## 3 Optimization Analysis Method  
### Structural Optimization Analysis  
Based on the sensitivity and dynamic response model of the humidity sensor constructed in the article, the relationship between the sensor sensitivity \(S\), the steady-state adjustment time \(t_{s}\), and the structural parameters is obtained, as shown in Figures 2 and 3. Among all the structural parameters of the sensor, the greater the interdigital length \(L\), width \(b\), the thickness of the moisture-sensing layer \(h_{1}\), and thickness of the electrode layer \(h_{2}\), the greater the sensitivity \(S\) of the sensor. The smaller the interdigital distance \(a\), the smaller the sensor sensitivity \(S\). In terms of dynamic adjustment time, the change of \(L\) will not affect the adjustment time of the sensor, but smaller \(a\), \(h_{1}\), and \(h_{2}\) with a larger \(b\) can contribute to a shorter adjustment time and system's better dynamic performance.  
To ensure that the sensor has high dynamic performance with high sensitivity, in the structural design process, the influence of structural parameters on the sensor's sensitivity and dynamic performance must be considered simultaneously. Through theoretical modeling analysis, the smaller the interdigital spacing \(a\), the larger the interdigital width \(b\), the higher the sensitivity, and the better the dynamic performance. Therefore, when designing and processing the sensor, it is sufficient to ensure that \(a\) and \(b\) can obtain the optimum extreme values of their performances within the acceptable error range. For the thickness of the moisture-sensitive layer \(h_{1}\) and the electrode layer \(h_{2}\), the larger the value, the higher the sensitivity and the worse the dynamic performance. The improvement of sensor sensitivity and dynamic performance are contradictory. Therefore, determining the appropriate parameter values of \(h_{1}\) and \(h_{2}\) to make the sensor take into account both high  
Figure 2: Influence of interdigital capacitive humidity sensor structure on sensitivity.  
sensitivity and high dynamic performance has become a critical step in the design and processing of the sensor.  
Sensitivity \(S\) and conditioning time \(t_{s}\) were chosen as two key metrics for sensor performance optimization. In order to ensure that the variables of different units are in the same magnitude, the two indicator functions are normalized. The sensitivity \(S\) and adjustment time \(t_{s}\) are normalized to the interval 0-1, and the normalization function can be expressed as:  
\[S_{nor}(a,b,h_{1},h_{2},L,N,RH,T)=\frac{S(a,b,h_{1},h_{2},L,N,RH,T)-\min\{S(RH,T)\}}{\max\{S(RH,T)\}-\min\{S(RH,T)\}} \tag{15}\]  
\[t_{s,nor}(a,b,h_{1},h_{2},L,N,RH,T,e_{ss})=\frac{t_{s,nor}(a,b,h_{1},h_{2},L,N,RH,T)-\min\{t_{s,nor}(RH,T)\}}{\max\{t_{s,nor}(RH,T)\}-\min\{t_{s,nor}(RH,T)\}} \tag{16}\]  
where \(S_{nor}\) and \(t_{s,nor}\) are the normalized sensitivity and steady-state time, respectively.  
The objective function taking into account the sensitivity and dynamic response performance of the interdigital capacitive humidity sensor is established:  
\[f(a,b,h_{1},h_{2},L,N,RH,T)=\min[t_{s,nor}(a,b,h_{1},h_{2},L,N,RH,T)-S_{nor}( a,b,h_{1},h_{2},L,N,RH,T)] \tag{17}\]  
The value range of the constructed sensor structure optimization objective function is \((-1,1)\). The larger the \(S\), the higher the sensitivity of the sensor, and the smaller the sensor \(t_{s}\), the better the dynamic performance. The purpose of the optimization design is to obtain the most suitable sensor structure parameters and to ensure that the value of the objective function is minimized.