J. Cent. South Univ. (2019) 26: 1934-1945

DOI: https://doi.org/10.1007/s11771-019-4144-1

Evaluating performance of cutting machines during sawing dimension stones

Mohammad ATAEI¹, Sadjad MOHAMMADI¹, Reza MIKAEIL²

1. School of Mining Engineering, Petroleum and Geophysics, Shahrood University of Technology,Shahrood, Iran;

2. Department of Mining and Metallurgical Engineering, Urmia University of Technology, Urmia, Iran

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract: The performance of cutting machines in terms of energy consumption and vibration directly affects the production costs. In this work, our aim was to evaluate the performance of cutting machines using hybrid intelligent models. For this purpose, a systematic experimental work was performed. A database of the carbonate and granite rocks was established, in which the physical and mechanical properties of these rocks (i.e., UCS, elastic modulus, Mohs hardness, and Schmiazek abrasivity factor) and the operational parameters (i.e., depth of cut and feed rate) were considered as the input parameters. The predictive models were developed incorporating a combination of the multi-layered perceptron artificial neural networks and genetic algorithm (GANN-BP) and the support vector regression method and Cuckoo optimization algorithm (COA-SVR). The results obtained indicated that the performance of the developed GANN-BP and COA-SVR models was close to each other and that these models had good agreements with the measured values. These results also showed that these proposed models were suitable tools in evaluating the performance of cutting machines.

Key words: dimension stone; cutting machine; energy consumption; vibration; hybrid intelligent method

Cite this article as: Mohammad ATAEI, Sadjad MOHAMMADI, Reza MIKAEIL. Evaluating performance of cutting machines during sawing dimension stones [J]. Journal of Central South University, 2019, 26(7): 1934-1945. DOI: https://doi.org/10.1007/s11771-019-4144-1.

1 Introduction

Forecasting and evaluating the performance of cutting dimension stones can be a major step in understanding the process as well as evaluation of the performance of cutting machines. The performance evaluation of cutting machines is very important in estimating the costs and designing a dimension stone cutting factory. Predicting the performance of cutting machines leads the designers to improve the processing speed and increase the production. The most important parameters involved in the evaluation of the performance of cutting machines are the energy consumption and the vibrations generated in them. The ampere consumption is one of the most important economic issues in the stone cutting factories and, the amount of vibration of a cutting machine has a direct impact on the production quality. Therefore, a correct prediction of these parameters can lead to the best design of the stone processing factories.

Up to the present time, many research works have been carried out to evaluate the process of cutting dimension stones and the performance of cutting machines during this process. In 1987, PAI [1] presented a classification based on the performance of disk wear and energy consumption. He investigated the feed rate, depth of cut, rotational speed of disk, and rock hardness as the most important parameters used to evaluate the energy consumption in a cutting process. JENNINGS et al [2] found that increasing the cutting rate increased the energy consumption, while the slope for energy change versus increase in the depth of cut was more than the slope for energy change versus the advance rate. Also in comparison with different types of stones, the highest energy consumption belonged to the granite, marble, and sandstone rocks, respectively. In 1997, CEYLANOGLU et al [3] investigated the relationship between the specific cutting energy and the production rate with some rock characteristics. The results of a statistical analysis showed that the specific energy of cutting and the production rate were in good relationships with the values for the uniaxial compressive strength, tensile strength, point load index, rock hardness, and Schmidt's hammer hardness. OZCELIK et al [4] investigated the relationship between the cutting depth and the vibration. In 2005, ERSOY et al [5] established a relationship between the specific energy SEcut of the sawblade operating parameters and the rock properties using multiple linear regression. In the same year, BUYUKSAGIS et al [6] separately studied the performance of cutting machines in the marble cutting process in a laboratory scale. In their work, they considered two parameters including the depth of cut and the feed rate as the cutting process variables and the amount of special cutting energy as a criterion for evaluation of the cutting performance. YILMAZ et al [7] studied the effect of cutting rate on energy consumption in the circular sawing of granites. The results of their work showed that in order to increase the cutting rate, increasing the cutting speed and reducing the depth of cut improved the efficiency of the process in terms of energy consumption. On the other hand, increasing the cutting phases was found to increase the energy consumption, and subsequently, increase the wear of the cutting tool. In 2009, IMEN et al [8] studied the effect of cutting speed on the energy consumption in marble cutting processing. They found that these two parameters had significant effects on the energy consumption. ATICI et al [9] studied the relationship between the specific energy of cutting saws and the drilling bits with rock brittleness and destruction energy. MIKAEIL et al [10] have published a series of papers for determination of energy consumption and system vibration during the cutting process. They studied the relationship between the power consumption and three different brittleness indices of rocks, and evaluated the power consumption in the carbonate rock cutting process using the fuzzy multi-criteria decision-making techniques [11]. On the other hand, in the vibration context, they studied the application of a fuzzy analytical hierarchy process to the prediction of vibration during the rock sawing process [12] and investigated the relationship between the system vibrations and the rock brittleness indices in the rock sawing process using statistical method [13]. OZCELIK et al [14] studied the effect of rock anisotropy on the vibration of cutting machines. The results obtained showed that the least vibration was achieved when the cutting angle along the z axis was 25°. In 2011, SENGUN et al [15] evaluated the specific energy and rock properties using a simple regression analysis, and developed empirical equations for carbonate rocks. CINAR et al [16] conducted a study on how to control the energy consumption in cutting marble rocks by controlling the parameters involved using floating and controlling the PID algorithm. In 2012, AYDIN et al [17] presented a statistical model for estimation of the specific energy depending on the operating variables and the rock properties. They concluded that, rather than the physico-mechanical properties, the mineralogical properties were the dominant rock properties affecting the specific energy. In 2013, explanation of the relationships between the specific energy values and the rock properties was given by ENGINE et al [18]. They found that Shore hardness and abrasion resistance were strongly related to the specific energy, and according to these parameters, the prediction charts of the specific energy values were created. In 2014, YARDAKUL et al [19] developed the SEcut prediction models using the AHI techniques. Their results showed that ANFIS gave the best SEcut prediction accuracy. In 2017, ALMASI et al [20] developed a new rock classification based on the abrasiveness, hardness, and toughness of rocks, and the pull-back amperage for the prediction of hard dimension stone sawability. In 2017, ARYAFAR et al [21] studied the ampere consumption of dimension stone sawing machines using the artificial neural networks.

A literature review showed that the researchers only focused on one aspect (either energy consumption or vibration) of the cutting machine performance. Furthermore, the soft computing approaches have been used in fewer studies, while this modelling approach has many advantages to develop predictive models. Therefore, the main goal of the present work was to provide an optimal model using the intelligence science techniques for evaluating the performance of cutting machines from two aspects including the amount of vibration and the energy consumption in the carbonate and granite rock cutting processes. This work has been divided into three parts: data collection and establishing a database; presentation of two hybrid soft computing models including artificial neural networks with genetic algorithm and support vector regression with cuckoo optimization algorithm; and finally, evaluation of the best model.

The rest of this paper is organized as what follows. In Section 2, a summary of the methodology and hybrid models will be introduced. In addition data collection and preparation are described in this section. In Section 3, the predictive model will be developed. Validation of the developed models is carried out in Section 4. In Section 5, the performance of models will be discussed. Finally, this paper concludes in Section 6.

2 Methods and materials

2.1 Method

Artificial neural networks (ANNs) and support vector regression (SVR) are the most used and common approaches for modeling and controlling complex systems and finding very difficult relationships between the input and output variables. Up to now, they have been used successfully in many research works, showing that they can be regarded as strong tools for developing predictive models. Despite aforementioned advantages, selection of optimal structures is a challenging issue in their practical applications. In this regard, the optimization algorithms are the best solutions. In this work, ANN and SVR were optimized by the genetic algorithm (GA) and the cuckoo optimization algorithm (COA), respectively. In what follows, the reasons for using these hybrid models and their implementation are described. It should be noted that for the sake of brevity, explanation of the basics of the methods is discarded.

2.1.1 GANN-BP

The back-propagation (BP) algorithm is one of the most useful and common types of neural networks in which the main aim is to converge a minimum error. In this type of network, the error is calculated and then according to the error rate, the weight communication and bias are updated [22]. In such a network, an optimum solution can be achieved by optimizing the weights of a BP neural network, parameters of learning step, and finding the network structure [23]. GA is a general stochastic search method that can solve a wide variety of optimization problems by the principles of Darwinian natural selection [24]. In this work, we applied GA to optimize the weights and threshold of the neural network of BP algorithm, and thus this approach was called GANN-BP. Figure 1 shows a flowchart of the prediction process using GANN-BP.

2.1.2 COA-SVR

Support vector regression (SVR) is a form of support vector machines (SVMs) that is based on the principle of structural risk minimization. The main advantage of SVR is to find the global optimum and control the over-fitting in the problems. Therefore, in this work, SVR was used for the aim of constructing the predictive models. The performance of SVR and the quality of its results are largely dependent on its structure parameters. Hence, the first step for training a SVR model is to choose the optimum SVR parameters. Among the meta-heuristic algorithms that can be utilized for selection of the SVR model by successfully mimicking the nature, the cuckoo optimization algorithm (COA) has some advantages including fast convergence and global optimum achievement. This optimization algorithm that is inspired by the life of the family of a bird called cuckoo was introduced by YANG et al [25] and modified by RAJABIOUN [26]. In this work, COA was employed to find out the model parameters. Accordingly, by combining SVR and COA, the presented method was called COA-SVR. Figure 2 shows a flowchart of the prediction process using COA-SVR.

Figure 1 Flowchart of using GA to optimize BP algorithm [23]

2.2 Data

In order to choose a wide range of the dimension stones to evaluate the performance of cutting machines from the energy consumption and system vibration viewpoints, it was important to choose the rocks with different properties. For this reason, sample blocks of two groups of dimension stones including seven carbonate and five granite rocks were collected from various quarries located in Iran. An attempt was made to collect the dimension stone samples big enough and without any macroscopic defects to perform the necessary physical and mechanical tests. In this work, the operational parameters affecting the sawing efficiency in the circular diamond saw and physical-mechanical rock properties were selected as the input parameters to predict the output parameters (i.e. energy consumption and vibration of machine). In what follows, the input and output parameter measurements are described.

Figure 2 Flowchart of using COA to optimize SVR parameters

2.2.1 Input parameters

An attempt to present a predictive model using all the mineralogical, petrographical, and physico- mechanical properties is impossible from a practical viewpoint. To select the input parameters of rock properties, the following three rules were considered: 1) the number of parameters used should be small; 2) equivalent parameters should be avoided; and 3) measurement of parameters should be easy. Accordingly, the parameters were selected as the rock characteristics listed below:uniaxial compressive strength (UCS), Schmiazek F-abrasivity factor (SF-a), Mohs hardness (MH), elastic modulus (YM).

To determine these parameters, experiments were carried out with high precision under the standards of the International Association of Rock Mechanics [27] in a laboratory in the Shahrood University of Technology. The results of the laboratory studies including the mechanical and physical properties are given in Table 1. On the other hand, the feed rate and depth of cut were selected as the operational input parameters, and the other operational parameters such as the peripheral speed, saw blade type, and saw blade diameter were kept constant. In the laboratory, each dimension stone was sawn at different feed rates, i.e., 100, 200, 300, and 400 cm/min, and at depths of cut of 35, 30, 22, and 15 mm.

Table 1 Physical and mechanical properties of studied rocks

2.2.2 Outputs parameters

In order to prepare the cutting experiments, a cutting machine was used in a laboratory scale. The mechanism of this machine was based on the principles of a cutting machine in a real scale. During the cutting test, the energy consumption and vibrations of machine were measured by an amperemeter and an accelerometer, respectively. The output signals from the accelerometer were amplified by the amplifier and then divided into digitized signals, and finally, were transferred to a computer for final processing. Data processing was done with the help of a computer program prepared in the LabView. Figure 3 shows an example of the recorded vibration signals.

2.2.3 Establishing database

After determining and measuring the input and output parameters by the laboratory test and cutting experiments, a database including 112 datasets for carbonate rocks and 111 datasets for granite rocks was established. After that, in order to develop the models and then to validate them, it was necessary to divide the database into two categories of data called the training data and test data. For this purpose, randomly, 75% of the total data was considered as the training data and the remaining 25% of data as the test data consists of Types A and B; data Type A included data for rock samples available at the learning stage and data type B included data for rock samples not available in the training phase. The number of training and test data for both types of studied rocks are given in Table 2. Table 3 shows the statistical data for the training data, and Tables 4 and 5 show the detailed statistical data for the test data Types A and B, respectively.

Figure 3 An example of recorded vibration signals

Table 2 Number of dataset in training and testing models

3 Developing predictive models

In the presentation of predictive models, it is always tried to make a comprehensive model as simple as possible. In this work, two operational parameters were considered as independent variables because they could be controlled in all models. However, selection of the inherent parameters should be done in a way that they are not correlated with each other. One of the criteria used to determine the correlation between two variables is the correlation coefficient.

A correlation coefficient measures the extent to which two variables tend to change together. This coefficient describes both the strength and the direction of the relationship between studied variables. The Pearson correlation is the most widely used statistical correlation to measure the degree of the relationship between the linearly related variables, and it is used for data with normal distribution or if there is a large amount of data. The Spearman rank correlation is a non-parametric one that does not assume any assumption about the distribution of the data, and it is an appropriate correlation when the variables are measured on a scale that is at least ordinal [28]. In this work, regarding the non-normal distribution of the inherent variables (based on the results of the skewness and kurtosis tests as well as the Shapiro-Wilk test), the Spearman rank correlation was used based on the following equation:

                          (1)

where ρ denotes the Spearman rank correlation, d_i is the difference between the ranks of the corresponding values X_i and Y_i, and n is the number of values in each dataset. Table 6 shows the strength of correlation based on the absolute value for ρ.

Table 3 Statistical data for training data

Table 4 Statistical data for type A test

Table 5 Statistical data for type B test

Table 6 Strength of correlation based on Spearman rank [29]

In this work, the SPSS software was used for the correlation test. According to this, if there is a significant level between two variables (sig) less than 0.05, there is a correlation between the two variables, and if it is more than 0.05, then the two variables are not correlated [29]. The results of the Spearman rank correlation for inherent variables in carbonate rocks are given in Table 7.

Table 7 Pearson correlation coefficient test for inherent variables in carbonate rocks

Table 8 shows that three parameters including uniaxial compressive strength, elastic modulus, and Mohs hardness are correlated with each other. On the other hand, these three parameters are not correlated with the Schmiazek F-abrasivity factor. Therefore, in carbonate rocks, 7 models can be considered, as shown in Table 8.

Table 9 shows the results of the Spearman rank correlation test for inherent variables in granite rocks.

Table 8 Acceptable models in carbonate rocks

Table 9 Pearson correlation coefficient test for inherent variables in granite rocks

From Table 9, it can be concluded that uniaxial compressive strength and elastic modulus are not correlated with each other and with the Schmiazek F-abrasivity factor significantly but they are correlated with the Mohs hardness. On the other hand, the Mohs hardness is correlated with other parameters except for the Schmiazek F-abrasivity factor. Based on the results obtained, 9 acceptable models were considered in granite rocks (Table 10).

Table 10 Acceptable models in granite rocks

The process of determining the candidate model(s) in the training phase was such that the acceptable models were developed, and the error value of each model based on RMSE was calculated as follows:

               (2)

where y_meas is the actual output value (measured), y_pred is the estimated output value by the model, and n is the total number of data. Then the model(s) with the minimum RMSE was (were) selected to evaluate its (their) performance in the test phase. In what follows, the developed models and their results are described.

3.1 Models developed using GANN-BP

A multi-layered perceptron artificial neural networks and genetic algorithm was used to develop a predictive model. The back-propagation algorithm was used for training the network; it does not always converge to the absolute minimum and has a weak rate of convergence. The connection weights of ANNs by the BP algorithm are only adjusted using the local angle, and the whole learning process from the global perspective is not examined. Therefore, it may be stopped in a local minimum [30]. To deal with this drawback, a hybrid model was used by combining BP and GA for increasing the training performance of the neural network works. In fact, GA was used to optimize the BP algorithm in order to overcome the BP disadvantage of being easily stopped in a local minimum. Besides, it is used to learn the connection weights and bias of ANNs. The best developed models using GANN-BP are listed in Table 11.

3.2 Models developed using COA-SVR

In order to find an optimal model for estimating the ampere consumption and vibration, an optimal network was used by combining the SVR method with the cuckoo optimization algorithm. Minimizing the root mean square error (RMSE) for SVR training was considered as the objective function of COA. Cross-validation or circular validation was also used to ensure a proper operation of the model. This approach is an evaluation method that determines the results of a statistical analysis on a dataset that can be generalized and is independent from the educational data. This technique is especially used in prediction applications to determine how useful the model will actually be. In general, one round of cross- validation consists of dividing the data into two complementary subsets, performing an analysis on one of those subsets (training data) and validating the analysis using the other dataset (test data). To reduce dispersion, validation was performed for several times with different partitions, and the average of the validation results was taken. One of

method. In this way, the data were partitioned into a K subset. From the K subset, each subset was used for validation and the K-1 subset was used for training. The K procedure was repeated and all data was used once for training and for validation purposes. Finally, the average results of the K validation were selected as a final estimate. Of course, other methods could be used to combine the results. In this work, the value for K was considered to be 10. Considering that the optimization algorithm had a random property, and, on the other hand, the optimal point was not unique, to determine the best parameters for each model, the optimization process and determination of the parameters were performed for 5 times. The characteristics of the optimal models are shown in Table 12.

4 Validation

In order to validate the models, their performance was evaluated in the estimation of both categories of testing data Types A and B, and compared with the measured values. Figures 4 and 5 show the estimated outputs compared with the measured values of Type A for the carbonate and granite rocks, respectively.

Figures 6 and 7 show the estimated ampere consumption and vibration compared with the actual measured values for the type B data using the developed models for the carbonate and granite rocks, respectively.

Table 11 Best developed models using GANN-BP and network architecture^*

Table 12 Optimum parameters of best developed models using COA-SVR

Figure 4 Comparison of measured and estimated outputs for data Type A in carbonate rocks:

Figure 5 Comparison of measured and estimated outputs for data Type A in granite rocks:

Figure 6 Comparison between measured and estimated outputs for data Type B of carbonate rocks:

5 Discussion

For the sake of a quantitative comparison, RMSE and R² were used. Smaller RMSE values produced higher coefficients of determination, leading to more accurate fitted curves. The calculated values for these indices for the proposed models are given in Table 13.

As can be seen from Table 13, COA-SVR model has better performance in estimation of the energy consumption of carbonate rocks for both type of validation data. The performance criteria show that COA-SVR model is superior to estimate vibration of data Type A in the carbonate rocks, while, the performance of GANN-BP and COA- SVR is almost the same to estimate vibration of data Type B in the carbonate rocks.

Figure 7 Comparison between measured and estimated outputs for data Type B of granite rocks:

Table 13 Performance of developed models

As can be seen from Table 13, COA-SVR model has better performance in estimation of the energy consumption of carbonate rocks for both type of validation data. The performance criteria show that COA-SVR model is superior to estimate vibration of data Type A in the carbonate rocks, while, the performance of GANN-BP and COA-SVR is almost the same to estimate vibration of data Type B in the carbonate rocks.

According to Table 13, COA-SVR model is superior to estimate the energy consumption of data type A in the granite rocks; while, GANN-BP possessed a higher performance to estimate the energy consumption in data Type B of granite rocks as well as to estimate system vibration of both data type in granite rocks.

The obtained results indicate that both hybrid intelligent models have almost the same performance to evaluate the performance of cutting machine in sawing the carbonate and granite rocks. In addition, comparison between measured and estimated values concludes that soft computing approach are reliable tool to estimate cutting machines performance. Finally, validation of the proposed models incorporating rock types which their samples not available in the developing phase indicates the generality of models that highlights the practical efficiency of them.

6 Conclusions

Two hybrid intelligent models including GANN-BP and COA-SVR were proposed to estimate the ampere consumption and vibration of cutting machines during sawing the carbonate and granite dimension stones. The performance of the proposed models was evaluated using two types of datasets: data Type A including data for rock samples available at the learning stage and data Type B including data for rock samples not available in the training phase. The following main conclusions could be drawn from this investigation:

1) The GANN-BP model was found to be superior in comparison with COA-SVR to estimate vibration of data Type A and both outputs of data Type B in the granite rocks.

2) The COA-SVR model possessed a higher performance in the estimation of both outputs of data Types A and B in the carbonate rocks and the ampere consumption of data Type A in granite rocks as well.

3) It could be deduced that the performance of GANN-BP and COA-SVR was close to each other. Generally speaking, it can be concluded that the proposed hybrid intelligent models are suitable approaches to evaluate the performance of cutting machines.

Acknowledgment

The authors would like to acknowledge the financial support of Shahrood University of Technology for this research work under the project No. 11039.

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(Edited by HE Yun-bin)

中文导读

切割机在切割块石时的性能评估

摘要：切割机的能耗和振动性能直接影响到生产成本。本研究的目的是通过系统的实验研究，使用混合智能模型来评估切削机床的性能。建立了一个关于碳酸盐岩和花岗岩的数据库，确定极限抗压强度、弹性模量、莫氏硬度、Schmiazek磨耗系数等物理力学参数和切削深度、进给速度等操作参数为输入参数。将多层感知器人工神经网络与遗传算法(GANN-BP)、支持向量回归法与布谷鸟优化算法(SCA-SVR)相结合，建立预测模型。结果表明，所建立的GANN-BP模型与COA-SVR模型性能相近，与实测值吻合较好。这些结果也表明，这些模型是评价切削机床性能的合适工具。

关键词：块石; 切割机; 能源消耗; 振动; 混合智能方法

Foundation item: Project(11039) supported by Shahrood University of Technology, Iran

Received date: 2018-05-02; Accepted date: 2018-12-08

Corresponding author: Mohammad ATAEI, PhD, Professor; Tel: +98-23-32395509; E-mail: ataei@shahroodut.ac.ir; ORCID: 0000- 0002-7016-8170