# A Crack Characterization Method for Reinforced Concrete Beams Using an Acoustic Emission Technique
## 1 Introduction
Such data related to concrete failure are very hard to collect in real-life scenarios, which may eventually lead to an inefficacious crack assessment indicator. * In many cases, the existing works have failed to precisely determine the time period of early crack occurrence, since used AE features have displayed discrete fluctuations, making it very problematic to sort out the time period. Additionally, nonmonotonic curves of these features even after the severity of cracks has increased can be observed as well. It may lead to false maintenance alerts resulting in a waste of resources. * The existing methods do not focus on the classification of crack types, even though machine learning-based classification methods can be effective measures to detect cracks. Very few methods that have adopted classification approaches fail to distinguish the micro-cracks from the macro ones. Considering the points mentioned earlier, it becomes a necessity to develop a robust concrete crack assessment indicator (CAI) that can coalesce the diagnostic capabilities of the individual features by suppressing noise in the curve of the indicator representing the time history. Previous works focus on load analysis against the AE history, fracture detection, fault classification (severe/minor), classification of tensile or shear cracks, etc. The existing literature lacks the development of a very accurate CAI for evaluating the crack development of concrete beams over time. The existing works found so far that made substantial effort to build a degradation indicator using AE burst (AEB) features did not consider the entire time history of the loading, while not allowing us to have full insight into the degradation process. To deal with the lacking capability and the above-mentioned challenges, this paper utilizes the Mahalanobis distance (MD) [26] accompanied by the Boruta feature selector algorithm [27] to fuse the important features from the AE feature pool and develop the CAI. Our proposed system combines the MD and Boruta feature selector algorithm (Boruta-Mahalanobis system (BMS)) in a multi-dimensional system. The MD is used so that we can build a measurement scale with multiple dimensions and establish the Mahalanobis space (MS) [26]. The MS acts as a point of reference of the scale considering a group of normal observations. It is possible to solve the class imbalance problem using MD by considering single-class samples. It is not necessary to use the entire data designated for training to construct the measurement scale. It is possible to calculate MD using the in-between distance of the center of the MS and the observations that are being evaluated. Observations having a MD smaller than the threshold are considered normal, whereas observations having a MD that exceeds the threshold are abnormal. Provided with robust and appropriate features, the MD alone can determine fractures in the concrete beam. Though the MD has been effectively used in many works [28; 29; 30; 31; 32], it does not provide a complete method to figure out appropriate features that can provide us with a reliable CAI. Therefore, we used Boruta, which is a wrapper-based feature selector algorithm capable of choosing the most intrinsic features of the system. However, the CAI developed using BMS can present a great deal of noise due to the scattered and fluctuating MD points. To alleviate noise and obtain a monotonic CAI, we suggested a noise-removal strategy (NRS) based on the cumulative sum (CUMSUM) algorithm [33]. In this study, the final time-dependent CAI has a duration of 872 s, with the first 300 s representing the normal condition. The following two 300 and 272-s periods represent micro-crack and fracture formations, respectively. This CAI is finally passed through a k-nearest neighbor classifier (k-NN) as an input to distinguish between the three mentioned states. The novel contributions of the work are presented in brief as follows:  
* A reliable CAI presenting the time history of crack formation in the concrete beam is proposed.