Artificial Intelligence (AI)-Based Evaluation of Bolt Loosening Using Vibro-Acoustic Modulation (VAM) Features from a Combination of Simulation and Experiments  
[PERSON]  
1 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200000, China 1  
[PERSON]  
2 Department of Mechanical Engineering, the Hong Kong Polytechnic University, Hong Kong 999077, China 2  
[PERSON]  
1 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200000, China 1  
[PERSON]  
1 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200000, China 1  
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the above-mentioned nonlinear features consist of a great proportion of nonlinear components (e.g., SOH) [10; 11] generated by the inspection system, when a single excitation is used in the inspection. Additionally, a single transducer can hardly provide enough information for the damage state in practical applications [12]. In order to enhance the inspection accuracy against the noises from instruments, vibro-acoustic modulation (VAM) has attracted increasing attention for SHM and NDT&E. The VAM technique adopts two excitation signals, namely a low-frequency (LF) pumping wave and a high-frequency (HF) probing wave. Nonlinear signal features are extracted at the frequencies and are the difference and sum of the frequencies of the two excitations. Therefore, a relatively low level of measurement noise is involved in the VAM test and, consequently, the nonlinear responses in signal spectra [13] (i.e., sidebands (SBs)) can be quantitatively correlated to the health condition of the inspected structure. [PERSON] et al. [4] proposed a monitoring method of bolt loosening in both composites and metallic joints using nonlinear sideband features, regardless of their working conditions. Considering the local material characters at the contact surface, [PERSON] et al. [13] developed a finite element (FE) model consisting of two Euler-Bernoulli beam components with two degrees of freedom (DOFs) to accurately predict the VAM responses of the bolted joints. To further improve the practical applicability of this method, [PERSON] et al. [14] applied a piezoceramic transducer, smaller than the conventional shaker, to excite the LF pumping wave and combined the linear swept and time reversal technique in the bolted joint to enhance the signal intensity of nonlinear features. In addition, [PERSON] and [PERSON] [15] proposed a novel method based on the Gnome entropy \(gEn\) and random forest to detect multi-bolt loosening. Even though many applications of nonlinear features in damage evaluation using the VAM technique have been conducted, the diverse nonlinear modulation mechanisms are still not clearly understood [16]. Some researchers [16; 17; 18; 19] have reported that the generation of nonlinear structural acoustic features may be a combined result of several different mechanisms besides CAN, such as dissipative nonlinearity (DN) and material intrinsic nonlinearity (MIN). Hence, the existing evaluations of bolt loosening using the nonlinear coefficients established by the CAN model are confronted with the following obstacles:  
1. The nonlinear coefficients are defined using the amplitudes of the spectral linear and nonlinear components.