## 1 Introduction  
In engineering applications, cracks can lead to structural failure, posing severe safety hazards in industrial fields such as transportation, energy, aircraft, and aerospace. Due to the continuous changing loads on aircraft during work, fatigue cracks will occur [1; 2], which is an important cause of safety accidents. Consequently, there is significant attentions paid to the initiation and propagation of cracks, leading to research efforts aimed at understanding the formation and expansion of cracks in engineering materials like aerod aluminum alloys [3; 4; 5; 6]. On the other hand, some of the attentions are involved in seeking the effective detection of cracks to ensure the safety operation of equipment [7; 8; 9]. The ability to accurately identifying and assessing cracks is integral to maintaining the structural integrity and performance of engineering systems.  
The detection of metal cracks heavily relies on non-destructive testing (NDT) techniques, which evaluate the integrity of materials and structures without causing any damage. Based on the different physical principles, a range of methods have been explored, including eddy current testing (ECT), magnetic particle testing (MPT), penetrant testing (PT), ultrasonic testing (UT), and radiographic testing (RT) [10]. Compared to other detection methods, ECT offers several distinct advantages in crack detection, such as being low cost, having a rapid response and no coupling agent, and being sensitive to both surface cracks and subsurface cracks. Additionally, the pulsed eddy current technique (PECT), which has evolved from the ECT method, is widely employed in defect detection due to its rich information in the frequency domain [11; 12; 13].  
In addition, artificial intelligence algorithms have also been more and more applied in non-destructive testing. [PERSON] proposed a genetic algorithm (GA) based backpropagation neural network (BPNN) to invert the defect size on the ferromagnetic material [14]. [PERSON] used an Artificial Neural Network (ANN) to show the parameters of the combined cracks through ECT signals and found some highly implicit nonlinear mapping relationships [15]. [PERSON] proposed the data enhancement method of principal component analysis (PCA) to solve the problem of insufficient data of the ANN algorithm used for ECT inversion [16]. Neural networks have become an effective way for defect inversion with ECT.  
But the existing investigation indicated that PECT is an appropriate way to quantitatively characterize the cracks in metallic specimens, such as aero-aluminum alloys. However, an issue is that numerous studies have primarily focused on regular artificial cracks as experimental specimens [17; 18; 19; 20]. Actually, the characteristics of natural cracks significantly differ from those of artificial cracks [21; 22].  
Therefore, the motivation of this paper is to promote a quantitative approach for the natural crack in aero-aluminum alloys based on PEC. Section 2 introduces the three-points bending experiment, and 7075 aero-aluminum alloy specimens with natural cracks are prepared based on this method. Moreover, the cracks are measured using the optical method. Then, in Section 3, the specimens with natural cracks are measured using PECT. The influence of the natural crack on the output of the PEC probe are analyzed according to the experiment results. In Section 4, an BPNN algorithm based on GA is proposed to improve the characterization accuracy for the natural cracks. In the proposed algorithm, the Latin Hypercube is explored to obtain the a more uniform population distribution in GA, and consequently to optimize the weights for BPNN. Finally, some conclusions are arrived at in Section 5.