## 3 Results
### Development of Offline (General) Thermal Comfort Model  
Figure 7 shows the acquired measurements from test subject 1, including environment-related variables, namely, ambient temperature (\(T_{a}\)), air velocity (\(\
u\)), helmet thermal resistance and applied power level (\(R_{h}\)) and the applied mechanical work rate (\(P\)). Bioresponse-related variables, including heart rate (\(H_{R}\)), the temperature difference (\(\Delta T\)) between the average temperature beneath the helmet and the ambient air temperature, the temperature difference (\(\Delta T_{var}\)) between the ear temperature and the ambient air temperature as well the thermal comfort (\(T_{C}\)), were considered. The graphs show the environmental variables (left graphs), including the ambient air temperature (\(T_{a}\), \({}^{\circ}\)C), fan set-points (\(\
u\), 1 = 4 ms\({}^{-1}\)), the helmet wearing level (0 = no helmet, 0.5 = helmet and 1 = helmet + aerosolell) and the applied mechanical work rate (power) level (\(P\), W). The measured variables related to the bioresponses of the test subject (right graphs) were heart rate (\(H_{R}\), ppm), the temperature difference (\(\Delta T\), \({}^{\circ}\)C) between the average temperature beneath the helmet and the ambient air temperature, the temperature difference (\(\Delta T_{var}\), \({}^{\circ}\)C) between the ear temperature and the ambient air temperature and the thermal comfort (red line) and sensation (blue line) scores. To investigate the effect of the different inputs on thermal comfort, different linear regression models (general models) were identified to estimate and predict the perceived under-helmet thermal comfort \(T_{C}\) (output) using continuously measured variables (inputs), including the aforementioned environmental and bioresponse-related variables. The most suitable combination of input variables was selected by retaining only the input variables with a significant (\(p<0.05\)) effect on thermal comfort. Additionally, the best model structure was selected based on two main selection criteria, namely, the goodness of fit (\(R^{2}\)) and Akaike information criterion (AIC). The results showed that the most suitable LR model structure, with the highest goodness of fit (average \(R^{2}\) = 0.87 \(\pm\) 0.05) and lowest Akaike  
Figure 7: The recorded measurements of the different variables obtained from test subject 1.  
information criterion (average AIC = \(138\pm 12\)), to predict the thermal comfort for all test subjects was as follows:  
\[T_{C}\ =\ \alpha+\beta_{1}T_{a}+\beta_{2}v+\beta_{3}P+\beta_{4}[T_{a}R_{h}]. \tag{2}\]  
The average parameter estimates, \(t\)-ratio and \(p\)-value of \(P>|t|\) for each selected input variable are given in Table 5. The results showed that the main effect of the thermal resistance \(R_{h}\) was not significant (\(p>0.05\)); however, the variable interaction of \(R_{h}\) with \(T_{a}\) showed a significant (\(p=0.015\)) effect on the prediction of the under-helmet thermal comfort. To understand the interaction effect of \(R_{h}\) and \(T_{a}\) on the prediction of thermal comfort, a prediction trace analysis of the model [27] was employed using prediction the JMP\({}^{\circledgtrgtr}\) profiler tool [28], as visualised in Figure 8. For convenience of this analysis, the values of each input variable were scaled (normalised) in such a way to lie in the closed interval [\(-1\), \(+1\)], where -1 indicates the variable's low level and \(+1\) indicates its high level (Figure 8). The scaling of each variable value \(i(k)\) was done according to the following formula:  
\[x_{i}(k)\ =\ \frac{i(k)-M_{i}}{\Delta_{i}}\]  
where \(x_{i}(k)\) is the scaled variable value at time instance \(k\), \(M_{i}\) is the midpoint (\(M_{i}\ =\ \frac{L_{i}+U_{i}}{2}\)) and \(L_{i}\) and \(U_{i}\) are the particular lower and upper limits of input variable \(i\), respectively. The term \(\Delta_{i}\left(\frac{L_{i}-U_{i}}{2}\right)\) is half of the range of the interval.