## 2 Four New Signal-Based Approaches to Be Compared
### Diagnosis-Oriented Data Filtering and Threshold-Based Classification (Approach B)  
Due to the motion of the wear surfaces friction appears. The friction can be represented by the force required for movement. The hydraulic pressure applied to move the surfaces is proportional to the force, and thus to the friction between the wear surfaces (for details, see [29; 30]). The following approach briefly introduced in [15] will be detailed in the sequel. The wear behavior is determined on a different time scale by measured signals. The successful compression of so-called macro-data introduced in [15] is employed in this contribution. The complete time behavior and history of the pressure measurements has to be taken during a load-cycle and is filtered to achieve an improved evaluation. The generation of characteristic values is calculated from the pressure behavior. The considered data are taken from the last 20 s of a load-cycle, so the results are not influenced by transient heating effects. For one load-cycle, the measured signal (20 s) is considered using a sliding window technique. Each window contains \(n=100\) data points, which equate to a time span of one second. The sliding effect is used to consider different data windows. The window step size is one data point, so for one load cycle, \(N=2000\) windows are considered. For one window \(j\), the arithmetic mean \(\overline{x}_{j}\) is calculated by  
\[\overline{x}_{j}=\frac{1}{n}\sum_{i=1}^{n}x_{i}. \tag{1}\]  
If  
computed during operation. After each load-cycle \(c\), all previous calculated damage increments are accumulated to obtain the accumulated damage increments  
\[AS_{c}=\sum_{k=1}^{c}S_{k} \tag{4}\]  
and plotted as a function of time corresponding to the load cycle \(c\) (see Figure 3 (second row)).  
The development of the \(AS\)-time behavior from \(c=1\) to \(M\), with \(M\) denoting the last realizable load cycle, exhibits changes in the gradient with an increasing number of cycles.  
Finally, the gradient of the \(AS\)-curve is smoothed using centered moving average. Specific numbers of values \(W=100\) before and after the actual value are used to calculate the mean value, e.g., for the load cycle \(c\), \(AS_{c,smooth}\) is calculated as  
\[\begin{split} AS_{c,smooth}=&\frac{1}{W}(AS_{c- \frac{W}{2}}+AS_{c-\frac{W}{2}+1}+...\\ &+AS_{c}+...+AS_{c+\frac{W}{2}-1}+AS_{c+\frac{W}{2}}).\end{split} \tag{5}\]  
In Figure 3 (third row) the centered moving average of the \(AS\) gradient is plotted on a logarithmic scale.  
Figure 3: Procedure of the diagnosis-based data-filtering (approach B and C); first row: time behavior of pressure equivalent value for a complete test-run; second row: time behavior of accumulated damage increments (\(AS\)); last row: time behavior of smoothed \(AS\) gradient.  
The amplitude of gradient of the curve can be used to representing the different states of the wear surface. From the time behavior shown in Figure 3 (third row), it can be concluded that the surface condition temporarily generates very high friction. In this contribution, it is assumed that four distinguishable states exist to be used for classification of the surface condition as follows:  
* State 1: Stable and error-free operation (below the green line).
* State 2: Stable with small changes in the surface condition (between the yellow and green lines).
* State 3: Acceptable changes in the surface condition (between the red and yellow lines).
* State 4: Significant changes in the surface condition (above the red line).  
If no measurement data are available (e.g., during stop of the experiment), the corresponding state is denoted as state 0. The threshold values are selected experimentally based on previous measurements. In [31] the threshold values are optimized according to the minimization of the difference between results generated using approach B and C.