## 3 Results and Discussion
### Experiment Verification
#### 3.2.2 Influence of Operating Conditions on Dynamic Weighing  
When the continuous system is in dynamic operation condition, the material flow, pressure, and other factors of the system will exert a load on the unit equipment. The exert load is superimposed on the change of the weighing measurement value and reflected as the change of the additional mass \(m_{D}\) in the mathematical model in Equation (16). In order to show the universality of the research, the gas-liquid reactor commonly used in the chemical production process is taken as an example. There are three main influencing factors:  
1. If the unit equipment is a pressure vessel, the strain generated by pressure load will be superimposed to the total strain of the system to affect the weighing measurement result; \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measurement System** & **Equation** & **R\({}^{2}\)** \\ \hline
1 & \(m_{1}\)= 1.0161\(m-1.6190\) & 0.99999 \\
2 & \(m_{1}\)= 1.0186\(m-1.7026\) & 0.99995 \\
3 & \(m_{1}\)= 1.0184\(m-1.5185\) & 0.99997 \\
4 & \(m_{1}\)= 1.0190\(m-1.5840\) & 0.99997 \\
5 & \(m_{1}\)= 1.0188\(m-1.6723\) & 0.99997 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Equation and coefficient of determination (R\({}^{2}\)) between the true value \(m\) and measured value \(m_{1}\). \begin{table}
\begin{tabular}{c c} \hline \hline  & **Measurement\%** \\ \hline Absolute maximum error & 0.0012 \\ Repeatability & 0.002 \\ Hysteresis & 0.001 \\ Linearity & 0.0014 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Absolute maximum error, repeatability, hysteresis, and linearity of measured data. The gas-liquid two-phase in the flowing state inside the unit equipment can generate dynamic load and act on the internal parts of the equipment, such as the additional load;  
Harmonic load or vibration load generated by power devices and attached to the system, such as stirring device and centrifugal pump. According to Equations (15) and (16), the relative mass change coefficient \(M^{*}\) under dynamic working conditions is:  
\[M^{*}=\frac{\Delta m}{m}=m^{*}+\frac{m_{D}}{m}=1-\frac{m_{1}}{kn} \tag{17}\]  
In order to investigate the combined influence of the connected piping and the dynamic load as a whole, the dynamic change curve of \(M^{*}\) with time under different experimental conditions is shown in Figure 7.  
The relative mass change coefficient \(M^{*}\) drops sharply at the beginning and the value soon comes within the required accuracy range (5%), as the internal mass increases. This is because the system needs a short period of stability under the impact of the stress of connected piping and dynamic load. Finally, the combined influence of connected piping and dynamic load can be controlled within the allowable precision range. From Figure 7,b, it can be seen that, within the same test time, the variation of the relative coefficient \(M^{*}\) generated by liquid flow rate is more obvious than pressure, but it is still within the standard deviation. The main reason is that the liquid shock dynamic load can be reflected as the superposition of a simple harmonic displacement wave, and each specific velocity corresponds to a frequency characteristic. In order to analyze the main reasons for data fluctuations and realize signal remolding and regression, the various frequency signals are decomposed through Fourier analysis to form waveforms with different frequencies and amplitudes [38]. As shown in Figure 8, the spectrum distributions at different flow rates are similar and the main peaks are all located at 0.2 HZ, which are inferred to be caused by the harmonic load generated by the liquid inlet device. The amplitude of the main peak of the spectrum increases obviously with the increase of the flow velocity. Therefore, the analysis results can be used as the basis for adjusting the liquid phase flow velocity. In addition, the spectrum reflects the overall vibration of the system, and the elastic coefficient of the connecting structure is far greater than the fluctuation caused by the impact load.