## 1 Introduction  
Ultrasonic testing (UT) has played a major role in the structural health monitoring (SHM) of various safety-critical structures. When a material is subjected to cyclic loading, it can lead to crack development, crack growth, and eventually structure failure. While ultrasound has been widely used for non-destructive testing, conventional ultrasound techniques are often limited by crack size and density--by the time the presence of cracks is detectable with such techniques, a structure may already have consumed 80-90% of its fatigue life and can be close to failure. Additionally, small cracks, sometimes termed micro-cracks or microstructural defects, can themselves compromise the mechanical strength and integrity of the structure [1]. As importantly, conventional ultrasonic techniques are also limited by the areal size and complexity of a structure, which makes comprehensive evaluation of real-world structures time-consuming, cumbersome, and incomplete [2, 3]. Nonlinear effects take advantage of the fact that micro-cracks can often make up in numbers what they lack in size [4]. Typically, a micro-crack can have two ends, although more complex shapes are possible. Each end of a micro-crack typically has an acute angle which can result in stress concentration. Closing and opening of the cracks can result in local stiffness changes in the presence of ultrasonic excitation [5, 6]. Common structural materials have second order elastic coefficients involved in linear scattering of ultrasonic waves and also have considerably smaller third order coefficients that can give rise to higher order scattering. Due to the relative size of the second and third order elastic coefficients,a smooth bore hole in a structure can have an insignificant nonlinear response. However, due to the combined effects of (i) stress buildup at crack ends and (ii) large numbers of micro-cracks, the aggregate nonlinear response of a field of micro-cracks can be substantial and readily detectable. Earlier studies show nonlinear ultrasonic testing (NUT) is able to detect plastic deformation or fatigue damage at an early stage [7; 8; 9; 10]. Conventional guided wave approaches have limitations for large-area inspection. They can only be used in relatively uniform structures that support specific guided ultrasonic modes. In addition, a careful interpretation of the interaction of the selected modes with the structure is required to satisfy the phase matching condition [9; 11]. In terms of mode analysis, mode identification for the guided wave generation condition has made NUT for complex structures challenging. In terms of the test system, inspection of a plate or a pipe using conventional approaches also relies on either specially designed angle beam transducers, magnetostrictive transducers (MSTs), PZT disk transducers, or arrays of such transducers [11]. The measurement setup with a large set of transducers is sometimes applicable to one geometry but not others due to different dispersion characteristics of different geometries. Restriction to specific geometries can render such approaches impractical for many SHM applications. [PERSON] et al. has proposed a new type of sensor for use with nonlinear elastic wave spectroscopy (NEWS) [12]. They used photonic crystal (PC) structures in order to filter out undesired frequencies on a damaged aluminum plate. A complicated design of the host structure is generally required for the tuning of band gaps, and thus it prevents their use in real applications. There have also been many studies on the feasibility and value of the nonlinear elastic wave spectroscopy method with a time reversal process for microdamage imaging [13; 14; 15; 16], which was accompanied by complex mathematical calculations. This paper aims to overcome these limitations and develop nonlinear ultrasonic test in more practical manner for industry use by proposing a simple measurement system and analysis algorithm.