## 4 Evaluation of the Optimized Design  
On the basis of the above analysis results, an optimized prodder with parameter values of \(m_{1}=0.1\) kg, \(k_{1}=1818\) N/m, \(c_{1}=0.1\) Ns/m, and \(k_{3}=100\) kN/m can obtain greater signal strength and larger detection depth. As shown in Figure 12, the plastic box's theoretical resonance vibration intensity, as measured with the optimized prodder, is 8.07 \(\times\) 10\({}^{-4}\), while the same value that was measured with the original prodder is 3.60\(\cdot\)10\({}^{-4}\), thus the signal strength increases by approximately 122.78%.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{3}{c}{**Prodder**} & \multicolumn{3}{c}{**Steel Rod**} & \multicolumn{3}{c}{**Buried Object**} \\ \cline{2-7}  & \(m_{1}\) & \(k_{1}\) & \(c_{1}\) & \(k_{3}\) & \(c_{3}\) & \(k_{2}\) & \(c_{2}\) \\ \hline Parameter value & \(\uparrow\) & \(\uparrow\) & \(\uparrow\) & \(\uparrow\) & \(\uparrow\) & \(\uparrow\) & \(\uparrow\) \\ The main resonance frequency & \(\downarrow\) & — & — & \(\uparrow\) & — & \(\uparrow\) & — \\ Vibrational amplitude & \(\uparrow\) & — & \(\downarrow\) & \(\downarrow\) & — & \(\downarrow\) & \(\downarrow\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Effects of Parameters of the System on Its Vibrational characteristics.  
Figure 11: Effects of \(c_{2}\) on the frequency response of the plastic box.  
Finally, Adams, which is a widely used multi-body dynamics simulation software, is used to conduct a simulation experiment to verify the numerical analysis results. The optimization function of this software allows for users to obtain the optimal parameter values for the design objectives within certain constraints. As shown in Figure 13a, a parametric dynamics model explaining the working principle of prodder is built in the Adams software. According to the above analysis results, \(k_{1}\) has few influence on the measured signal, smaller values for the damping coefficients \(c_{1}\) and \(c_{3}\) tend to enhance performance. Therefore, \(k_{3}\) and \(m_{1}\), the viscoelastic coefficients of steel rod and the mass of the moving part of prodder, are set as key design variables. The objective function is the mean value of the variance between the time domain vibration data measured with the original and new designed prodders. It is obvious that the maximum value of the objective function corresponds to the strongest difference of vibration intensity, as measured by these two prodders. The corresponding parameter values are optimal in the design of better performing prodder. The optimization result is shown in Figure 13b and the theoretical main resonance frequencies of vibration signal measured by the original and optimized prodders are 109.27 Hz and 76.5 Hz, respectively, which perfectly meets with the numerical analysis results that are shown in Figure 12. Due to Adams software taking earth gravity into account, the vibration intensity of simulation results increases 161.56%, which is larger than the numerical analysis result of 122.78%, but they are of the same order. The corresponding values for \(k_{3}\) and \(m_{1}\) are 100 \(\mathrm{kN/m}\) and 0.1 kg, respectively, which are equal to the results deduced by the mathematical method, which verifies this numerical analysis method and the optimal design. It should be noted that the value ranges of the above parameters are selected experientially, mainly for studying the parameter's effect on the prodder's performance. This paper principally provides an optimization analysis method for developing a better performance prodder used for landmine detection.  
Figure 12: Performances comparison between the optimized prodder and the original prodder.  
Figure 13: **(a)** Parametric dynamics model of prodder-object system; and, **(b)** Performance comparison between the original prodder and the prodder optimized with the function of Adams software.