## 4 Applying the CM Framework to a Case Study
### Results
For instance, in [24], the authors achieved accurate fault diagnosis using time-frequency signal analysis with the discrete wavelet transform and artificial neural network. [PERSON] et al. suggested using the neural network and wavelet multi-resolution analysis for diagnosis in Industrial Robots [31], while in [32], the authors proposed a deep transferable motion-adaptive fault detection method that uses torque ripples for the fault detection of industrial robot gearboxes. All these more advanced techniques could be used in the post-processing phase after the collection of torque data units to automatically detect and diagnose failures. To summarize, with respect to prior arts, our work proposes a CM architecture with a strategy to extract comparable data units which can be valid for applications with a low degree of repeatability, where it is difficult to establish a methodology to analyze data since the manipulator executes different combinations of motions in a single program--such as in applications where the trajectory is planned dynamically. This solution can be used in combination with many different post-processing methodologies for fault detection, isolation and diagnosis already consolidated in the literature. Using this ROS-based CM architecture can speed up the analysis and validation steps by helping to test different approaches for FDD (Fault Detection and Diagnosis) in collaborative manipulators implementing all the algorithms to control robot motions, data acquisition and data analysis in the same framework. Moreover, compared to most similar work [26], our solution shows its effectiveness in a real-industrial scenario without the need to develop data models to track all the programmable motion anomalies for all the possible combinations of movements in a cobot application. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Data Unit**} & \multicolumn{2}{c}{**Dominant**} & \multirow{2}{*}{**Wavelet Entropy**} & \multirow{2}{*}{**Kurtosis**} \\  & **Frequencies (Hz)** & & \\ \hline \multirow{3}{*}{Data unit 1} & \multirow{3}{*}{8.9, 12.1} & \(-1.9\times 10^{5}\) (h), & \multirow{3}{*}{2.38 (h), 2.78 (f)} \\  & & \(-2.4\times 10^{5}\) (f) & \\ \cline{1-1}  & & \(-1.3\times 10^{6}\) (h), & \\ \cline{1-1}  & & \(-1.6\times 10^{6}\) (f) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: HIs calculated after data unit extraction on signals represented in Figures 13 and 14. The values refer to data unit 1 and data unit 2 extractions in case of healthy (h) and faulty (f) conditions. Figure 12: Fourth joint torque acquisition in the case of healthy (in black, above) and faulty (in red, below). Figure 14: Data units 2 extraction. In this Figure, three subsequential joint torque units are represented, which were extracted with the label “PTP(2)” from the acquisition of 2750 sample at 40 Hz. In black and in red, respectively, the 4 th joint torque is under healthy and faulty conditions. Figure 13: Data unit 1 extraction. In this Figure, three subsequential joint torque units are represented, which were extracted with the label “PTP(1)” from the acquisition of 2750 sample at 40 Hz. In black and in red, respectively, the 4 th joint torque is under healthy and faulty conditions. Figure 15: FFT applied to data unit 1 extraction. In black, the FFT of the joint torque under healthy conditions is represented, while in red, it is under in faulty conditions.