# Algorithm for Fatigue Crack Initiation Assessment Based on Industrial Photogrammetry
## 1 Introduction  
Fatigue of welded structures is one of the critical factors affecting the structural integrity and durability of structural components in various industries such as aerospace, automotive, and civil engineering. The ability to accurately detect and predict the occurrence of fatigue cracks is crucial to ensure reliability, which is why advanced detection methods are required [1]. Traditional fatigue crack assessment methods are often invasive and time-consuming [2; 3; 4]. Therefore, there is a growing interest in non-destructive testing methods in various engineering tasks [5; 6] that allow for more accurate and earlier detection of potential defects spatially for monitoring [7; 8; 9]. Fatigue of welded steel details is a complex phenomenon due to the welding process which involves alternating phases of heating and cooling alongside the introduction of additional filler material. These factors lead to various imperfections, including inhomogeneities and unfavorable residual tensile stresses, which reduce the fatigue life of welded steel details [1]. To mitigate fatigue failure in welded steel details, strategies such as employing high-quality welds, reducing stress concentration, and situating welds in areas of lower stress are often employed. However, in certain cases, these measures may prove insufficient, so additional post-weld treatment methods are developed [10]. The HFMI (High-Frequency Mechanical Impact) method has been one of the most popularpost-weld treatment methods in the last few decades [2; 9; 11]. The HFMI method increases the fatigue life of welded steel components by taking three key parameters into account: First, it reduces the stress concentration at the weld toe by refining the geometry; second, it introduces residual compressive stresses to counteract unfavorable tensile residual stresses resulting from welding; and third, it increases the material hardness at the weld toe by work hardening [9]. The fatigue life of welded steel components comprises different phases, namely crack initiation (N\({}_{\text{J}}\)) and crack propagation (Np), and the HFMI method significantly prolongs the initiation phase, especially compared to as-welded (AW) components. In the AW condition, the majority of the fatigue life is due to crack propagation. To assess the fatigue life of AW and HFMI-treated welded longitudinal and transverse attachments, the Two-Stage Model (TSM), which takes both periods into account, was developed [9]. For TSM calibration based on fatigue tests, it is necessary to determine the fatigue crack initiation period. Industrial photogrammetry as part of close-range photogrammetry, an image-based measurement technique, has proven to be a promising tool in the field of non-destructive testing [12; 13; 14; 15]. Its ability to capture detailed surface information from a safe distance without physically touching the object is a significant advantage, especially in hazardous environments or with sensitive materials. However, the application of photogrammetry to detect fatigue crack initiation is not straightforward and requires sophisticated algorithms to interpret the complex patterns and anomalies that precede failure. In previous research [9; 11], the fatigue crack initiation period was determined by manual visual assessment based on industrial photogrammetry data and from recorded data from a hydraulic press. In previous research [9; 16; 17], image correlation approaches based on data captured with digital cameras [7; 13; 14] have been proposed for automatic detection of crack initialization [7; 13; 14]. Authors propose an Image-based Method for Crack Analysis BARA [18] or a Vision-Based approach [19] for automatic algorithms to detect and monitor cracks in 2D or 3D.