## 2 Data Acquisition and Methodology
 \tag{1}\]  
where \(j\) is the spring constant of the single degree of freedom (SDOF) system, \(\ddot{x}_{j}\) is the absolute acceleration, \(\xi\) is the damping ratio of the system, \(\omega_{n}\) is the natural frequency, \(\omega_{d}\) is the damped natural frequency, \(n\) is the number of SDOF systems, \(\Delta t\) is the time difference and \(\ddot{y}_{j}\) is the input shock. Lastly, correlation analysis was used to detect any significant change away from the best health profile or condition. In this case, Pearson's correlation coefficient was used due to its sensitivity to outliers and its measurement of the degree to which two variables coincide [36]. A correlation value of 1 means that the profile is perfectly symmetrical with the best health profile, and the impact force of the two profiles are the same. Hence, correlation worked well to compare the repetitive, mechanical movements. The formula used is given by [PERSON] [33] in Equation (2):  
\[Correlation\ Coefficient=\sum_{i}^{N}(x_{i}-\overline{x})(y_{i}-\overline{y})/ \left[\sqrt{\sum_{i}^{N}(x_{i}-\overline{x})^{2}}\sqrt{\sum_{i}^{N}(y_{i}- \overline{y})^{2}}\right] \tag{2}\]  
where \(x_{i}\) and \(y_{i}\) are the input and output of variable \(i\), \(\overline{x}\) and \(\overline{y}\) are the average values of \(x_{i}\) and \(y_{i}\), respectively, and \(N\) represents the number of samples. Correlation using Equation (2) was done on the extracted section of the force profiles and the force SRS profiles obtained from the SRS program to check for deterioration in the health condition of the machine over time on the assumption that such deterioration would be attributed to fault occurrences, including normal wear. The first force profile obtained 10 min after the six-die nut manufacturing machine began operating was assumed to be the best health profile compared to profiles for the remaining time period up to the next maintenance shutdown, as shown in Figure 3. In Figure 3a, 16:10 is the 4P die best health force signal and 19:50 is the impaired health force signal prior to 4P breakage at 19:51 on 9 March. The damage is reflected in the voltage loss as the contact of the die to the surface is reduced by the bending of the 4P die before its failure. The same is depicted for the force SRS signal profiles in Figure 3b. The SRS peak impact from 1 Hz to 60 Hz notably reduced, as the energy of the frequency fell from the reduction of the force impact transmission to the workpiece due to the 4P die damage. Figure 3: Best health and impaired health profiles for 4P on 9 March for **(a)** force signals and **(b)** force SRS signals. On this machine, maintenance was conducted after a fixed amount of production due to the emphasis on quality. As a consequence, parts were changed even though wear was minimal. The analytical tool, therefore, had to be very sensitive to detect the faults of concern under such a maintenance system. A maintenance log was kept of the time, duration, and description of works done on the machine. The maintenance log in Table 1 is for the three days that were analysed to test for the detection of the types of maintenance works and faults that occurred during this period. The findings were then verified against a longer time period spanning the last half of February, March, and the first half of April.