## 2 Data Acquisition and Methodology  
The six-die nut manufacturing machine used in this research already had proximity sensors and five force sensors--one force sensor for each of the first, second, third, and fourth die and one for the fifth and sixth dies. The proximity sensors trigger the capture of the force impact data. The sampling frequency of the force sensors was 20,000 Hz, and the sensors are mounted onto a common plate in close proximity to the moulds. In this machine, the fourth, fifth, and sixth dies break the most frequently. Consequently, force impact data were collected from the force sensor for the fourth die--commonly denoted as 4P--and the force sensor for the fifth and sixth dies--commonly denoted as 5P and 9P, respectively--as shown in Figure 1. Firstly, data capture was triggered by the fourth and fifth proximity sensors when the dies neared the workpiece. Under the cooperation agreement with the manufacturer, the dimensional specifications of the machine studied, the die materials and dimensions, nut dimensions, and the force sensor specifications are considered commercially sensitive. Secondly, the force sensors were connected to a computer that displayed the force signal profiles and stored the force data in an external hard drive for later analysis using the Visual Signal Version 1.6 software. The force data was collected continuously. Thirdly, and for analytical purposes, one force signal impact was selected every 10 min, which provided six data profiles for every hour of manufacturing. Closer to the maintenance period, one force signal was acquired every 5 min to enable observation of the gradual deterioration in die and non-die condition. Following machine start-up at the beginning of the workday or after maintenance, the first force signal impact was acquired at the end of ten minutes, a run-in period that allowed the signal to stabilise and reflect the improvements effected to machine condition and operation. Fourthly, the force data was graphed to observe the change of the impact on the workpiece over time. The profile of the 4P force signal is shown in Figure 2a. Due to its location, the 9P force sensor provided the force signal profiles illustrated in Figure 2b for the 5P die--shown in the blue box--and the 9P die--shown in the red box. The force signal profile has an inverted bell shape with the downward slope representative of increasing die contact on the workpiece until the maximum impact force is achieved at the minima, after which die retraction is reflected by the upward slope that levels off when the die has been completely removed from the workpiece surface. Fifthly, the analysis was conducted only on the first half of each force impact signal--as indicated by the green box in Figure 2b--because this section contained the information on actual die impact and was necessary for fault detection. Sixthly, this extracted section of each signal was exported to a text file and imported into MATLAB 2016 Version 16.1.0.0. The SRS analysis was performed to show the damage induced by the die impact using the equation and open source code taken from Irvine [35]. Figure 1: 4P and 9P sensor locations. Figure 2: Force signals from (**a**) 4P and (**b**) 5P and 9P. Equation (1) gives the formula for the absolute acceleration for each natural frequency in the data analysed by:  
\[ \begin{array}{rl}\ddot{x}_{j}=&2e^{-\xi\omega_{n}\Delta t}\cos(\omega_{d} \Delta t)\ddot{x}_{j-1}-e^{-2\xi\omega_{n}\Delta t}\ddot{x}_{j-2}+2\xi\omega_{n} \Delta t\ddot{y}_{j}\\ &\qquad\qquad+\omega_{n}\Delta te^{-\xi\omega_{n}\Delta t}\Big{\{}\Big{[} \frac{\omega_{n}}{\omega_{d}}\big{(}1-2\xi^{2}\big{)}\Big{]}\sin(\omega_{d} \Delta t)-2\xi\cos(\omega_{d}\Delta t)\Big{\}}\ddot{y}_{j-1}\end{array}