# Structural Health Monitoring Using Machine Learning and Cumulative Absolute Velocity Features
###### Abstract  
Machine learning (ML)-aided structural health monitoring (SHM) can rapidly evaluate the safety and integrity of the aging infrastructure following an earthquake. The conventional damage features used in ML-based SHM methodologies face the _curse of dimensionality_. This paper introduces low dimensional, namely, cumulative absolute velocity (CAV)-based features, to enable the use of ML for rapid damage assessment. A computer experiment is performed to identify the appropriate features and the ML algorithm using data from a simulated single-degree-of-freedom system. A comparative analysis of five ML models (logistic regression (LR), ordinal logistic regression (OLR), artificial neural networks with 10 and 100 neurons (ANN\({}_{10}\) and ANN\({}_{100}\)), and support vector machines (SVM)) is performed. Two test sets were used where Set-1 originated from the same distribution as the training set and Set-2 came from a different distribution. The results showed that the combination of the \(CAV\) and the relative \(CAV\) with respect to the linear response, i.e., \(R_{CAV}\), performed the best among the different feature combinations. Among the ML models, OLR showed good generalization capabilities when compared to SVM and ANN models. Subsequently, OLR is successfully applied to assess the damage of two numerical multi-degree of freedom (MDOF) models and an instrumented building with \(CAV\) and \(R_{CAV}\) as features. For the MDOF models, the damage state was identified with accuracy ranging from 84% to 97% and the damage location was identified with accuracy ranging from 93% to 97.5%. The features and the OLR models successfully captured the damage information for the instrumented structure as well. The proposed methodology is capable of ensuring rapid decision-making and improving community resiliency. c 2021 14 June 2  
data [2]. Conventional ML tools were, however, limited in their ability to process the large amounts of measured sensor data in their raw form, particularly before deep learning (DL) tools emerged. As such, careful engineering and considerable domain knowledge have been utilized to extract damage-sensitive features from the raw data which were subsequently fed into a suitable ML model. Many of these features were based on modal properties of the structure, such as modal frequencies, mode shapes, curvature of mode shapes, modal assurance criteria, and power spectral densities [3; 4; 5; 6; 7; 8]. Although these damage-sensitive features produced promising results [9; 10], they were also shown to be sensitive to operational or environmental conditions [11]. Therefore, researchers have studied alternative features not based on modal properties, such as the cumulative absolute velocity (\(CAV\)) [12; 13], higher exponentiations of the acceleration intensity [14], standardized \(CAV\) (\(CAV_{STD}\)) [15], and instantaneous power (\(IP\)) [16], which also showed promising results for SHM [17]. Applications of ML in vibration based-SHM have been studied by several researchers [18; 19; 20]. Among different ML models, multi-layer perceptrons (MLP) have been applied the most [21; 22; 23; 24]. [PERSON] et al. [18] proposed a Bayesian artificial neural network (ANN) method for SHM and showed its applicability for a truss bridge. [PERSON] et al. [25] used Fourier coefficients of the mode shapes with ANN to detect and locate damage. [PERSON] et al. [26] used an ANN based system identification method to estimate damage percentage of joints for a truss bridge structure. More recently, developments of convolutions neural network (CNN) based SHM techniques are increasing. [PERSON] et al. [27] trained CNN models for different damage cases and successfully classified damage. [PERSON] et al. [28] applied two dimensional (2D) CNN for the overall assessment of concrete bridges. Support vector machine (SVM) is another ML classifier that researchers found effective in damage detection. [PERSON] et al.