## 1 Introduction
Identifying the sub-surface cracks also involves the simple magnetization of the material and obtaining the flux leakage output by using a hall sensor [6]. The periodic checking and verification of sub-surface cracks in critical areas may avoid drastic incidents. Magnetic flux testing (MFL) techniques are required in the inspection of steel tubes and pipes in the petrochemical industry, rope cars, nuclear reactor tubes, etc. [PERSON] and [PERSON] et al. [7] designed and produced two different PIGs to inspect pipelines using the flux leakage method. The authors also developed a new magnetic measurement system to investigate the effect of the speed variation of the produced PIGS. [PERSON] et al. [8] introduced the principle, measuring methods, and quantitative analysis of the MFL method. The authors used statistical identification methods to establish the relationship between the defect shape parameter and magnetic flux leakage signals. [PERSON] et al. [9] developed a bobbin coil magnetizer arrangement to inspect the defects in small-diameter tubes and used an ANSYS Maxwell EM V-16-based Finite Element Method (FEM) and analytical model to support the experimental results. For improving model accuracy, recently support vector regression (SVR), a machine learning tool, has gained focus among researchers in various fields to minimize prediction error. [PERSON] et al. [10] proposed an internal crack-defect-detection method based on the relief algorithm and Adaboost-SVM, to overcome the problems of poor generalization and low accuracy in the existing defect detection process. [PERSON] et al. [11] developed an SVR regression model to forecast the stock price by optimizing the SVR parameters using dynamic adjustment and the opposition-based chaotic strategy in the Firefly Algorithm (FFA), termed the Modified Firefly Algorithm (MFFA). [PERSON] et al. [12] implemented the SVR model with a Genetic Algorithm (GA) technique to forecast the dissolved gas content in power transformers to maintain the safety of the power system. [PERSON] et al. [13] used a twin support vector regression model to forecast the wind speed by tuning the SVR parameters by implementing the Particle Swarm Optimization (PSO) algorithm. [PERSON] et al. [14] presented a novel Sine Cosine Algorithm-SVR model to select the penalty and kernel function of SVR and validated the effectiveness by solving benchmark datasets. [PERSON] et al. [15] introduced the GA-SVR model in forecasting sales volume to achieve better forecasting accuracy and performance than traditional SVR and Artificial Neural Network (ANN) prediction models. [PERSON] et al. [16] investigated the efficiency of the SVM forecasting model for the next-day directional change of electricity prices and reported 76.12% forecast accuracy over a 200-day period. Several other applications of SVR models exist in literature, ranging from process parameter prediction [17; 18] to flow estimation [19] and from 3D-printing applications [20] to battery monitoring [21]. From the literature, it is understood that the SVR model, a machine learning tool, has been used by researchers in different areas like stock-market prediction, electricity prices, dissolved gas content, wind speed, etc. In this work, the SVR model is to be developed to predict the SGT's defect in terms of length, width, and depth of cracks from the given gray level co-occurrence matrix feature from the Magnetic Flux Leakage (MFL) image. The selection of parameters, such as kernel function, solver type, and validation scheme, along with % of test data, will affect the performance of the SVR models. The root means square error, mean absolute error, and \(R^{2}\) values are considered to measure the performance of the SVR model. Multiple contradictory performance measures require the conversion of multi-objectives into a single objective that initiated the implementation of the TOPSIS method. The Moth Flame Optimization Algorithm (MFO) is proposed to select the optimal parameters of SVR to minimize the prediction error.