**A New Closed-Form Solution for Acoustic Emission Source Location in the Presence of Outliers**

**Zilong Zhou 1, Yichao Rui 1,\*, Jing Zhou 1, Longjun Dong 1, Lianjun Chen 2,\*, Xin Cai <sup>1</sup> and Ruishan Cheng <sup>1</sup>**


Received: 21 April 2018; Accepted: 5 June 2018; Published: 8 June 2018

**Abstract:** The accuracy of an acoustic emission (AE) source location is always corrupted by outliers due to the complexity of engineering practice. To this end, a preconditioned closed-form solution based on weight estimation (PCFWE) is proposed in this study. Firstly, nonlinear equations are linearized, and initial source coordinates are obtained by using equal weights. Residuals, which are calculated by source coordinates, are divided into three regions according to normal distribution. Secondly, the weight estimation is developed by establishing the relationship between residuals and weights. Outliers are filtered by the iteration between the weight estimation and source location. Subsequently, linear equations are reconstructed with the remaining measurements containing no outliers, while they are ill-conditioned. Finally, the preconditioning method is applied to weaken the ill condition of the reconstructed linear equations, so as to improve the location accuracy. This new method is verified by a pencil-lead break experiment. Tests results show that the location accuracy and stability of the new method are superior to traditional methods. In addition, outlier tolerance and the velocity sensibility of the new method are investigated by simulating tests.

**Keywords:** acoustic emission; closed-form solution; outlier; time difference of arrival; weight estimation
