PSI - Issue 39

Nabam Teyi et al. / Procedia Structural Integrity 39 (2022) 608–623 Author name / StructuralIntegrity Procedia 00 (2019) 000–000

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into a set of wavelets. The CWT is used to break down a signal into wavelets. Wavelets are very small oscillations with a lot of temporal localization. The DWT divides a signal into sets, each of which is a time series of coefficients characterizing the signal’s time evolution in the frequency range in question. Gómez et al. (2016) did a comprehensive review of advances made in the use of the WT in the diagnosis of cracked rotors. Babu and Reddy (2021) used WTs at stress concentration points to detect open cracks on a rotating stepped shaft with several discs. One dimensional WTs were used to the response curves or mode shapes. Rotational response curves were more sensitive to shaft cracks and helped locate cracks than translation response curves. The effectiveness of wavelet detection for single and multiple grooves increased with groove depth. Response curves were evaluated for crack location using white Gaussian noise with low signal to noise ratio. ANNs receiving data from discrete wavelet coefficients were used to locate and measure cracks. 4.6. Adaptive Neuro Fuzzy Inference System Jang invented the ANFIS (Jang, 1991). In the process, a feed-forward neural network, similar to fuzzy inference methods, is used. This design can simulate complex, nonlinear, and non-homogeneous functions. It is a hybrid neuro fuzzy method. It converts input characteristics to input MFs, MFs to a collection of if-then rules, rules to a set of output characteristics, and output MFs to a single-valued output or an associated decision. Nanda et al. (2014) investigated the effect of crack sites and sizes on vibration parameters on a transversely loaded cantilever shaft with several cracks. The experimental investigation examined the dynamic response of uncracked and cracked mild steel shaft specimens. The theoretical answer was tested using an ANFIS and the shaft’s modal parameter. The surface plots proved the ANFIS methodology’s efficacy. The residual plots were eliminated by comparing the ANFIS predicted data to the theoretical data. The ANFIS segment ended with normal probability charts. Nanda et al. (2014) again used ANFIS optimization technique to locate and measure the depth of a crack in a simply supported shaft under axial and bending loads. The cracked shaft’s vibration parameters were calculated theoretically. The changes in natural frequencies caused by cracks were used as an input parameter for ANFIS crack detection. Nanda and Parhi (2013) simulated the dynamic response of an axial and bending load on a steel shaft with two transverse cracks fixed at both ends by bearings. The MANFIS methodology located cracks at any depth and location. The first three natural frequencies and the first three mode shapes were sent into MANFIS. The proposed experimental setup was used to validate the MANFIS projected outcome (relative crack position and depth). Das et al. (2015) used ANFIS for nonlinear function approximation, combining it with neural network learning capabilities and a fuzzy inference system. They employed grid partitioning to simulate a single output Sugeno type fuzzy inference system (FIS) to explore the influence of an open fracture on the modal characteristics of a cantilever shaft subjected to free vibration. Shim and Shuh (2002) proposed a synthetic AI system using eigen frequencies, for crack detection in a planar frame. The ANFIS architecture was used to approximate the eigen frequencies as functions of the crack parameters. Estimation was within 4% error in the clamped plane frame problem. Shim and Shuh (2002) also proposed the use of Pareto-based CEA for Multiobjective Optimization (MOPCEAs) to identify fracture patterns. MOPCEAs identified the crack location and depth by minimising three objective functions defined by the estimated eigen frequency and the measured/reference one. MOPCEA was useful for inverse and crack identification problems, but was computationally expensive. MOPCEAs must be parallelized to reduce processing time. Additionally, Shim and Shuh (2003) proposed a method for crack localization and depth using ANFIS solved via a hybrid learning algorithm and CEAs capable of solving single objective optimization problems with a continuous function and continuous search space. The fractured structure was broken down into a number of parts, with the crack considered to be within one of them. From the dataset generated by the FEA for various crack sizes and locations, ANFIS architecture for the cracked structure was created to simulate the structure’s response. The clamped-free beam problem’s crack parameters were approximated to within 3 percent inaccuracy. 4.7. Machine Learning Models As with mathematical functions, machine learning models take input data, predict what will happen, and then respond accordingly. Models describe signals in the noise or patterns found in training data in supervised and unsupervised machine learning. ML models are essentially algorithms that have been trained; they are generated when