Citation: Hassan, F.; Rahim, L.A.; Mahmood, A.K.; Abed, S.A. A Hybrid Particle Swarm Optimization- Based Wavelet Threshold Denoising Algorithm for Acoustic Emission Signals. Symmetry 2022, 14, 1253. https://doi.org/10.3390/sym14061253 Academic Editors: Marcin Kami ´ nski, Zbigniew Pozorski and Anna Knitter-Pi ˛ atkowska Received: 23 March 2022 Accepted: 21 April 2022 Published: 16 June 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). symmetry S S Article A Hybrid Particle Swarm Optimization-Based Wavelet Threshold Denoising Algorithm for Acoustic Emission Signals Farrukh Hassan 1, * , Lukman Ab. Rahim 1 , Ahmad Kamil Mahmood 2 and Saad Adnan Abed 3 1 Department of Computer and Information Sciences, High Performance Cloud Computing Centre (HPC3), Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia; lukmanrahim@utp.edu.my 2 Interventure Tech, 4 Laluan Tronoh 9, Desa Tronoh, Tronoh 31750, Malaysia; kamilmhpet@gmail.com 3 College of Medicine, University of Fallujah, Fallujah 31002, Iraq; saad.adnan@uofallujah.edu.iq * Correspondence: farrukh_18001246@utp.edu.my Abstract: Acoustic emission (AE) as a non-destructive monitoring method is used to identify small damage in various materials effectively. However, AE signals acquired during the monitoring of oil and gas steel pipelines are always contaminated with noise. A noisy signal can be a threat to the reliability and accuracy of the findings. To address these shortcomings, this study offers a technique based on discrete wavelet transform to eliminate noise in these signals. The denoising performance is affected by several factors, including wavelet basis function, decomposition level, thresholding method, and the threshold selection criteria. Traditional threshold selection rules rely on statistical and empirical variables, which influence their performance in noise reduction under various conditions. To obtain the global best solution, a threshold selection approach is proposed by integrating particle swarm optimization and the late acceptance hill-climbing heuristic algorithms. By comparing five common approaches, the superiority of the suggested technique was validated by simulation results. The enhanced thresholding solution based on particle swarm optimization algorithm outperformed others in terms of signal-to-noise ratio and root-mean-square error of denoised AE signals, implying that it is more effective for the detection of AE sources in oil and gas steel pipelines. Keywords: discrete wavelet transform; acoustic emission; particle swarm optimization; local search; genetic algorithm; late acceptance hill climbing; signal-to-noise ratio; mean square error 1. Introduction A great deal of attention has been paid to the acoustic emission (AE) method for fault diagnosis in various fields such as civil engineering, big data analytics, and aerospace engineering, because of its convenience in data acquisition. The operation of the sensor, the difference in travelling path and the process of data acquisition adds noise to the signal. The complex noises in the AE signals make it difficult to extract the signal characteristics. The reduction in noise is indispensable for successful and reliable processing of AE signals [1]. Several strategies have been developed in recent years to reduce noise and improve the signal-to-noise ratio (SNR) [2–7]. For denoising a noisy signal with a fixed noise frequency, the Fourier transform filter (FFT) approach is often applied. It is determined by withdraw- ing Fourier components with frequencies beyond a cutoff frequency. Nevertheless, it is dif- ficult to determine the noise frequency [8]. Therefore, it makes the conventional technique inappropriate when dealing with AE signals [9]. Singular value decomposition (SVD) is a numerical approach for noise reduction using matrix decomposing [10]. SVD offers a good noise reduction performance for fault signals with low background noise. However, when there is a lot of background noise, the SVD decomposition is imperfect, and the components still have a lot of noise. Singular spectrum analysis (SSA) requires manually setting the em- bedded dimension, and good results can only be obtained by selecting the proper embedded dimension [11]. Mallat suggested the wavelet transform (WT) for the first time in 1989 [12]. Symmetry 2022, 14, 1253. https://doi.org/10.3390/sym14061253 https://www.mdpi.com/journal/symmetry