# Phase Reversal Method for Damage Imaging in Composite Laminates Based on Data Fusion
## 1 Introduction  
Composite materials have been widely used in the fields of aerospace, defense industry, and civil industry because of their excellent properties, such as low density and high specific strength and modulus. However, due to the complex manufacturing technology of composite materials and harsh service environment, damage is inevitable. This damage can reduce the strength of a structure and endanger its safety. Although most composite structures are designed according to the damage-tolerance criteria [1], it is still important to detect and evaluate damage before it occurs and spreads out. Structural health monitoring (SHM) technology has attracted great attention in the field of damage assessment of composite materials [2]. Many damage-detection methods have been proposed and improved in recent years [3, 4, 5]. Among them, the damage-detection method based on the ultrasonic Lamb wave has been particularly efficient for large plate structures [6, 7, 8]. [PERSON] et al. [9] developed a theoretical model for the analysis of PWAS-related Lamb-wave time reversal. The theoretical model is first used to predict the existence of single-mode Lamb waves. Both numerical and experimental results show that the use of PWAS-tuned single-mode Lamb waves can greatly improve the effectiveness of the time-reversal damage-detection procedure. [PERSON] et al. [10] proposed a modified time-reversal method (MTRM) which requires only one transducer to actuate signals, while the other transducer acts as a sensor for any signal path. The development of MTRM paves the way for implementing time reversal of signals by using a single actuator and multiple sensors, including non-contact sensors, such as a laser vibrometer. [PERSON] et al. [11] combined the refined time-reversal method (RTRM) and the reconstruction algorithm for probabilistic inspection of defects (RAPID) to predict the damage location on an aluminum plate. TheLamb-wave time-reversal method is an effective baseline-free damage-detection technique for structural health monitoring. However, the parameters of the composite laminates, including dispersion characteristics and anisotropy, reduce the accuracy of the PRM in locating damage to composite laminates. Lamb waves have dispersion and multimode characteristics [12; 13; 14; 15], and composite laminates have features of anisotropy and heterogeneity, which makes the signal analysis using the damage-detection methods based on Lamb waves challenging. Therefore, to improve the accuracy of damage detection, dispersion removal [16; 17; 18] and direction-dependent damage-detection methods [19; 20] have been proposed. These methods generally require users to obtain prior information on the structural parameters of composite materials, and this information is often difficult to obtain in practical applications. In damage imaging, phase and noise artifacts, as well as distortion, may occur due to changes in external environmental parameters, such as temperature and uneven material surface, the dependence of the wave velocity and wavelength on the frequency, and different interactions between defects and material geometrical structure. [PERSON] et al. [21] proposed an image-data-fusion method suitable for elliptic positioning where the amplitude was used as a damage index. The accuracy of the damage location was improved by using the combined amplitude addition and multiplication method. This paper presents a new damage-detection method, the phase-reversal method (PRM), for composite laminates. The proposed method uses a linear sensor array to receive a Lamb-wave signal and analyzes damage according to the scattering signal phase change. Then it applies the inverse Fourier transform to the damage scattering wave and uses its similarity as a damage index to obtain the damage location. Finally, it calculates the correlation coefficient and uses the data-fusion method to improve the damage-imaging accuracy.