## 3 Optimization Analysis Method
### Heat Transfer Analysis  
The amount of moisture the air can hold is proportional to the temperature. When moist air encounters a cooler surface, the temperature of the humid air drops accordingly, reducing its ability to retain moisture. If the temperature is lower than a specific limit, moisture will be precipitated on the surface, resulting in condensation and affecting the humidity sensor's performance [39]. By adding a heating layer to the humidity sensor to make its surface temperature higher than the ambient temperature, the problem of sensor condensation is solved. In addition, based on the sensor sensitivity and dynamic response model established in the article, there is a strong relationship between temperature and the  
Figure 3: Influence of interdigitated capacitive humidity sensor structure on dynamic adjustment time. sensor. Increasing the sensor temperature within a certain range can further improve the sensor's sensitivity and dynamic response performance, as shown in Figure 4.  
To optimize the design of the sensor heating layer and realize the optimal sensor heating strategy, it is necessary to analyze the heat exchange between the sensor and the external environment. The humidity sensor is abstracted as a uniform cuboid with area \(S\) and height \(H\). The heat transfer process of the humidity sensor can be divided into three parts: thermal conduction \(\phi_{Cond}\), thermal convection \(\phi_{Contv}\), and thermal radiation \(\phi_{Rad}\)[40], as shown in Figure 5. \(T_{s}\) is the surface temperature of the sensor, and \(T_{e}\) is the ambient temperature. The total heat dissipation of the entire humidity sensor structure can be expressed as:  
\[\phi=\phi_{Cond}+\phi_{Rad}+\phi_{Conv} \tag{18}\]  
Figure 4: (**a**) The effect of temperature on the sensitivity of the humidity sensor. (**b**) The effect of temperature on the dynamic response time of the humidity sensor. Figure 5: Humidity sensor heat exchange analysis. Thermal conduction is the process of transferring thermal energy from a high temperature to a low temperature. The heat conduction equation of the humidity sensor can be expressed as:  
\[d\phi_{Cond}=-\lambda S(dT/dx) \tag{19}\]  
where \(\lambda\) is the thermal conductivity, \(S\) is the area of the heated zone, and \(dT/dx\) is the temperature gradient. The established sensor model assumes thermal conductivity is a specific value inside the sensor. The sensor heat transfer \(\phi_{Cond}\) is obtained by integrating both sides of the equation:  
\[\phi_{Cond}=\frac{\lambda S(T_{s}-T_{e})}{H} \tag{20}\]  
Thermal radiation refers to the phenomenon that an object radiates electromagnetic waves due to its temperature. The thermal radiation equation of the humidity sensor can be expressed as:  
\[\phi_{Rad}=2\varepsilon\sigma S(T_{s}^{4}-T_{e}^{4}) \tag{21}\]  
where \(\varepsilon\) is the emissivity of the object. Assuming the sensor is an ideal black body with \(\varepsilon=1\). \(\sigma\) is the Boltzmann constant, \(\sigma=5.67\times 10^{-8}\)\(\mathrm{W}/(\mathrm{m}^{2}\cdot\mathrm{K}^{4})\). Since the thermal radiation of the system is related to the Boltzmann constant, it is much smaller than thermal convection and thermal conduction. Therefore, in order to simplify the analysis process, the thermal radiation effect of the sensor can be ignored. Thermal convection is the process of transferring heat through a flowing medium. The thermal convection equation of the humidity sensor can be expressed as:  
\[\phi_{Cond}=\mu(T_{s}-T_{e}) \tag{22}\]  
where \(\mu\) is the air convection coefficient, generally \(\mu=5/(\mathrm{m}^{2}\cdot\mathrm{K})\). Through analysis, the total heat dissipation of the humidity sensor structure is:  
Figure 4.0  
It can be seen that when the ambient temperature and heating temperature are constant, the total heat transfer of the sensor is closely related to the structure of the heating layer. By designing the installation of the heater and optimizing the heating strategy, the system can be more suitable for extreme weather detection.