Low-rise gable roof buildings pressure prediction using deep neural networks

Journal of Wind Engineering & Industrial Aerodynamics xxx (xxxx) xxx

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Journal of Wind Engineering & Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia

Low-rise gable roof buildings pressure prediction using deep neural networks Jianqiao Tian a, Kurtis R. Gurley c, Maximillian T. Diaz a, Pedro L. Fern
andez-Cab
an b, d, c a, * Forrest J. Masters , Ruogu Fang a

J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, 32611, USA Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, 20742, USA Department of Civil and Coastal Engineering, University of Florida, Gainesville, FL, 32611, USA d Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY, 13699, USA b c

A R T I C L E I N F O

A B S T R A C T

Keywords: Deep neural network Machine learning Low-rise buildings Wind-induced pressure Prediction Super-resolution

This paper presents a deep neural network (DNN) based approach for predicting mean and peak wind pressure coefficients on the surface of a scale model low-rise, gable roof building. Pressure data were collected on the model at multiple prescribed wind directions and terrain roughness. The resultant pressure coefficients quantified from a subset of these directions and terrains were used to train a DNN to predict coefficients for directions and terrains excluded from the training. The approach can leverage a variety of input conditions to predict pressure coefficients with high accuracy, while the prior work has limited flexibility with the number of input variables and yielded lower prediction accuracy. A two-step nested DNN procedure is introduced to improve the prediction of peak coefficients. The optimal correlation coefficients of return predictions were 0.9993 and 0.9964, for mean and peak coefficient prediction, respectively. The concept of super-resolution based on global prediction is also discussed. With a sufficiently large database, the proposed DNN-based approach can augment existing experimental methods to improve the yield of knowledge while reducing the number of tests required to gain that knowledge.

1. Introduction The distribution of wind-induced pressures acting on buildings has a critical role in structural design. The pressure distribution for a specific building is generally collected from scale model experiments in a boundary layer wind tunnels (BLWTs). Experiments in BLWTs have to be conducted for all combinations of building shape and wind parameters of interest. This process can be time and resource intensive, and resource or physical testing constraints may prevent the capture of desired data. Therefore, it is desired to find a reliable approach to cyber-enhance data collection procedures in BLWTs. Recent developments stand to benefit from such enhancement. As evidenced by the National Science Foundation Natural Hazards Engineering Research Infrastructure (NHERI) program, facilities to study wind effects have begun to evolve into cyberphysical facilities (Whiteman et al., 2018a, 2018b). This paper explores how machine learning techniques can cyberenhance the conventional BLWT modeling to extend the knowledge yielded from tests while commensurately reducing the effort required to

perform them. The larger contextual question centers on how a machine learning enhanced method can ultimately lead to approaches that learn as data are collected and subsequently optimizes the execution of experiments (presumably by automation) to reduce the time required to achieve user-specified objectives, e.g., determine the worst-case envelope of peak loads for unmeasured wind directions. Deep neural network (DNN) based methods have been shown to be a robust solution to predict pressure coefficients distributed over a relatively local scale (prediction of pressure at locations in close physical proximity to the training data). In this paper, we explore taking a DNNbased prediction method to a more global prediction level, which improves prediction accuracy and expands the applicability of the tool. The current study addresses the role of machine learning as a robust tool to numerically predict wind-induced pressure loads for a model (a) absent experimental data for a specified incident wind direction and terrain exposure but (b) with data collected in other wind directions and terrains. Besides predicting the pressure distribution under absent wind condition, this proposed DNN based method is also applied to achieve a

* Corresponding author. E-mail address: ruogu.fang@ufl.edu (R. Fang). https://doi.org/10.1016/j.jweia.2019.104026 Received 4 June 2019; Received in revised form 8 August 2019; Accepted 2 November 2019 Available online xxxx 0167-6105/© 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Tian, J. et al., Low-rise gable roof buildings pressure prediction using deep neural networks, Journal of Wind Engineering & Industrial Aerodynamics, https://doi.org/10.1016/j.jweia.2019.104026

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∙ Predictions are conducted at a relatively local scale. This local predicting scale is mainly expressed with two perspectives: (a) localization: the function maps were generated based on a relatively small hand-picked neighborhood, and (b) planarization: prediction involves limited flow regions, e.g., the roof. Prediction at a single location was based on the measurements four neighboring locations to the predicted location. This localization restricts prediction into a small scale of a neighborhood and discards information beyond this neighborhood. When the target neighborhood was located around the boundaries of separating/reattaching flow regions, information beyond this narrow neighborhood will be more critical. Moreover, for spatial pressure distribution, some teams flattened sensors’ 3D locations in a 2D plan, by either converting the sensors’ location or simply removing z coordinate, to predict wind load over roofs (Chen et al., 2002, 2003; Fu et al., 2006). Some others adopted 3D locations as their inputs; but the predictions were performed exclusively for building roofs as well (Gavalda et al., 2011; Hu and Kwok, 2019; Fu et al., 2007a). This planarization scheme, i.e., only focusing on relatively flat plan or flattening a 3D space into a 2D plane, removes potentially important 3-dimensional spatial information and limits the flexibility of the model. For example, in (Bre et al., 2018) the objective is to predict surface-average pressure coefficients for varying wind angles. This pressure coefficient is the average result for each face, i.e., for one surface under one wind direction, there is only one number to predict. Therefore, this work is incapable of having any spatial resolution in the prediction. On the other hand, in our work, the prediction result has a higher spatial resolution. It is the pressure coefficients at multiple sensor locations that we predicted, i.e., under one prediction condition, there are 206 or 266 coefficients to predict at once. Detailed discussion regarding the global prediction and its impact of improving prediction performance is discussed in Sec. 5.1. To our best knowledge, our proposed work is the first-of-its-kind to globally predict the entire building surface pressure distribution with spatial resolution.

spatial interpolation to increase the spatial resolution of the pressure distribution. This interpolation is further expanded to the concept of super-resolution, where pressure distribution can be spatially interpolated at an arbitrary location on the surface. Proof of concept is given for implementing the proposed approach in conjunction with experiments in this study. The specific prediction task involves predicting pressure distribution over the whole building surface for unseen wind directions and unseen upstream terrain conditions. In this study DNN is utilized to predict both mean and peak pressure coefficients. Major contributions contained in this paper include (a) advancing prediction from a local level to a global level, (b) predicting peak pressure coefficient distributions using a DNN-based method, which is the first such study of its kind to our best knowledge, and (c) introducing the concept of super-resolution, a natural benefit of the global prediction. It is demonstrated that DNN-based prediction algorithms possess superior generality for various prediction tasks. A brief discussion regarding the effect of low resolution on prediction accuracy and confidence is also presented in the context of sensor placement optimization. The paper is organized as follows. In Sec. 2, the background on the DNN-based method in load prediction is presented. In Sec. 3, we introduce the database used in this study. Sec.4 provides brief but essential DNN-related concepts. In Sec. 5, we provide the detailed experiment setup and result for the global prediction. A discussion of popular error metrics for wind load prediction is also presented here, along with a novel error metric defined in this work. With Sec. 6, we focus on the concept of super-resolution, demonstrating the feasibility of this concept with experimental results. Lastly, discussion regarding the benefit of employing a global prediction and super-resolution is analyzed in Sec.7, followed by the conclusion in Sec.8. 2. Background 2.1. DNN-based methods

Despite their limitations, these works demonstrate that a DNN-based algorithm is a potential solution to predict wind loads on bluff bodies. The focus of this present paper is to discuss DNN’s ability to handle larger prediction scale, i.e., global prediction scale, to enhance prediction accuracy. Further, new DNN algorithms are presented to demonstrate the efficacy of peak coefficient prediction to complement the existing literature’s focus on mean coefficients. This greatly expands the utility of DNN as a tool to inform design. The performance comparison between DNN and other machine learning techniques for wind engineering has not been usually reported. However, DNN has been often reported to be a universal machine learning method for nonlinear regression tasks with higher generality and flexibility (Zhang et al., 2001). In other fields such as computer vision and pattern recognition, shallow machine learning techniques, such as support vector machines (SVM), can be seen as a viable alternative for DNN (Akande et al., 2014). In this work, we concentrated on utilizing DNN to discuss the feasibility of conducting the global pressure distribution and the advantage brought by the global prediction. The performance comparison between different machine learning techniques is another topic we would like to include in our future works.

DNN-based approaches have been reported as a robust solution for accurately predicting wind-induced pressures acting on building models. Predictions have been conducted with a single building model and between multiple building models, in varying forms such as pressure time series (Chen et al., 2002), mean pressure coefficients (Fu et al., 2007a, 2007b; Gavalda et al., 2011; Fern
andez-Cab
an et al., 2018; Chen et al., 2003), face-averaged mean pressure coefficients (Bre et al., 2018), root-mean-square (RMS) pressure coefficients (Gavalda et al., 2011; Chen et al., 2003), power spectrum (Dongmei et al., 2017; Fu et al., 2006), fluctuating pressure coefficients (Hu and Kwok, 2019), and interference factor between buildings (Zhang and Zhang, 2004). As acknowledged in the previous references, DNN’s application to wind load prediction has been limited to a relatively elementary level due to the lack of computational resource and suitable databases. ∙ Current predictions can be performed with a limited number of input variables. Typical input variables include sensors’ locations, building model geometry, and flow conditions, e.g., incident wind direction, upstream terrain conditions. Most previous works involve a limited combination of these variables. Works that have multiple variables as the network inputs failed to conduct prediction with regards to every input variable. For example, the team in (Gavalda et al., 2011) trained a network, with sensors’ 3D locations, wind direction, and roof slope as inputs and mean coefficients as output. However, they solely validated the prediction accuracy for unseen wind direction, but not for unseen roof slope. Therefore, we couldn’t verify whether the DNN captured the physical meaning of roof slope, or if the roof slope did not contribute to the final prediction in the DNN. To be practically useful, such predicting methods are expected to predict pressure distribution with multiple variables. This goal has not been fully achieved due to the lack of a suitable database.

3. BLWT dataset For DNN-based methods, the training database plays a critical role in the overall performance. A useful database should have sufficient size, sufficient variety, and suitable quality for the application. Such a database should include multiple scenario parameters, such as building geometry, terrain condition, wind direction, etc. Moreover, the size of such a database needs to be sufficient to allow comparison within each parameter, or cross multiple parameters, to be performed. The multisensor configuration should contain sufficient spatial resolution to 2

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pressure coefficients for nearly 300 different upwind terrain conditions. The terrain condition is simulated by combinations of varying roughness element heights, from 0 to 160 mm, increment as 10 mm, and varying roughness elements orientations, precisely configured by an automated roughness grid actuation system. The building dimension ratio is 3:5 : 2:3 : 1 (L: W: H). Three model scales are provided in this database: 1 : 20, 1 : 30, and 1 : 50 with the roof slope as 14 : 12 . Thus, the model is intentionally the same dimension ratios and roof slope as the ST3 dataset in the NIST-UWO database. Each set of data has 266 available sensors installed on the whole surface. The sensor configuration is shown in Fig. 2. A given test was measured for 20, 180, and 300 s for the 1:50, 1:30, and 1:20 models, respectively, at a sampling rate of 625 Hz. In this study, a 3rd order low pass digital Butterworth filter with cutoff frequency as 150 Hz is applied to the raw data. 4. DNN methodology Fig. 1. Sensor Configuration of ST3, NIST-UWO database.

4.1. Concept Deep neural network (DNN) has been a popular machine learning tool since it was introduced. DNNs are well known for their ability to reveal complex non-linear dependency relations between input-output pairs. As its name implies, DNN is inspired by the mechanism of biological neural networks, where learning is popularly assumed to be a process of dynamically adjusting connection maps between neurons (Nagy et al., 2002; Zhang, 2000). In a DNN, there are several layers, including one input layer, one output layer, and one or more hidden layers. Each hidden layer contains several neurons. A general notation to describe the network structure goes like this: I-h1 -h2 -O, referring to a network with I input variables, O output variables, h1 and h2 neurons contained in the first and second hidden layer respectively. For example, Fig. 3 presented a simple 4-4-3-1 ~ DNN. It has four input variables: x, y, z, and α, one output variable: C. First and second hidden layers have four and three neurons, respectively. Each neuron is a basic computation unit. The specific computation operated in the neuron is called activation function. Neurons, within two successive hidden layers, are cross-connected with varying weights and biases. Computation results from the previous neurons are sent to neurons at the next layer as input. This process, from network input to output, through lower layer to higher layer, is referred to as feed-forward. At the end of one feed-forward procedure, the error between truth and output is calculated with specific functions, i.e., a cost function to evaluate the current performance of the network. Within one neuron, the forward computation contains two parts: multiplication-addition, and activation function, as shown in Fig. 4. The multiplication-addition process is responsible for gathering inputs in a weighted approach, followed by adding with a bias. This weighted summation, noted as zl in Fig. 4, is then sent to the activation function to generate an activation, noted as al in Fig. 4, which will be sent to next layer as input. Here, the superscript l indicates that this variable exists in the l-th hidden layer. DNN simulates the overall function map by combining a set of activation functions with optimal weights-bias configuration. The overall system function, as well as cost function, are functions of network inputs, and weights-biases at every layer. Training, i.e., the process of finding the optimal weights/bias, is achieved by minimizing cost (errors) between network output and truth. Training is usually performed in a highly automated fashion. This automation is a result of advanced learning algorithms, such as LevenbergMarquardt back-propagation algorithm, which is used in this paper. Specifically, for the Levenberg-Marquardt back-propagation algorithm in our work, we set the initial learning rate to be 0.001, learning rate decrease factor to be 0.1, learning rate increase factor to be 10, and maximal training epochs to be 1500. However, it should be pointed out that this parameter setting might be database dependent. A trained DNN

Fig. 2. Sensor Configuration of DesignSafe-CI database.

capture the fluctuating pressure in different flow regions over the surface of the model. Two suitable databases, NIST-UWO and DesignSafe-CI database, were chosen to serve our focus on predicting pressure coefficients for unseen (untrained) wind directions and terrain conditions. 3.1. NIST-UWO database The NIST-UWO database was created at University of Western Ontario boundary layer wind tunnel facility (Nist aerodynamic database, 2019; Ho et al., 2003). It contains wind pressure coefficients over the entire surface of a given model and includes varying building geometries and wind directions. For this study, the ST3 dataset from Test-7 is used, since its sensor configuration fits our experiment requirements the best among the options in that database. The ST3 dataset contains 22 sets of data; each set includes 206 available sensor points. It covers wind directions from 0
to 80
, with increment as 5
, and 90
, 135
, 180
, 225
, 270
, 315
. The building dimensions ratio is 3:5 : 2:3 : 1 (L: W: H), with a 1 4:12 roof slope gable roof, and a scale as 1 : 100. Pressure sensors are distributed on both of the roof and standing walls. In this database, the ST3 Test-7 dataset includes 20 repeated measurements at 45
, which we later found critically valuable. This repeated measured dataset is named as STR in Test-7. The sensor configuration is shown in Fig. 1. 3.2. DesignSafe-CI database The DesignSafe-CI database (Fern
andez-Cab
an and Masters, 2018a, 2018b) was created at the University of Florida Natural Hazard Engineering Research Infrastructure Experimental Facility. It contains 3

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Fig. 3. Illustration of the structure and computation flow for a 4-4-3-1 DNN.

Fig. 5. Backward computation within one neuron. Fig. 4. Forward computation within one neuron.

and Mahmoud, 2004; Günaydın and Do gan, 2004; Dreiseitl and Ohno-Machado, 2002). One critical issue in training DNNs is over-fitting. Over-fitting refers to a situation where the DNN is trained to be too specific for the training database, therefore losing generality. When an over-trained neural network is employed in predicting/generating new data, it fails to use the correct general functional relations. Over-fitting could be loosely analogized to “memorizing” training examples, while ideal learning is to “understand” the patterns that exist in the training samples (Long et al., 2005; Tetko et al., 1995). To avoid this over-fitting problem, two major principles should be followed:

is expected to have the capability of obtaining complex function map between input-output pairs. One complete training iteration contains three major steps: feed-forward, cost computation, and back-propagation, as shown in Fig. 3. In the backward computation within one neuron, the outcome of cost function will be taken as input. Since cost function can be written as a function of every weight and bias, i.e., Jðw1 ;w2 ;w3 ;w4 ;bÞ, the gradient of the cost function can also be calculated for each weight and bias. Therefore, weight and bias ought to be updated to minimize the overall dJ . This process is illustrated in Fig. 5. cost function, e.g., w ¼ w  dw Some other concepts have been developed to improve the training performance of DNN-based approaches, such as gradient approximation, parameter initialization, mini-batch training, etc. Since this paper is rather a preliminary discussion of the ability/possibility of using DNN to handle wind load prediction, only the most essential concepts used in DNN-based prediction were presented in this paper. With DNN attracting more and more attention from the research community, we believe that interested readers could easily find more detailed information regarding the theory and history of DNN (Zhang, 2000; Hill et al., 1994; Ben-Nakhi

4.2. Principle one Train the DNN with the proper database. Since the DNN is trained by minimizing the error between network outputs and truth, if the training database contains “wrong” data, then the trained DNN will be influenced by the “wrong” samples. Here, “wrong” data refers to data samples that do not represent target function well or with limited generalization. This 4

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2011; Dongmei et al., 2017). The major drawback in hand-picked configurations is that information beyond this neighborhood will not be taken into consideration at all. This would require training a series of DNNs, each trained only using a subset of inputs to predict locally. Conversely, the global prediction would train the DNN using all taps on the whole surface without any discrimination. All available taps are used for training the network, and the well-trained network will make a final prediction based on all reference points. Thus, no hand-picked local neighborhood is necessary to assign. The global prediction can be simply described as an “all-to-one” method. We also extend our experiment to show that the global prediction is an “all-to-any” method, which leads to the concept of superresolution. A strong motivation for developing a global prediction network is that when the prediction location does not contain sufficient sensor resolution, a local prediction leads to lower accuracy and stability. To illustrate the benefit of a global prediction, consider the NIST Test7 database. Face Three has 27 sensors, as shown in Fig. 1, which we take as an example to demonstrate the performance between a global prediction and a local prediction. The experiment configuration is summarized in Table 1. For the case of an approach wind direction of 45
, locally predicting mean pressure coefficients with the method presented in (Chen et al., 2003), i.e., predicting the pressure distribution for the unseen wind angle based on all sensors from Face Three, delivered a final prediction with a correlation coefficients of 0.9444. Fig. 6 presents the actual and predicted mean pressure coefficients for each of the 27 locations on Face Three. The global prediction is then conducted by training the network on the whole surface, instead of only sensors from Face Three. When predicting the pressure distribution of Face Three with unseen wind direction as 45
, the network returns a more accurate final prediction result with a correlation coefficients of 0.9995 (see also Fig. 6. The sensor series number is illustrated in Fig. 1). The prediction result is shown in Fig. 7, where we use the standard box-plot to describe the distribution of correlation coefficients between prediction results and truth. These correlation coefficients are from ten independently repeated training instances. In a box plot, the box includes 25% to 75% of these coefficients, and extreme data point,

Table 1 Global and local prediction on Wall Three. Global Prediction Input Table Training Dataset Training Wind Direction Testing Dataset Prediction Accuracy (Correlation Coefficient)

Local Prediction

x; y; z, wind direction α 206 sensor on the whole 27 sensor on Wall Three surface  6 wind direction  6 wind directions 30
, 35
, 40
, 50
, 55
, 60
27 sensor locations on Wall Three, under wind direction 45
0.9995 0.9444

principle implies that the quality of training database should be examined so that the interference introduced by the training database can be rejected, while the generality is preserved as much as possible. 4.3. Principle two Stop the training when it is good enough, before the network overfitted. There are several stop criterion available, such as performance criterion, converging rate criterion, validation checks criterion, and maximal training iterations criterion. 5. DNN application to wind tunnel data 5.1. Global vs local prediction Within the context of the wind pressure application, consider the locations of the pressure measurements in Fig. 1, where each measurement location (each tap) is indicated by an x-mark. The local prediction would predict pressure at a given tap (one x-mark in Fig. 1) using input from only the taps within a hand-picked neighborhood. This neighborhood could be a small 4-by-4 neighborhood or relatively larger area such as the whole roof. Regardless how specifically large this area is; a handpicked region was always defined in previous studies (Chen et al., 2002, 2003; Zhang and Zhang, 2004; Fu et al., 2006, 2007a; Gavalda et al.,

Fig. 6. Global prediction of mean coefficients for Face Three. 5

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Fig. 7. Correlation coefficients distribution from ten repeated training-prediction procedure.

i.e., outlier, is represented by “ þ ”-marks (McGill et al., 1978). In terms of DNN training, a shorter box is better than a more extended box; a higher box is better than a lower box (higher correlation coefficients); and outliers closer to the box are better than farther from the box. We can see that global prediction promotes both prediction accuracy and prediction stability, and therefore stronger prediction confidence. This performance improvement demonstrates the benefit of conducting the prediction at a global level. By including all locations on the surface into one integrated prediction framework, the training database was expanded and assisted the DNN to train better. The price for upgrading a local prediction to a global prediction is mainly higher computational cost. To our observation, a global prediction requires more training iterations than the local prediction, approximately five-fold to ten-fold. However, with advancing computation speed, the extra computational price could be negligible. In 2003, 151 training iterations of 246 parameters took an IBM workstation 10 min to achieve. Today an Apple laptop can finish 1300 training iterations of 390 parameters within 45 s. The global concept can certainly be expanded to include training data on the other surfaces beyond Face Three to promote the prediction accuracy of areas with less dense sensor configuration. In previous studies (Chen et al., 2003; Fu et al., 2007a; Gavalda et al., 2011; Dongmei et al., 2017), such loosely related data was generally considered less useful, and for the sake of simplicity, these data were discarded. However, DNN-based method allows us to fully use these data since well-trained DNN will “decide” how to use each data or assign importance to each data point. To further validate DNN’s ability to conduct such a global predictions (using all faces to train), we designed three experiments to predict the spatial distribution of both mean and peak pressure coefficients for both unseen wind direction and terrain condition. Mean pressure coefficients were predicted for unknown incident wind direction (Experiment 1), and unknown upstream terrain roughness conditions (Experiment 2). Peak pressure coefficients (typically the basis for design loads) were predicted for unknown incident wind direction in Experiment 3. The concept of Super-Resolution is then introduced and demonstrated in Experiments 4 and 5.

Fig. 8. Example prediction-truth pairs used to compare error metrics.

5.2. Error metric During our reviewing of related references (Chen et al., 2002, 2003; Zhang and Zhang, 2004; Fu et al., 2006, 2007a; Gavalda et al., 2011; Dongmei et al., 2017; Bre et al., 2018), we find that there are several error metrics used to evaluate the prediction accuracy, such as Root-Mean-Square Error (RMSE), Mean-Square Error (MSE) and correlation coefficients, R. However, there is a lack of common error metric that is used in every work. This leads to a situation where cross-reference comparison is difficult to conduct. We hereby compare each error metric and propose to employ a standardized error metric that is suitable for different prediction tasks. To make the comparison straightforward, we employ an example prediction-truth pair to illustrate the features of each metric, shown in Fig. 8. Additionally, for demonstrating each error metric’s performance with different data scenarios, e.g., different flow 6

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Consequently, for the prediction-truth pair in Fig. 8, the correlation coefficients of original, uplifted, and enlarged pairs all equal to 0.9988. These two properties free us from troubles when we need to perform some specific transformations on pressure coefficients. RMSE and MSE do not share the same property. Another valuable property of correlation coefficients is that the absolute value of the correlation coefficient is normalized between ½0; 1, and enables us to conduct cross-reference comparison efficiently. A critical drawback of the correlation coefficient is that correlation coefficient could only reflect the similarity of the shapes but not range, nor bias, i.e., RðA; BÞ ¼ RðA þ c; BÞ ¼ RðA  c; BÞ. Therefore, when correlation coefficients are used to estimate prediction accuracy, both scale and mean values should be given to comprehensively reflect the accuracy. Otherwise, correlation coefficients should also be provided in addition to plot figures. In the following parts of this paper, we choose the correlation coefficient as our accuracy estimator.

regions, or varying conditions, the original prediction-truth pairs are uplifted by 0.5 units, and enlarged 2 times, respectively. A distorted uplifted prediction was used to represent a “bad” prediction. 5.2.1. Mean square error Mean square error (MSE) is defined in (Chen et al., 2003) as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ffi 1 N pi  mi MSE ¼ Σ N i¼1 mi where, N is the number of pressure sensors; pi is the i-th data in a predicted dataset; mi is the i-th data in a measured dataset, i.e., the ground truth. MSE has been employed in (Chen et al., 2003; Zhang and Zhang, 2004; Fu et al., 2006; Gavalda et al., 2011), and it is one of the most popular error metrics for pressure distribution prediction on the roof area. However, for a global prediction, MSE is not a suitable error metric, because when additional standing walls were included in the prediction, some walls might introduce pressure coefficients that are very close to zero. These “near-zero” pressure coefficients could cause a dramatic rise in the MSE as the normalizing denominator. For the example prediction-truth pair, shown in Fig. 8, MSE of the original pair is 2.0709, while MSE of uplifted pair is only 0.0176. Even though they share the same fitting accuracy, the MSE says otherwise. The MSE between distorted prediction and corresponding truth is 0.1019, still smaller than the MSE of original prediction, even though the distorted prediction possesses lower fitting accuracy. This shows the major drawback of using MSE as it is insufficient to measure the fitting accuracy if no other restriction was given. This problem has not been pointed out previously because previous works concentrated in roof prediction. And roof area doesn’t tend to include such “near-zero” points.

5.3.2. Fit rate An additional limitation in previously employed error metrics has been noticed. These three error metrics considered only one measurement as ground truth. However, repeated wind tunnel pressure measurements in turbulent flows, conducted with identical measurement setup, contain observation uncertainty between measurements. This variability is much more pronounced for observed peaks and the resultant peak coefficients than for mean coefficients. This has been commonly observed and attributed to the chaotic nature of nonlinear turbulent fluid mechanics (Fu et al., 2006; Holmes and Cochran, 2003; Chen et al., 2003). The influence of peak coefficient variability will later be shown to present a challenge DNN prediction of peaks, which perhaps motivates the relative lack of attention to DNN based prediction of peak coefficients in the literature. Therefore, when evaluating the accuracy, we should also compare the prediction result with repeated measurements to avoid the observation uncertainty. If the prediction shares an accuracy close to repeated measurement statistical property, then it is fair to say the prediction is accurate enough to be used as a supplement for wind tunnel measurement. Therefore, we propose an accuracy estimator, based on observation uncertainty, called Fit Rate:

5.3. Root mean square error Root mean square error (RMSE) is defined in (Fu et al., 2007a) as: RMSE ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N Σ ðpi  mi Þ2 N i¼1

Step 1. calculate mean, μi , and standard deviation, σ i , of pressure coefficients from repeated measurement, at i-th sensor location;

where, N is the number of pressure sensors; pi is the i-th data in a predicted dataset; mi is the i-th data in a measured dataset, i.e., the ground truth. RMSE doesn’t suffer from the problem of “near-zeros”. This is because RMSE doesn’t include a normalization factor in the calculation. Nevertheless, the lack of normalization can also be viewed as a limitation as well, especially when the scale of pressure coefficients has been changed. For the original prediction-truth pair in Fig. 8, RMSE of the original pair is 0.98%, while, RMSE of enlarged pair is 1.96%. The RMSE doubled since the data scale doubled. Therefore, when RMSE is to be used in cross-reference comparison, it will be necessary to normalize the scale of pressure coefficients into a standardized range. Otherwise, RMSE is not sufficient to be used for evaluating the performance of the prediction accuracy.

Step 2. calculate difference, di ¼ mi  pi , between prediction, pi , and truth, mi , at i-th sensor location; Step 3. if jdi j < σ i , we say, at i-th sensor location, prediction fits within one standard deviation interval. Otherwise, it does not fit; Step 4. Fit Rate¼(Number of Fitted Sensor Location)/(Number of Total Sensors)  100% Prediction results at different sensor locations might have the same absolution error, but with different significance. Fit Rate expresses the significance by normalizing the error over observation uncertainty, i.e., standard deviation from the repeated measurement, at each sensor location. The major advantage of employing Fit Rate is that it enables us to diagnose prediction result at each single sensor location, with the comparison to repeated measurements, to interpret which sensor location, or which area is more difficult to predict. Fit Rate can also be employed as a complement to the correlation coefficient. For example, if we have two predictions, A and B, with same correlation coefficients, but A has a higher fit rate, then, we can interpret that A has an overall better fitting accuracy, except for a few prediction locations that prediction errors are more severe than prediction B. The fit rate distribution of these 20 repeated measurements in the form of mean coefficients, contained in NIST Test-7 database, is shown in Fig. 9 for one standard deviation interval. From this figure, we can see that this observation uncertainty is significant. Accordingly, when

5.3.1. Correlation coefficients Correlation coefficient, R, is defined in (Fu et al., 2007a) as: Σi¼1 ððmi mÞðpi pÞÞ ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffiWhere, N is the number of Correlation Coef. ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 N N N

Σi¼1 ðmi mÞ 

Σi¼1 ðpi pÞ

pressure sensors; pi is the i-th data in a predicted dataset; mi is the i-th data in a measured dataset, i.e., the ground truth. The correlation coefficient provides a very reliable approach for estimating prediction accuracy for both the local and the global prediction tasks. It measures how similar two sets of data are, but remain constant regardless of changes of bias and scale of data pairs, i.e., RðA;BÞ ¼ RðA þ c; B þ cÞ ¼ RðA  c; B  cÞ; c 6¼ 0. 7

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Fig. 9. Fit rate analysis for 20 repeated measurements of mean coefficients, within one standard deviation interval.

Table 2 Network configuration for Exp. 1, 2, and 3. Exp. 1

Exp. 2

Exp. 3 1st-Stage Network

2nd-Stage Network

Network structure 1st hidden layer activation function 2nd hidden layer activation function Inputs

4-18-15-1 Tangent Sigmoid function

4-15-13-1

4-18-15-1

5-20-15-1

3D prediction location coordinates: x; y; z; incident wind direction: α

3D prediction location coordinates: x;y;z; roughness elements length: L

3D prediction location coordinates: x; y; z; incident wind direction: α

Outputs

Cp

Cp

Cp

3D prediction location coordinates: x; y; z; incident wind direction: α; predicted mean pressure coefficients: Cp fp C

Training database size Training condition Target testing dataset Target testing condition

266(data/set)*5(set)

206(data/set)*10(sets)

266(data/set)*5(set)

α ¼ ½30
; 35
; 40
; 50
; 55
; 60
 266(data)*1(set)

L ¼ ½00; 10; 20; 30; 40; 60; 70; 80; 90; 100 (mm) 206(data)*1(set)

α ¼ ½30
; 35
; 40
; 50
; 55
; 60


α ¼ 45


L ¼ 50mm

α ¼ 45


Logarithmic Sigmoid function

266(data)*1(set)

e.g., from roof to the whole surface, and (b) defining the network inputs as prediction location in the form of 3D spatial coordinates on the whole surface, instead of 2D coordinates on roofs. To demonstrate the performance of a global prediction, two experiments, i.e., Exp. 1 and Exp. 2, are conducted. Table 2 summarized network configuration for Exp. 1, 2, and 3. In Exp. 1, mean pressure coefficients distribution is to be predicted for an unseen incident wind direction. The network inputs are defined as prediction location, x; y; z, and incident wind direction, α. A global prediction requires more neurons than a local prediction. Therefore, the DNN used in this experiment is configured as a 4  18  15  1 network. Network output is set as mean pressure coefficients, Cp . Tangent sigmoid (tansig) function and log-sigmoid (logsig) function are employed as activation functions at the first and second hidden layer respectively. These two activation functions, illustrated in Fig. 10 and 11 are utilized to add tunable non-linearity into regression problems. The entire available training database is divided into three sub-groups, i.e., training set,

justifying prediction accuracy, we also should bring this observation uncertainty into consideration. If we compare prediction with only one measurement, we abandon an acceptable error tolerance. A reasonable error tolerance will be more critical when a “bad” measurement is taken as ground truth. Fit Rate is also useful to determine an acceptable error level associated with statistical significance (seeFig. 9). 5.4. Mean pressure coefficients prediction for unseen wind direction (Exp. 1) Mean pressure coefficients, Cp , have been the subject of prediction in previously works (Fu et al., 2007a; Gavalda et al., 2011; Chen et al., 2003). The earliest attempt to predict mean pressure coefficients for unseen wind direction was found in (Chen et al., 2003), in which only pressure on the roof was considered. The global prediction can be conveniently transformed from a local prediction by (a) expanding the training database from the local area, 8

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Fig. 10. An illustration of tangent-sigmoid function used as activation function at 1st hidden layer.

Fig. 11. An illustration of log-sigmoid function used as activation function at 2nd hidden layer.

validation set, and test set, with a ratio as 85%, 10%, and 5%. Validation set and test set only serve a monitoring purpose, and they did not participate in error back-propagation. Therefore, they do not change the weights-biases configuration. The target wind direction to predict is chosen as 45
for two reasons. First, the repeated measurement provided by NIST-UWO database is only available for α ¼ 45
. Setting αtarget ¼ 45
allows us to utilize these

repeated measurements to calculate Fit Rate. Secondly, pressures associated with cornering incident wind direction, such as 45
, is generally more challenging to predict, due to stronger corner vortices and higher gradients (Chen et al., 2003). Therefore, if our prediction result is satisfactory under this cornering wind direction, we are confident that the prediction result for other wind direction will be equally satisfactory, if not better.

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Fig. 12. Prediction of mean pressure coefficients for unseen wind direction ¼ 45
(Exp. 1).

are a good illustration of the generality of the DNN-based predicting framework: to make the DNN suitable for different prediction tasks, only some minor modifications needed to be made. The DesignSafe-CI database is employed to train and validate prediction accuracy since it focused on varying the approach wind roughness condition. The unseen roughness element length L is arbitrarily chosen as 50 mm, while the training roughness element length is elected as: L ¼ 0; 10; 20; 30; 40; 60; 70; 80; 90; 100 mm. The details of this experiment are provided in Table 2. Again, to evaluate the stability of the training procedure, we repeat the procedure ten times. The correlation coefficient between ground truth and the average of predicted mean pressure coefficients result is 0.9995. The averaged prediction result is shown in Fig. 13. The correlation coefficients from ten repeated predictions are: [0.9988; 0.9990; 0.9992; 0.9992; 0.9993; 0.9993; 0.9994; 0.9994; 0.9994; 0.9994]. This set of correlation coefficient reflects that the training procedure is stable and accurate. From Exp. 1 and 2, we can observe that different prediction tasks can be solved with almost identical network structures. This observation demonstrates the generality of DNN-based approaches, which is not generally found in conventional methods such as linear interpolation or computational flow dynamics (CFD)-based methods.

We found that the range of training wind direction has an important role to play in the overall prediction accuracy. For example, if α ¼ 45
was to be predicted, concentrating αtrain ¼ ½30
; 35
; 40
; 50
; 55
; 60
, will deliver a correlation coefficient accuracy as 0.9993. While setting the training wind direction αtrain ¼ ½0
; 45
Þ [ð45
; 180
, with an increment as 5
, returns an accuracy of 0.9950, which aligns with the result in (Fu et al., 2007a), with minor difference. The authors in (Chen et al., 2003) narrowed their training wind direction into [270
, 360
] to predict unseen wind direction as 300
, 320
, and 340
. Their reason for narrowing down the training pool is their consideration of symmetry of the building. Even though the size of the training database decreases by narrowing the training wind direction, accuracy improves. When training the DNN, the weights/bias within the DNN needs to be randomly initialized. Repeatedly training a DNN with identical training conditions but different random initialization is a common approach to evaluate the training performance. In this study, the training-predicting procedure has been repeated ten times with differing initialization conditions. The correlation coefficients between these ten repeated predictions and the truth, are: [0.9983; 0.9990; 0.9991; 0.9991; 0.9992; 0.9992; 0.9993; 0.9994; 0.9995; 0.9995]. The average of predicted mean pressure coefficients result from these ten repeated training-predictions has a correlation coefficient of 0.9997. The fit rate of the averaged prediction is 33.0097%, 66.0194%, and 91.7476% for one, two, and three standard deviations intervals, respectively. The averaged prediction result is shown in Fig. 12. The prediction is in a strong agreement with measured truth.

5.6. Peak pressure coefficients prediction for unseen wind direction(Exp. 3) To our best knowledge, peak pressure coefficient prediction has not been accurately achieved with DNN-based methods. Exp. 3 is designed to globally predict peak pressure coefficients for unseen wind direction. The peak pressure coefficient is an expected value based on multiple sequential observed peaks fitted to a Gumbel distribution using the Gumbel-Lieblein BLUE algorithm, with the expected peak value corresponding to a probability of non-exceedance of 80% (ISO 4354, 2009). For peak pressure prediction, two prediction strategies have been tested in our experiments. The first strategy is passed from Exp. 1 and 2, namely, employing a single network with network inputs defined as prediction location: ðx; y; zÞ, wind direction, α, and setting the network fp . However, to our observation, output as peak pressure coefficients, C

5.5. Mean pressure coefficients prediction for unseen roughness condition (Exp. 2) The objective of Exp. 2 is to predict mean pressure coefficients for varying upstream terrain roughness conditions, presented as roughness element length, L. The experiment configuration in Exp. 2 is almost identical as in Exp. 1 except for two modifications: (a) one input variable, i.e., wind direction, α, is replaced with roughness element length, L; and (b) network structure is changed to 4-15-13-1. These slight modifications 10

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Fig. 13. Prediction of mean pressure coefficients for unseen L ¼ 50 mm (Exp. 2).

Fig. 14, achieving a correlation coefficient as 0.9964. The ten-timesrepeated correlation coefficients of peak positive pressure coefficients are:[0.9837; 0.9851; 0.9903; 0.9906; 0.9912; 0.9915; 0.9920; 0.9924; 0.9928; 0.9947]. Fit rate, of the averaged prediction, are 50.00%, 81.07%, and 95.63% for one, two, and three standard deviation intervals. The average of predicted peak negative pressure coefficients from ten repeated training-testing procedures are shown in Fig. 15, achieved a correlation coefficient as 0.9951. The ten-times-repeated correlation coefficients of peak negative pressure coefficients are:[0.9617; 0.9731; 0.9774; 0.9783; 0.9882; 0.9884; 0.9908; 0.9923; 0.9926; 0.9929]. Fit rate, of the averaged prediction, are 60.19%, 89.81%, and 98.06% for one, two, and three standard deviation intervals, receptively. The truth and prediction result for peak pressure coefficient are presented in the form of contour maps. Fig. 17 and Fig. 18 present maximal peak coefficient truth and prediction, respectively. Fig. 19 and Fig. 20 present truth and prediction result for minimal peak pressure coefficient, respectively. Prediction error is represented by the white dots in Figs. 17 and 19, where larger dots represent large prediction error. These prediction errors are defined by normalizing the absolute error over the standard deviations of repeated measurements at a corresponding location. From Figs. 18 and 20 we can see the prediction results are smoother than the truth. Smoothness and symmetry of the contour map are generally used to evaluate the accuracy (Fu et al., 2006; Chen et al., 2003). The nature of the variability in wind tunnel tests results in less smooth maps. The roof surface tends to have a larger prediction error than the walls. Peak pressure coefficient prediction contains larger errors than then mean coefficients prediction in Exp. 1 and 2. First, mean and peak pressure coefficients might not be closely correlated. If this statement stands, there will be a natural barrier to overcome before we can further improve the prediction from mean to peak coefficients. Second, the activation functions used in the present neural network do not sufficiently represent the dependency between mean and peak pressure coefficients. Peak pressure coefficients involve more complex turbulence characteristic, including certain stochastic features. The activation function we choose might not be able to represent those stochastic features, and therefore, returns larger prediction errors. Finally, the previously discussed larger variability of peak coefficients may inherently result in less accurate predictions, even with the two stage network

even with the optimal network configuration, the return result is less satisfactory, with correlation coefficients around 0.9269. Peak pressure coefficients are more challenging to predict than mean pressure coefficients without significant modification made to the DNN. Expanding the discussion at the beginning of Sec. 5.2.4, the inherent variability of pressure observations among experiments with identical inputs is more extreme for peak coefficients than for mean coefficients. Peak coefficients are more directly the product of chaotic nonlinear turbulent fluid mechanics and estimated based on a small number of observed peaks which vary from one experiment to the next. Mean coefficients are estimated utilizing the entire time history rather than a small subset of observed peaks. Therefore, peak coefficients are less likely to be repeated with precision than mean coefficients. This inherent variability in peak coefficients under identical inputs of course translates to more uncertainty in the DNN’s ability to map the relation between inputs and peak coefficients. This motivates the following alternative strategy. The second strategy is to break peak pressure coefficients prediction into two parts, separately performed by two neural networks. The firststage network predicts the mean pressure coefficients distribution, utilizing the same network structure as Exp. 1 and 2. The second-stage network performs prediction/translation from the mean pressure coefficient to the peak pressure coefficients. The result shows accuracy improvement. The input of the second stage network is defined as prediction location coordinates in 3D format, x;y;z, incident wind direction, α, and predicted mean pressure coefficients Cp , returned from the firstfp . This strategy stage network, while the network output is defined as C is illustrated in Fig. 16. This strategy can be regarded as a reflection of the idea of ensemble methods (Zhou, 2012), which is an effective solution for solving tricky problems with simple networks with limited learning abilities. For both of the first-stage and second-stage network, the first and second hidden layers are assigned with tangent sigmoid (tansig) function and logarithmic sigmoid (logsig) function as their activation functions respectively. We found that a 5-20-15-1 DNN structure is sufficiently optimal for the second stage network (See Table 2). The training set, validation set, and test set are divided from utilized DesignSafe-CI database with a ratio as 85%, 10%, and 5% as well. The training process has been performed ten times as well to evaluate training stability. The average of predicted peak positive pressure coefficients from ten repeated training-testing procedures are shown in

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Fig. 14. Prediction of maximal peak pressure coefficients for unseen wind direction ¼ 45
(Exp. 3).

Fig. 15. Prediction of minimal peak pressure coefficients for unseen wind direction ¼ 45
(Exp. 3).

networks are generally considered to have better performance than broad but shallow networks. Stacking two separated neuron networks into a deeper network also offers us with two major benefits. First, it allows us fp , and therefore gives us to monitor the relationship between Cp and C

employed. Even though the DNN method is capable of handling complex nonlinear function relation, there still exist certain limitations. Meanwhile, the improvement, achieved by the second strategy, implies that breaking a complex task into pieces, and handle them separately could be an efficient solution. Essentially, the second strategy represents a deeper DNN than the first strategy by stacking two networks together. Deeper

more potentially valuable insight. Second, it reduces the difficulty in developing a new network. In the second strategy, first-stage and secondstage networks share two very similar network structure, and the same 12

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Fig. 16. Illustration of the second strategy for predicting peak pressure coefficients.

Fig. 19. Contour Map for measured minimal peak pressure coefficients, wind direction ¼ 45
, with prediction error represented by white dots.

Fig. 17. Contour Map for measured maximal peak pressure coefficients, wind direction ¼ 45
, with prediction error represented by white dots.

Fig. 20. Contour map for predicted minimal peak pressure coefficients, wind direction ¼ 45
.

essential number of sensors, and increase the sensor resolution by prediction? This question is rather critical in optimizing sensor configuration for wind tunnel tests. We now introduce the concept of super-resolution into this wind load prediction problem. Super-resolution refers to the ability to determine pressure coefficients at arbitrary locations based on limited measured locations. It is an extension of spatial inter-/extra-polation to a global scale. Unlike conventional spatial interpolation, which generally relies on reference sensors within a specific neighborhood, the super-resolution is derived from a global pressure prediction function, f ðx; y; zÞ, without consideration of any particular hand-picked neighborhood. (Alternatively, it could be viewed as extending the neighborhood to the whole surface.) Also, conventional interpolation is incapable of extending prediction for unseen flow properties. The super-resolution, on the other hand, is capable of predicting pressure coefficients at unknown locations under unseen flow properties, e.g., incident wind directions. For validation purposes, we cannot choose any arbitrary location to predict, since we have ground truth only at measured locations. Thus, an approximation is made by compressing the size of the training dataset. The training dataset is segmented into two groups: known group and hidden group. Only the known group is revealed to the network during the training procedure. The hidden group is utilized only for a final evaluation of prediction. The Known-Hidden ratios investigated are: 7 : 1, 5 : 1, 4 : 1, 3 : 1, 5 : 2, 2 : 1, 1 : 1, 1 : 2, and 1 : 3, where a KnownHidden ratio of 1 : 1 means that half of the total sensor locations are known to the neural network during the training procedure. The other half is hidden from the algorithm and has to be predicted as “arbitrary”

Fig. 18. Contour map for predicted maximal peak pressure coefficients, wind direction ¼ 45
.

activation functions. Tuning these two similar networks will be much easier than tuning a deeper network, especially when we already have the first-stage network well-tuned. 6. Super-resolution A meaningful question to ask when designing a wind tunnel experiment is: What is the minimal sensor density needed to conduct robust/ reliable prediction with DNN? Take our Exp. 1 and a similar work (Chen et al., 2003) as an example. Both of these two works concentrate on predicting mean pressures for unseen incident wind angle. The major difference is that Exp. 1 predicts globally on the whole surface, while prediction in (Chen et al., 2003) is limited to the roof. The team in (Chen et al., 2003) employ a database that has 335 sensors on the roof, while our database has 92 sensors located on the roof. The return result of our prediction has MSE ¼ 10.57% within roof area, while (Chen et al., 2003) has the MSE ¼ 11.60%. It seems 92 sensors could be as sufficient as 335 sensors. Thus, can we predict the pressure distribution based on a minimally 13

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the original serial number of pressure sensors defined in the database. By doing so, the Known sensor is distributed on the whole surface equally. Fig. 21 shows the equally distributed sensor configuration for Known/ Hidden ratio as 3:1 in Exp. 4. Prediction accuracy based on this sensor configuration is calculated in the form of correlation coefficients and shown in Fig. 22. Each box in Fig. 22 contains correlation coefficients between the truth and ten predictions from ten repeated training instances. Also, we include the correlation coefficients between truth and the averaged prediction in Fig. 22. This averaged prediction is the prediction of mean pressure coefficients, generated by averaging ten predictions from ten training instances. Rather than equally distributing the Known/Unknown sensors, another strategy that we also consider is a more corner-focused configuration. This configuration has a higher sensor density on corners and edges. Fig. 23 illustrates this sensor configuration for Known/Hidden ratio as 3:1 in Exp. 4. The prediction result based on this configuration is shown in Fig. 24. By comparing the results in Figs. 22 and 24, we can conclude that when employing DNN-based method to achieve pressure prediction, the known sensor location plays a fundamentally important role in the overall prediction performance. Different sensor configurations do not preserve pressure distribution character equally well. A more careful and optimal sensor configuration will be the subject of sensor optimization and requires further studies. With that being said, the prediction accuracy of averaged prediction remains at a pretty high level, higher than 0.900 in Fig. 22. Even when the prediction accuracy could be less satisfactory, these predictions can be readily improved with a more optimized sensor configuration. Figs. 22 and 24 can also indicate what the lowest sensor density to meet different error tolerances is. Therefore, it is fair to say, the DNN-based prediction method has a strong potential in predicting wind-induced pressure with minimal sensors. To demonstrate this super-resolution concept is useful for other prediction tasks, we also tested it for the unknown roughness condition in Exp. 5. Exp. 5 shares the same experimental configuration as Exp. 2, except that we reduce the size of training dataset similarly to Exp. 4. The

Fig. 21. The equally distributed sensor configuration with Known/Hidden ratio as 3:1 in Exp. 4.

location for the unseen condition. Consequently, the spatial resolution increases from 133 sensors to 266 sensors on the whole surface. Exp. 4 is conducted to demonstrate that super-resolution is an applicable concept to predict mean pressure coefficients for unknown incident wind directions. Exp. 4 inherits the same experimental configuration from Exp. 1 without any modification (See Table 2), except for the changing size of the training dataset to simulate various sensor density. Even though the network configuration for Exp. 1 might not be optimal for Exp. 4, using the identical experiment configuration allows us to discuss the generality of super-resolution better. Super-resolution is an inherent feature from a global prediction. If the correct function, i.e., Cp ¼ f ðx; y; z; αÞ are captured by a global prediction, based on limited measurement, then this function should be able to return Cp for any given x; y; z, or α. Two sensor configuration strategies are considered in Exp. 4. The first strategy is to separate the Known and Hidden group simply according to

Fig. 22. Accuracy of predicted mean pressure coefficients with varying resolutions for unseen wind direction (Exp. 4). 14

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least, this accuracy decrease is not in a monotonic fashion. Understandably, the overall accuracy decreases with lower sensor resolution. And we assume the non-monotonic decrease of prediction accuracy is caused by the process of separating Known/Hidden groups. 7. Discussion We have demonstrated DNN’s ability to handle wind-induced pressure distribution at a global level. By rising the prediction scale from local to global, the presented prediction framework shows strength in (a) predicting with high accuracy in an automated fashion and (b) enabling the concept of super-resolution. With advancing computational resources, the global prediction could be easily achieved with a nearly realtime fashion. Conventional analysis methods, such as computational fluid dynamic (CFD)-based methods, tends to have limited generality, i.e., for different flow regions, turbulence characters ought to be analyzed separately. With this restriction, the wind load analysis is usually limited to the roof areas. It will be beneficial if standing walls are also brought into the analysis. The DNN-based global prediction is highly suitable for such a task. Not only because the training-prediction is highly automatic, but it also has been shown that containing the whole surface in the prediction improves prediction accuracy, especially for corners and edges. Including surrounding walls doesn’t introduce interference to prediction result on another flow region, because well trained DNN is assumed to have the ability to “decide” which area should be taken as reference. Moreover, we believe in the strong potential of DNN-based prediction method in optimizing sensor configuration for a wind tunnel test. This will be extending work for further studying the concept of superresolution. However, in spite of the obvious robustness of DNN-based prediction methods, there are definite drawbacks or opportunities for improvements. The first limitation lays in the determination of optimal network

Fig. 23. The corner-focused sensor configuration with Known/Hidden ratio as 3:1 in Exp. 4.

size of the training dataset is gradually decreased by separating the database into known and hidden groups with the same set of ratios as in Exp. 4. The sensor configuration for the known group and the hidden group are equally distributed. The prediction results are presented in Fig. 25. From Figs. 22, 24 and 25, we can make four valuable observations. First, lower resolution leads to lower prediction confidence. With smaller Known-Hidden ratio, the accuracy distribution appears to be more divergent, (i.e., longer box in the box-plot), meaning that the probability of making a bad prediction increases. Second, the averaged prediction shows improvement compared to individual predictions. We could, therefore, take averaging individual predictions as a remedy when the prediction confidence is less satisfactory or less stable. Third, the overall trend of prediction accuracy decreases with lower resolution. Last but not

Fig. 24. Prediction accuracy of mean pressure coefficients with varying resolution for unseen wind direction (Exp. 4) based on corner-focused sensor configuration. 15

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Fig. 25. Accuracy of predicted mean pressure coefficients with varying resolution for unseen EH (Exp. 5).

DNN-based methods is a critical question to answer in future work.

structures. The optimal network structures used in this work are chosen either by the inspiration from previously published references or by experience and observations. There is a lack of theoretical support for optimizing network structure. Even though experience and observation remain a practical approach for determining optimal network structure at this point, this limitation will inevitably limit the generality of the proposed DNN-based method, if the targeted problem became more complicated. Another major challenge is how to pre-process training database properly. DNN-based methods, as with many other machine learning methods, have a high reliance on utilized databases. The learning machine cannot obtain the “correct” patterns by learning from “wrong” examples. This reliance requires the quality of utilized databases to be strictly monitored and controlled. Besides the quality of databases, the differences in the configuration in varying databases are another critical factor. When combining multiple databases, pre-processing these utilized databases becomes more significant. The third limitation is that DNN-based prediction couldn’t leverage numerous input variables into predictions simultaneously at this point. For example, in this paper, we achieved mean pressure coefficients prediction for unseen wind direction and terrain condition separately, however, we cannot predict the pressure distribution for these variables jointly. This limitation is a result of the lack of a suitable database. To release the power of machine learning-based method to a higher level, either a more comprehensive unified database ought to be built, or existing databases ought to be combined. Finally, we have observed that some prediction tasks, such as predicting peak pressure distribution, are more challenging for the employed DNN-based method. However, breaking the big problem into smaller and easier parts improved the overall performance. Therefore, when we are targeting complex predictions, an ensemble network architecture could compensate DNN’s limitation. A more delicately comprehensive database could also help address this problem. Shown as in Figs. 22 and 24, difference of sensor configuration can impact the overall prediction performance. Therefore, how to optimally define the sensor configuration during the data collection procedure specifically for

8. Conclusion In this paper, we propose to employ DNN to achieve global wind load predictions. The major innovation of employing the global prediction includes improving prediction accuracy, particularly for low measurement sensor resolution, and enabling the concept of super-resolution. Although a global prediction imposes a strong challenge for computation, we found that with advancing computation platform and algorithms, it can still be performed in a relatively nearly real-time fashion. The DNN-based method is shown to be a reliable and robust approach to achieve cyber-physical enhancement for wind load measurement. This enhancement includes two perspectives: (a) expanding the existing database for unknown measurement conditions, such as unseen wind directions or terrain conditions; (b) expanding the resolution/sensor density by prediction. Acknowledgment Support for this research was provided by the National Science Foundation Natural Hazards Engineering Research Infrastructure program (NHERI, CMMI-1520843), No. IIS-1564892, IIS-1908299, the UF Clinical and Translational Science Institute, which is supported in part by the NIH National Center for Advancing Translational Sciences under award number UL1 TR001427, and the University of Florida Informatics Institute Junior SEED Program (00129436). Also, our appreciation goes to Dr. Eric Ho at the University of Western Ontario, for his help in providing additional data. References Akande, K.O., Owolabi, T.O., Twaha, S., Olatunji, S.O., 2014. Performance comparison of svm and ann in predicting compressive strength of concrete. IOSR J. Comput. Eng. 16 (5), 88–94. Ben-Nakhi, A.E., Mahmoud, M.A., 2004. Cooling load prediction for buildings using general regression neural networks. Energy Convers. Manag. 45 (13–14), 2127–2141. 16

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