, wind. 20, x, xFOR FOR PEER PEER REVIEW REVIEW 9 9of of 20 20 To extract the time-varying characteristics of the nonstationary wind speed, as shown in FigureToTo5, extract theextract abovementioned the the time time-varying-varying DB10 characteristics characteristics wavelet matrix of of the the nonstationary multiscale nonstationary method wind wind speed, was speed, used as as shown forshown a 10-levelin in Figure Figure decomposition5,5 , the the abovementioned abovementioned[6,21]. With DB10 the DB10 increase wavelet wavelet in level matrix matrix number, multiscale multiscale the filtered method method frequency was was used component used for for aa becomes 1010-level-level smallerdecompositiondecomposition and the approximate[6,21]. [6,21]. With With the valuethe increase increase better in representsin level level number, number, the time-varying the the filtered filtered meanfrequency frequency value. component component Figure6 compares becomes becomes thesmallersmaller Typhoon and and the Lekima the approximate approximate constant value mean value better wind better speedrepresents represents model the the and time time the-varying- time-varyingvarying mean mean meanv valuealue.wind Figure. Figure speed 6 6compares compares model. Itthethe can Typhoon Typhoon be seen from Lekima Lekima Figure constant constant6 that the mean mean time-varying wind wind speed speed mean model model wind and and speed the the calculatedtime time-varying-varying by using mean mean the wind wind wavelet speed speed matrixmodel.model. algorithm It It can can be be seen fluctuates seen from from Figure around Figure 6 the 6that that constant the the time time mean-varying-varying wind mean mean speed wind wind calculated speed speed calculated by calculated the stationary by by using using wind the the speedwaveletwavelet model. matrix matrix Its 10-min algorithm algorithm constant fluctuates fluctuates mean along around around the the windthe constantconstant speed is mean12.33 mean m wind/ winds, the speed time-varying speed calculated calculated mean by bywind the the speedstationarystationary fluctuates wind wind betweenspeed speed model. model. 8.7 and Its Its 17.2 10 10- mmin-min/s, andconstant constant the crosswind mean mean along along speed the the iswind wind close speed tospeed the is constantis 12.33 12.33 m/s, m/s, mean the the speed. time time- - Itvaryingvarying can be seenmean mean that wind wind the speed time-varyingspeed fluctuates fluctuates mean between between wind 8.7 speed 8.7 and and can 17.2 17.2 better m/s, m/s, reflectand and the the crosswind trendcrosswind of the speed speed nonstationary is is close close to to windthethe constant constant speed. mean mean speed. speed. It It can can be be seen seen that that the the time time-varying-varying mean mean wind wind speed speed can can better better reflect reflect the the trendtrend of of the the nonstationary nonstationary wind wind speed. speed.

FigureFigureFigure 5.5. 5. Wavelet-matrixW Waveletavelet-matrix-matrix transformtransform transform (WMT)(W (WMTMT) decompositiondecomposition) decomposition ofof of thethe the LekimaLekima Lekima data.data data. .

(a()a ) (b(b) )

FigureFigureFigure 6.6. 6. ComparisonComparison Comparison ofof of thethe the constantconstant constant meanmean mean andand and time-varyingtime time-varying-varying meanmean mean windwind wind speeds:speeds: speeds: ((a a)()a longitudinal)longitudinal longitudinal component;component;component; ((bb ()b) laterallateral) lateral component.component. component.

4.4. Field Field M Measurementseasurements and and W Windind C Characteristicsharacteristics

4.1.4.1. Turbulence Turbulence I ntensityIntensity TurbulenceTurbulence intensity intensity is is an an important important characteristic characteristic to to describe describe the the variation variation in in wind wind speed speed with with timetime and and space space and and the the relative relative intensity intensity of of the the fluctuating fluctuating wind wind speed. speed. Based Based on on the the turbulence turbulence intensityintensity calculation calculation formula formula of of the the stationary stationary wind wind speed speed model, model, the the time time-varying-varying mean mean wind wind speed speed ofof the the nonstationary nonstationary wind wind speed speed model model and and the the corresponding corresponding fluctuating fluctuating wind wind speed speed are are substituted. The turbulence intensity of the nonstationary wind speed model, I  , is expressed as the substituted. The turbulence intensity of the nonstationary wind speed model, Ii ,i is expressed as the ratioratio of of the the standard standard deviation deviation of of the the fluctuating fluctuating wind wind speed speed to to the the interval interval TT, ,the the time time-varying-varying meanmean wind wind speed: speed:  (30) I==i i ,, i u v (30) Ii i==,, i u v UU

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4. Field Measurements and Wind Characteristics

4.1. Turbulence Intensity Turbulence intensity is an important characteristic to describe the variation in wind speed with time and space and the relative intensity of the fluctuating wind speed. Based on the turbulence intensity calculation formula of the stationary wind speed model, the time-varying mean wind speed of the nonstationary wind speed model and the corresponding fluctuating wind speed are substituted.

TheSensors turbulence 2020, 20, x FOR intensity PEER REVIEW of the nonstationary wind speed model, Ii∗, is expressed as the ratio10 of of the 20 standard deviation of the fluctuating wind speed to the interval T, the time-varying mean wind speed:   ==i (31) Ii σi  ,, i u v Ii = , i = u, v (30) UU  where Ii and Ii are the stationary wind speed model and nonstationary wind speed model σi I∗ = ∗ , i = u, v (31) turbulence intensities, respectively;  andi   the corresponding standard deviations; u and v u Uu∗ represents the bridge in the longitudinal and lateral, respectively; and, according to China’s code, T where Ii and Ii∗ are the stationary wind speed model and nonstationary wind speed model turbulence = 10 min this study. [14]. intensities, respectively; σu and σu∗ the corresponding standard deviations; u and v represents the bridge   in theIt longitudinal can be seen and from lateral, Figure respectively; 7 that, in the and, typhoon according period, to China’s the turbulence code, T = 10intensities min this study.Iu and [14 I].v calculatedIt can based be seen on from the nonstationary Figure7 that, wind in the speed typhoon model period, in the thedownwind turbulence and intensitiescrosswind directions,Iu∗ and Iv∗ calculated based on the nonstationary wind speed model in the downwind and crosswind directions, respectively, are lower than those in the stationary wind speed models ( Iu and Iv ), which are quite respectively, are lower than those in the stationary wind speed models (I and I ), which are quite different in some periods, indicating that the results of the stationary windu speed vmodel offer greater different in some periods, indicating that the results of the stationary wind speed model offer greater safety. The turbulence intensity along the wind direction is greater than that across the wind safety. The turbulence intensity along the wind direction is greater than that across the wind direction. direction. Values of the average I and I of Typhoon Lekima based on the stationary wind speed Values of the average Iu and Iv ofu Typhoonv Lekima based on the stationary wind speed model are 19.52% and 12.4%, respectively, while the values of average I and I based on the nonstationary wind model are 19.52% and 12.4%, respectively, while the valuesu∗ of averagev∗ Iu and I v based on the speednonstationary model are wind 18.07% speed and model 11.56%. are 18.07% and 11.56%.

FigureFigure 7.7. ComparisonComparison ofof thethe turbulenceturbulence intensitiesintensities ofof TyphoonTyphoon LekimaLekima withwith aa 10-min 10-min duration. duration.

4.2. Gust Factor In the traditional stationary model, the gust factor is defined as the ratio of the maximum gust

wind speed during the gust duration Tg to the mean wind speed in the basic time interval T. For the nonstationary gust factor, it is expressed as the maximum ratio of the mean value of the original wind speed to the mean value of the time-varying average wind speed during the gust duration. These are expressed as follows

max[Ut (gT )] (32) Gug(,) t T = U

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4.2. Gust Factor In the traditional stationary model, the gust factor is defined as the ratio of the maximum gust wind speed during the gust duration Tg to the mean wind speed in the basic time interval T. For the nonstationary gust factor, it is expressed as the maximum ratio of the mean value of the original wind speed to the mean value of the time-varying average wind speed during the gust duration. These are expressedSensors 2020 as, 20 follows, x FOR PEER REVIEW 11 of 20 max[U(t )]  g T Gu(tg, T) = Ut() (32) Sensors 2020, 20, x FOR PEER REVIEW G ( t , T )= max U g  11 of 20 (33) ug     Ut()  U(tg)g    T Gu∗ (tg, T) = max Ut()g  (33)     (33) Gug( t , T )= max Ue (t ) where Gug(,) t T and Gug(,) t T are the gust factors ∗ ing theT stationary model and the gust factors Ut()  g  where G (t , T) and G (t , T) are the gust factors in the stationaryT model and the gust factors in the in the nonstationaryu g u∗ model,g respectively; Ut()g is the mean value of the original wind speed where Gug(,) t T and Gug(,) t T are the gust factors in the stationary model and the gust factors nonstationary model, respectively; U(tg) is the mean value of the original wind speed recorded during recordedin the during nonstationary the gust model, duration respectively; tg ; and UtUt()() gis theis the mean mean value value of the of theoriginal variable wind mean speed wind the gust duration tg; and Ue∗(tg) is the mean valueg of the variable mean wind speed during the gust  durationspeed duringtg. the gust duration tg . recorded during the gust duration tg ; and Ut()g is the mean value of the variable mean wind AsAs shown shown in in Figure Figure8 ,8 the, the gust gust factors factors of of the the stationary stationary wind wind speed speed model model and and the the nonstationary nonstationary speed during the gust duration tg . windwind speed speed model model are are compared. compared. It It can can be be seen seen from from that that the the gust gust factors factors of of stationary stationary wind wind speed speed model andAs nonstationary shown in Figure wind 8, the speedgust factor models of the have stationary a similar wind fluctuation speed model trend and the and nonstationary amplitude size, modelwind and speed nonstationary model are comparedwind speed. It canmodel be seen have from a similar that the fluctuation gust factors trend of stationary and amplitude wind speed size , but but the gust factor of the stationary model is larger than that of the nonstationary model. the gustmodel factor and nonstationaryof the stationary wind model speed modelis larger have than a similar that of fluctuation the nonstationary trend and amplitudemodel. size, but the gust factor of the stationary model is larger than that of the nonstationary model.

FigureFigureFigure 8. 8.Comparison Comparison 8. Comparison of of of the the the gust gust gust factors factors of ofof Typhoon Typhoon Lekima Lekima Lekima with with with a 10 a a 10-min- min10-min duration. duration. duration.

TaoTao [21 Tao [21]] and [21] and He and He [17 He ] [17] reported [17] reported reported that the that that gust the factor g gustust was factor factor closely wa was s closely related closely related to relatedthe longitudinal to the to longitudinalthe longitudinal turbulence intensity.turbulenceturbulence Figure intensity. 9 intensity. shows Figure the Figure relationship 9 9shows shows between the the relationship the gust between factor between and the the longitudinal gust gust factor factor and turbulence andlongitudinal longitudinal intensity turbulence intensity under the stationary model and nonstationary model. underturbulence the stationary intensitymodel under andthe stationary nonstationary model model. and nonstationary model.

FigureFigure 9. Stationary 9. Stationary and and nonstationary nonstationary gustgust factors versus versus turbulence turbulence intensity. intensity.

Many scholars have fitted the relationship between gust factor and longitudinal turbulence Figure 9. Stationary and nonstationary gust factors versus turbulence intensity. intensity [26,27]. The expressions of the relationship between gust factor and the intensity of longitudinal turbulence are presented based on the linear model and the nonlinear model, which can Many scholars have fitted the relationship between gust factor and longitudinal turbulence be expressed in one equation as follows: intensity [26,27]. The expressions of the relationship between gust factor and the intensity of longitudinal turbulence are presented based on the linear model and the nonlinear model, which can be expressed in one equation as follows:

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Many scholars have fitted the relationship between gust factor and longitudinal turbulence intensity [26,27]. The expressions of the relationship between gust factor and the intensity of longitudinal turbulence are presented based on the linear model and the nonlinear model, which can be expressed in one equation as follows:

k2 T Gu(tg, T) = 1 + k1Iu In( ) (34) tg where Ishizaki suggested k1 = 0.5, k2 = 1.0 for typhoons [28]; Choi suggested k1 = 0.62, k2 = 1.27 [29]; Cao suggested k1 = 0.5, k2 = 1.15 for Typhoon Maemi [30]; Tao et al. suggested k1 = 0.26, k2 = 0.91 for a nonstationary model [21]; and He et al. suggested k1 = 0.45, k2 = 0.96 for a nonstationary model [17]. The relationship between gust factor and turbulence intensity under typhoon Lekima were fitted for comparison. Where the stationary model suggests k1 = 0.57, k2 = 1.12 and the nonstationary model suggests k1 = 0.49, k2 = 1.18. As shown in Figure 10, the stationary model proposed in this study is similar to the He model, and the nonstationary model proposed in this study is similar to Cao model. The two fitting models proposed in this study can well describe the stationary and nonstationary relationshipsSensors 20 between20, 20, x FOR the PEER gust REVIEW factor and turbulence intensity. 13 of 20

FigureFigure 10. Comparison10. Comparison of of thethe measured longitudinal longitudinal spectra spectra of Typhoon of Typhoon Lekima Lekimaand the Kaimal and the Kaimalspectrum. spectrum.

4.3. TurbulenceAs shown Power in Spectral Figure Density10, the low frequency part of the power spectral density values based on the stationary model are smaller than the power spectral density values based on the nonstationary Amodel. fluctuating The windestimated speed power can be spectral regarded density as the values superposition based on ofthe vortices stationary with and di ff nonstationaryerent frequency componentsmodels inare space. slightly Tolarger determine than the Kaimal the contribution spectrum of the of high different frequency frequency part. In componentsthe low frequency to the fluctuatingpart, windthe power energy, spectral the power density spectral values density of the ofstationary the fluctuating model were wind smaller can be than obtained the Kaimal by using the Fourierspectrum, transform while ofpower the autocorrelationspectral density values function of the of the nonstationary fluctuating model wind. were Through consistent numerous with the field measurementsKaimal spectrum. of strong wind, many effective models of fluctuating wind spectra have been established. Among them, the Kaimal spectrum is adopted by China’s Code for “Wind-resistant Design of Highway 5. Buffeting Response Analysis of the Cables Based on the Measured Data Bridges” as the downwind fluctuating wind spectrum model [14]. For example, the expressions for the Kaimal5.1. spectrum The RMS corresponding Value of the Measured to the Cable stationary Acceleration and nonstationary Response wind speed models are as follows: As one of the main load-bearing components of cable-stayed bridges, the cables themselves are nS(n) 200(nz/U) flexible components. With the rapid growth= of the span of cable-stayed bridges, wind load plays a(35) 2 5/3 key role in cable design, as wind loadu can seriously[ + endanger( )] the durability and safety of cable-stayed ∗ 1 50 nz/U bridges. Cables become a vulnerable component [31]. Therefore, field testing of cable vibration response is crucial [3]. In this study,nS∗( then) acceleration200(nz response/U∗) of the longest stay cable of the Jintang = (36) Bridge was analysed. Figures 11 and2 12 shows the vibration5/3 response of this stay cable during eu ∗ Typhoon Lekima captured by the SHMS.∗ [1 + 50(nz/U )]

(a)

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In Equations (35) and (36), the power spectral density for stationary and nonstationary is expressed, respectively; z is the height from the ground; n is the natural frequency of fluctuating wind; and u and eu are the stationary and nonstationary friction wind speed, respectively. The friction wind speed cannot be measured directly but, because it is related to the mean square deviation of fluctuating wind, it can be obtained by the following energy normalization formulas:

2 2 Figure 10. Comparison of the measured longitudinalσ = 6u spectra of Typhoon Lekima and the Kaimal (37) ∗ spectrum. σ2 = 6u2 (38) ∗ ∗ As shown in Figure 10, the low frequency part of the power spectral density values based on the As shown in Figure 10, the low frequency part of the power spectral density values based on the stationary model are smaller than the power spectral density values based on the nonstationary stationary model are smaller than the power spectral density values based on the nonstationary model. model. The estimated power spectral density values based on the stationary and nonstationary The estimated power spectral density values based on the stationary and nonstationary models are models are slightly larger than the Kaimal spectrum of the high frequency part. In the low frequency slightly larger than the Kaimal spectrum of the high frequency part. In the low frequency part, the power part, the power spectral density values of the stationary model were smaller than the Kaimal spectral density values of the stationary model were smaller than the Kaimal spectrum, while power spectrum, while power spectral density values of the nonstationary model were consistent with the spectral density values of the nonstationary model were consistent with the Kaimal spectrum. Kaimal spectrum. 5. Buffeting Response Analysis of the Cables Based on the Measured Data 5. Buffeting Response Analysis of the Cables Based on the Measured Data 5.1. The RMS Value of the Measured Cable Acceleration Response 5.1. The RMS Value of the Measured Cable Acceleration Response As one of the main load-bearing components of cable-stayed bridges, the cables themselves are flexibleAs components. one of the main With load the- rapidbearing growth components of the span of cable of cable-stayed-stayed bridges, bridges, the windcables load themselves plays a key are roleflexible in cable components. design, as With wind the load rapid can growth seriously of the endanger span of the cable durability-stayed andbridges, safety wind of cable-stayed load plays a bridges.key role in Cables cable design, become as a wind vulnerable load can component seriously endanger [31]. Therefore, the durability field testing and safety of cable of cable vibration-stayed responsebridges. is Cables crucial become [3]. In this a vulnerable study, the componentacceleration [31]. response Therefore, of the longest field testing stay cable of cable of the vibration Jintang Bridgeresponse was is analysed. crucial [3]. Figures In this 11 study, and 12 the shows acceleration the vibration response response of the of longest this stay stay cable cable during of the Typhoon Jintang LekimaBridge captured was analysed. by the Figure SHMS.s 11 and 12 shows the vibration response of this stay cable during Typhoon Lekima captured by the SHMS.

Sensors 2020, 20, x FOR PEER REVIEW 14 of 20 (a)

(b)

Figure 11. Measured acceleration of the upstream stay cable: (a) in plane; (b) out of plane. Figure 11. Measured acceleration of the upstream stay cable: (a) in plane; (b) out of plane.

(a)

(b)

Figure 12. Measured acceleration of the downstream stay cable: (a) in plane; (b) out of plane.

Figure 13 shows the relationship between the root mean square value of the 1-min-average acceleration and the 1-min-average wind speed. With the increase in wind speed, the in-plane and out-of-plane acceleration responses of the upstream and downstream stay cables exhibited a certain randomness, without obvious regularity, but the in-plane vibration was slightly greater than the out- of-plane vibration, and the vibration response was small and thus the control effect of the damper was very good.

(a)

SensorsSensors 20 202020, ,20 20, ,x x FOR FOR PEER PEER REVIEW REVIEW 1414 ofof 2020

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((bb)) (b) FigureFigure 11. 11. Measured Measured acceleration acceleration of of the the upstream upstream stay stay cable: cable: ( (aa)) in in plane; plane; ( (bb)) out out of of plane. plane. Sensors 2020, 20, 4520 14 of 20 Figure 11. Measured acceleration of the upstream stay cable: (a) in plane; (b) out of plane.

((aa)) (a)

((bb)) Figure 12. Measured acceleration of the downstream(b) stay cable: (a) in plane; (b) out of plane. FigureFigure 12. 12. Measured Measured acceleration acceleration of of the the downstream downstream stay stay cable: cable: ( (aa)) in in plane; plane; ( (bb)) out out of of plane. plane. FigureFigure 13 12.shows Measured the relationship acceleration of between the downstream the root stay mean cable: square (a) in plane; value (b of) out the of 1-min-average plane. accelerationFigureFigure and 1 133 showsshows the 1-min-average the the relationship relationship wind between between speed. With the the root root the meanincrease mean square square in wind value value speed, of of the the the 1 1 in-plane--minmin--averageaverage and out-of-planeaccelerationaccelerationFigure 1 accelerationand3and shows thethe 1 1- the-minmin responses relationship--averageaverage of windwind the between upstream speed.speed. the WithWith and root thethe downstream mean increaseincrease square ininstay wind wind value cables speed,speed, of exhibited the thethe 1- mininin--planeplane a-average certain andand out-of-plane acceleration responses of the upstream and downstream stay cables exhibited a certain randomness,accelerationout-of-plane andacceleration without the 1- obviousmin responses-average regularity, windof the speed. butupstream the With in-plane and the downstream increase vibration in waswindstay slightlycables speed, exhibited greaterthe in-plane thana certain and the randomness, without obvious regularity, but the in-plane vibration was slightly greater than the out- out-of-planeoutrandomness,-of-plane vibration,acceleration without obvious and responses the vibrationregularity, of the response but upstream the in was-plane and small downstream vibration and thus was the stay slightly control cables greater e ffexhibitedect of than the a damperthe certain out- of-plane vibration, and the vibration response was small and thus the control effect of the damper wasrandomness,of-plane very good.vibration, without and obvious the vibration regularity, response but the was in-plane small vibration and thus was the slightlycontrol effectgreater of than the thedamper out- ofwaswas-plane very very vibration, good. good. and the vibration response was small and thus the control effect of the damper was very good.

Sensors 2020, 20, x FOR PEER REVIEW 15 of 20 ((aa))

(a)

(b)

FigureFigur 13.e 13.Root Root mean mean square square stay stay cable cable acceleration acceleration response response versus versus mean mean wind wind speed: speed (:a ()a Upstream;) Upstream; (b()b Downstream.) Downstream.

5.2.5.2. Spectral Spectral Analysis Analysis of of the the Cable’s Cable’s Measured Measured Acceleration Acceleration Response Response TheThe fast fast Fourier Fourier transform transform method method was used was to usedanalyze to theanalyze in-plane the and in out-of-plane-plane and acceleration out-of-plane responseacceleration of the response cable, andof the the cable, results and are the shown results in are Figure shown 14. in The Figure amplitude 14. The of amplitude the in-plane of the and in- plane and out-of-plane vibration on the same cable was different, but the vibration characteristics were very similar, with the frequency values of each order being nearly the same.

Figure 14. Spectra of the stay cable acceleration response.

5.3. Wavelet Packet Energy Analysis of the Cable’s Measured Acceleration Response To investigate the wavelet packet energy distribution of the stay cable of the Jintang Bridge during Typhoon Lekima, the acceleration response data collected by the longest stay cable sensor of the Jintang Bridge was used to calculate the wavelet packet energy spectrum over 1-min intervals. It has been pointed out that the multi-scale analysis of the bridge’s structure vibration response using DB wavelet can achieve good results [32–34]. The DB10 wavelet function was used, the decomposition level was 5, and the characteristic frequency band was the band of the first 32 largest energy coefficients.

Sensors 2020, 20, x FOR PEER REVIEW 15 of 20

(b)

Figure 13. Root mean square stay cable acceleration response versus mean wind speed: (a) Upstream; (b) Downstream.

5.2. Spectral Analysis of the Cable’s Measured Acceleration Response The fast Fourier transform method was used to analyze the in-plane and out-of-plane Sensors 2020, 20, 4520 15 of 20 acceleration response of the cable, and the results are shown in Figure 14. The amplitude of the in- plane and out-of-plane vibration on the same cable was different, but the vibration characteristics out-of-planewere very similar, vibration with on the the frequency same cable values was diofff eacherent, order but thebeing vibration nearly the characteristics same. were very similar, with the frequency values of each order being nearly the same.

Figure 14. Spectra of the stay cable acceleration response. Figure 14. Spectra of the stay cable acceleration response. 5.3. Wavelet Packet Energy Analysis of the Cable’s Measured Acceleration Response 5.3. Wavelet Packet Energy Analysis of the Cable’s Measured Acceleration Response To investigate the wavelet packet energy distribution of the stay cable of the Jintang Bridge during TyphoonTo Lekima, investigate the acceleration the wavelet response packet dataenergy collected distribution by the longestof the stay stay cable sensor of the of Jintang the Jintang Bridge Bridgeduring was Typhoon used to Lekima, calculate the the acceleration wavelet packet response energy data spectrum collected over by the 1-min longest intervals. stay cable It has sensor been of pointedthe Jintang out that Bridge the multi-scale was used to analysis calculate of thethe bridge’swavelet structurepacket energy vibration spectrum response over using 1-min DB intervals. wavelet It canhas achieve been pointed good results out that [32– the34]. multi The DB10-scale wavelet analysis function of the bridge was used,’s structure the decomposition vibration response level was using 5, andDB the wavelet characteristic can achieve frequency good band results was the [32 band–34 of]. theThe first DB10 32 largest wavelet energy function coeffi cients. was used, the decompositionAs shown in Figurelevel was 15, the5, and energy the characteristic of Typhoon Lekima frequency was mainlyband was distributed the band in of the the first first frequency 32 largest bandenergy (0–4 coefficients. Hz), with an average energy ratio of 96.1%. The acceleration signals of the stay cables were analysed through wavelet energy analysis at the same time. As shown in Figure 16, the in plane vibration was mainly distributed in the 11th frequency band (31.25–34.375 Hz), with the upstream and downstream parts accounting for 51.6% and 27.1%, respectively, while the out of plane vibration was mainly distributed in the first frequency band, with the upstream and downstream parts accounting for 22.2% and 17.1%, respectively. It can be concluded that the out of plane vibration of the stay cables mainly occurred during the typhoon and these vibrations were of low frequency. In addition, the distribution of the typhoon energy in the high-frequency band was narrow, but the in-plane vibration energy of the stay cable was distributed over a wide range, which shows that a certain out of plane vibration mode of the stay cable existed in the 11th band. Sensors 2020, 20, x FOR PEER REVIEW 16 of 20 Sensors 2020, 20, x FOR PEER REVIEW 16 of 20 As shown in Figure 15, the energy of Typhoon Lekima was mainly distributed in the first As shown in Figure 15, the energy of Typhoon Lekima was mainly distributed in the first frequencyfrequency band band (0 –(04– Hz),4 Hz), with with an an average average enenergy ratioratio of of 96.1%. 96.1%. The The acceleration acceleration signals signals of the of staythe stay cablescables were were analysed analysed through through wavelet wavelet energy energy analysis atat the the same same time. time. As As shown shown in Figurein Figure 16, the16, the in planein plane vibration vibration was was mainly mainly distributed distributed inin the 11th11th frequencyfrequency band band (31.25 (31.25–34.375–34.375 Hz), Hz), with with the the upstreamupstream and and downstream downstream parts parts accounting accounting forfor 51.6% and and 27.1%, 27.1%, respectively, respectively, while while the the out outof plane of plane vibrationvibration was was mainly mainly distributed distributed in in the the firstfirst frequency band,band, with with the the upstream upstream and and downstream downstream partsparts accounting accounting for for 22.2% 22.2% and and 17.1%, 17.1%, respectively. respectively. ItIt cancan be be concluded concluded that that the the out out of planeof plane vibration vibration of theof thestay stay cables cables mainly mainly occurred occurred during during thethe typhoon andand these these vibrations vibrations were were of lowof low frequency. frequency. In addition,In addition, the t hedistribution distribution of of the the typhoon typhoon energyenergy inin thethe high high-frequency-frequency band band was was narrow, narrow, but butthe the in-plane vibration energy of the stay cable was distributed over a wide range, which shows that a in-plane vibrationSensors 2020 20energy of the stay cable was distributed over a wide range, which shows that a certain out of plane, , 4520 vibration mode of the stay cable existed in the 11th band. 16 of 20 certain out of plane vibration mode of the stay cable existed in the 11th band.

Figure 15. Energy distribution of the typhoon wavelet packet . FigureFigure 15. Energy 15. Energy distribution distribution of of the the typhoon typhoon wavelet wavelet packet. packet.

FigureFigure 16. 16. EnergyEnergy distribution distribution of of the the cable cable wavelet wavelet packet. packet. In view of the above energy analysis of the typhoon and stay cables, we again make a separate In comparativeview of the analysis above ofenergy the data analysis in the first of frequencythe typhoon band and and stay the 11th cables, frequency we again band betweenmake a separate comparativethe period analysis of Typhoon Figureof the Lekima data16. Energy andin the the distribution normalfirst frequency climate of conditions the band cable and windwavelet the period. 11th packet Itfrequency can. be seen band from between the periodFigures of Typhoon17 and 18 that, Lekima in the 1stand frequency the normal band, climate for the normal condition climates wi conditions,nd period. the windIt can period be seen from FigureIn viewsfor 17 theof and in-planethe18 abovethat, and in out-of-planeenergy the 1st analysisfrequency vibrations of band, of the the staytyphoonfor cablesthe normal upstreamand stay climate and cables, downstream condition we again weres, the higher make wind aperiod separate comparativefor the inthan- planeanalysis those and during ofout thethe-of typhoon- planedata period, invibrations the whereas, first of frequency the in the stay 11th cables frequency band upstream and band, the for and the11th typhoondownstream frequency period, thewereband higher between in-plane vibrations of the stay cables upstream and downstream were higher than those in the normal the thanperiod thoseclimate of Typhoonduring conditions the Lekima ty windphoon period, and period, which the indicateswhereas,normal that climate in the the high-order 11th condition frequency vibrations wi ofband,nd the stayperiod. for cable the isIttyphoon caused can be period seen from, Figurethes in 17-planeby and the18 typhoon.vibrations that, in Attention theof the 1st should stay frequency thereforecables upstream band, be paid tofor theand the high-order, downstreamnormal vortex-induced climate were condition higher vibrations thans, of the thethose wind in theperiod for thenormal in-planestay climate cables, and condition to out avoid-of fatigue-splane wind damage vibrationsperiod to, which the stayof theindicates cables. stay cables that the upstream high-order and vibration downstream of the stay were cable higher thanis those caused during by the the typhoon. typhoon Attention period, whereas, should therefore in the 11th be paid frequency to the band,high-order for the, vortex typhoon-induced period , the vibrationsin-plane vibrations of the stay cablesof the, tostay avoid cables fatigue upstream damage and to the downstream stay cables. were higher than those in the normal climate conditions wind period, which indicates that the high-order vibration of the stay cable is caused by the typhoon. Attention should therefore be paid to the high-order, vortex-induced vibrations of the stay cables, to avoid fatigue damage to the stay cables.

Sensors 2020, 20, x FOR PEER REVIEW 17 of 20 SensorsSensors2020 2020, 20, 20, 4520, x FOR PEER REVIEW 1717 of of 20 20

(a) (a)

(b) (b) Figure 17. Energy distribution of the wavelet packet in the first frequency band of the cable: (a) FigureFigure 17. 17.Energy Energy distribution distribution of of the the wavelet wavelet packet packet in in the the first first frequency frequency band band of of the the cable: cable (: a()a) Upstream; (b) Downstream. Upstream;Upstream; (b ()b Downstream.) Downstream.

(a) (a) Figure 18. Cont.

SensorsSensors2020 2020, 20, 20, 4520, x FOR PEER REVIEW 1818 of of 20 20

(b)

FigureFigure 18. 18.Energy Energy distribution distribution of of wavelet wavelet packet packet in in the the 11th 11th frequency frequency band band of of the the cable: cable (:a ()a Upstream;) Upstream; (b()b Downstream.) Downstream.

6.6. Conclusions Conclusions TheThe nonstationary nonstationary characteristics characteristics of of Typhoon Typhoon Lekima Lekima and and the the energy energy bu buffetingffeting response response distributiondistribution of of the the cable cable acceleration acceleration of of the the Jintang Jintang Bridge Bridge were were analysed. analysed. The The following following conclusions conclusions cancan be be drawn: drawn: 1. The1. turbulenceThe turbulence intensity intensity in the in nonstationary the nonstationary model model is smaller is smaller than that than in thethat stationary in the stationary model, and themodel, safety and factor the safety of the factor stationary of the stationary model is higher, model whichis higher, is relatively which is relatively conservative. conservative In the . engineeringIn the engineering application, application, the stationary the modelstationary can bemodel used can for be design used reference.for design reference. 2. The2. twoThe fitting two fitting models models proposed proposed in this study in this can well study describe can well the stationary describe theand stationarynonstationary and relationshipsnonstationary between relationships the gust factor between and the turbulence gust factor intensity. and turbulence The stationary intensity. model The proposed stationary in thismodel study proposed is similar in to thisthe He study model, is similar and the to nonstationary the He model model, and proposed the nonstation in thisary study model is similarproposed to the Cao in this model. study is similar to the Cao model. 3. In3. theIn low the frequencylow frequency part, thepart, power the power spectral spectral density density values ofvalues the stationary of the stationary model were model smaller were thansmaller the Kaimal than spectrum, the Kaimal while spectrum, the power spectralwhile the density power values spectral of the density nonstationary values model of the werenonstationary consistent with model the Kaimal were spectrum. consistent It shows with thatthe theKa nonstationaryimal spectrum. model It is shows more suitable that the for windnonstationary spectrum model estimation. is more suitable for wind spectrum estimation. 4. The4. measuredThe measured vibration vibration characteristics characteristics of the of the upstream upstream and and downstream downstream cables cables have have obvious obvious regularity.regularity. The in-planeThe in-plane vibration vibration or out or of out plane of plane vibration vibration of the of same the same cable cable is very is similar,very similar, and the outand of the plane out vibration of plane isvibration greater than is greater the in-plane than the vibration, in-plane which vibration, shows which that the shows damper that has the a gooddamper effect has on suppressinga good effect the on in-planesuppressing vibration. the in-plane vibration. 5. The5. energyThe energy distribution distribution in and in out and of out the cableof the plane cable are plane diff erent are different between between the typhoon the typhoon period and theperiod normal and climatethe normal condition climate wind condition period. wind It is period mainly. It concentrated is mainly concentrated in the first frequency in the first bandfrequency (0–3.125 Hz)band and (0– the3.125 11th Hz) frequency and the 11th band frequency (31.25–34.375 band Hz);(31.25 so,–34.375 we should Hz); so pay, we special should attentionpay specialto the high-order, attention tovortex-induced the high-order vibration, vortex of-induced the cables vibration during ofa typhoon. the cables during a typhoon. In general, considering the difference in wind environments in different regions, it is necessary to study theIn g extremeeneral, considering value distribution the difference of the nonstationary in wind environment buffeting responses in different of long-span, regions, it cable-stayed is necessary bridgesto study in the a sea extreme environment, value distribution and form of the the engineering nonstationary practice buffeting that canresponse accurately of long simulate-span, cable the - bustayedffeting bridges response in undera sea environment, extreme wind and conditions form the to engineering guide the design. practice that can accurately simulate the buffeting response under extreme wind conditions to guide the design. Author Contributions: This paper is a scientific manuscript incorporating contributions from all the authors. J.G. wroteAuthor the manuscriptContributions: and wasThis responsiblepaper is a scientific for the field manuscript measurement incorporating data analysis contributions in this study. from X.Z. all provided the authors. the necessaryJ.G. wrote help the in manuscript the writing and and analysis was responsible and made for detailed the field revisions. measurement All authors data have analysis read andin this agreed study. to the X.Z. publishedprovided version the necessary of the manuscript. help in the writing and analysis and made detailed revisions. All authors have read and Funding:agreed toThe the support published of the version KeyR&D of the Program manuscript. Projects in Zhejiang Province (2019C03098), the National Natural Science Foundation of China (U1709207, 51578506), The Program for Science and Technology of Zhejiang Provincial DepartmentFunding: The of Transportation support of the (2017027). Key R&D Program Projects in Zhejiang Province (2019C03098), the National Natural Science Foundation of China (U1709207, 51578506), The Program for Science and Technology of Conflicts of Interest: The authors declare no conflict of interest. Zhejiang Provincial Department of Transportation (2017027).

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References

1. Guo, J. Key technical innovation of Xihoumen Bridge—The longest steel box gird in the world. Eng. Sci. 2010, 8, 18–22, CNKI:SUN:ENSC.0.2010-04-004. 2. Xu, Y.L.; Zhu, L.D. Buffeting response of long-span cable-supported bridges under skew winds. Part 2: Case study. J. Sound. Vib. 2005, 281, 675–697. [CrossRef] 3. Ni, Y.Q.; Wang, X.Y.; Chen, Z.Q.; Ko, J.M. Field observations of rain-wind-induced cable vibration in cable-stayed Dongting Lake Bridge. J. Wind Eng. Ind. Aerodyn. 2007, 95, 303–328. [CrossRef] 4. Liu, M.; Liao, H.L.; Li, M.S.; Ma, C.M.; Yu, M. Long-term field measurement and analysis of the natural wind characteristics at the site of Xi-hou-men Bridge. J. Zhejiang Univ. Sci. A 2012, 13, 197–207. [CrossRef] 5. Guo, Z.W.; Yuan, H.; Wang, X.S. Field measurement of non-stationary characteristics at site of Qingcaobei Yangtze River Bridge in Three Gorges. J. Build. Struct. 2019, 40, 11–18. [CrossRef] 6. Wang, H.; Wu, T.; Tao, T.Y.; Li, A.Q.; Kareem, A. Measurements and analysis of non-stationary wind characteristics at Sutong Bridge in Typhoon Damrey. J. Wind Eng. Ind. Aerodyn. 2016, 151, 100–106. [CrossRef] 7. Fenerci, A.; Oiseth, O. Strong wind characteristics and dynamic response of a long-span suspension bridge during a storm. J. Wind Eng. Ind. Aerodyn. 2018, 172, 116–138. [CrossRef] 8. Davenport, A.G. The spectrum of horizontal gustiness near the ground in high wind. Q. J. R. Meteorol. Soc. 1961, 87, 194–211. [CrossRef] 9. Kaimal, J.C.; Wyngaard, J.C.; Izumi, Y.; Cote, O.R. Spectral characteristics of surface layer turbulence. Q. J. R. Meteorol. Soc. 1972, 98, 563–589. [CrossRef] 10. Panofsky, H.A.; Singer, I.A. Vertical structure of turbulence. Q. J. R. Meteorol. Soc. 1965, 91, 339–344. [CrossRef] 11. Harris, R.I. Some further thoughts on the spectrum of gustiness in strong winds. J. Wind Eng. Ind. Aerodyn. 1990, 33, 461–477. [CrossRef] 12. Shiotani, M.; Iwatani, Y. Horizontal Space Correlations of Velocity Fluctuations during Strong Winds. J. Meteor. Soc. Jpn. 1976, 54, 59–67. [CrossRef] 13. Architectural Institute of Japan. Recommendations for Loads on Buildings; Architectural Institute of Japan: Tokyo, Japan, 2004. 14. Professional Standard PRC. Wind-Resistant Design Specification for Highway Bridges; China Communications Press: Beijing, China, 2004. 15. American Society of Civil Engineering. Minimum Design Loads for Buildings and Other Structures; ASCE 7-10: Reston, VA, USA, 2010. 16. Su, Y.W.; Huang, G.Q.; Xu, Y.L. Derivation of time-varying mean for non-stationary downburst winds. J. Wind Eng. Ind. Aerodyn. 2015, 141, 39–48. [CrossRef] 17. He, X.H.; Qin, H.X.; Tao, T.Y.; Liu, W.S.; Wang, H. Measurement of Non-Stationary Characteristics of a Landfall Typhoon at the Jiangyin Bridge Site. Sensors 2017, 17, 2186. [CrossRef][PubMed] 18. Chen, J.; Hui, M.C.H.; Xu, Y.L. A comparative study of stationary and non-stationary wind models using field measurements. Bound.-Lay. Meteorol. 2007, 122, 105–121. [CrossRef] 19. Failla, G.; Pappatico, M.; Cundari, G.A. A wavelet-based spectrum for non-stationary processes. Mech. Res. Commun. 2011, 38, 361–367. [CrossRef] 20. Xu, Y.L.; Chen, J. Characterizing nonstationary wind speed using empirical mode decomposition. ASCE J. Struct. Eng. 2004, 130, 912–920. [CrossRef] 21. Tao, T.Y.; Wang, H.; Wu, T. Comparative Study of the Wind Characteristics of a Strong Wind Event Based on Stationary and Nonstationary Models. ASCE J. Struct. Eng. 2017, 143, 04016230. [CrossRef] 22. Huang, G.Q.; Chen, X.Z. Wavelets-based estimation of multivariate evolutionary spectra and its application to nonstationary downburst winds. Eng. Struct. 2009, 31, 976–989. [CrossRef] 23. Xiang, Z.G.; Lu, Y.L. An effective wavelet matrix transform approach for efficient solutions of electromagnetic integral equations. IEEE. Trans. Antenn. Propag. 1997, 45, 1205–1213. [CrossRef] 24. Muralidharan, K.; Mishra, S.K.; Frantziskonis, G.; Deymier, P.A.; Nukala, P.; Simunovic, S.; Pannala, S. Dynamic compound wavelet matrix method for multiphysics and multiscale problems. Phys. Rev. E. 2008, 77, 026714. [CrossRef][PubMed] 25. Zhang, X.J. The improvement of orthogonality of Daubechies wavelet by wavelet matrix. Jiangxi Electr. Power 2013, 4, 56–59. [CrossRef] Sensors 2020, 20, 4520 20 of 20

26. Cao, S.Y.; Tamura, Y.; Kikuchi, N.; Saito, M.; Nakayama, I.; Matsuzaki, Y. A case study of gust factor of a strong typhoon. J. Wind Eng. Ind. Aerodyn. 2015, 138, 52–60. [CrossRef] 27. Yan, L.; Ren, L.; He, X.; Lu, S.; Guo, H.; Wu, T. Strong Wind Characteristics and Buffeting Response of a Cable-Stayed Bridge under Construction. Sensors 2020, 20, 1228. [CrossRef] 28. Ishizaki, H. Wind profiles, turbulence intensities and gust factors for design in typhoon-prone regions. J. Wind Eng. Ind. Aerodyn. 1983, 13, 55–66. [CrossRef] 29. Choi, E.C.C. Gradient height and velocity profile during typhoons. J. Wind Eng. Ind. Aerodyn. 1983, 13, 31–41. [CrossRef] 30. Cao, S.Y.; Tamura, Y.; Kikuchi, N.; Saito, M.; Nakayama, I.; Matsuzaki, Y. Wind characteristics of a strong typhoon. J. Wind Eng. Ind. Aerodyn. 2009, 97, 11–21. [CrossRef] 31. Matsumoto, M.; Saitoh, T.; Kitazawa, M.; Shirato, H.; Nishizaki, T. Response characteristics of rain-wind induced vibration of stay-cables of cable-stayed bridges. J. Wind Eng. Ind. Aerodyn. 1995, 57, 323–333. [CrossRef] 32. Guo, J.; Hang, D.; Zhu, X.J. Prediction of crack propagation in U-rib components based on the Markov chain. ASCE J. Bridge. Eng. 2020. accepted. [CrossRef] 33. Yi, T.H.; Li, H.N.; Gu, M. Wavelet based multi-step filtering method for bridge health monitoring using GPS and accelerometer. Smart Struct. Syst. 2013, 11, 331–348. [CrossRef] 34. Meo, M.; Zumpano, G.; Meng, X.L.; Cosser, E.; Roberts, G.; Dodson, A. Measurements of dynamic properties of a medium span suspension bridge by using the wavelet transforms. Mech. Syst. Signal Process. 2006, 20, 1112–1133. [CrossRef]

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