# Algorithm for Fatigue Crack Initiation Assessment Based on Industrial Photogrammetry
## 3 Results  
Figure 5 shows the procedure for the first part of the algorithm, i.e., the result of the ORB method and the classification of key points. It also shows the coordinates of the difference based on which the displacement of the test specimen is calculated. Figure 6 shows the displacements obtained along the Y-axis during the test of a single sample. The display clearly shows the oscillations and the tendency of the sample to stretch until it breaks. The test data for the method for determining the crack initialization moment are based on specimens S355-TA-AW-02, S355-TA-AW-03, S355-TA-AW-04, S355-TA-HFMI-03, and S355-TA-HFMI-04 [9;11]. Figure 5: Showcase of ORB method, sorted key points, and calculated differences from Equations (1) and (2). Figures 7 and 8 show a visualization of the moving average of the sample data defined based on a window of five data. From the graph, the tendency of material separation is clear, but due to the fluctuation of the value, it is difficult to filter out a specific moment that can be defined as the moment of the beginning or only the break of the test specimen. Also shown in the same figures is a visualization of the moving minimum mean of the data defined based on a window of five data. The graph clearly shows the tendency of material separation, much more clearly than with the moving average method. An increase in the minimum value may indicate an increase in the stretching of the material and that it no longer returns to its initial state, which is the result of material fatigue. However, due to oscillations in the value, as with the previous method, it is not possible to precisely model a specific moment that can be defined as the moment of the beginning or just the crack of the test specimen. In addition to the mentioned methods, Figures 7 and 8 show the visualization of the moving maximum mean of the data. Comparing this method with the two mentioned, it is concluded that this method best indicates the final crack of the test specimen. The value line does not show the progression of the material strain as strongly as with the other methods. The conclusion from the mentioned methods is that they cannot serve well enough as part of the modeling of the moment or the detection of the crack itself. Figure 9 visualizes the approximation of the data by a polynomial of the \(n^{\text{th}}\) degree. Lower-degree polynomials tend to generalize the data, resulting in a poor representation of the data oscillations. Therefore, a higher degree polynomial was chosen, in this case of the \(20^{\text{th}}\) degree and higher [34]. After analysing and predicting which degrees of the polynomial would be best for use in the algorithm, the size of the percentage deviation that gives the best solution without large oscillations from the reference solutions must be determined. Figure 10 shows the peak value and the test deviation to visualize the effect of deviation on the final solution. Figure 6: Algorithm raw Y-axis displacement during the test for test specimen S355-TA-AW-02. Figure 8: Applying and testing moving average, minimum, and maximum methods on last 250 image data of S355-TA-AW-02 test specimen. Figure 7: Applying and testing moving average, minimum, and maximum methods on test specimen S355-TA-AW-02 data. Table 1 clearly shows that the approximation by the 26 th-degree polynomial has the lowest average percentage deviation from the reference value [11]. Due to the inhomogeneity of the data, the smallest average percentage deviation from the reference value was taken, which would mean that the chosen parameters of the method are not necessarily the best for each individual sample, but at the group level. The 22 nd- and 24 th-order polynomials have very small deviations from the chosen 26 th order, only 0.02% difference. The value of the average percentage deviation does not exceed 1.06%, and the smallest value has a critical value of 5% deviation, amounting to 0.39%.