# A Vision-Based Bolt Looseness Detection Method for a Multi-Bolt Connection
## 1 Introduction  
Bolt connections play a crucial role in uniting various components within structures and are indispensable in diverse industries like civil engineering, aerospace engineering, and mechanical engineering [1; 2]. Ensuring the quality and stability of these bolt connections is paramount to maintaining the overall security of the structure. However, under adverse environmental conditions, intense shocks, or other external factors, removable bolt connections can become vulnerable points in a structure. This vulnerability poses a significant threat to the safety and reliability of the entire structure. Startlingly, statistical data reveal that over 20% of the accidents in mechanical systems, resulting in substantial losses, are attributed to bolt looseness [3]. In contemporary settings, torque wrenches are widely employed for detecting loosened bolts. Nevertheless, this method is prone to measurement errors of up to 50%, and it involves labor-intensive and hazardous processes [4; 5]. Moreover, existing studies on bolt loosening detection predominantly focus on single-bolt structures, with limited research dedicated to multi-bolt connections. Many of these methods either lack accuracy or fail to recognize all potential cases of loosening [6; 7]. Consequently, there is an urgent need to develop an automated method with a high detection accuracy to ensure the safety and reliability of multi-bolt connections. For this subject, researchers have proposed various sensor-based methods, including piezoelectric-based methods, impedance-based methods, and acoustic-based methods [1; 2]. The frequency selection is very important in ultrasound methods, which decides theaccuracy and robustness of the method. In 2018, [PERSON] and [PERSON] [8] detected the looseness of a three-bolt connection with a piezoelectric transducer array. They used a cross-correlation method to find higher harmonics or special frequency pairs that could identify loose bolts. In 2019, they [6] evaluated several nonlinear-ultrasound methods to identify the looseness of a four-bolt connection. They tried some nonlinear algorithms to recognize the individual frequency corresponding to each bolt. When one of the bolts is loose, it will produce more nonlinearities in the corresponding frequencies, so they can identify the loose one. But the method can only recognize several loosening cases in which just one bolt is loosened. [PERSON] et al. [9] evaluated a nonlinear vibro-acoustic modulation (VM) approach and a linear acoustic method to detect loose bolts. They found that the VM method had higher sensitivity and accuracy, and their method could even deal with multi-type connections. [PERSON] et al. [10] proposed a bolt looseness detection method based on machine learning (ML) and vibration frequency recognition. They compared various ML algorithms based on accuracy and training time. The random forest (RF) algorithm was finally chosen for further studies. The piezoelectric active sensing method represents another avenue of research in contacted sensor-based approaches. However, it faces challenges as energy-based indicators are susceptible to saturation and fluctuation. [PERSON] et al. [11] extracted some nonlinear stress wave features and chose the recursive entropy of the signal as the indicator to detect loose bolts. [PERSON] et al. [12] found that the bolt looseness caused a shift in the impedance of the multi-bolt connection, so they used a fusing multi-frequency-based electro-mechanical impedance (EMI) method to identify loose bolts. But this method cannot identify all the 16 cases of the 4-bolt connection. Feature extraction is a problem in wave signal processing-based methods. In 2020, [PERSON] et al. [13] trained a support vector machine (SVM) network based on a genetic algorithm. That network could recognize all the looseness cases of a four-bolt connection. They developed another novel indicator from the multi-variate multi-scale fuzzy entropy (MMFE) as the input of the classifier.