# Metaheuristics and Support Vector Data Description for Fault Detection in Industrial Processes
## 1 Introduction  
Currently, machine learning and nature-inspired algorithms are being applied in several research fields to obtain optimal results. Some real applications include medical diagnosis based on the patient's symptoms [1], fraud detection in economic transactions [2], identification of patterns of investment in order to buy/sell in a more efficient manner [3], image detection to predict city traffic, machine failure and the design of autonomous vehicles, among others [4]. There are some previous studies regarding fault detection and fault diagnosis based on Dynamic Weight Principal Component Analysis (PCA) [5], Principal polynomial analysis [6], PCA and a Bayesian network [7], deep convolutional neural network [8], Hidden Markov Model and Bayesian Network [9], among others. However, statistical assumptions about the distribution of the process data should be made in some of these approaches. Support Vector Data Description (SVDD) [10] and Artificial Neural Networks (ANN) algorithms share the same concept using the linear learning model for pattern recognition. ANN tries to converge to a local minimum using the gradient descent learning algorithm and suffers from overfitting problems. On the other hand, SVDD tends to find a global solution during training since the complexity of the model has been taken into account as a structural risk in SVDD formation. ANN minimizes only empirical risk learned from training samples and SVDD considers not only the empirical risk but the structure risk. Thus, SVDD training results show better generalization capability than those obtained with ANN. In industry, machine learning classifiers are implemented to focus on faults detection. In [11; 12], reviews of machine learning applications in the manufacturing industry are presented. The use of artificial neural networks in the modeling and optimization of processes is emphasized as well as the application of SVM for quality assessment in industries. Another application of SVM for the early failure prediction in the oil and gas industry is shown in [13]. In [14], a monitoring platform using Artificial Neural Network and the Support Vector Machine is proposed and applied to the prediction of the performance of aeronautical engines and health diagnosis. Nevertheless, conventional algorithms are also created to perform two-class or multi-class classification tasks. Because of this, data containing all class of information on the processes are required. Recently, machine learning algorithms have been used in fault detection, but there is sometimes the downside of having more information available from one of the kind. For example, if a relatively new machine is in operation, it is very likely that only the data corresponding to normal operation are available. In this study, a method for fault detection is proposed which is able to deal with processes or machines where observations or data about the faults are scarce for the training phase by using the one class classifier known as Support Vector Data Description (SVDD) [10]. The choice of hyper-parameters is one of the most important features for SVDD. These parameters are associated with the hyper-sphere as well as with the kernel function chosen for the classification. In this study, these hyper-parameters are simultaneously optimized using metaheuristic techniques. Furthermore, a comparison among four optimization techniques is reported in order to evaluate the quality of the obtained results. The results are satisfactory when applied to a process of fault detection at low computational cost. There are some studies covering different SVDD algorithm applications [15; 16; 17]--most of them optimizing the hyper-parameters using approaches like grid search, which is computationally expensive. To obtain these parameters in a more efficient manner, some authors have considered metaheuristic algorithms. Particle swarm optimization (PSO) and genetic algorithms can be often found in literature. Ref.