Estimation and Optimization of Tool Wear in Conventional Turning of 709M40 Alloy Steel Using Support Vector Machine (SVM) with Bayesian Optimization

Cutting tool wear reduces the quality of the product in production processes. The optimization of both the machining parameters and tool life reliability is an increasing research trend to save manufacturing resources. In the present work, we introduced a computational approach in estimating the tool wear in the turning process using artificial intelligence. Support vector machines (SVM) for regression with Bayesian optimization is used to determine the tool wear based on various machining parameters. A coated insert carbide tool 2025 was utilized in turning tests of 709M40 alloy steel. Experimental data were collected for three machining parameters like feed rate, depth of cut, and cutting speed, while the parameter of tool wear was calculated with a scanning electron microscope (SEM). The SVM model was trained on 162 experimental data points and the trained model was then used to estimate the experimental testing data points to determine the model performance. The proposed SVM model with Bayesian optimization achieved a superior accuracy in estimation of the tool wear with a mean absolute percentage error (MAPE) of 6.13% and root mean square error (RMSE) of 2.29%. The results suggest the feasibility of adopting artificial intelligence methods in estimating the machining parameters to reduce the time and costs of manufacturing processes and contribute toward greater sustainability.


Introduction
Tool life is one of the main parameters in machining. Tools that wear or fail a comparably lengthy duration life service can lead to a decreased production rate and surface finish capacity [1]. Tool wear is an important parameter in machining as its increase not only increases cutting forces and cutting temperatures but also produces poor finished and inaccurately machined surfaces. Rapid tool wear also increased the lead time spent in the replacement of tools, thereby reducing the production rate [2]. Worn tools reduce the quality of the production and might harm the machine as well as the workpiece. Furthermore, the cutting force might increase, which elevates the temperature and intensifies the tool wear. Breakdown of the tool may result in more significant repercussions like scraping as well as scratching and might cause the workpieces and tool holder to be catastrophic. Increased cutting forces and power consumption, declining dimensional accuracy as well as surface quality are indicators of failure of the tool [3]. However, the turning process has become one of the major metal production processes among metal-cutting procedures and is frequently used for industrial applications in the area of high technology [4]. In the turning process, tool wear occurs because of the contact between the workpiece and cutting tool, which is directly affected by the cutting parameters, cutting forces, tool geometry, power consumption, etc. Feed rate, depth of cut, and cutting speed are the common ("backpropagation neural network") based on iterative gradient convergences for the estimation of tool life by evaluating its stability and convergence.
Iterative convergence estimation techniques include ADAM (adaptive moment), Adadelta (adaptive delta), Adagrad (adaptive gradient), momentum, and SGD (stochastic gradient descent) algorithms. The outcomes of these techniques demonstrate that the best prediction for the BNN model is the convergence of the ADAM gradient for tool wear in all instances. To predict tool wear, Wang et al. [21] introduced a new physics-guided neural network model. As a modeling strategy for the combination of secret data examined by a data-driven model and a physics-based model, a cross-physical data fusion system (CPDF) was introduced, then the data hidden in the unlabeled sample were examined by the physics-based model of tool cutting influenced by semi-supervised learning. The benefit of the proposed approach is that it examines adequate physics and data domain information to remove physical inconsistency from standard data-driven models.
The deep learning network is known as the deep belief network, DBN, which was introduced by Chen et al. [22] to forecast the wear of a cutting tool on the flank. The performance of a DBN was compared against the performance of SVR and ANNs on an MSE basis ("mean-squared error") and the coefficient of determination (Rˆ2), taking into consideration the data of over 900 tests to determine the superiority of the DBN in forecasting the tool wear. Wu et al. [23] applied BiLSTM (bidirectional long short-term memory) as well as SVD (singular value decomposition) neural network for the projection of tool wear. The results of the experiments revealed that the suggested SVD-BiLSTM model can efficiently estimate the tool wear and provide better prediction than other comparative models.
Shen et al. [24] developed a predictive model by employing innovative techniques of machine learning with a multi-feature multi-model ensemble and dynamic smoothing method with machining parameters (i.e., feed rate, depth of cut as well as cutting speed) as model inputs, where the main characteristics for estimations were therefore generated. With prediction outcomes, the trials revealed great agreement in terms of predictive trends and the precision of the average values of RMSE.
This work proposes the SVM with Bayesian optimization for regression for estimating the nose wear in the turning of 709M40 alloy steel. This research contributes to the investigation of artificial intelligence approaches in estimating the machining parameters to reduce the processing time, resources, and labor. In addition, the research investigates the efficacy of the SVM model with Bayesian optimization in estimating the tool wear in the turning process. Moreover, the research highlights the importance of utilizing artificial intelligence in contributing toward more sustainable manufacturing.

Materials and Methods
The experimental work provided by the College of Technological Studies was conducted at the workshop on machining at the Department of Manufacturing Engineering Technology. This work aimed to obtain appropriate dependent values in terms of machining parameters from independent input values of machining parameters. A series of turning trials were performed by utilizing a multicoating composed of TiCN + Al 2 O 3 + TiN deposited by CVD carbide removable inserts as part of a coupled project for optimizing machining operations (SPUN 12 03 12 2025) with four squared working edges [25] for cutting alloy steel-709M40. Insert configurations were 30 • , 60 • , 0 • , 5 • , 6 • , side approach and approach angles, inclination, clearance, and normal rake, respectively.
Turning experiments were performed in dry conditions using lathe type Harrison 600 with spindle speed range of 10-1800 rpm. The required tool holder type was a CSBPL 2020K 12. The workpiece was a 709M40 alloy steel bars, which were around 410 mm long with a diameter of 100 mm. The workpiece is often supplied in the hardened and tempered condition with a tensile strength ranging from 850-1000 N/mm 2 due to its good ductility and shock resistance and resistance to wear properties [26]. The treatment condition used for the workpiece was soft annealed. The chemical composition, mechanical, and physical properties of the 709M40 alloy steel is given in Table 1. However, to match the practical rough turning, criterion values of nose wear were considered in this study.

Support Vector Machine with Bayesian Optimization for Regression
A SVM for regression is one of the well-known machine learning methods that was first introduced by Drucker et al. [29]. SVM has been widely adopted for various regression problems and has achieved results with high accuracy when compared to other machine learning models. SVM can provide predictions for small and high dimensional data, data with local minima, and nonlinear problems [30].
SVM is based on a mathematical basis and statistical learning approaches that can improve the generalization capability by employing the structural risk minimization (SRM) principle [29,30].
For the training dataset Y = {(a 1 , b 1 ), (a 2 , b 2 ), (a 3 , b 3 ), . . . , (a n , b n )}, a i , b I ∈ R, where a i represents the feature vector of the input sample and b i is the corresponding labels to each sample for i = 1, 2, 3, . . . , n. The fundamental concept of SVM is to build a nonlinear map between output and input and then map the input data into the high dimensional feature space from low dimension using kernel as a function. A simple SVM model is shown in Figure 1.
where ϕ(x) is a nonlinear function in which a low dimension feature input will be converted into high dimensional feature space. In SVM, W contains the coefficients of the data, and b is the learnable constant. The SVM objective function can be formulated as: In the above equation where ε * i and ε i are the upper and lower slack variables. This is subject to ε -deviation y i − f(a i ) ≤ ε, the term 1 2 w 2 is a regularization that improves the generalization of the model.
The regularization constant parameter C determines the trade-off between experiential error and believing risk. In Equation (3), the ε denotes the loss parameter. Equation (2) constraint suggests that the loss will be ignored if the difference between the real and predicted values is less than ε. As shown in Figure 1, the actual value of the data a i is under the ε, where the chance of getting an error is quite a low estimate as zero. On the other hand, if the actual values b i are outside the ε , then the error will be ε i or ε * i .  Machine learning models are prone to underfitting and overfitting during a t phase. Thus, to avoid this problem, the regularization term, 1 2 || || 2 as well as training error is minimized [30] Hyperparameters play an important role in fine the performance of machine learning models [31]. The tuning of hyperparameters either a manual or optimized approach. Manual approaches are time-consuming a not achieve optimal performance. Due to this, various optimization approaches integrated into the selection of hyperparameters of machine learning models Bayesian optimization, heuristical optimization approaches, random search, an search methods. In this research, Bayesian optimization is utilized to optimize perparameters of the SVM model.

Bayesian Optimization
In the Bayesian theory concept, by calculating the objective function of the p distribution, which captures the updated belief for the known objective function. jective function f(a), Bayesian optimization constructs a probabilistic model. The m exploited to predict the unknown next point to evaluate the bounded set A. Fr preceding evaluation f(a) to make full use of predicted information and is not limit on the Hessian approximations or local gradient, it can also find the maximum c of non-convex functions [32].
There are two-parts that play a role with Bayesian optimization. The first on Gaussian process prior and the second one is the acquisition function that is used uate the subsequent point by constructing a utility function.
The Gaussian process is an effective and powerful prior distribution over th smooth function. It is based on a random variable that has no limit (e.g., an infini ber), where any finite random variable is subjective to combined Gaussian distr [32].
The Gaussian distribution (GP) is expressed as: where µ( ) is a mean function of a and the ( , * ) value data is a covariance f of data , * . There are many ways to choose an acquisition function like expected impro Machine learning models are prone to underfitting and overfitting during a training phase. Thus, to avoid this problem, the regularization term, 1 2 w 2 as well as c , the training error is minimized [30] Hyperparameters play an important role in fine-tuning the performance of machine learning models [31]. The tuning of hyperparameters can be either a manual or optimized approach. Manual approaches are time-consuming and may not achieve optimal performance. Due to this, various optimization approaches can be integrated into the selection of hyperparameters of machine learning models such as Bayesian optimization, heuristical optimization approaches, random search, and grid search methods. In this research, Bayesian optimization is utilized to optimize the hyperparameters of the SVM model.

Bayesian Optimization
In the Bayesian theory concept, by calculating the objective function of the posterior distribution, which captures the updated belief for the known objective function. For objective function f(a), Bayesian optimization constructs a probabilistic model. The model is exploited to predict the unknown next point to evaluate the bounded set A. From the preceding evaluation f(a) to make full use of predicted information and is not limited only on the Hessian approximations or local gradient, it can also find the maximum complex of non-convex functions [32].
There are two-parts that play a role with Bayesian optimization. The first one is the Gaussian process prior and the second one is the acquisition function that is used to evaluate the subsequent point by constructing a utility function.
The Gaussian process is an effective and powerful prior distribution over the space smooth function. It is based on a random variable that has no limit (e.g., an infinite number), where any finite random variable is subjective to combined Gaussian distribution [32].
The Gaussian distribution (GP) is expressed as: where µ(a) is a mean function of a and the k(a, a * ) value data is a covariance function of data a, a * . There are many ways to choose an acquisition function like expected improvement (EI) as well as probability of improvement (PI). The PI function is written as where ( ) and ( ) indicate the predictive variance and mean function of the objective function. Φ(.) and ɤ(.) express the PDF as well as CDF of standard normal distribution. The current best observation is donated by = ∈ : ( ), respectively. In the SVM model, there are three parameters (C, ϵ, σ) to optimize, where C is the penalization coefficient; the kernel parameter is denoted by σ, when σ value is larger, the structural risk will be small; and ϵ is the insensitive loss coefficient that controls the gap (width) of the regression function on the insensitive area [33]. Table 2 illustrates twenty-four experiments with varied cutting parameters that were carried out under dry conditions. The trials were performed in a single-path double-pass system. Based on the second pass in each pass, the response was computed. This was provided to facilitate considerable wear for a 709M40 steel alloy to take place with 24 experimental trials. Scanning images of the nose wear were measured by field-emission scanning electron microscope (FESEM), as shown in Figure 1. The figure illustrates the micrographs of nose wear for different cutting speeds and feed rates. Nose wear was found to be the dominant wear mechanism than the flank and crater wear [34]. Figure 2 shows a comparison of tool edge performance in three experiments where low, moderate, and high cutting speed are used in association with a moderate feed of 0.2 mm/rev and a depth of 2.25 mm. To match the practical rough turning operations, nose wear was considered as a criteria in the experiment. A Zeiss Gemini SEM 500 field emission scanning electron microscope (FESEM) equipped with an energy-dispersive x-ray (EDX) microanalysis system was utilized to examine the worn tool inserts. (.) express the PDF as well as CDF of standard normal distribution. The current best observation is donated by a best = arg max a i ∈a 1:t f (a i ), respectively. In the SVM model, there are three parameters (C, , σ) to optimize, where C is the penalization coefficient; the kernel parameter is denoted by σ, when σ value is larger, the structural risk will be small; and is the insensitive loss coefficient that controls the gap (width) of the regression function on the insensitive area [33]. Table 2 illustrates twenty-four experiments with varied cutting parameters that were carried out under dry conditions. The trials were performed in a single-path doublepass system. Based on the second pass in each pass, the response was computed. This was provided to facilitate considerable wear for a 709M40 steel alloy to take place with 24 experimental trials. Scanning images of the nose wear were measured by field-emission scanning electron microscope (FESEM), as shown in Figure 1. The figure illustrates the micrographs of nose wear for different cutting speeds and feed rates. Nose wear was found to be the dominant wear mechanism than the flank and crater wear [34]. Figure 2 shows a comparison of tool edge performance in three experiments where low, moderate, and high cutting speed are used in association with a moderate feed of 0.2 mm/rev and a depth of 2.25 mm. To match the practical rough turning operations, nose wear was considered as a criteria in the experiment. A Zeiss Gemini SEM 500 field emission scanning electron microscope (FESEM) equipped with an energy-dispersive X-ray (EDX) microanalysis system was utilized to examine the worn tool inserts.

Training Dataset
To train the SVM model for determining the tool wear, data from experiments in the literature were extracted. Table A1 depicts the training data from [5] that was used to train the SVM model on the different feed rate, depth of cut, and cutting speed. It can be seen that the training data had 82 experiments for the CVD coated tool and similarly for the PVD coated tool, it added to a total of 162 experiments for the training dataset. The depth of cut ( ), feed rate ( ), and cutting speed ( ) were considered as the input parameters

Training Dataset
To train the SVM model for determining the tool wear, data from experiments in the literature were extracted. Table A1 depicts the training data from [5] that was used to train the SVM model on the different feed rate, depth of cut, and cutting speed. It can be seen that the training data had 82 experiments for the CVD coated tool and similarly for the PVD coated tool, it added to a total of 162 experiments for the training dataset. The depth of cut (d), feed rate ( f ), and cutting speed (V) were considered as the input parameters whereas the wear of the cutting tool insert was considered as the response. The selection of the training dataset was based on the large numbers of experiments presented in [5], where large datasets are preferable in training artificial intelligence algorithms. In addition, the data present the input parameters of interests such as depth of cut, feed rate, and cutting speed with a comparable range, in terms of standard deviation of depth of cut, to our conducted experiment of the validation dataset of Table 2.
The SVM with the Bayesian optimization model was executed with an acquisition function defined as the probability of improvement with 30 iterations. Figure 3 illustrates the estimation of the tool wear of the CVD-coated cutting tool wear of the training dataset, while Figure 4 presents the estimation of the cutting tool wear of the PVD coated tool wear of the training dataset. It can be observed that the SVM model with Bayesian optimization achieved a high extent of accuracy by closely estimating the experimental training dataset. Table A2 presents the estimated value of the tool wear parameter of each experiment in the training dataset. To further assess the performance of the estimation results, statistical measures were calculated as the MAPE ("mean absolute percentage error"), RMSE ("root mean square error"), and CVRMSE ("coefficient of variation of root mean square error"), which are calculated in Equations (6)-(8), respectively, as: where y denotes the experimental data point;ŷ denotes the estimated data point; andy as the average value.

Validation Dataset
The promising trained model was then exported and used to estimate the cutting tool wear of the validation dataset that was presented in Table 2. Figure 5 illustrates the experimental and predicted data of the cutting tool wear of the validation dataset with various depths of cuts of 1.5 mm, 2 mm, 2.25 mm, 2.5 mm, and 3 mm. The estimated data points by the SVM model with Bayesian optimization closely matched the experimental data points of the validation dataset. Table 4 depicts the estimated individual values of the cutting tool wear parameter for each experiment in the validation dataset. The performance metrics of the SVM model with Bayesian optimization on the validation dataset were calculated and are presented in Table 5. It can be noted that the proposed SVM model achieved a high extent of accuracy in estimating the cutting tool wear parameter of the validation dataset with a MAPE of 6.13%, RMSE of 2.29%, and CVRMSE of 9.02%. The results validate the model performance and the feasibility of estimating the cutting tool wear computationally based on the previous training dataset and thus can reduce the experimental work and resources.
where y denotes the experimental data point; ̂ denotes the estimated data as the average value. Table 4 presented the calculated performance metric model with Bayesian optimization for the training dataset. The model resulte performance in terms of the MAPE, RMSE, and CVRMSE with an average of and 15.9%, respectively.

Metric
Training Dataset were calculated and are presented in Table 6. It can be noted that the proposed achieved a high extent of accuracy in estimating the cutting tool wear para validation dataset with a MAPE of 6.13%, RMSE of 2.29%, and CVRMSE o results validate the model performance and the feasibility of estimating the wear computationally based on the previous training dataset and thus can re perimental work and resources.

Conclusions
This research explored the performance of the artificial intelligence-based estimation approach of tool wear in a turning process of 709M40 alloy steel. Support vector machine for regression with Bayesian optimization model was employed to estimate the tool wear value based on the depth of cut and cutting speed as well as feed rate inputs. The proposed model was trained on a training dataset of 162 data points and was then used to determine the tool wear of our validation dataset. The reported results suggest the feasibility of the SVM model in estimating the tool wear with high accuracy of MAPE of 6.13%, RMSE of 2.29%, and CVRMSE of 9.02% for the validation dataset. The estimated values closely match the conducted experimental tool wear values. The approach was validated for the 709M40 alloy steel based on depth of cut, feed rate, and cutting speed for a certain range of values. For other materials with a different range of input values, it would require retraining the algorithm using the transfer learning approach. The proposed approach contributes more toward saving the cost, time, and labor in the manufacturing process. Moreover, adopting artificial intelligence estimation methods saves resources and enables more efficient and sustainable manufacturing processes.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.