# Adaptive Sensor Array Error Calibration Based Impact Localization on Composite Structure
## 1 Introduction  
Structural health monitoring is an emerging technology with signal processing technology to monitor the status of composite structures in real time or whenever necessary [1; 2; 3]. Defect would be induced during service, such as from impacts by a foreign object. Despite the advantages of composite structure, they are susceptible to barely visible impact damage [4; 5]. Therefore, impact localization is an important part of structural health monitoring system to ensure the safety of composite structure. Array signal processing for source localization is one of the major interests in many applications. Over several decades, this topic was extensively studied and many algorithms have been proposed, such as spatial filter based method [6] and phased array based method [7]. Among these existing localization methods, the multiple signal classification (MUSIC) algorithm is easy implementation with arbitrary array configurations [8]. [PERSON] et al. [9] proposed a MUSIC method based on array signal processing for impact source localization in a plate. [PERSON] et al. [10] developed an imaging method based on the time-reversal operator and MUSIC algorithm for damage imaging in a metallic plate. [PERSON] et al. [11] presented a near-field impact monitoring method based on the two-dimensional multiple signal classification method for the composite structure. [PERSON] et al. [12; 13] proposed a plum-blossom sensor array-based 2D-MUSIC method to realize omnidirectional impact localization of composite structures. [PERSON] et al. [14] presented a model-based 2D-MUSIC damage identification algorithm for plate-like structures. However, those MUSIC based methods in the literature mentioned above require precise knowledge of the signals received from a standard source located at any direction. The performance of those methods depend strongly on the accuracy of the observed array signal vector from sensor array. In fact, array signal vectors have various error forms including array element position error, gain-phase error caused by structural propagation path deviation, etc. Therefore, imprecise sensor array signal vectors would significantly degrade the performance of the MUSIC algorithm, and there is still the problem of ensuring array steering vector calibration for practical engineering applications. To reduce the localization error caused by sensor phase errors, [PERSON] et al. (2015) presented an anisotropy compensated MUSIC algorithm. This method experimentally verifies that the correction of the sensor phase error makes the MUSIC algorithm more accurate and reliable for the damage localization on composite structures. However, the process of measuring the sensor phase error by experiments may be time consuming and expensive. A practical approach to alleviating the problems introduced by imprecise array calibration is to use the received signals to adjust or fine-tune the array calibration. In radar fields, self-calibrating antenna arrays have been developed and tested by [PERSON] (2016) and others. However, self-calibration sensor array for composite structural health monitoring seen to have received little attention. In this study, adaptive sensor array error calibration based method is proposed for impact localization on composite structure. First, observed signal vector from the sensor array is represented by error calibration matrix with unknown gains and phases, and then it used to construct the cost function including sensor array parameters. Second, 2D-MUSIC algorithm based on linear attenuation calibration in ref. (2011) is applied for estimating the initial estimate of impact location. Finally, substituting the initial estimate, the cost function is minimized by adaptive iterative to calculate the sensor array error parameters and the exact location of the impact source. This study is organized as follows. Section 2 introduces the signal modal of imprecise sensor array and Section 3 simulates a FEA model which was created in ABAQUS.