3.1. Mask Model Evaluation
The discussion consists of the model accuracy performance and the physical meaning of the predicted droplets. The simulation is firstly carried out by comparing various FFNN configurations. The 4000 hidden is selected because it has better accuracy than the fewer hidden node number and almost the same in terms of root mean square error (RMSE) with the higher hidden node number. The computational time is also quite acceptable, with training time less than 1 s while being simulated in Matlab installed in a computer with AMD processor Ryzen 3 and RAM 8 GB. After running the simulation, the results has shown a good agreement with the RMSE value of 0.0022 for the training case and 0.0042 for testing. The prediction of the efficiency can be checked visually in
Figure 7. The
of the training and testing data of the mask, the model is more than 0.997 and 0.989, respectively, which is considered high for correlation, as shown in
Table 2.
Table 3 describes the droplet number after coming out of the mask, the percentage of the outlet volume compared to the initial volume, and the escaped droplet’s diameters average. N95 has the highest capability as it traps the most number of droplets compared to others, with gauze as the least. The data is highly dependent on the training data. If the droplet diameter more than the maximum value of the training data, the efficiency values in
Table 1 are employed depending on the mask type. The droplet number comparison of the procedure, surgical and N95 mask is almost the same. In reality, the N95 mask should have more efficiency compared to the surgical mask. The cause can be the reference for the cough droplet data distribution [
1], where the small diameter droplet number with a size of less than 10
m is quite few. An addition simulation is added to check the mask accuracy further by adding the droplet number up to 100 for the range between 0 and 10
m, the comparison is shown in the form of box plot for 50 times simulation as shown in
Figure 8. The difference between N95 and surgical mask becomes more apparent. From the results, it can be said that the proposed mask model can predict the escaped droplets. The comparison between the surgical and N95 mask can be further compared in the future, therefore it can be almost the same as in [
3], especially in terms of the trapped droplet number. In the future, the mask training data will be updated according to the latest and more accurate sources.
3.2. The Droplet Evaporation and Penetration
As discussed in the methodology, the model consists of two parts, the reduced diameter of the droplet and the penetration capability. Both models were modeled using FFNN trained by ELM algorithms. The predicted reduced diameters were compared with the data from [
37] or data in
Figure 5. As shown in
Figure 9, the predicted data has shown a good agreement with the training data. Although some slight errors have been found in the small value of diameter data, the overall regression analysis between the predicted droplet diameter and the training and testing data’s diameter has shown a high correlation with 0.999 and 0.994 of
, respectively. The model represented by
Figure 9 is to predict the droplet diameter reduction behavior after escaping from mouth or mask.
Figure 9b,c shows the comparison of the predicted diameter at a certain timestamp. The model range is actually up to 1500
m to accommodate the no mask condition. Furthermore, for the droplets with diameter less than 10
m, the evaporation process will be very fast about less than 1 s and will not move too faraway from the initial position (except there is wind from external environment). Therefore, while observing the horizontal distance, the error can be ignored. However, to reduce the indicated error of the small particles in
Figure 9c, the proposed methods will be refined in the future by accommodating more comprehensive training data or by applying another machine learning method.
The first and second data of
Figure 10 shows reduced diameter and time as a function of the diameters. The
y-axis is the predicted diameter at a specific timestamp from the first figure’s FFNN model. As described in
Section 2.3, the model’s input is the time stamp and the initial diameter. The second figure is the input to obtain the
y-axis of the first figure. The input data from [
36] represents the falling time and evaporation time for various diameters. In other words, there are two regions. The first figure shows that the boundary’s right side has a predicted diameter with negative values. In other words, the volume droplet is zero, or it has evaporated completely.
Figure 10 also confirms that the model has shown its capability to predict the droplet behavior outside of the training data range or unlearned data. The training data only consist of the reduced diameter up to the evaporation time. In contrast, the data for what happens after the designated time is unknown from the model point of view. After running the simulation, the result has shown the negative value that can be interpreted to be evaporated completely. In summary, the model’s capability to predict the evaporation condition and the final state of the diameter after a specific timestamp has been demonstrated.
Table 4 shows the evaporated droplets at specific timestamps, which are 2 and 10 s. Besides N95 with no escaped droplet, the droplets from other mask types have shown a considerable number of the evaporation process after a duration of 2 s flowing to the ambient air. After 10 s, most of the droplets have evaporated while the diameter of the rest continuously decreases. For example, the remaining droplet number of the cotton mask is about 94, with the average diameter is 197.56
m which should be less than the initial diameter. Furthermore, the other remaining droplets would be evaporated completely or falling to the ground after a certain period, which one comes first. The analysis of the obtain data from this part of the model can be combined with the data from the next model that predicts horizontal distance coverage.
The horizontal distance predictor or the second model has been compared with the training data from [
37], as depicted in
Figure 11a as the function of diameter and b regression analysis. The model has a relatively high correlation value for training and testing, which are 0.990 and 0.933, respectively, as shown in
Table 2. The model also can follow the training data pattern by showing the furthest distance of the droplet is covered by droplets with a diameter of about 30
m. If the input droplet diameter value is more than the training data’s coverage, the highest value of diameter input is considered, which is the same as in the mask model. The horizontal distance coverage is affected by various variables, such as humidity, the initial velocity of the droplet, wind velocity from ambient or ventilation that can be considered in the future.
Table 5 shows the predicted droplet number at various ranges of horizontal distance. N95 and surgical mask show zero value of droplets because the escaped droplets have a relatively small size and will be evaporated at a relatively short distance. The highest droplet number is found at no mask condition, followed by gauze, cotton, and procedure. The droplet number at a horizontal distance of less than 50 cm is not shown in the model because the number is only minority and the droplets will be completely evaporated because of the small diameter. From the table, N95 and the surgical mask has the safest condition because of the minimum values of droplet number at a distance of more than 50 cm. From the droplet generators’ point of view, if the droplet number for small size diameter is added in the cough droplet distribution, the higher number escaped droplets from the mask will be likely evaporated before reaching a distance of more than 50 cm because of the small size of the droplet. For the procedure mask, 5 droplets are detected at a distance of more than 100 cm, significantly lower than cotton and gauze masks. When considering the no-mask condition, the droplet number majority is found between 100 and 140 cm. The droplet can be 3 times lower than the no mask condition by putting the gauze mask on. The droplet population can be further reduced by half of the original by putting on the cotton mask. In other words, although the gauze mask has significantly low effectiveness compared to the surgical mask and N95 mask, the gauze mask still can considerably reduce the droplet volume three times than the no mask condition.
In summary, the proposed model has successfully demonstrated the capability to predict the droplet behavior at various mask types. The simulation time is also relatively fast. While the training time is less than one second, the prediction time can be faster. The duration to complete 50 times simulation involving 3000 droplets at 6 different mask conditions for the three models is about 312 s which is relatively fast. The manuscript’s main novelty is about a framework to predict droplet behavior based on various literature’s available data. Therefore, the method can be extended into some possible directions. Firstly, the model can be developed to accommodate the most updated training data due to the quality of a machine learning-based model depending on the quality of the data. Therefore, if a new finding appears in the future, the research can be accommodated by the model by including the training data’s data. Secondly, the model can be developed further by accommodating more independent variables. For the droplet generator, another droplet distribution data at different human activities can be added in the future. For the mask models, the droplet’s velocity can be added to the model input by accommodating the change velocity or reduced diameter before and after various mask types. For environmental models, the horizontal velocity, humidity, and wind velocity of the falling droplets can be added to the model by adding the training data according to the desired variables.
The proposed methods have potential functions as the fast prediction, interconnecting one research to another, gaining insight into unknown phenomena by working together with the numeric model. The model can duplicate the experimental or numerical data pattern; hence fast prediction of output or dependent variable with different input values or independent variables is possible without redo the simulation or experiment. Therefore, when predicting a situation or variable at a particular condition, the prediction can be carried in a short time. The model can also be employed to integrate one research to another, as demonstrated in the current paper, where the knowledge of two different research is integrated to predict the droplet flow from outlet mouth to the environment at various mask type conditions. Furthermore, the model can be employed to gain insight into an unknown phenomenon, mainly when reinforcement learning can be applied in the future.