# Acoustic-Based Engine Fault Diagnosis Using WPT, PCA and Bayesian Optimization
###### Abstract
After signal decomposition, relevant time-frequency information can be extracted, and it can be used as the input for fault classification. Most fault diagnosis models in the literature follow a single classification algorithm or attempt to compare among few classification algorithms to find the best model [20; 21; 22; 23]. However, it has to be noted that each emerging fault has different characteristics and the appropriate algorithm has to be chosen according to their corresponding classification performance. There has been considerable work on optimization of model hyperparameters [24; 25]. However, there are limited approaches for the combined model selection with hyperparameter optimization in literature. One useful methodology is the utilization of meta learning procedures which employ information from previous data to find the optimal algorithm or hyperparameter configuration [26]. This is not practical in many cases due to its computational complexity in evaluating a huge amount of previous data. Bayesian optimization is an adequate method to overcome this issue [27], which has been shown to outperform other optimization techniques on several of challenging benchmark problems [28; 29]. The objective of Bayesian optimization is to find a point that minimizes an objective function using cross-validation classification error [30; 31]. The function evaluation itself could involve an onerous procedure, and this is addressed in [30] by using a conventional dimensionality reduction technique--Principle Component Analysis (PCA). By reducing the feature space to smaller number of Principle Components (PCs), the computational complexity is reduced, lowering the evaluation time [32; 33]. PCA has been proven to reduce training time and improve the classification performance in very large datasets as shown in [34]. Nonetheless, the utilization of PCA to reduce the feature set for Bayesian optimization and its effect on the optimization performance have not been addressed critically in the known literature. The aim of this paper is to present a new fault diagnosis method for a gasoline ICE with various fault conditions by analyzing its acoustic signals. This starts with Model 1, which contains the selection of standard classifiers. It evolves to Model 2, which uses Bayesian optimization for both model selection and model hyperparameter optimization, so that an optimal model with its selected features and parameters is provided. Finally, Model 3 is proposed, which applies PCA alongside Bayesian optimization to reduce the complexity of the feature space for the optimization problem. All three models use WPT for signal analysis and the statistical features computed from the high- and low-level WPT coefficients. Hence, the main contributions of this paper are as follows:  
* Exploring the viability of the use of acoustic signals for engine fault classification under different fault scenarios and different operating conditions
* Evaluating the performance and the use of Bayesian optimization on standard classification models for fault diagnosis of an ICE
* Evaluating the effect of PCA on the optimized fault classification model in terms of classification accuracy, other performance metrics and the evaluation time  
The remainder of this paper is structured as follows. Section 2 presents the experimental set up and the engine fault characteristics. Section 3 describes the general workflow and the detailed methodology employed. Section 4 describes the results and the comparison of the three models using various performance metrics. Section 5 concludes the paper.