## 3 Results and Discussions
### Temperature Compensation System  
In addition to the large temperature difference between day and night on the sea, the operating temperature of the instruments onboard also varies from moment to moment. To overcome the sensitivity drift due to the temperature variation, a practical and flexible pressure measurement system with temperature compensation is developed to calibrate the drift caused by the ambient temperature variation. The design purpose of the embedded digital compensation system is to simplify the complexity and reduce the cost to satisfy the requirement of marine engineering. Hardware of the compensation system consists of a commercial monolithic-integrated 24-bit analog-digital convertor and signal amplifier, a high-precision temperature sensor, power management system, and a low-cost MCU. The system diagram is shown in Figure 8.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Test Cycle** & **Protective Layer** & **Pressure** & **1** & **2** & **3** \\ \hline \multirow{4}{*}{Cycle 1} & \multirow{2}{*}{Silicone rubber} & 3 MPa & Pass & Pass & Pass \\  & & 4 MPa & Pass & Pass & Abnormal \\  & & 3 MPa & Pass & Pass & Pass \\  & & 4 MPa & Pass & Pass & Pass \\  & & 5 MPa & Pass & Pass & Pass \\ \hline \multirow{4}{*}{Cycle 2} & \multirow{2}{*}{Silicone rubber} & 3 MPa & Pass & Pass & Pass \\  & & 4 MPa & Abnormal & – & – \\ \cline{1-1}  & & 3 MPa & Pass & Pass & Pass \\ \cline{1-1}  & & 4 MPa & Pass & Pass & Pass \\ \cline{1-1}  & & 5 MPa & Pass & Pass & Pass \\ \hline \end{tabular}
\end{table}
Table 4: Encapsulation stability tests.  
Generally, the output of the pressure sensor at a constant voltage can be expressed as follows:  
\[V_{out}=S_{T}\times P+V_{0} \tag{2}\]  
where \(S_{T}\) is the sensitivity at T \({}^{\circ}\)C, P denotes the incentive pressure, and \(V_{0}\) represents the zero-drift voltage due to fabrication error when no incentive pressure exists.  
Firstly, the zero-drift voltage \(V_{0}\) is compensated by average approximation. The compensation value is obtained preliminarily by averaging the zero-drift voltages at various temperatures. After compensation, the output voltage can be described as a proportional function:  
\[V_{Z}=V_{out}-\overline{V_{0}}\approx S_{T}\times P \tag{3}\]  
Secondly, the temperature-drift voltage is compensated by a sensitivity coefficient. After compensation, the output voltage can be described as follows:  
\[V_{comp}=K\times V_{Z}\approx K\times S_{T}\times P \tag{4}\]  
where \(K\) denotes the compensation coefficient of \(S_{T}\) The coefficient \(K\) can be calculated from:  
\[K=\frac{S_{ref}}{S_{T}}=\parallel S_{T}=a_{1}T^{2}+a_{2}T+a_{3},S_{ref}=22.99\parallel \tag{5}\]  
where \(a_{1}\), \(a_{2}\), and \(a_{3}\) are the coefficients of the rational polynomial model, and \(S_{ref}\) is the sensitivity at 25 \({}^{\circ}\)C (which is defined as the reference). After the curve fitting of the sensitivity, the polynomial coefficients \(a_{1}\), \(a_{2}\), and \(a_{3}\) were obtained: \(1.657\times 10^{-4}\), \(-0.06873\), and \(24.58\), respectively.  
By simultaneously collecting output data from the pressure sensor and the temperature sensor through the serial ports of the microcontroller, the voltage of the pressure sensor at different temperatures can be mapped to that at the reference temperature (i.e., 25 \({}^{\circ}\)C). Therefore, the output voltage of the measurement system becomes weakly correlated with the temperature. The output characteristics of the pressure measurement system before and after compensation are shown in Figure 9a,b. The results show that the temperature  
Figure 8: The diagram of the digital pressure measurement system with temperature compensation.  
compensation system for the pressure sensor could successfully implement the sensitivity drift compensation. The maximum error of the output value after compensation was 0.43% F.S.