# Adaptive Sensor Array Error Calibration Based Impact Localization on Composite Structure
## 5 Conclusions  
This article presents an adaptive piezoelectric sensor array calibration based method for composite structure impact localization. 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. [11] 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.  
Both FEM simulations and experiment results on carbon-fiber composite panel with the imprecise PZT sensor array have demonstrated the validity and effectiveness of the proposed method. Compared with classical 1D-MUSIC and standard 2D-MUSIC method, the proposed method has more accurate localization results. The maximum direction and distance estimation error of the proposed method is 2\({}^{\circ}\) and 2.2 cm, respectively. It shows that the proposed adaptive sensor array error calibration based 2D-MUSIC method is effective for impact localization on a real composite structure. In addition, the beam-formings both of 1D-MUSIC and 2D-MUSIC algorithm are getting better after sensor array error calibration.  
Further research is still worth doing to address systematically the influence of environmental factors to sensor array and to establish the signal model within environmental influence to improve the accuracy of impact localization.  
Y.Z. and J.X.; methodology, Y.Z. and L.R.; software, L.R.; validation, L.R., Y.Z., J.X. and Z.W.; formal analysis, L.R.; investigation, L.R.; data curation, L.R.; writing--original draft preparation, L.R.; Y.Z. and J.X.; writing--review and editing, Y.Z. and J.X.; supervision, Y.Z. and J.X.; project administration. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China [No. U1909217, 51905242], the Zhejiang Special Support Program for High-level Personnel Recruitment of China [No. 2018R52034] and the Qing Lan Project of Jiangsu Province of China.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Impact Case**} & \multicolumn{2}{c}{**Classical 1D-MUSIC**} & \multicolumn{2}{c}{**Standard 2D-MUSIC**} & \multicolumn{2}{c}{**Proposed Method**} \\ \hline \(r\)/mm & \(\theta\)/\({}^{\circ}\) & \(\widehat{\theta}_{c}\)/\(E_{c}^{0}\) & \(\widehat{\theta}_{ac}\)/\(E_{ac}^{0}\) & \(\widehat{r}_{f}\)/\(E_{s}^{\circ}\) & \(\widehat{\theta}_{f}\)/\(E_{p}^{\circ}\) & \(\widehat{r}_{f}\)/\(E_{p}^{\circ}\) & \(\widehat{\theta}_{f}\)/\(E_{p}^{\circ}\) \\
131 & 108 & 105/3 & 108/0 & 114/17 & 104/4 & 114/17 & 106/2 \\
189 & 102 & 98/4 & 105/3 & 176/13 & 100/2 & 176/13 & 102/0 \\
76 & 121 & 112/9 & 116/5 & 72/4 & 117/4 & 72/4 & 119/2 \\
190 & 76 & 74/2 & 76/0 & 167/22 & 75/1 & 167/22 & 76/0 \\ \hline \hline \multicolumn{2}{c}{Note: \(\widehat{\theta}_{c}\)/\(E_{c}^{0}\) and \(\widehat{\theta}_{ac}\)/\(E_{ac}^{0}\) are estimated direction and error of classical and error calibration based 1D-MUSIC, \(\widehat{r}_{f}\)/\(E_{s}^{\circ}\) and \(\widehat{\theta}_{f}\)/\(E_{p}^{\circ}\) are estimated direction and error of standard 2D-MUSIC, \(\widehat{r}_{f}\)/\(E_{p}^{\circ}\) and \(\widehat{\theta}_{f}\)/\(E_{p}^{\circ}\) are estimated direction and error of the proposed method.} \\ \end{tabular}
\end{table}
Table 3: Summary of estimated results and errors.