## 1 Introduction  
The development and miniaturization of acousto-electronics [1; 2] and acousto-optics modulation filters [3; 4] are primarily based on surface acoustic waves (SAWs) in anisotropic piezoelectric crystals, such as Lithium Niobate (LiNbO\({}_{3}\)) and Lithium Tantalate. Among the various piezoelectric crystals, LiNbO\({}_{3}\) has generated considerable interest as a potential material for acoustic device applications, due to its high electromechanical coupling coefficient (\(K^{2}\) = 5.3%) [5]. The generation and detection of acoustic waves in piezoelectric crystals with the aid of inter-digital transducers (IDTs) have attracted widespread scientific interest for signal processing and filtering applications, and also been used as sensor for pressure, temperature, traces of vapor and gases [6; 7]. The SAWs transducers are fabricated using electrically conductive comb-shaped structures (digital and inter-digital transducers; DT, IDT) in the frequency range varying from the upper GHz range (of typically up to 15 GHz) to the lower MHzrange [8]. It has several advantages like; small volume, high sensitivity, diverse type and convenient process which made it used in several measurement areas. In last few decades, a significant number of non-destructive evaluation (NDE) and structural health monitoring (SHM) techniques have been implemented for detecting the failure in critical structures. Currently, the emphasis of SHM techniques is on global and local damage detection using vibration-based techniques [9] and guided wave-based techniques [10]. Guided waves such as Lamb waves and SAW have been explored for detection of surface and subsurface defects/delamination [11; 12; 13; 14]. Recently, highly sensitive strain sensors employing SAW resonator have been developed for SHM applications [15; 16; 17]. It was demonstrated that the strain induced in the structure could be sensed using SAW sensors, and macroscale damage could be quantified. These SAW-based piezo-sensors also act as a self-sensing device which is capable of detecting surface and subsurface aberrations and damages. Investigations using several methods have been conducted on the experimental and theoretical aspects of acoustic wave propagation in anisotropic piezoelectric sensors [18]. The experimental investigations were mainly focused on the characterization of piezo-electric sensors and determination of elastic constant of the anisotropic crystals [19]. The dispersion relationship and phase velocity information have been experimentally determined using neutron scattering [20], Brillouin scattering [21], pulse superposition, and pulse-echo overlapping technique [22; 23]. Based, on the anisotropy of the sensors, complex patterns of caustic wave propagation are observed [24]. Scanning acoustic microscopy is another sensitive technique used for sensors or material characterization that could be used both in reflection and transmission modes [25; 26; 27; 28; 29; 30]. Ultrasonic point source-point receiver [31] and coulomb coupling techniques employed by [PERSON] et al., have explored piezoelectric coupling for acoustic waves propagation in the piezo-electric sensors [32; 33; 34; 35]. In conventional SHM, the underlying assumption is that the sensors are inherently healthy and calibrated to compensate for error and noise arising from the harsh environmental conditions. In harsh environmental conditions and extreme loadings, such as fatigue, corrosion and high temperature, hidden damage is induced within the sensor. The sensors which are sensitive to active devices usually suffer more damage compared to the structure. However, both in research and practice, limited considerations are devoted to quantifying the health of the sensors. The error induced due to the degraded sensor is circumvented by correcting the acquired response by a baseline compensation factor. Instead of ignoring the performance deterioration of the sensors, we focused our efforts on detecting the damage in the sensors.