# Machine Learning Techniques in Structural Wind Engineering: A State-of-the-Art Review
## 4 Summary of Tools of Performance Assessment of ML Models  
The performance of the ML models in wind engineering applications throughout the reviewed literature was assessed through at least one or more forms of different standard statistical error and standard indices. It is important for any ML model to evaluate the performance of the model using some error metrics or factors. Thus, this section aims to provide future researchers with a summary of all the tools and equations that have been used up to this date in structural wind engineering ML applications along with an assessment of which tools are more appropriate for the applications at hand. The compiled list of metrics, or factors, calculates the error to evaluate the accuracy between the ML predicted data and a form of ground truth such as experimental data or independent sets of data that were not used in training among others. There is always a lack of consensus on the most accurate metric that can be used. Nonetheless, this section attempts to provide more guidance on which methods are preferred based on the surveyed studies. Several error metrics were used throughout the reviewed literature which include: Akaike information criterion (AIC), coefficient of efficiency (E\({}_{\text{f}}\)), coefficient of determination (R\({}^{2}\)), Pearson's correlation coefficient (R), mean absolute error (MAE), mean absolute percentage error (MAPE), mean square error (MSE), root mean square error (RMSE), scatter index (SI), and sensitivity error (Si). For the convenience of the readers and for completeness, the equations used to express each of these error metrics for assessing predicted data (\(p_{i}\)) against measured data (\(m_{i}\)) are summarized below (Equations (9)-(18)). For \(N\) number of data points (e.g., \(N\) could be the number of pressure tabs used to provide experimental data), some of the error calculation equations also use average or mean values for predicted data (\(\overline{p}\)) as well as measured data (\(\overline{m}\)). \[AIC\ =\ N\ \log(\frac{1}{N}\sum_{i}^{N}(p_{i}-m_{i})^{2})+2k \tag{9}\]  
\[E_{f}\ =\ 1-\frac{\sum_{i}^{N}|m_{i}-p_{i}|}{\sum_{i}^{N}p_{i}} \tag{10}\]  
\[R^{2}\ =\ \frac{\sum_{i}^{N}(m_{i}-\overline{m})(p_{i}-\overline{p})}{\sqrt{ \sum_{i}^{N}(m_{i}-\overline{m})^{2}\sum_{i}^{N}(p_{i}-\overline{p})^{2}}} \tag{11}\]  
\[R\ =\ \sqrt{\frac{\sum_{i}^{N}(m_{i}-\overline{m})(p_{i}-\overline{p})}{ \sqrt{\sum_{i}^{N}(m_{i}-\overline{m})^{2}\sum_{i}^{N}(p_{i}-\overline{p})^{2 }}}} \tag{12}\]  
\[MAE\ =\ \frac{1}{N}\ \sum_{i}^{N}|m_{i}-p_{i}| \tag{13}\]  
\[MAPE\ =\ \frac{1}{N}\sum_{i}^{N}\left(\frac{p_{i}-m_{i}}{p_{i}}\right)\times 1 00\% \tag{14}\]  
\[MSE\ =\ \sqrt{\frac{1}{N}\sum_{i}^{N}\left(\frac{p_{i}-m_{i}}{m_{i}}\right)^{2}} \tag{15}\]  
\[RMSE\ =\ \sqrt{\frac{1}{N}\sum_{i}^{N}(p_{i}-m_{i})^{2}} \tag{16}\]  
\[SI\ =\ \sqrt{\frac{\sum_{i}^{N}[(p_{i}-\overline{p}\ )-(m_{i}-\overline{m})]^{2}}{ \sum_{i}^{N}\left(m_{i}\right)^{2}}} \tag{17}\]  
\[S_{i}\ =\ \frac{X_{i}}{\sum_{i=1}^{n}X_{i}}\times 100;\ \text{where}\ X_{i}\ =\ f_{max}\ (x_{i})-f_{min}\ (x_{i}), \tag{18}\]where \(f_{max}\left(x_{i}\right)\) and \(f_{min}\left(x_{i}\right)\), are the corresponding maximum and minimum values for the predicted output over the ith input factor while using the mean values for the other factors. In general, MSE was employed in most of the studies and is considered one of the most common error metrics for pressure distribution prediction, but it is not always an accurate error metric. The MSE accuracy decreases when the pressure among the walls is included in the prediction because walls might introduce a pressure coefficient near zero which may cause a great rise as the normalizing denominator [90]. Nevertheless, MSE is generally stable when used in RF models when the number of trees reaches 100 [88]. The RMSE is not affected by the near-zero pressure coefficient as with MSE because it does not include a normalization factor in the calculation.