## 4 Case Study Verification
### Data Collection for Indicators of the Equipment under Evaluation  
For the qualitative indicators of the quayside container crane equipment under evaluation, experts provide their evaluations for each indicator using Pythagorean hesitant fuzzy numbers. It should be noted that the indicators for strength, stiffness, deformation, corrosion, and cracks under the metal structure subsystem can be quantified. Decision-making experts will provide corresponding linguistic evaluations based on experimental data, thereby obtaining the Pythagorean hesitant fuzzy evaluation matrix. Relevant test data are shown in Tables 3-7. Resistance strain gauges were meticulously affixed at critical stress points on the principal components of the quayside container crane under evaluation. These gauges were linked to a strain gauge meter to measure the stress experienced by each component when subjected to the equipment's rated load. Due to the numerous test points, only the maximum stress test values for each part are displayed in Table 3.  
Use a total station to measure the deflection at various test points under different operating conditions of the quayside container crane under evaluation. Record the initial height values of the test points when the trolley is unloaded and at the parking position. Then, lift the test load with the trolley and move it to the corresponding position. After stabilization, record the height values of the test points under load. The deflection displacement of the main beam at that test point position is determined by the change in height of the test point before and after loading. The results are shown in Table 4.  
In Figure 2, point A is located near the end of the front girder of the quayside container crane, point B is at the connection between the front girder and the front strut, point C is situated at the midpoint of the front girder, and point D is positioned at the rear part of the front girder. Using a steel ruler, the local waviness of each component of the assessed equipment was quantitatively measured, focusing on the extent of protrusion or indentation over a span of 1 m. The results of these measurements are systematically compiled in Table 5.  
Key welds of the metal structure of the quayside container crane equipment under evaluation are subjected to spot checks using the magnetic particle inspection method. Due to the numerous inspection points, this paper only displays the locations that did not meet the criteria. The results are shown in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Crack Location** & **Right Main Beam** & **Right Main Beam** & **Right Main Beam** &
\begin{tabular}{c} **Connection Point of** \\ **Left Gantry Leg and** \\ **Lower Crossbeam** \\ \end{tabular} \\ \hline Crack Length/mm & 22 & 25 & 18 & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Crack detection for critical parts of the quayside container crane equipment under evaluation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Area** & **Measurement Point A** & **Measurement Point B** & **Measurement Point C** & **Measurement Point D** \\ \hline No-Load Test Value/m & 35.2007 & 35.1977 & 35.2075 & 35.2067 \\ Rated Load Test & 35.0304 & 35.1420 & 35.1461 & 35.1978 \\ Value/m & \(-\)0.1703 & \(-\)0.0557 & \(-\)0.0614 & \(-\)0.0089 \\ Deflection Amount/m & \(\begin{array}{c}\hline \hline \end{array}\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Stiffness test values for critical parts of the quayside container crane equipment under evaluation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Area** & **Main Beam** & **Gantry Leg** & **Truss Frame** & **Tie Rod** & **Crossbeam** \\ \hline Deformation & & & & & \\ Amount/mm & - & 4.2 & 2.7 & - & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Local waviness test values for critical parts of the quayside container crane equipment under evaluation.