Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge

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1 Engineering, 21, 2, doi:1.4236/eng Pblished Online November 21 ( Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge Xhi He 1, Jn Fang 1, Andrew Scanlon 2, Zhengqing Chen 3 1 School of Civil Engineering, Central Soth University, Changsha, China 2 Department of Civil and Environmental Engineering, The Pennsylvania State University, State College, USA 3 College of Civil Engineering, Hnan University, Changsha, China xhihe@mail.cs.ed.cn Received Agst 28, 21; revised October 26, 21; accepted October 28, 21 Abstract The wind-rain indced vibration phenomena in the Dongting Lake Bridge (DLB) can be observed every year, and the field measrements of wind speed data of the bridge are sally nonstationary. Nonstationary wind speed can be decomposed into a deterministic time-varying mean wind speed and a zero-mean stationary flctating wind speed component. By sing wavelet transform (WT), the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed in this paper. The wind characteristics of trblence intensity, integral scale and probability distribtion of the bridge are calclated from the typical wind samples recorded by the two anemometers installed on the DLB sing the proposed nonstationary wind speed model based on WT. The calclated reslts are compared with those calclated by the empirical mode decomposition (EMD) and traditional approaches. The compared reslts indicate that the wavelet-based nonstationary wind speed model is more reasonable and appropriate than the EMD-based nonstationary and traditional stationary models for characterizing wind speed in analysis of wind-rain-indced vibration of cables. Keywords: Time-Varying Mean Wind Speed, Nonstationary Wind Speed Model, Cable-Stayed Bridge, Wavelet Transform (WT), Wind Characteristic, Wind-Rain-Indced Vibration 1. Introdction Under the simltaneos occrrence of moderate wind and rain, cables in cable-stayed bridges are prone to excessive and nanticipated vibration de to large flexibility, relatively small mass and low inherent damping have been reported in a nmber of cable-stayed bridges worldwide [1-3]. This vibration can case redced cable and connection life de to fatige or rapid deterioration of the corrosion protection system and may reslt in the loss of pblic confidence in the bridge [4]. Excessive stdies have been ths carried ot to explore the mechanism and explain the complex phenomenon of wind-rain-indced excessive vibration of stay cables. The main research methods on wind-rain-indced cable vibration inclde theoretical analyses [5], wind tnnel simlation tests [6] and field observation [1,7,8]. Some main featres for wind-rain-indced vibration have been captred. However, almost all previos researches were based on the assmption of considering wind as a stationary random process. In fact, the wind speed cannot keep a stationary level for a long time [7] and errors may be reslted if the stationary-assmed approach is still adopted. This paper aims to seek a wavelet-based method to investigate wind characteristics on basis of the field measred wind data of the Dongting Lake Bridge (DLB) in Hnan, China. The DLB is a three-tower prestressed concrete cable-stayed bridge, shortly after opening to traffic in 2, several times excessive cable vibration nder wind and rain conditions were observed. A series of field observation and measrements have been carried ot to investigate the characteristics of wind and rain and cable vibration responses, and magneto-rheological (MR) dampers have been sccessflly sed to mitigate the cable vibration in 23 [3]. Combining the field measrements of wind and wavelet mltiscale analysis, the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed based on the typical. The wind parameters in rain-wind-indced vibration are obtained by sing the proposed nonstationary model and compared with previos research reslts based on the stationary assmption. It is conclded that the wavelet-based approach is more rea- Copyright 21 SciRes.

2 896 X. H. HE ET AL. sonable and appropriate than traditional and EMD-based approaches for characterizing wind speed in analysis of wind-rain-indced vibration of cables. 2. Wind Speed Models 2.1. Stationary Wind Speed Model The actal wind field near the grond shold inclde three orthogonal components sch as a vertical wind speed component Wt (), a longitdinal wind speed component Ut (), and a lateral wind speed component Vt (), and the descriptions of their relative characteristics. In the traditional stationary wind speed model, the bondary layer longitdinal wind speed component Ut () at a given height is assmed as an ergodic random process consisting of a constant mean wind speed component U, and a longitdinal flctating wind speed component t (), i.e. Ut () = U+ t () (1) The mean wind speed component U prodces static effects on strctres and the flctating wind speed component t () prodces dynamic effects. The mean wind speed denotes an average over a time interval T, which is commonly taken as 3 s, 1 min or 1 h with respect to wind effects on strctres, leading to the so-called 3 s gst, 1 min or horly mean wind. 1 T U = U () t dt T (2) The mean wind speed of Wt () and Vt () are assmed zero and the relevant flctating wind speed components vt () and wt () are assmed zero-mean stationary random process Nonstationary Wind Speed Model Some research stdies [7,9] have shown that based on field measrements, wind speed cannot maintain a stationary level for a long time and sally has obvios nonstationary characteristics. The characteristics of nonstationary random process represent that the information of time-domain, freqency-domain etc. are related with time and are not ergodic. The nonstationary wind speed can be modeled as the sm of a deterministic time-varying mean wind speed pls a zero-mean stationary random process for flctating wind speed [1]. Ut () = Ut () + () t (3) where Ut () is a deterministic time-varying mean wind speed reflecting the temporal trend of wind speed; and () t is a flctating wind speed of a zero-mean stationary process. The above nonstationary model can be expanded to lateral and vertical wind speed. In fact, if wind speed Ut () is a strictly stationary random process, the time-varying mean wind speed Ut () will be the constant mean wind speed component U defined in Eqation (1). The stationary wind speed model Eqation (1) ths can be looked at as an especial case of the nonstationary model Eqation (3). 3. Time-Varying Mean Wind Speed Extraction Based on WT 3.1. Wavelet Transform Traditional Forier transform (FT) decomposes a signal into freqency components and determines the strength of each component. This decomposition is represented by a power spectrm of a signal. However, sch an analysis does not indicate if a particlar freqency component of significant (local) variations occrred, and is not sitable for nonstationary signals. A short-time Forier transform (STFT) moves a fixed-dration window over a signal and extracts the freqency content in that interval. The STFT overcomes limitations of FT and has been sccessflly applied in analysis of globally nonstationary signals. However, a fixed size of a filter window was fond to be a limiting factor de to the reslting fixed freqency resoltion. The wavelet transform (WT) overcomes the limitations of FT and STFT. It can be thoght of as a generalized STFT, with a freqency-dependent window size [11]. A wavelet family ψ ab, is the set of elementary fnctions generated by dilations and translations of a niqe admissible mother wavelet ψ (t) : ψ () 1 t b ab, t = a ψ (4) a where ab, R, a, are the scale and translation parameters, respectively, and t is the time. At b the wavelet fnction is centered, and as a increases, the wavelet becomes narrower. The signal is then decomposed into a series of basis fnctions of length consisting of dilated (stretched) and translated (shifted) versions of the mother fnction, i.e., wavelets of different scales and positions in time or space [12]. Therefore, the wavelet fnction can provide a good local freqency resoltion for both low and high freqency components of a signal. The continos wavelet transform (CWT) of signal 2 xt () L( R) (the space of real sqare smmable fnctions) is defined as the correction between the fnction xt () with the family wavelet ψ ab, for each a and b : 1 t b W ( a, b) x() t dt x, ψ ab, a ψ = =< a ψ > (5) For special election of the mother wavelet fnction ψ () t and for the discrete set of parameters, = 2 j and a j Copyright 21 SciRes.

3 X. H. HE ET AL. 897 b, 2 j jk = k, with jk, Z (the set of integers), the family ψ /2, ( t ) = j j jk 2 ψ (2 t k ) jk, Z (6) constittes an orthonormal basis of the Hilbert space L 2 ( R) consisting of finite-energy signals. The correlated decimated discrete wavelet transform (DWT) is obtained by j/2 j W jk, = 2 x( t) ψ(2 t k) dt =< x, ψ jk, > (7) where j = N,, 1, N = log 2 ( M). Eqation (7) provides a nonredndant representation of signal and its vales constitte the coefficients in a wavelet series. These wavelet coefficients provide fll information in simple way and direct estimation of local energies at different scales. Moreover, the information can be organized in hierarchical scheme of nested sbspaces called mltiresoltion analysis in L 2 ( R ). If the decomposition is carried ot over all resoltions levels, the sampled signal can be expressed as below [13]: 1 1 (8) xt () = W ψ () t = r() t jk, jk, j j= N k j= N where t = 1, 2,, M, wavelet coefficients W jk, can be interpreted as the local residal errors between sccessive signal approximations at scales j and j + 1, and rj () t is the residal signal at scale j Time-Varying Mean Wind Speed Extraction Since the wavelet fnction family {, () t jk } ψ is an orthonormal basis for L 2 ( R ), the concept of energy is linked with the sal notions derived from the Forier theory. Then, the wavelet coefficients are given in Eqation (7), the nmber of coefficients at each resoltion level is N 2 j j = M. Note that this correlation gives information on the signal at scale 2, and time 2 j k. j The set of wavelet coefficients at level j, { Cj,( k )} is also a stochastic process where k represents the discrete time variable [14]. It provides a direct estimation of local energies at different scales. The energy at resoltion level is given by 2 2 j j jk, k E = r = W (9) For a complex nonstationary signal, the longest period component obtained by WT decomposing in maximm layers, is not always the optimal component reflecting the local information of nonstationary time-varying mean. Therefore, the key isse in sing WT to extract the trend in nonstationary signals is how to make sre the most reasonable nmber of decomposition layers is considered. Based on the wavelet theory, the wavelet has the character of conservation of energy when the wavelet fnction is a series of orthogonal basis fnctions. For a discrete WT, the energy of each layer detail coefficient can be obtained sing Eqation (9). The appropriate levels for decomposing the time-varying mean wind speed were qantitatively determined by the sdden change of simple scale wavelet energy. The accrate time-varying mean wind speed was then obtained by the inverse discrete orthogonal wavelet transforms of approximate coefficients [15] Wavelet Selection and Comparison In order to verify the effectiveness and veracity of time-varying mean extraction by sing WT, in this paper, a set of zero mean stationary wind speeds were simlated by adopting harmonic sperposition method, as shown in Figre 1. The time-varying mean vale is obtained by modlating constant mean U based on different modlation fnctions, and the nonstationary wind speed Ut () can be obtained by sperposition of the dispersed time-varying mean vale and stationary wind speed. This paper considers constant amplitde cosine fnction, linear fnction and exponential fnction as constant mean modlation fnctions. The fnctions are shown in Eqations (1)-(12), respectively, π Ut ( ) = U(1 + cos t), U= 2 m/ st, [,36] (1) 9 [ ] [ ] Ut ( ) = U(1 + t/ 36), U= 2 m/ st,,36 (11) t /3.6 U( t) = Ue, U = 2 m / s, t,36 (12) The time-varying mean nonstationary wind speeds by sing Eqations (1)-(12) are obtained and shown in Figres 1-(d), respectively. The first step in sing WT to extract time-varying mean is selecting an appropriate wavelet fnction family. In the wavelet tool box of MATLAT R27, some orthogonal wavelet families sch as Dabechies wavelet, Symlets wavelet, Coiflets wavelet and Discrete Meyer wavelet can be sed to extract the trend component, and some Biorthogonal and Reverse Biorthogonal wavelets can also be sed for trend extraction. Since the wavelets db, and sym have compactly spported orthogonality [16], they ths adapt well to DWT. db N ( N is the wavelet order nmber) indicates the Dabechies wavelet family with vanishing moment N, wavelet and scale fnctions effective spported length 2N 1; coif N indicates the biorthogonal Coiflet wavelet family with vanishing moment N, effective spported length 2N 1 and filtering length 6N ; and sym N indicates the orthogonal Symlets wavelet family with vanishing moment N, effective spported length 2N 1 and filtering length Copyright 21 SciRes.

4 898 X. H. HE ET AL. U(t) (d) Figre 1. Original stationary wind speed and nonstationary time-varying wind speeds: Original stationary wind speed; Nonstationary wind speed with cosine fnction; Nonstationary wind speed with linear fnction; (d) Nonstationary wind speed with exponential fnction. 2N. The trend extraction precision of sing orthogonal wavelets of db1, coif5, sym7 and dmey are compared in this paper. By sing db1 wavelet, coif5 wavelet, sym7 wavelet, dmey wavelet and the empirical mode decomposition (EMD) [17], the time-varying mean extraction of nonstatioary wind speeds shown in Figres 1-(d) are carried ot, respectively. Shown in Figre 2 are the time-varying wind speeds extracted by wavelets and EMD. Table 1 lists the comparison of mean sqare deviation (MSD) between the extracted and theoretical means by sing optimal wavelet fnctions of the 4 wavelets and EMD. From the Figre 2 and Table 1, it is seen that: 1) The MSD between the extracted and theoretical mean vale obtained by EMD is mch bigger than those obtained by all the aforementioned wavelets; 2) Among the different wavelets, the extracted precision of the nsymmetrical wavelet db1 is better than those of symmetrical wavelets coif5, ym7 and dmey, and wavelet coif5 is better than wavelet sym 7 and dmey; and 3) The extracted precisions of linear fnction are better than cosine and exponential fnctions. It is fond that too large or too small a wavelet order nmber can affect the extracted precision, and wavelet db1 has higher precision for any mean extraction. In fact, the for wavelet fnctions db, coif, sym7 and dmey all can be sed to extract the time-varying mean wind speed. In order to gain better application effects, wavelet db1 is selected to extract the time-varying mean wind speed from the measred typical wind samples of the Dongting Lake cable-stayed bridge in this paper. 4. Description of Bridge and Field Measrements The Dongting Lake Bridge (DLB), as shown in Figre 3, is the first three-tower prestressed concrete cable-stayed bridge located in the inflx of Dongting Lake into the Yangtze River, China. The bridge consists of two main spans of 31 m each and two side spans of 13 m each with 25. m clearance height above water level. The deck is 23.4 m wide with for lanes of traffic. The central tower is m high and side towers are 99.3 m Table 1. Comparison of MSD between extracted and theoretical mean wind speeds. Modlation fnctions Wavelet (m/s) db1 coif5 sym7 dmey EMD (m/s) Cosine fnction Linear fnction Exponential fnction Copyright 21 SciRes.

5 X. H. HE ET AL Cosine fnction Linear fnction Exponential fnction North Anemometer 13 m 31 m 31 m 13 m Figre 3. Elevation of Dongting Lake Bridge (DLB). A12 cable series of field observation and measrements were condcted, and finally MR dampers were installed on the cables (see Figre 4) to mitigate cable vibration [3,7]. Soth U(t) Cosine fnction Linear fnction Exponential fnction Cosine fnction Linear fnction Exponential fnction Cosine fnction Linear fnction Exponential fnction (d) Figre 2. Extracted time-varying mean wind speeds: Obtained by wavelet db1; Obtained by wavelet coif5; Obtained by wavelet sym7; (d) Obtained by EMD. high each. There are a total 222 cables with size ranging from 28 to 21 m in length and 99 to 159 mm in diameter with polyethylene (PE) pipes. Shortly after it opened to traffic in 2, excessive and nanticipated wind-rainindced cable vibrations were observed every April, Jly. The large-amplitde cable vibration cases concerns to the bridge administrative athority and engineers. A Figre 4. Dongting Lake Bridge: MR dampers installed on the cables; Anemometer at deck level; Anemometer at top of soth side tower. Copyright 21 SciRes.

6 9 X. H. HE ET AL. The field tests inclded measrements of wind and rain characteristics, cable vibration and its mitigation by sing MR dampers. Two three-axis ltrasonic anemometers were installed on the top of the soth side tower and deck level near cable A12, respectively. Deck level one is sitated at an elevation of 26 m, 4 m stretching ot from the deck edge with a horizontal cantilever (see Figre 4). Tower top one is sitated at an elevation of 12 m, 2 m high above the tower top cantilever (see Figre 4). One data acqisition and processing system in the bridge site can record the data while wind-rain-indced vibration occrs. The sample freqencies of wind speed and acceleration response are 4 Hz and 1 Hz, respectively. Continos field measrements were condcted for 47 days from 24 March to 11 May Wind Characteristics of DLB 5.1. Typical Wind Speed Samples Dring the field testing period in 23, significant wind-rain-indced vibrations were observed, and the corresponding wind speed and direction, rainfall and cable acceleration response data were recorded. The for typical measred wind speed data segments (1 h) from anemometers installed on the top of the soth side tower and bridge deck level dring wind-rain-indced vibration dration on 1 April 23 are considered here. Shown in Figres 5 and are the 1h dration wind speed samples from bridge deck level anemometer between 17:1 to 18:1 and 22:2 to 23:2, 1 April 23, respectively. Shown in Figres 5 and (d) are the 1 h dration wind speed samples from the tower top anemometer between 17:1 to 18:1 and 22:2-23:2, 1 April 23, respectively. By sing the nonstationary wind speed model based on WT proposed in this paper, the timevarying mean wind speeds of the for typical wind samples obtained are shown in Figres 5-(d). Figres 5-(d) also show the time-varying mean wind speeds obtained by EMD and the traditional constant mean wind speeds for comparison. It is seen that the mean wind speed in 1h is time-varying, and it is not appropriate to adopt the constant mean wind speed assmption. The time-varying mean wind speeds obtained by WT and EMD are a continos fnction of time with a designated freqency level, which is more natral than the traditional time-averaged mean wind speed with the certain time interval [1]. If the traditional stationary approach is sed, the errors may reslt in the calclated wind characteristics. Wind speed (m/s) Wind speed (m/s) Wind speed (m/s) Wind speed (m/s) Original measred wind speed Constant mean wind speed Time-varying mean wind speed by EMD Time-varying mean wind speed by WT Original measred wind speed Constant mean wind speed Time-varying mean wind speed by EMD Time-varying mean wind speed by WT Original measred wind speed 8 Constant mean wind speed Time-varying mean wind speed by EMD 6 Time-varying mean wind speed by WT Original measred wind speed 8 Constant mean wind speed 6 Time-varying mean wind speed by EMD Time-varying mean wind speed by WT (d) Figre 5. Typical wind speed samples and their timevarying and horly mean wind speeds: Deck wind sample 1 (17:1-18:1, 1 April 23); Deck wind sample 2 (22:2-23:2, 1 April 23); Tower wind sample 1 (17:1-18:1, 1 April 23); (d) Tower wind sample 2 (22:2-23:2, 1 April 23). Copyright 21 SciRes.

7 X. H. HE ET AL Trblence Intensity For stationary wind speed, the ratio of the standard deviation of flctating wind to mean wind speed is traditionally defined as the trblence intensity. The trblence intensity of longitdinal flctating t () for a given dration T is expressed by with standard deviation σ I = (12) U 1 T 2 σ = () t dt T (13) For nonstationary wind speed, however, the mean wind speed is time varying, and trblence intensity is also time dependent over time interval T. To be consistent with the trblence intensity by the traditional method, the mean vale of the time varying trblence intensity over the interval T I σ = (14) Ut () where σ means the standard deviation of flctating wind speed over the interval T, and () t is a flctating wind speed of a zero-mean stationary process. To have a comparison of trblence intensities obtained by WT, EMD and traditional stationary model, the average vales of longitdinal trblence intensity of 1h dration are compted sing the typical wind samples from the two anemometers installed on the bridge deck and tower top compared in Table 2. It is fond that the mean vales of trblence intensities compted by nonstationary models are smaller than those obtained by the traditional stationary model. The maximm difference between the nonstationary model based on WT and traditional stationary model is 12.4%, and the mean difference is 9.1%. The trends of wind speed vary rapidly, as shown in Figre 5, which can lead to the overestimation of trblence intensity by the traditional stationary approach. Among the two nonstationary approaches based on WT and EMD, the reslts by WT are slightly smaller than those by EMD, the maximm and mean differences are 7.8% and 4.7%, respectively Integral Scale Integral scales were calclated by fitting an exponential crve throgh the atocorrelation fnction for each 1h sample segment. Using the typical wind samples from the two anemometers installed on the bridge deck and tower top (see Figre 5), the calclated average vales of integral scale of 1h dration are com- Table 2. Comparison of average vales of longitdinal trblence intensity. Wind speed record Deck level Tower top Nonstationary model Based on WT Based on EMD Stationary model Sample Sample Sample Sample Table 3. Comparison of average vales of integral scale. Wind speed record Deck level Tower top Nonstationary model Based on WT Based on EMD Stationary model Sample Sample Sample Sample pted by WT, EMD and traditional stationary approach, and compared in Table 3. Like the compared reslts of trblence intensity, the average vales of integral scale calclated by nonstationary models based on WT and EMD are larger than those obtained by the traditional stationary model. The maximm and mean differences between the nonstationary model based on WT and traditional stationary model are 62.9%, 53.8%, respectively. The trends of wind speed vary rapidly, as shown in Figre 5, which can lead to overestimation of integral scale by the traditional stationary approach. Among the two nonstationary approaches based on WT and EMD, the reslts by WT are slightly smaller than those by EMD, the maximm and mean differences are 27.3% and 14.8%, respectively Probability Distribtion For stationary wind speed, the probability distribtion of longitdinal flctating wind speed is assmed follow the Gassian distribtion given by σ p ( ) = e (15) 2πσ where σ is the standard deviation aforementioned. For nonstationary wind speed, however, the mean wind speed is time varying, and trblence intensity is also time dependent over time interval T. To be consistent with the trblence intensity by the traditional method, the mean vale of the time varying trblence intensity over the interval T Copyright 21 SciRes.

8 92 X. H. HE ET AL. ( ) p σ = e (16) 2πσ where σ is the standard deviation of flctating wind speed over the interval T, and () t is a flctating wind speed of a zero-mean stationary process. To investigate probability distribtions of nonstataionary wind samples, for typical wind speed samples recorded at the two anemometers installed on the top of the soth side tower and deck level, as shown in Figre 5 are taken as examples. Displayed in Figre 6 are the probability distribtions of two typical flctating wind speeds recorded from the deck level anemometer (see Figres 5 and ) and two typical flctating wind speeds recorded from soth tower anemometer (see Figres 5 and (d)) together with Gassian density fnctions, respectively. The probability distribtions based on WT are calclated from flctating wind speed obtained by sbtracting the time-varying mean wind speed at a freqency level of 1/36 Hz from original wind sample. The probability distribtions based on EMD nonstationary and traditional stationary wind speed models are also compted and compared in Figre 6. It is seen that the probability densities obtained by the nonstationary model based on WT comply with the Gassian distribtion better than those calclated by nonstationary model based on EMD and traditional stationary model. Especially, as shown in Figre 6(d), the probability distribtion of the flctating wind speed obtained based WT from tower original wind sample 2 (22:2-23:2, 1 April 23) complies with Gassian distribtion well, bt the reslts obtained based EMD and traditional stationary model deviate from the Gassian distribtions significantly. Ths, it may be conclded that wavelet-based stationary model is more reasonable and reliable for characterizing field measred nonstationary wind speeds. 6. Conclsions Wind-rain-indced vibration of stay cables in cablestayed bridge is very complicated. It is necessary to establish a reasonable wind speed model for frther analysis of cable wind-rain indced vibration. A waveletbased method for analyzing wind measrement data has been proposed in this paper. Since field measred wind samples are sally nonstationary, the proposed approach can release the limitation of stationary wind assmption of the traditional approach. The time-varying mean wind speed is more reasonable than the traditional time-averaged mean wind speed for a nonstationary wind speed record. Thogh the wavelet fnction selection problem of discrete orthonormal WT exists, there is a reasonable space for wavelet fnction Probability dentsity Probability dentsity Probability dentsity Probability dentsity Stationary wind speed model Nontationary wind speed model based on EMD Nontationary wind speed model based on WT Gassian fit Flctating wind speed (m/s) Stationary wind speed model Nontationary wind speed model based on EMD Nontationary wind speed model based on WT Gassian fit Flctating wind speed (m/s) Stationary wind speed model Nontationary wind speed model based on EMD Nontationary wind speed model based on WT Gassian fit Flctating wind speed (m/s) Stationary wind speed model Nontationary wind speed model based on EMD Nontationary wind speed model based on WT Gassian fit Flctating wind speed (m/s) (d) Figre 6. Comparison of probability densities: Deck wind sample 1(17:1-18:1, 1 April 23); Deck wind sample 2 (22:2-23:2, 1 April 23); Tower wind sample 1 (17:1-18:1, 1 April 23); (d) Tower wind sample 2(22:2-23:2, 1 April 23). Copyright 21 SciRes.

9 X. H. HE ET AL. 93 selection, and the inflence is very limited. The analysis process is simple and has higher precision once an appropriate wavelet fnction is selected. The comparison reslts indicate that wavelet db1 is the best one from the orthogonal wavelet families which can be sed to extract the time-varying mean wind speed. Based on the typical field measrement wind samples recorded from the two anemometers installed on the tower top and deck level of the DLB dring wind-rain-indced vibration on 1 April 23, the timevarying mean wind speed and the wind are calclated by the nonstationary wind speed model based on WT, and the calclated reslts are compared with those obtained by the EMD nonstationary and stationary models. The comparison reslts show that: 1) the trblence intensities and integral scales of longitdinal flctating wind speed calclated by nonstationary wind speed models based on WT and EMD are smaller than those obtained by traditional stationary model; 2) the flctating wind components after wiping off the time-varying mean wind speeds from original wind records are more complied with the standard Gassian distribtion; 3) The comparison of WT and EMD indicates that the time-varying mean wind speed extracted by WT is more reliable and effective than EMD de to its end effect. It can be conclded that the wavelet-based method proposed in this paper is more appropriate than the traditional and EMD-based methods for characterizing wind speed in analysis of wind-rainindced vibration of cables. 7. Acknowledgements The work described in this paper was spported by the China National Science Fondation (Grant no ) to which the athors grateflly appreciate. 8. References [1] Y. Hikami and N. Shiraishi, Rain-Wind Indced Vibrations of Cables in Cable Stayed Bridges, Jornal of Wind Engineering and Indstrial Aerodynamics, Vol. 29, No. 1-3, 1988, pp [2] J. A. Main, N. P. Jones and H. Yamagchi, Evalation of Viscos Dampers for Stay-Cable Vibration Mitigation, Jornal of Bridge Engineering, Vol. 6, No. 6, 21, pp [3] Z. Q. Chen, X. Y. Wang, J. M. Ko, Y. Q. Ni, B. F. Spencer, G. Yang and J. H. H, MR Damping System for Mitigating Wind-Rain Indced Vibration on Dongting Lake Cable-Stayed Bridge, Wind & Strctres, Vol. 7, No. 5, 24, pp [4] I. Hwang, J. S. Lee and B. F. Spencer, Isolation System for Vibration Control of Stay Cables, Jornal of Engineering Mechanics, Vol. 135, No. 1, 29, pp [5] D.Q. Cao, R. W. Tcker and C. Wang, A Stochastic Approach to Cable Dynamics with Moving Rivlets, Jornal of Sond and Vibration, Vol. 268, No. 2, 23, pp [6] M. Matsmoto, N. Shirashi and H. Shirato, Rain-Wind Indced Vibration of Cables of Cable-Stayed Bridges, Jornal of Wind Engineering and Indstrial Aerodynamics, Vol. 43, No. 3, 1992, pp [7] Y. Q. Ni, X. Y. Wang, Z. Q. Chen and J. M. Ko, Field Observations of Rain-Wind-Indced Cable Vibration in Cable-Stayed Dongting Lake Bridge, Jornal of Wind Engineering and Indstrial Aerodynamics, Vol. 95, No. 5, 27, pp [8] D. Zo, N. P. Jones and J. A. Main, Field Observation of Vortex- and Rain-Wind-Indced Stay-Cable Vibrations in a Three-Dimensional Environment, Jornal of Wind Engineering and Indstrial Aerodynamics, Vol. 96, No. 6-7, 28, pp [9] Q. S. Li, C. K. Wong, J. Q. Fang, A. P. Jeary, and Y. W. Chow, Field Measrements of Wind and Strctral Responses of a 7-Storey Tall Bilding nder Typhoon Conditions, Strctral Design of Tall Bildings, Vol. 9, No. 5, 2, pp [1] Y. L. X and J. Chen, Characterizing Nonstationary wind Speed Using Empirical Mode Decomposition, Jornal of Strctral Engineering, Vol. 13, No. 6, 24, pp [11] B. Bienkiewicz and H. J. Ham, Wavelet Stdy of Approach Wind Velocity and Bilding Pressre, Jornal of Wind Engineering and Indstrial Aerodynamics, Vol , 1997, pp [12] K. Grley and A. Kareem, Applications of Wavelet Transforms in Earthqake, Wind, and Ocean Engineering, Engineering Strctres, Vol. 21, No. 2, 1999, pp [13] O. A. Rosso, S. Blanco, J. Yordanova, V. Kolve, A. Figliola, M. Schrmann and E. Basar, Wavelet Entropy: a New Tool for Analysis of Short Dration Brain Electrical Signals, Jornal of Neroscience Methods, Vol. 15, No. 1, 21, pp [14] L. Znino, D. G. Perez, M. Garavaglia and O. A. Rosso, Wavelet Entropy of Stochastic Processes, Physica A (Netherlands), Vol. 379, No. 2, 27, pp [15] J. H. Shen, C. X. Li and J. H. Li, Extracting Time- Varying Mean of the Non-Stationary Wind Speeds Based on Wavelet Transform (WT) and EMD, Jornal of Vibration and Shock, in Chinese, Vol. 27, No. 12, 28, pp [16] H. J. Li, B. Q. Feng and G. C. W, The Compactly Spported Cardinal Orthogonal Vector-Valed Wavelets with Dilation Factor α, Applied Mathematics and Comptation, Vol. 25, No. 1, 28, pp [17] N. E. Hang, Z. Shen, and S. R. Long, The Empirical Mode Decomposition and Hilbert Spectrm for Nonlinear and Nonstationary Time Series Analysis, Proceedings of Royal Society, London A, Vol. 454, 1999, pp Copyright 21 SciRes.