## 2 Four New Signal-Based Approaches to Be Compared
### Condition Evaluation Based on a Sensitivity Matrix (Approach C)  
The approach uses data generated by diagnosis-oriented data filtering (see Section 2.2) to further reduce the complexity by compressing the signal information into three states according to an operation-related judgment of the system state.  
This approach differs from those described previously due to the advanced evaluation goal. Thus, instead of using thresholds to classify the states here the relationship between the actual value of a characteristic and the previous ones is employed to determine whether the actual value is greater, less, or about the same as previous values.  
Thus, a strong state-related evaluation is possible using the diagnosis-based data filtering approach. From Figure 3 (last row), it can be concluded, that two main aspects become important when assessing the real state of the system related to wear: (I) the absolute level of wear (due to operation) defined by the absolute level of integrated \(AS\) and (II) the observation of actual changes. By combining both aspects, a sensitivity matrix can be built. The procedure was firstly introduced in [16] and is explained in detail in the following.  
To consider the history of the absolute level of wear the left-sided mean (LM) of a specific number of the last load-cycles is calculated (shown in black in Figure 4 (first row)). This value considers specific numbers of load-cycles before the actual load-cycle to calculate the mean value of the previous characteristic values. The actual value of the centered moving average is compared to the LM-value: (I) if the actual value is less than LM-value, the trend is denoted as \(-1\); (II) the trend is 0 if the actual value is in the same range as LM-value; and (III) the trend is 1 if the actual value is greater than LM-value. A short section of the time behavior (Figure 4 first row, dashed box) is used to show the calculation of the trend in Figure 4 (second row). The comparison shows that the actual load-cycle is related to the history of the wear level. The actual changes in the wear level are shown by the steps in the trend behavior. The algorithm employed is as follows: (I) if the last step is \(\pm 2\), the changes are more significant than those with \(\pm 1\); and (II) the last step is denoted as 0 if no step occurred during the last 50 load-cycles.  
By combining the last step of the trend (\(x\)-axis) and the actual value of the trend (\(y\)-axis), the sensitivity matrix shown in Figure 5 can be built and detailed based on the experimental data. Depending on the actual value and the last step of trend value, nine different combinations can be distinguished, as shown in Figure 5. A short section of the trend value is depicted in Figure 4 (second row). The calculating steps are numbered from 1 to 13. A transition connects two steps. Assuming that there are connections between the actual changes (last step) and the actual integrated damage increment, nine combinations can be combined as three states (denoted by green, yellow, and red) based on heuristic experience.  
Figure 4: Sequence developing the process of state transition and classification using sensitivity matrix (approach C); first row: time-behavior of smoothed \(AS\) gradient (blue) and left-sided mean (LM)-value (black); second row: short section of trend value showing 13 states of this trend; third row: sensitivity matrix showing the above mentioned 13 states with state transition; last row: evaluated machine state.