# Machine Learning Techniques in Structural Wind Engineering: A State-of-the-Art Review
## 3 Prior Studies on Applying ML Techniques in Structural Wind Engineering
### Prediction of Wind-Induced Pressure
The predicted mean pressure coefficients, using the Tokyo Polytechnic University (TPU) database [98] as input data, were reasonable when compared to the \"M&P\" parametric equation [99] and the \"S&C\" equation [100]. Those two equations are provided here (Equations (5) and (6), respectively) for convenience. \[\overline{Cp}\bigg{(}\theta,\frac{D}{B}\bigg{)}\ =\ \frac{a_{0}+a_{1}G+a_{2} \theta+a_{3}\ \theta^{2}+a_{4}G\theta}{1+b_{1}G+b_{2}\theta+b_{3}\ \theta^{2}+b_{4}G\theta} \tag{5}\]  
\[\overline{Cp}\bigg{(}\theta,\frac{D}{B}\bigg{)} =\ \overline{Cp(0^{\circ})}\ \ln[1.248-0.703\sin\bigg{(}\frac{\theta}{2}\bigg{)}-1.175\sin^{2}( \theta) \tag{6}\] \[+0.131\sin^{3}(2G\theta)+0.769\cos\bigg{(}\frac{\theta}{2}\bigg{)} +0.07G^{2}\sin^{2}\bigg{(}\frac{\theta}{2}\bigg{)}\] \[+0.717\cos^{2}\bigg{(}\frac{\theta}{2}\bigg{)}.\]  
where \(a_{\rm i}\) and \(b_{i}\) are adjustable coefficients, \(\theta\) is the wind angle, \(D/b\) is the side ratio, \(G=\ln(D/B)\), and \(\overline{Cp(0^{\circ})}\) is assumed by [PERSON] and [PERSON] [100] equal to 0.6 independent from \(D/B\). [PERSON] and [PERSON] [66] successfully predicted the wind pressures around cylinders using different ML techniques for Reynolds numbers ranging from 104 to 106, and turbulence intensities levels ranging from 0% to 15% using several data from previous literature. In this particular study, the RF and GBRT performed better than the single regression tree model. [PERSON] et al. [86] used ANN to predict the mean, RMS and peak pressure coefficients on low-rise building flat roofs for three different scaled models. The predicted mean and RMS pressure coefficient show a very good agreement with the experimental data, especially for the smaller-scale model. [PERSON] and [PERSON] [88] investigated the wind pressure on tall buildings under interference effects using different ML models. The models were trained by different portions of the dataset ranging from 10% to 90% of the available data. The results showed that the GANs model could predict wind pressures based on 30% training data only, which may eliminate 70% of the wind tunnel test cases and accordingly decrease the cost of testing. In addition, RF exhibited a good performance when the number of grown trees, the n number of features and the maximum depth of the tree were set to 100, 3 and 25, respectively. Likewise, [PERSON] [101] predicted wind pressure coefficients  
Figure 5: Illustration of the \(k\)-fold cross-validation method. for box-shaped obstructed building facades using ANN with a \(\pm\)0.05 confidence interval for a confidence level of 95%. [PERSON] et al. [90] focused on predicting the mean and the peak pressure coefficient on a low-rise gable building using a deep neural network (DNN). This study presented a strategy to predict peak pressure coefficients which is considered a more challenging task when ML models are used. The strategy is used to predict first the mean pressure coefficient and then use the predicted mean pressure as an input with other input variables to predict peak pressure coefficients. This strategy is a reflection of the ensemble methods idea [58], which is an effective method for solving complex problems with limited inputs. FNN models were also successfully used in several studies [53; 54; 102] to predict mean pressure distribution and power spectra of fluctuating pressures. The most significant feature of FNN models is the capability of approximating any nonlinear continuous function to a desired degree of accuracy. Thus, this family of methods can capture the non-linearity relationship between the different input variables such as wind pressures, wind directions, and coordinates of pressure taps. Another technique that is based on the methodology of applying ANN was used by [PERSON] et al. [92] in predicting surface mean pressure coefficients using equations for the group method of data handling neural networks (GMDH-NN)--a derivative method from ANN.