## Materials and Methods
### Machine Learning Methods  
Regress function achieved by MATLAB is an orthogonal least squares method for multiple linear regression; it has been applied in the fields of meteorology, economics [33; 34; 35]. The least-square algorithm is used in the REGRESS function. Furthermore, REGRESS divides the residuals of observed values of y by an estimate of their standard deviation. The obtained values present t-distributions under a certain degree of freedom. The intervals returned in this function are shifts of the confidence intervals of these t-distributions and centered at the residuals [36]. The F statistic is used to evaluate the significance of the model, the significance level is set to 0.05, and the confidence interval of the coefficient estimation value is set to 95% in this study. Support vector machine (SVM) is a widely used modeling method, but problems like large workload and long training time occur when this method being used in large size sample. Least squares support vector machines (LS-SVM) can solve these problems with its high efficiency [37]. It is a support vector machine version that involves equality constraints and works with a least-squares cost function [38]. LS-SVM regression used in this study is highly related to regularization networks, Gaussian processes, and reproducing kernel Hilbert spaces, emphasizing the primal-dual interpretations of constrained optimization problems [39]. LS-SVM can solve small-sample, nonlinear, and high-dimensional problems, and the selection of kernel function will affect the final result [40]. Kernel functions are important in SVM with its ability to transform original data from low dimension space to high dimension space. We used the LS-SVM method and chose the radial basis function (RBF) as the kernel function in this study. The penalty coefficient and bandwidth of the RBF (\(\gamma\)) kernel must be determined for better performance. Extreme learning machine (ELM) is a feedforward neural network and has an extremely fast learning speed with a single hidden layer; it can be easily used to many applications by only setting the number of neurons in the hidden layer. It shows the advantage of generalization comparing with \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Calibration Set**} & \multicolumn{3}{c}{**Prediction Set**} \\
**Groups** & **Sum** & **Range** & **Mean** & **S.D.** & **Sum** & **Range** & **Mean** & **S.D.** \\ \hline A & 46 & 151.26-182.19 & 165.25 & 8.13 & 15 & 150.53-172.00 & 163.09 & 5.64 \\ B & 72 & 154.20-183.00 & 170.99 & 7.08 & 24 & 156.23-182.30 & 170.79 & 7.06 \\ C & 72 & 10.082-3.2137 & 1.9144 & 0.4711 & 24 & 1.1818-3.1031 & 1.8962 & 0.4609 \\ D & 66 & 154.20-183.82 & 171.15 & 7.49 & 22 & 156.23-182.74 & 170.95 & 7.44 \\ \hline \hline \end{tabular} Group A means the group for measured volume medium diameter (VMD) values of the single nozzle (\(\mu\)m); Group B represents all measured volume medium diameter (VMD) values of twin nozzles (\(\mu\)m); Group C represents measured deposition values of twin nozzles (\(\mu\)m/cm\({}^{2}\)); Group D represents overlapping measured volume medium diameter (VMD) values of twin nozzles (\(\mu\)m). “S.D.” means standard deviation.  
\end{table} 
Table 1: Measured values of volume medium diameter (VMD) and deposition.