14 In wind engineering, t o accurately estimate the nonlinear dynamic response of structures while considering 15 uncertainties of hurricanes, a suite of wind records representing the hurricane hazards of a given location is 16 of great interest. Such a suite generally consists of a large number of hurricane wind records, which may 17 lead to highly computational cost for structural analysis . To reduce the computational demand while still 18 preserving the accuracy of the uncertainty quantification process , this paper proposes a machine learning 19 approach to select a representative subset of all collected hurricane wind records for a location. First, 20 hurricane wind records , which are expressed as time series with information that includes both wind speed 21 and direction, are collected from a synthetic hurricane catalog. The high-dimensional hurricane wind 22 2 records are then compressed into a set of low -dimensional latent feature vectors using an artificial neural 23 network, designated as an autoencoder. The latent feature vectors represent the important patterns of wind 24 records such as duration, magnitude and the changing of wind speed s and direction s over time. The wind 25 records are then clustered by apply ing the k- means algorithm on the latent features, and a subset of records 26 is selected from each cluster. The wind records selected from each cluster are those whose latent feature 27 points are closest to the centroid of all latent feature points in that cluster. In order to do regional analysis 28 while taking into account that the hurricane wind records are site- specific, this paper suggest s that a region 29 can be discretized into a set of grids, with the proposed hurricane selection approach applied to each grid. 30 This procedure is demonstrated using Massachusetts as a testb ed. 31 Keywords: hurricane selection , time series clustering , autoencoder , k-means , uncertainty quantification , 32 regional analysis, wind direction 33 Introduction 34 Nonlinear dynamic analysis is increasingly being considered in wind design of buildings and other 35 structures as performance -based design becomes an increasingly popular option (ASCE 2019) , where 36 controlled inelastic deformations are allowed under strong winds (Wang and Wu 2022) . In the fully 37 probabilistic performanc e-based hurricane engineering framework (Barbato et al. 2013) , fragility curves of 38 structures are commonly adopted to do probabilistic damage assessment . Strength limit sta tes of structures 39 usually involve nonlinear behavior that is then integrated into the predictions of likelihood of damage that 40 is offered through fragility analysis. Fragility functions are defined as the failure probability of a structure 41 conditional on t he intensity measure of hazards, including hurricanes in this work . If only the failure 42 probability or fragility is of interest for a hurricane event (i.e., at the end of the load ing time history) instead 43 of for a certain time interval within the hurricane duration, the uncertainties in the load ing time histories 44 can be accounted for through running a series of nonlinear dynamic analysis with a s uite of hurricane wind 45 records. The hurricane wind records should include time histories that incorporat e the wind directions as 46 well as wind speeds, because the changing of wind directions during hurricanes has significant effects on 47 3 the structural response. Consequently, the wind records in this research are time series of both wind speed 48 and direction. To develop accurate fragility curves, the structures should be analyzed with a suite of 49 hurricane wind records that can cover the record -to-record uncertainties in the changing of wind speeds and 50 directions within the hurricane durations . A large amount of hurricane wind records can be collected for a 51 location considering the existing historical and synthetic hurricanes (ASCE 2016b; Vickery et al. 2010; 52 Vickery et al. 2009b; Vickery et al. 2009c) . However, it is challenging to run nonlinear dynamic analysis 53 for all of the collected hurricane records due to the high computational demand of finite element analysis 54 of structures ; thus, a minimu m number of hurricane records should be selected to represent the uncertainties 55 in all of the collected hurricane records. 56 In prior work, Li (2005) and Li and Ellingwood (2006) developed hurricane fragility curves f or wood -frame 57 residential construction with a simplified limit state function, where the nonlinea r and dynamic effects are 58 neglected . Cui and Caracoglia (2015) carried out fragility analysis on tall buildings only for the 59 serviceability limit state , so frequency domain a nalysis is adopted , and duration and nonstationary effects 60 of hurricanes cannot be considered. In order to avoid performing structural analysis for long durations of 61 windstorms , the dynamic shakedown method was utilized by researchers to model the inelastic behavior of 62 buildings (Chuang and Spence 2019, 2020; Tabbuso et al. 2016) . Other researchers tried to develop 63 hurricane fragility curves using nonlinear dynamic analysis only for a fixed time interval with a constant 64 wind direction. For example, Hallowell et al. (2018) used wind records with 1 -hour time intervals , whi le 65 Ma et al. (2021) used wind records with 2- minute time intervals . The fragility developed for this certain 66 time interval cannot represent the fragility for a whole hurricane because of dynamic effects, yielding and 67 changes in wind speeds and directions. Of course, one can discretize the hurricane duration into a series of 68 short time interval s and apply the devel oped fragility curves to each short time interval ; however, the failure 69 probabilities within those short time intervals are correlated (Der Kiureghian 2005; Kim et al. 2019; Straub 70 et al. 2020) . This correlation is difficult to quantify from the view of time -variant reliability and is not 71 considered by the above authors. Given the limitations of the previous research, this paper consider s the 72 4 failure probabilit y for a hurricane event instead of a certain time interval during a hurricane and tries to 73 select hurricane wind records that can account for the record -to-record uncerta inties in hurricanes. The 74 selected wind records can be used to estimate failure probabilit ies of structures with nonlinear time history 75 analysis. Through this way it is no longer needed to estimate the correlations of failure probabilities in the 76 short time interval s within a hurricane. 77 In performance -based earthquake engineering (Moehle and Deierlein 2004) , a probabilistic framework has 78 been proposed to integrate seismic hazard analysis and structural damage analysis, where a suite of ground 79 motions are adopted to represent the un certainties in earthquake ground motions. Ground motion selection 80 has been widely studied in the literature (Baker and Lee 2018; Bojórquez et al. 2013; Du and Padgett 2021; 81 Jayaram et al. 2011; Naeim et al. 2004) . Some generally used ground motions suites are the SAC 82 (Somerville et al. 1997) records, LMSR (Krawinkler et al. 2003) records, and FEMA -P695 records (FEMA 83 2009) . Recently, machine learning approaches have also been introduced to ground motion selection, where 84 a reduced number of ground motions ar e obtained through clustering of a large number of ground motions 85 (Bond et al. 2022; Kim et al. 2021; Zhang et al. 2020) . However, there is no similar re search in the literature 86 for selection of hurricane wind records. There are two instances of prior research that consider uncertainties 87 in hurricane wind hazards using a set of wind records, but they do not use a selection procedure. Vickery 88 et al. (2006) studied hurricane fragilit y curves for bu ilding envelope components that were developed in 89 the Hazus- MH software by comparing the wind pressure demand and the capacity of the envelope 90 components. The record- to-record uncertainties of hurricane wind speeds were accounted for through the 91 use of a 2 0,000- year simulation of hurricanes created by employing the hurricane model described by 92 Vickery et al. (2000a) and Vickery et al. (2000b) . The simulated hurricanes inherently incorporate d many 93 of the duration effects associated wit h the changes in wind speed and direction which accompany hurricane 94 winds. Joyner and Sasani (2018) developed fragility curves for the windborne debris damage of building 95 glazing, where eight hurricanes that made landfall in the U.S. in the last 10 years were adopted. 96 Uncertainties in the record -to-record variability for different hurricanes were accounted for by employing 97 5 the eight hurricane records in the damage analysis. Vickery et al. (2006) used all hurricanes in the 20,000 - 98 year simulation, which may address the uncertainties in hurricanes, but is not suitable for nonlinear dynamic 99 analysis considering the computational demand. On the contrary, Joyner and Sasani (2018) only used eight 100 hurricanes without an analysis of the hazard uncertainties, which may not be able to represent the 101 uncertainties in hurricanes for a specific location. 102 This paper proposes a procedure to select a suite of hurricane wind records that can be used for performance- 103 based design and fragility analysis. The wind speed and direction records for a location are collected from 104 a synthetic hurricane catalog (Liu 2014) with some preprocessing, after which t he collec ted wind records 105 have du rations that are short enough to make a nonlinear time history analysis feasible. The collected wind 106 records are then compressed into low -dimensional latent feature vectors using a neural network designated 107 as an autoencoder (Aggarwal 2018) , so that it is easier to measure similarity of different wind records and 108 apply the standard clustering algorithms such as the k -means algorithm (Aggarwal et al. 2001; Shalev- 109 Shwartz and Ben- David 2014) . Autoencoder is an artificial neural network in which the input and output 110 layers have the same number of neurons, while the number of neurons in the middle is constricted. The 111 training algorithm tries to reconstruct the input data in the output layer; however, this reconstruct ion is not 112 exact because t he neurons in the middle only carry a reduced representation of the input data . The data held 113 by the neurons in the middle (i.e., the low dimensional vectors compared to the input and output layer) are 114 called latent features, to which the clustering algorithm i s applied. This means that only important 115 information in the wind records is preserved for clustering. T he latent features representing hurricane wind 116 records are then clustered into several groups using the conventional k-means algorithm (Shalev -Shwartz 117 and Ben- Davi d 2014) . Finally, only a few hurricane wind record s are selected from each cluster for fragility 118 development or design checks , which significantly reduce s the number of required time history analyses , 119 while still ensuring that the uncertainties of diffe rent hurricanes are covere d with a limited number of wind 120 records. Since the properties of hurricanes for different locations have significant differences , a hazard map 121 can be developed for hurricane wind records so that users are able to choose appropriate records for their 122 6 locations of interest . As an example, the Commonwealth of Massachusetts has been divided into 92 grids 123 and a suite of hurricane wind records has been selected for each grid using the proposed hurricane selection 124 approa ch. To demonstrate the usefulness and effectiveness of t he selected wind records, they have been 125 adopt ed to develop fragility curves for electrical transmissions towers in Massachusetts, which can be found 126 in Du et al. (2022) and Du and Hajjar (2022) . 127 Hurricane simulation 128 Synthetic hurricanes are widely used for risk analysis and structural design in wind engineering, which 129 evolved from the single site probabilistic model (Russell 1971) to Vickery’s hurricane track m odel (Vickery 130 et al. 2000a) . For example, ASCE 7 has adopt ed the hurricane track model when generating the wind hazard 131 maps (ASCE 2016b) . This research also uses a 10,000 year synthetic hurricane catalog developed by Liu 132 (2014) for the Atlantic basin based on Vickery’s hurricane track model , which consists of a hurricane 133 genesis model, a track model, an central pressure model , a decay model and a boundary layer model . The 134 temporal and spat ial evolution of thousands of hurricanes from emergence to dissipation wa s modeled using 135 the Monte Carlo method. The HURDAT database (Jarvinen et al. 1984) for historical storms was adopted 136 for building the hurricane model through regression and calibrating the simulated results. In this simulation, 137 the state of a hurricane can be determined with 7 parameters: the hurricane eye ’s latitude and longitude, 138 storm translation speed, storm heading angle, storm central pressure , radius to maximum w inds (describing 139 storm size) , and Holland’s radial pressure profile parameter (i.e., the Holland B parameter (Holland 1980) ). 140 These parameters are updated at each 6-hour point. As suggested by Vickery et al. (2000a) , linear 141 interpolation is perform ed within each 6- hour interval, which results in 10- min updates of the parameters 142 as used in Vickery et al. (2009c) . Examples of the simulated h urricane track s are shown i n Fig. 1. In this 143 research, the gradient wind speeds are calculated by employ ing Georgiou’s model (Georgiou 1985) , which 144 gives the 10- min sustained wind speed s at 500 m to 2000 m above the ground surface (Cui and Caracoglia 145 2019; Pei et al. 2014, 2018) . An example of the calculated gradient wind field is shown i n Fig. 2. 146 7 147 Fig. 1. Examples of the simulated hurricane tracks 148 149 Fig. 2. Example of hurricane gradient wind field (m/s) 150 The obtained hurricane gradient wind speeds 𝑉𝑉𝑔𝑔 need to be converted to surface wind speed s 𝑉𝑉10 (10 m 151 above the ground or water) for wind force calculation on structur es. The reduction factor 𝑉𝑉𝑔𝑔𝑉𝑉10⁄ over water 152 proposed by Batts et al. is used in this research (Batts et al. 1980; Vickery et al. 2009a) . A sea-land transition 153 factor obtained from the model given in Simiu and Scanlan (1996) is then utilized to calculate the surface 154 wind over land (open terrain with surface roughness 𝑧𝑧 0=0.03 𝑚𝑚) from the surface wind over water ( 𝑧𝑧0= 155 0.0013 𝑚𝑚). In addition, the surface wind speed over land approaches the fully transit ioned value 156 asymptotically over a fetch distance as the wind moves from sea to land; therefore, the transition function 157 proposed in Vickery et al. (2009b) is employed here, which defines the percentage of the sea- land transition 158 8 as a function of the fetch distance. With the method s discussed in this section, the time series of the 10-min 159 sustained wind speed s at 10 m height and the corresponding wind direction s at a location of interest 160 (assuming open terrain) during a hurricane may be obtained. 161 Hurricane wind records collection and preprocess 162 ASCE 7 wind hazard maps display wind speeds with a certain mean recurrence interval (MRI) for the entire 163 U.S., including hurricane prone regions (ASCE 2016b) . However, much information regarding hurricane 164 winds is omitted in the ASCE 7 wind hazard map s, such as the variation of wind speeds and directions 165 during a hurricane, and the duration s of hurricane wind s. This kind of information , which are contained in 166 the time series of hurricane wind speeds and directions, are critical for structural response estimation and 167 risk analysis . Thus, in this section, a number of hurricane wind speed and direction records are collected 168 for a location of interest . In order to collect hurricane wind records for a region, the region is first discretized 169 into a series of grids and t hen hurricane wind records are c ollected for each grid. 170 Wind records for a location of interest 171 A location in Massachusetts with latitude 41.7 and longitude -70.1 is used as an example in this section. 172 Wind records are collected for this specific location from 10,000- year synthetic hurricanes developed by 173 Liu (2014) . Examples of the collected 10- min sustained wind speed and wind direction records at the 174 location of interest are shown in Fig. 3 to Fig. 5 with the corresponding hurricane tracks. It is seen in Fig. 175 3(a), Fig. 4(a) and Fig. 5(a) that the hurricane eye usually moves thousands of miles from a hurricane’s 176 genesis to dissipation . It is reasonable to assume that the wind speed induced by a hurricane that is very far 177 away is relatively small and can be neglected. Th erefore , as suggested by Vickery et al. (2009c) , hurricane 178 winds are considered only when the location of interest is within 250 km of the hurricane eye (see the blue 179 circles in Fig. 3 to Fig. 5). This limit on distance also provides a limit for the durations of the hurricane 180 wind r ecords. Figure 3(c), Fig. 4(c) and Fig. 5(c) illustrate the absolute values of the wind speeds and the 181 wind directions in a polar coordinate system, while Fig. 3(d), Fig. 4(d) and Fig. 5(d) illustrate the hurricane 182 wind speeds in the North and East directions in a Cartesian coordinate system. Note that the wind direction 183 9 in the polar coordinate system is clockwise positive fro m the North direction. It is seen that the pattern of 184 wind speed and direction records are different for different hurricanes, which depends on a number of 185 factors , including the 7 parameters defining the hurricane eye tracks and wind fields . While the imp acts of 186 the hurricane wind field as shown in Fig. 2 on the wind records is complex, a qualitative analysis of the 187 impact of hurricane eye tracks on the wind records pro vides examples of the range of loading developed 188 during hurricanes. Specifically, when the location of interest is very close to the hurricane eye track, the 189 record of the absolute values of the wind speed s usually has two peaks and the drop of the wind speed in 190 the middle is due to the near zero wind speed in the hurricane eye ( see Fig. 3(c)). On the contrary, if the 191 location of interest is further from the hurricane eye track, the record of the absolute values of the wind 192 speed s will typically only have one peak ( see Fig. 4(c) and Fig. 5(c)). The difference between Fig. 4 and 193 Fig. 5 is that the hurricane eye pass es by the West or East side of the location of interest, which dominates 194 the variation of the wind directions as presented in the se two figures . 195 196 (a) The whole hurricane track (the blue circle represent s the 250 km limit) 197 10 198 (b) The hurricane track within the 250 km limit (blue circle) of the location of interest (blue dot ) 199 200 (c) Wind speed and direction records 201 202 (d) Wind speed record s in the North and East directions 203 Fig. 3. An example of hurricanes going through the location of interest 204 11 205 (a) The whole hurricane track (the blue circle represents the 250 km limit) 206 207 (b) The hurricane track within the 250 km limit (blue circle) of the location of interest (blue dot) 208 209 (c) Wind speed and direction records 210 12 211 (d) Wind speed record s in the North and East directions 212 Fig. 4. An example of hurricanes passing by the West side of the location of interest 213 214 (a) The whole hurricane track (the blue circle represents the 250 km limit) 215 216 (b) The hurricane track within the 250 km limit (bl ue circle) of the location of interest (blue dot) 217 13 218 (c) Wind speed and direction records 219 220 (d) Wind speed record s in the North and East directions 221 Fig. 5. An example of hurricanes passing by the Ea st side of the location of interest 222 Wind records are first collected through applying the 250 km distance limit between the hurricane eye and 223 the location of interest. Hurricanes with very low wind speeds are then filter ed out through a strategy that 224 only hurricanes whose maximum wind speed s at the location of interest are great er than the 50 -year MRI 225 wind speed at the same location are considered . The 50 -year MRI wind speed obtained from the ASCE 7 226 Hazard Tool (ASCE 2016a, b) is a 3- second gust wind speed at 10 m above ground ( 47 m/s for this location), 227 which is then converted to 10- min sustained wind speed at 10 m above ground (32.4 m/s for thi s location) 228 following the approach proposed by Simiu and Scanlan (Simiu and Scanlan 1996) . This 50- year MRI 10- 229 min sustained wind speed is used as the threshold for comparison with the collected hurricane wind records 230 to get rid of those with small maximum wind speeds . Thus, a total of 162 hurricane wind records are 231 collected from the 10,000- year synthetic hurricanes, of which 160 records are shown in Fig. 6 within a 232 Cartesian coordinate system and are used in the following sections for clustering. Only 160 records are 233 included because 162 cannot be divided by the batch size (i.e., 16) employed in the training process of the 234 14 autoencoder , as will be introduced in the following section s. In addition, Fig. 7 presents the histogram of 235 the durations of all of the collected hurricanes with a mean duration of 12.4 hours . To avoid the impulse 236 effects, a 1 -hour linear ramp- up and a 1- hour linear ramp- down are attached to the beginning and the end 237 of the collected w ind records, respectively, as recommended in the Prestandard for Performance- Based 238 Wind Design (ASCE 2019) . To be consistent with the hurricane wind records with 10 -min intervals, the 239 ramp is added as six 10- min steps with a constant wind direction. Note that the ramps are not included in 240 Fig. 3 to Fig. 5 but included in Fig. 6 and Fig. 7. Moreover, as will be discussed in the following sections, 241 the collected wind records may have different durations , but the autoencoder needs the same size for the 242 input data of each r ecord . Therefore, to facilitate training the autoencoder , zero paddings are added to the 243 beginning and the end of the records that are shorter than the longest one. Consequently, all records after 244 preprocess have the same length as the longest one. For each record, zero paddings at the beginning and the 245 end have the same length, which means all records after preprocessing have a midpoint that is usually 246 recorded when the hurricane eye is closest to the location of interest . 247 248 Fig. 6. The 160 collected hurricane wind records resolved in two directions 249 15 250 Fig. 7. Histogram of the durations of the collected hurricane wind reco rds 251 Wind records for a region 252 Hurricane wind records for different locations have different patterns. Consequently, it is appropriate to 253 select site- specific wind records instead of generic wind records for all locations. Compared to generic wind 254 records, site- specific wind records have lower uncertainties and thus can be used to predict response s of 255 structures at a given location more accurately. To collect and select site- specific hurricane wind records for 256 a region of interest , this research propose s that this region can be discretized into a set of grids and the 257 centroid of each grid is used to represent the whole grid for recording wind speeds and directions . Thus, 258 hurricane wind records can be collected for all centroids of the grids. To demonstrate this idea, Fig. 8 show s 259 Massachusetts as a testbed, which i s divided into 0.2 ° by 0.2° grids. In Fig. 8, the red dots represent the 260 centroids of the grid s that are not associated with Massachusetts, while the 92 blue dots represent the 261 centroids of the grids that are associated with Massachusetts. The hurricane wind records collection 262 procedure proposed in the previous section s is then run for all 92 grids. Note that when generating the wind 263 records, the percentage of the sea- land transition is calculated for the centroid of each grid based on its fetch 264 distance. In addition, the 50-year MRI wind speeds for the centroids of some grid s cannot be obtained from 265 the ASCE 7 Hazard Tool because these centroids are over the ocean (see Fig. 8); therefore, for these cases , 266 16 locations within the same grids but on the land are used to find the 50 -year MRI wind speeds. Figure 9 267 presents the histogram of the number of hurricanes collected for all 92 grids , with a mean value of 202. 268 269 Fig. 8. Massachusetts is discretized into grids 270 271 Fig. 9. Histogram of the number of collected hurricanes for the 92 grids 272 Wind records clustering and selection 273 The a pproximate ly 200 collected hurricane wind records for each grid are still too many for design check s 274 and fragility development, especially considering the long durations of the wind records. Incremental 275 dynamic analysis (IDA) may be used to estimate collapse probability of structures under hurricanes (Du et 276 al. 2022; Vamvatsikos and Cornell 2002) . This approach is computationally intensiv e because direct 277 integration of the nonlinear dynamic governing equations is required over the entire duration of the 278 hurricane wind records and this nonlinear time history analysis need s to be run multiple times with sc aled 279 17 wind records . As such, it is important to limit the number o f records used. Therefore, in this research , the 280 collected wind records for each grid are first clustered using a machine learning approach and then 281 approximate ly 1/10 of the wind records in each cluster are selected , which are combined together to create 282 approximate ly 20 selected wind records for each grid. This significantly reduce s the number of nonlinear 283 time history analyses required , while still preserving the uncertainties in the collected records. This 284 procedure is similar to stratified sampling in statistics. Sampling is the process of selecting a subset from a 285 population so that the characteristics of the whole population can be estimated using this subset , while 286 stratified sampling is used by div iding the population into subpopulations (i.e., clusters in this paper) , where 287 the elements within each subpopulation are similar, and perform ing sampling on each subpopulation. 288 Stratified samplin g may improve the precision o f the sample because sampling variability within each 289 subpopulation is smaller than the sampling variability on the entire population (Botev and Ridder 2017; 290 Parsons 2014) . Specifica lly, the selected wind records can cover a spread of properties such as durations, 291 patterns of wind speed records, and patterns of wind direction records, because the collected wind records 292 are divided into clusters based on these properties. 293 Fully connected autoencoder 294 Since the collected hurricane wind records are time series of both wind speed and direction with different 295 duration s, it is challenging to cluster the records directly. To facilitate the clustering process, the high 296 dimensional wind r ecords are first transform ed into low dimensional latent features using an artificial neural 297 network named autoencoder (Aggarwal 2018; Bond et al. 2022; Tavakoli et al. 2020) . The architecture of 298 the autoencoder for wind records at the location of interest given in the previous section is presented in Fig. 299 10. It is seen that the input matrix is the original wind speed records in the Cartesian system, which has two 300 columns with each column representing wind speed time historie s in the North and Eas t direction s, 301 respectively . The input matrix is first flattened into a vector as the input layer of the fully connected 302 autoencoder and then passed through other hidden layers to reconstruct the data as another vector in the 303 output layer , which is finally reshaped to a matrix as the reconstructed wind speed record s in the Cartesian 304 18 system . Even though the two columns of the input matri x are correlated time series of wind speeds in two 305 directions , this “flatten” and “reshape” process is reasonable because the correlations are considered in the 306 flattened vectors (input and output layers) through the weights of the fully connected layers. In another 307 word, “flatten” and “reshape” only change the appe arance of the data while retain ing the relationships and 308 correlations of the elements within the data. A fully connected autoencoder means that all the neurons in 309 one layer are connected to all the neurons in the next layer . The autoencoder architecture consists of two 310 parts: the encoder that compresses the high dimensional input data into the small -size latent feature vector, 311 and the decoder that utilize s the latent features to reconstruct the input data. In this example, the flattened 312 wind speeds in the i nput layer are transform ed into 5 latent features through the encoder process, which are 313 then expanded to form the reconstructed but still flattened wind records in the output layer through the 314 decoder process. The hidden layers with a nonlinear activation function (Tanh) are included to enhance the 315 power of this autoencoder so that it can map the input data into much smaller dimensional spaces . Here 316 Tanh is adopted because it has better performance than other ac tivation functions based on numerical tests 317 in this research . This autoencoder architecture requires that all input matrices have the same size ; thus, the 318 size of the longest wind record is used as the size of the input matrices and zero padding is added t o the 319 beginning and the end of all other short er wind records. This strategy retain s all information in the wind 320 records. In this example, the longest record has 156 data points (including the ramp -up and ramp- down) 321 with 10- min intervals, so the number of rows of the input matrices is 156. 322 19 323 Fig. 10. The proposed autoencoder architecture 324 The training of this autoencoder is conducted by minimizing the error between the reconstructed data in the 325 output layer and the input data , which ensures that the latent features can represent the important patterns 326 of the wind records. The Adaptive Moment Estimation (Adam) algorithm is adopted for stochastic 327 optimization and batch normalization is added to some hidden layers as show n in Fig. 10 to address the 328 exploding and vanishing gradient problems (Aggarwal 2018) . Since the chosen batch size is 16, only 160 329 of the collected 1 62 wind records are used for the training process. In addition, Fig. 11 illustrates the 330 reconstructed 160 wind records in the North and East directions after training the proposed autoencoder 331 neural network. The histogram of the reconstruction error between the original and the reconstruct ed wind 332 records is shown in Fig. 12, which demonst rates that the reconstructed records match well with the original 333 ones and the latent features hold the most important characteristics of the wind records . It should be noted 334 that since the 312 data points in the input layer is compressed into only 5 latent features, there must be some 335 loss of information in this process and the discrepancies between the original and the reconstructed records 336 are inevitable. However, these discrepancies are u sually induced by noise or other nonsignificant factors; 337 20 therefore, the low dimensional latent features should be adequate for clustering because the important 338 information has been extracted through the autoencoder . 339 340 Fig. 11. The 160 reconstructed wind records in two directions for the location of interest 341 342 Fig. 12. Histogram of the reconstruction error 343 344 345 21 Clusterin g and selection based on latent features 346 The location of interest studied in the previous s ection s is used here as an example. After the training 347 process, all wind speed time series are converted into latent feature vectors, on which the k- means algorithm 348 is applied for clustering. The goal of clustering is to maximize the similarity of data wit hin each cluster and 349 maximize the dissimilarity of data in distinct clusters. Therefore, one can take a subset of the data in a 350 cluster to represent all data in that cluster , the accuracy of which depends on the number of clusters used. 351 Here, the elbow rule is adopt ed to find an optimal number of clusters (Thorndike 1953) . To do so, the k- 352 means algorithm has been run multiple times on the latent features with different number of clusters ranging 353 from 2 to 20. F or this example, when the number of clusters k eq uals 8, the Within- Cluster -Sum of Squared 354 Errors (WSS) curve reaches its elbow as shown in Fig. 13. Therefore, the 160 hurricane wind records are 355 divided into 8 clusters . Since it is difficult to show the 5 latent features on a 2D or 3D figure, principal 356 component analysis is performed o n the latent features and the first 3 principal components are plotted in 357 Fig. 14 to demonstrate the results of the k -means clustering. This is acceptable because the first 3 principal 358 components possess 82% of the variation of the 5 latent features and it is believed that the 5 latent features 359 must show better performance than the 3 principal components if they can be plotted in a figure . In Fig. 14, 360 the first 3 principal component s are presented using 8 different colors for the 8 clusters, from which it may 361 be seen that the hurricane wind record s are clustered well because the principal component s of different 362 clusters have rare overlap s and the principal component s of each cluster are gathered closely around their 363 centroid. 364 22 365 Fig. 13. The WSS for differe nt number of clusters 366 367 Fig. 14. Principal components of the latent features for the 8 clusters 368 To demonstrate the effectiveness of the proposed clustering approach, Fig. 15 to Fig. 22 illustrate the 369 hurricane wind speeds and tracks of the 8 clusters. It is seen that the clustering results are successful, 370 because hurricane wind speeds and durations within each cluster have similar patterns. Specifically, 371 23 Clusters 2 and 7 have hurricanes whose tracks pass by the East side of the location of interest , while other 372 clusters have hurricanes whose tracks pass by the West side of the location of interest. The number of 373 hurricanes in each cluster from Cluster 1 to Cluster 8 are 31, 17, 31, 13, 20, 12, 19 and 17, respectively. So 374 much more hurricanes pass by the West side of the location of interest than the East side. The main 375 difference between Cluster 2 and Cluster 7 is that the dur ations of hurricanes in Cluster 7 is longer. For the 376 clusters passing by the West side of the location of interest, Cluster 3 and Cluster 4 has the shortest and the 377 longest durations, respectively, while Clusters 1, 5, 6 and 8 have durations in the middle. Clusters 6 and 8 378 have very similar durations , but they are divided into two clusters because they have different shapes for 379 the profile of the wind speed time histories . There are outliers in some clusters such as the one with abrupt 380 changing of the storm heading direction as seen in the figure of hurricane track s of Cluster 2 . This can be 381 expected because the k -means algorithm cannot eliminate all outliers, but instead assign s outlier s to their 382 closest cluster. Usually, outlier s are rare and their latent feature point s are far from the centroid of all points 383 in a cluster . Therefore, the outlier commonly will not be includ ed to the final s uite of wind records 384 considering the selection strategy within a cluster that will be introduced below . The wind field shown in 385 Fig. 2 also ha s impacts on the clustering results, which cannot be explained explicitly here because its 386 information is included in the latent features through the operations on the wind records during the training 387 of the autoencoder . 388 Considering the computational demand of nonlinear time -history analys es that these wind records will be 389 used to perform , approximately 1/10 of the hurricanes in each cluster are selected and combined together 390 as the final s uite of hurricane wind records . The number of record s selected from each cluster is proportional 391 to the total number of record s in each cluster, which results in 3, 2, 3, 1, 2, 1, 2 and 2 record s from each 392 cluster , respectively . This strategy is used to make sure the proportions of different patterns of wind records 393 are similar in the selected 16 hurricanes and the original 160 ones. It is also reasonable to make sure the 394 selected records from each cl uster are the most representative ones. To achieve this goal, the clustering 395 results of the latent features are used , and for each cluster it is recommended to select those records whose 396 24 latent feature points are the closest to the centroid of all latent f eature point s in that cluster. The selected 397 records for each cluster are highlighted in bold solid lines as shown in Fig. 15(a) to Fig. 22(a) , which is a 398 demonstration of the validity of this selection strategy within a cluster . In Fig. 15 (a) to Fig. 22(a) , all wind 399 records are shown in different colors and curves resolved from the same record are shown in the same color 400 in the upper subplot and lower subplot. It is seen that the selected records are representative, as they are 401 near the middle of all the records . The total of 16 selected hurricanes can be employed to represent 402 uncertainties in wind loading for design check and fragility development for structures at th e location of 403 interest . Note that these selected wind records are only time series of 10 -min mean wind speed at 10 meters 404 height. If one wants to use them for structural dynamic analysis , the fluctuating wind speeds and the 405 atmospheric boundary layer should be considered. 406 407 (a) Wind records of Cluster 1 408 25 409 (b) Hurricane eye tracks of C luster 1 410 Fig. 15. Hurricanes in C luster 1 411 412 (a) Wind records of C luster 2 413 414 (b) Hurricane eye tracks of C luster 2 415 Fig. 16. Hurricanes in C luster 2 416 26 417 (a) Wind records of C luster 3 418 419 (b) Hurricane eye tracks of C luster 3 420 Fig. 17. Hurricanes in C luster 3 421 27 422 (a) Win d records of C luster 4 423 424 (b) Hurricane eye tracks of C luster 4 425 Fig. 18. Hurricanes in C luster 4 426 28 427 (a) Wind records of Cluster 5 428 429 (b) Hurricane eye tracks of C luster 5 430 Fig. 19. Hurricanes in C luster 5 431 29 432 (a) Wind records of C luster 6 433 434 (b) Hurricane eye tracks of C luster 6 435 Fig. 20. Hurricanes in C luster 6 436 30 437 (a) Wind records of C luster 7 438 439 (b) Hurricane eye tracks of C luster 7 440 Fig. 21. Hurricanes in C luster 7 441 31 442 (a) Win d records of C luster 8 443 444 (b) Hurricane eye tracks of C luster 8 445 Fig. 22. Hurricanes in C luster 8 446 Wind records selection for a region 447 As a case study for region al analysis, Massachusetts has been divided into 92 girds and wind records has 448 been collected for each grid . Here t he procedures for wind records clustering and selection introduced in 449 the previous s ections are applied to all 92 grids. The same autoencoder architecture is used for all grids 450 except for the slightly different sizes of the input vectors for different grids, which is because the maximum 451 duration of the collected records for different grids may be different. The same k -means algorithm is also 452 adopt ed for clustering on the latent features; however, the number of clusters may vary for different grid s 453 because it is dynamically determ ined using the elbow rule . The histogram of the number of clusters for all 454 32 grids is presented in Fig. 23 with a mean value of 5.65. Since approximately 200 hurricane wind records 455 are collected for each grid , then approximately 20 records are selected for each grid according to the method 456 introduc ed in the previous s ection s. Finally, a wind map is generated so that a s uite of hurricane wind speed 457 and direction records can be provided for any location s in Massachusetts. For example, Fig. 24(a) gives 16 458 wind records selected from 8 clusters for a grid whose centroid has a lat itude of 41.7 and a longitude of - 459 70.1 (this location is used in the previous s ections), while Fig. 24(b) gives 19 wind records selected from 4 460 clusters for a grid whose centroid has a latitude of 42. 1 and a longitude of -72.5. Here the wind records 461 selected from the same cluster are shown in the same color, and it is seen that wind records within the same 462 cluster have similar characteristics in terms of wind speeds, directions, and durations. This approach 463 provides an alternative to the ASCE 7 wind map. T he ASCE 7 wind map can only provide a wind speed 464 without any information of variation of the wind speed and direction during a hurricane. This methodology 465 can be generalized to any other regions besides Massachusetts. 466 467 Fig. 23. Histogram of the number of clusters for all grids 468 33 469 (a) For a grid whose centroid has a latitude of 41.7 and a longitude of - 70.1 470 471 (b) For a grid whose centroid has a latitude of 4 2.1 and a longitude of - 72.5 472 Fig. 24. Examples of selected hurricane wind records 473 Conclusions 474 This paper presents a machine learning approach for collecting and selecting hurricane wind speed and 475 direction records for a location and a region, which can be used for efficiently developing fragility curves 476 or assessing probabilistic behaviors of structures considering uncertainties in hurricanes . The selected 477 hurricane wind records are supposed to address the uncertainties in hurricanes because 1) they are selected 478 34 from 10,000- year synthetic hurricanes and 2) the collected records with similar properties are first divided 479 into clusters and then the most representative ones are selected from each cluster. The pr eprocess of the 480 wind records is also important since i t can remove hurricanes with very small wind speeds and limit the 481 durations of the records to a relatively short time. The proposed autoencoder architecture is shown to be 482 able to reconstruct the wind speed time series and compress them into low dimensional latent features. The 483 clustering results based on the latent features using the k -means algorithm are successful, because the points 484 in the latent space are divided clearly into s everal clusters , and the wind records in the same cluster exhibit 485 similar properties in duration, hurricane track, and changing of wind speed and directions. A method is also 486 proposed to select the most representative records from each cluster based on the clustering results of latent 487 features. This hurricane selection procedure is demonstrated using wind records from both a location and a 488 region. For the regional hurricane selection, Massachusetts is used as a testbed, and it is discretized into a 489 set of grids with performing the proposed hurricane selection procedure on each grid. Usually, approximate 490 20 wind records are selected for a location, which make th e nonlinear structural analysis feasibl e for 491 uncertainty propagation simulation under hurricanes . 492 Data availability 493 Some or all data, models, or code that support the findings of this study are available from the corresponding 494 author upon reasonable request. Some or all data, models, or code used during the study were provided by 495 a third party. Direct r equests for these materials may be made to the provider as indicated in the 496 Acknowledgements. 497 Acknowledgement 498 The authors wish to thank Dr. Weichiang Pang of Clemson University for providing the synthetic hurricane 499 catalog . The material presented in this p aper is based upon work supported by National Science Foundation 500 under Grant No. CRISP -1638234 and Northeastern University . This support is gratefully acknowledged. 501 502 35