# A Vibration Based Automatic Fault Detection Scheme for Drilling Process Using Type-2 Fuzzy Logic
## 1 Introduction
The continuity of this new defuzzification process was demonstrated utilising several well-known Hausdorff metric properties, Aumann integration, and the continuity of the Lebesgue measure on the class of compact-convex subsets. Defuzzification processes are well-known as important tools in control systems with uncertainty. From a practical standpoint, the following characteristics are arguably the most crucial for a defuzzification procedure: consistency and computing efficiency. [PERSON] et al. [40], in their work, developed a new IT2 FLS, called an m-m IT2 FLS, that is a simplified version of the WM UB IT2 FLS.The m-m IT2 FLS has allowed for rigorous evaluations of IT2 fuzzy controllers, has lately been deployed in a number of applications, and has shown tremendous potential as a viable IT2 FLS that is not confined to control. They use a limits technique to quantitatively study the structure of the m-m IT2 FLS and identify the conditions under which the m-m IT2 FLS approaches the WM UB. These circumstances will also serve as guidance for the m-m IT2 FLS design parameters, which will aid designers in selecting these parameters for their applications. [PERSON] et al. [41] presented an overview of the uses of interval type-2 fuzzy logic in intelligent control. The paper's main focus is on the underlying reasons for employing type-2 fuzzy controllers in various applications. Bio-inspired algorithms have recently emerged as effective optimization algorithms for handling complicated issues. The use of bio-inspired optimization approaches in the design of type-2 fuzzy controllers for specific applications has aided in the difficult work of determining the suitable parameter values and fuzzy system topology. The associated cutting forces in this work have nonlinearities embedded in the drilling process, which is an important aspect and should be dealt with in an efficient manner using fuzzy techniques. A combination of PD and PID with Type-2 fuzzy logic system for the chatter control in milling process was proposed by [PERSON] et al. [42]. An innovative model-based fault detection (FD) system in combination with an interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy system for detecting faults in downhole drilling systems was proposed by [PERSON] et al. [43]. A novel fault detection methodology for interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems with sensor fault on the basis of novel fuzzy observer was illustrated by [PERSON] et al. [44]. In their study, [PERSON] and [PERSON] pioneer the use of Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) for gas turbine problem diagnostics. A bank of IT2 FLSs trained for state detection and health assessment of an industrial gas turbine under varied operating conditions makes up the proposed FDI system. In order to achieve this, train and test data are produced by adding mechanical fault signs to the mathematical model of the gas turbine. turbine. The Interval Type-2 Fuzzy C-Means (IT2 FCM) clustering method is then used to construct a fuzzy rule base, and a metaheuristic approach is used to optimise the parameters of the IT2 FLSs [45]. In order to enhance decision-making in fault detection, [PERSON] and [PERSON] suggested a method for leveraging the prediction uncertainty information produced by Bayesian deep learning models. Automatic Differentiation Variational Inference (ADVI) is used for inference, and the resulting prediction uncertainty information is used to improve defect identification. An actual case study on vertical continuous plating (VCP) of printed circuit boards is used to test the proposed methodology [46]. An innovative method for rotating machinery defect diagnosis and detection was presented by [PERSON] et al. Fast Fourier Transform (FFT), Continuous Wavelet Transform (CWT), and statistical features of raw signals were combined to create a novel feature engineering paradigm [47]. An automatic fault detection technique with model based methodology is depicted in this paper.