## 1 Introduction  
In order to make power lithium-ion battery systems for electric vehicles with higher energy densities, a significant amount of aluminum alloy and composite materials are used in the battery shell. As an important material in electric vehicle power batteries, shells, and cover plates, 3003 aluminum alloy plays an important role in new energy vehicles. However, corrosion, wear, and other defects that may occur during the use of this material pose a serious threat to safety, making it necessary to find defects quickly and accurately in order to avoid great losses.  
Pulsed eddy current (PEC) testing is a nondestructive and effective electromagnetic inspection technique [1; 2; 3; 4; 5; 6; 7]. PEC testing exhibits many advantages over conventional nondestructive testing (NDT). First of all, as opposed to ultrasonic inspection, PEC testing does not require an acoustic couplant, so it does not pollute the material being tested. Moreover, PEC testing can detect deeper defects than infrared and thermal NDT, which is normally used to detect shallow defects [8]. In addition, PEC testing is more economical and less hazardous than radiography inspection [9]. PEC testing has more advantages than ordinary eddy current (EC) testing, such as: a deeper detection depth [10], easier generation and control [11; 12], and richer information in frequency domains. Therefore, it is widely used not only for the measurement of the conductivity and thickness of metal [13], but also in defect characterization [14; 15; 16; 17; 18]. In fact, this nondestructive testing method can not only detect the surface defects and subsurface defects of stainless steel materials [19], but also of nonferrous metal materials such as aluminum, magnesium and its alloy materials [20; 21; 22; 23; 24], and carbon fiber reinforced plastics (CFRPs) [25].  
The probe in EC testing is usually comprised of excitation and detection units. The excitation unit inducing the eddy current in materials being tested is usually a cylindrical coil [26; 27; 28; 29; 30; 31; 32]. As a comparison, a rectangular coil can induce uniform and unidirectional eddy currents in the detected material, and has been devised particularly for EC testing [33] and alternating current field measurement (ACFM) testing [34]. In 2006, a rectangular coil was proposed and researched in PEC testing [10; 35]. In 2010, the defect classification and defect edge identification were studied using a rectangular PEC sensor [36; 37]. In 2012, a study showed that a rectangular sensor can induce a uniform eddy current on aluminum plates and that the size of a crack can be quantitatively detected by analyzing the three signals (\(Bx\), \(By\), and \(Bz\)) [38]. The author and his team proposed a PEC method based on a rectangular excitation coil (REC) and an axial parallel pickup coil for metal loss evaluation and imaging [23; 39]. This article is the continuation and expansion of the original research. However, the detection coil used the most in all of these studies was a \(Bz\) pickup coil, which is orthogonal to an REC and a specimen. In 2009, three-dimensional detection coils (\(Bx\), \(By\), and \(Bz\)) were investigated to detect the magnetic field of an eddy current induced by rectangular coil and to identify the defect. The experimental results showed that three-dimensional detection coils could obtain more information about defect sizing than uniaxial coils (\(Bz\)) [36], yet the study did not go deep into the field of imaging. A \(By\) pickup coil orthogonal to an REC and parallel to a specimen--which may have the potential to discover plane shape defect--has not been researched until now. Therefore, this paper mainly studies a PEC detection method based on a rectangular coil and a \(By\) pickup coil for mapping a plane shape defect. Previous research on pulsed eddy current detection involved the \(z\)-axis, and the authors' earlier paper focused on the \(x\)-axis. The novelty of this paper is reflected in the fact that it studies the magnetic field of the coil along the \(y\)-axis.