Parametric optimization of Nd:YAG laser microgrooving on aluminum oxide using integrated RSMANNGA approach
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Abstract
Nowadays in highly competitive precision industries, the micromachining of advanced engineering materials is extremely demand as it has extensive application in the fields of automobile, electronic, biomedical and aerospace engineering. The present work addresses the modeling and optimization study on dimensional deviations of squareshaped microgroove in laser micromachining of aluminum oxide (Al_{2}O_{3}) ceramic material with pulsed Nd:YAG laser by considering the air pressure, lamp current, pulse frequency, pulse width and cutting speed as process parameters. Thirtytwo sets of laser microgrooving trials based on central composite design (CCD) design of experiments (DOEs) are performed, and response surface method (RSM), artificial neural network (ANN) and genetic algorithm (GA) are subsequently applied for mathematical modeling and multiresponse optimization. The performance of the predictive ANN model based on 5883 architecture gave the minimum error (MSE = 0.000099) and presented highly promising to confidence with percentage error less than 3% in comparison with experimental result data set. The ANN model combined with GA leads to minimum deviation of upper width, lower width and depth value of − 0.0278 mm, 0.0102 mm and − 0.0308 mm, respectively, corresponding to optimum laser microgrooving process parameters such as 1.2 kgf/cm^{2} of air pressure, 19.5 Amp of lamp current, 4 kHz of pulse frequency, 6% of pulse width and 24 mm/s of cutting speed. Finally, the results have been verified by performing a confirmatory test.
Keywords
Laser microgrooving Aluminum oxide RSM ANN GAIntroduction
Advanced engineering ceramics have been widely used in the development of critical components, because of their superior characteristics such as electrical insulation, high hardness, low thermal expansion coefficient, corrosion resistance, high temperature resistance and low weighttostrength ratio (Doloi et al. 2007; Hafezalkotob and Hafezalkotob 2016), and particularly these are extremely hardtocut materials due to extreme brittleness. Owing to these complexities, the task to machine a component with deterministic precision becomes challenging. In the recent past, laser beam machining (LBM) has been explored as an effective and emerging process for shaping ceramic materials. Pulsed laser is efficient for micromachining of hardtocut material because of low pulse width with high peak power. Nd:YAG laser beam emits light or photons of shorter wavelength generating high power densities and small, focused spot diameter better than the benefits offered by conventional CO_{2} laser. Laser microgrooving operation considers various micromachining input process parameters like laser power, pulse width, spot size and cutting speed, which are quite compatible as well as in close agreement with derived energy equation of heat transfer (Chryssolouris 1991; Olsen and Alting 1995). Assist gas pressure also substantially affects the shape, geometry and dimension of cut during laser micromachining operation (Darwish et al. 2017; Farooq and Kar 1998). During square microgrooving operation, maintaining of squareness and depth is an essential factor to inherent focusing quality of laser machining process. The abovementioned parameters are usually adjusted and utilized for machining to give the quality of microgroove desired, but this consumes exhaustive amounts of time and effort, and still there is scope of researchers for goodquality microgrooving conditions. Moreover, to improve its machining performance effectively and efficiently, the optimized process parameters and predictive models are also essentially required.
When manufacturers deal with multiple conflicting objectives, modeling technique helps in enhancing the efficacy of machining process. Although many theoretical models involve simplifications, assumptions and approximations for approaching real machining process, they do not consider any undesirable deficiency in the process. Therefore, analytical solutions cannot be easily extended to practical usage (Davim 2001), and for this reason, adequate modeling is essential to do quality predictions in a function of cutting conditions. The model development by RSM and ANN is a convenient method for the product as well as process improvement and has received a considerable attention by the researchers in the last two decades.
However, due to the complex behavior of the machining processes, where a few distinctive and contradictory objectives must be simultaneously optimized, at the same time the monoobjective optimization techniques do not permit to find the comprehensive optimal cutting conditions value which fulfills all the execution attributes in machining; hence, the multiobjective optimization has turned into an increasingly important and challenging task (Khamel et al. 2012; Das et al. 2015). Indeed, it offers most prominent measure of data with a specific end goal to make a decision on choosing process parameters in machining process. Earlier researchers have applied different optimization techniques, like Taguchi method (Shivade and Shinde 2014), Grey relation analysis (Kumar A, Soota T, Kumar J Optimisation of wirecut EDM process parameter by Greybased response surface methodology. J Ind Eng Int. https://doi.org/10.1007/s4009201802648), desirability function (Kumar et al. 2015), for finding out the optimal process parameter values. Researchers are now focusing on employment of artificial intelligence (AI) techniques, viz. ANN, GA and fuzzy logic (Markopoulos et al. 2016; Qian X, Ma Y, Feng H Collaboration space division in collaborative product development based on a genetic algorithm. J Ind Eng Int. https://doi.org/10.1007/s4009201802577; Moghaddam and Kolahan 2016), for the process modeling and optimization of manufacturing processes which are expected to overcome some limitations of conventional process modeling techniques. Due to the ability to find a set of tradeoff solutions in a single simulation run, inclination toward the adaptation of AIbased optimization methods especially evolutionary multiobjective optimization (EMO) algorithm shows a growing interest not only to control and predict the behavior of the phenomenon, but also to accomplish a common goal of improving machining performance. Various researchers have employed methods which include statistical and analytical approaches for mathematical modeling (Ciurana et al. 2009; Kibria et al. 2013; Mishra and Yadava 2013; Madić et al. 2015) in order to predict the responses and for multiresponse optimization (Dhupal et al. 2008; Wang et al. 2016; Giorleo et al. 2016) in order to control the process parameters during laser micromachining process. Recently, Shivakoti et al. (2017) highlighted the use of fuzzy TOPSIS method for the selection of optimal laser micromarking process parameters to improve the marking performance on high strength temperature resistance material such as gallium nitride (GaN). In an another study Kalita et al. (2017) performed an investigation with same workpiece material for optimization of process parameters in laser beam micromarking using genetic algorithm (GA) and particle swarm optimization (PSO). The results showed that there is a close agreement between the GA parameter settings with PSO results. Kibria et al. (Kibria et al. 2014) modeled the relationship between the laser microturning process parameters (laser power, pulse frequency, rotational speed, air pressure and feed rate) and quality characteristics using ANN and performed multiobjective optimization using RSM in order to achieve the desired surface roughness and minimum depth deviation of turned part. Mukherjee et al. (Mukherjee et al. 2013) used artificial bee colony (ABC) algorithm for parametric optimization of two different Nd:YAG laser beam micromachining processes (microdrilling and microgrooving).
From the existing literature, most of the studies are on laser micromachining, viz. microdrilling (Biswas et al. 2010; Kuar et al. 2012; Nandi and Kuar 2015; Biswas et al. 2015; Zhang et al. 2015), microturning (Dhupal et al. 2008; Kibria et al. 2010, 2012, 2013; Hao et al. 2018), micromilling (Campanelli et al. 2013; Mohammed et al. 2017; Darwish et al. 2017; Yang et al. 2018) and micromarking (Shivakoti et al. 2017; Kalita et al. 2017; Peter et al. 2013; BrihmatHamadi et al. 2017); work in the field of laser microgrooving (Dhupal et al. 2007; Kuar et al. 2008) is very limited. Laser microgrooving is based on the interaction of a laser beam with the workpiece surface, nonuniform melting and ejection of material from the groove walls, and laser power reduction, as the beam propagates into the groove, can be identified as a cause for the variation in lower width and depth formation which is of prime importance to enhance the product quality. With the intention of achieving goodquality microgroove machined surface and better dimensional accuracy on alumina ceramic workpiece, intensive research is needed. Also, an extensive research work is much needed to develop a technology guidance for laser microgrooving of such a useful material for modern manufacturing industries. Moreover, appropriate combination and utilization, along with proper adjustment of precited machining parameters, are of prime importance for acquiring good grade of microgroove, which is a challenging task as it consumes precious time and effort due to the dynamic behavior of the laser micromachining process. Yet almost no systematic study has been reported in laser microgrooving operation that would ensure scope for researchers, and also no method currently results in the same level of efficiency for all processes. The novelty aspect of the present study focuses on the development of computational as well as empirical models and multiresponse parametric optimization in microgrooving of alumina (Al_{2}O_{3}) ceramic material through Nd:YAG laser treatment. Particularly, design of experiments (DOEs), response surface methodology (RSM), artificial neural network (ANN) and genetic algorithm (GA) have been applied to process improvement. The following dimensional deviations of the microgroove are addressed: upper width deviation, lower width deviation and depth deviation. The manuscript is arranged in the following form: “Introduction” section contains a brief overview of the motivation of the problem and shows the updated progress. “Experimental setup and procedure” section provides a brief description of the experimentation process, the material and the methods involved. “Results and discussion” section critically discusses the results obtained. The statistical analysis of the experiments and formation of the mathematical model are covered in section “Results and discussion.” This section also highlights the use of ANN and GA as a suitable optimization technique for the current problem. Additionally, the final part of the manuscript derives conclusions based on the study.
Experimental setup and procedure
Properties of workpiece material (alumina, Al_{2}O_{3})
Properties  Units  Value 

Density  gm/cc  3.96 
Specific heat  J/kgk  775 
Thermal conductivity  (cal/s)/(cm^{2}C/cm)  0.072–100 °C 
0.15–1000 °C  
Compressive strength  MPa  2500 
Modulus of elasticity  GPa  393 
Hardness  GPa  1800, HB30 
Fracture toughness  MPa√m  4 
Sintering temperature  °C  1600 
Melting temperature  °C  2050 
Process parameters and levels
Parameters  Unit  Levels  

−2  −1  0  1  2  
Air pressure (X_{1})  kgf/cm^{2}  0.4  0.8  1.2  1.6  2.0 
Lamp current (X_{2})  Amp  14.5  17  19.5  22  24.5 
Pulse frequency (X_{3})  kHz  1  2  3  4  5 
Pulse width (X_{4})  %  0  2  4  6  8 
Cutting speed (X_{5})  mm/s  12  16  20  24  28 
Design of experimental plan and experimental results
Test no.  Actual setting of parameters  Dimensions of microgroove (mm)  Dimensional deviations of microgroove (mm)  

X _{1}  X _{2}  X _{3}  X _{4}  X _{5}  Upper width  Lower width  Depth  Upper width deviation  Lower width deviation  Depth deviation  
1  1.6  17.0  2  2  16  0.1967  0.1390  0.160  − 0.003  − 0.061  − 0.040 
2  0.8  22.0  2  2  16  0.2210  0.2020  0.200  0.021  0.002  0.000 
3  1.6  17.0  4  6  16  0.1840  0.1550  0.168  − 0.016  − 0.045  − 0.032 
4  1.6  22.0  4  6  24  0.2154  0.1910  0.212  0.0154  − 0.009  0.012 
5  0.8  17.0  4  2  16  0.1930  0.1280  0.162  − 0.007  − 0.072  − 0.038 
6  1.2  24.5  3  4  20  0.2330  0.2005  0.234  0.033  0.001  0.034 
7  1.2  19.5  3  4  28  0.2490  0.1620  0.209  0.049  − 0.038  0.009 
8  1.2  19.5  3  4  20  0.2210  0.1355  0.165  0.011  − 0.064  − 0.035 
9  1.2  19.5  3  4  20  0.2054  0.1525  0.176  0.005  − 0.047  − 0.024 
10  1.2  19.5  3  0  20  0.2137  0.1565  0.142  0.013  − 0.043  − 0.058 
11  1.6  22.0  4  2  16  0.2062  0.1495  0.164  0.006  − 0.050  − 0.036 
12  1.2  19.5  3  4  20  0.1950  0.1350  0.202  − 0.005  − 0.065  0.002 
13  0.4  19.5  3  4  20  0.1853  0.1295  0.164  − 0.014  − 0.070  − 0.036 
14  1.2  19.5  3  8  20  0.1792  0.1295  0.149  − 0.021  − 0.070  − 0.051 
15  0.8  22.0  4  2  24  0.1915  0.1365  0.185  − 0.008  − 0.063  − 0.015 
16  1.2  19.5  3  4  12  0.2090  0.1265  0.189  0.009  − 0.073  − 0.011 
17  0.8  17.0  4  6  24  0.2040  0.1135  0.159  0.004  − 0.086  − 0.041 
18  0.8  17.0  2  6  16  0.1956  0.1255  0.136  − 0.004  − 0.074  − 0.063 
19  1.6  22.0  2  6  16  0.1915  0.1745  0.193  − 0.008  − 0.025  − 0.006 
20  1.2  19.5  5  4  20  0.1996  0.1700  0.163  − 0.001  − 0.030  − 0.037 
21  1.2  19.5  3  4  20  0.2060  0.1430  0.155  0.006  − 0.057  − 0.045 
22  2.0  19.5  3  4  20  0.1995  0.1470  0.142  − 0.001  − 0.053  − 0.058 
23  1.2  19.5  3  4  20  0.1992  0.1420  0.142  − 0.001  − 0.058  − 0.057 
24  0.8  17.0  2  2  24  0.2040  0.1440  0.132  0.004  − 0.056  − 0.067 
25  0.8  22.0  4  6  16  0.2050  0.1425  0.228  0.005  − 0.057  0.028 
26  0.8  22.0  2  6  24  0.2370  0.1735  0.183  0.037  − 0.026  − 0.016 
27  1.6  22.0  2  2  24  0.2316  0.1700  0.205  0.032  − 0.030  0.005 
28  1.2  14.5  3  4  20  0.1940  0.1190  0.117  − 0.006  − 0.081  − 0.083 
29  1.6  17.0  2  6  24  0.1907  0.1255  0.120  − 0.009  − 0.074  − 0.080 
30  1.6  17.0  4  2  24  0.2160  0.1535  0.126  0.016  − 0.046  − 0.074 
31  1.2  19.5  1  4  20  0.2125  0.2091  0.170  0.012  0.009  − 0.030 
32  1.2  19.5  3  4  20  0.2067  0.1630  0.168  0.006  − 0.037  − 0.032 
Results and discussion
Model prediction using response surface methodology
The empirical models in the form of quadratic regression equations to predict the various dimensional deviations of microgroove (Y_{UWD}, Y_{LWD} and Y_{DD}) with air pressure (X_{1}), lamp current (X_{2}), pulse frequency (X_{3}), pulse width (X_{4}) and cutting speed (X_{5}) are given below.
Results of ANOVA for dimensional deviations model
Source  DOF  Sequential SS  Adjusted SS  Adjusted MS  F  P value  Remark 

(a) Upper width deviation, Y_{UWD} model  
Regression  20  0.007120  0.007120  0.000356  6.26  0.002  Significant 
Linear  5  0.003599  0.000640  0.000128  2.25  0.121  
Interaction  10  0.001786  0.001786  0.000179  3.14  0.037  
Square  5  0.001735  0.001735  0.000347  6.11  0.006  
Residual error  11  0.000625  0.000625  0.000057  
Total  31  0.007745  
(b) Lower width deviation, Y_{LWD} model  
Regression  20  0.017356  0.017356  0.000868  6.04  0.002  Significant 
Linear  5  0.009493  0.001259  0.000252  1.75  0.203  
Interaction  10  0.004190  0.004190  0.000419  2.92  0.047  
Square  5  0.003672  0.003672  0.000734  5.11  0.011  
Residual error  11  0.001580  0.001580  0.000144  
Total  31  0.018935  
(c) Depth deviation, Y_{DD} model  
Regression  20  0.025359  0.025359  0.001268  4.61  0.006  Significant 
Linear  5  0.017916  0.002651  0.000530  1.93  0.169  
Interaction  10  0.003912  0.003912  0.000391  1.42  0.286  
Square  5  0.003531  0.003531  0.000706  2.57  0.089  
Residual error  11  0.003027  0.003027  0.000275  
Total  31  0.028386 
Model prediction using artificial neural network
Artificial neural network has been designed to mimic the linear order characteristics of structure interlinked nerve cells of human brain called biological neurons. Briefly, a group of certain inputs are mostly employed; each one designates the output of any other neuron. Each input is multiplied by a corresponding weight analogous to a synaptic strength, and these are summed up to determine the activation level of the neuron.
Check data set for testing ANN model and comparison results of predicted and measured dimensions of microgroove
Test no.  Responses in mm  

Upper width  Lower width  Depth  
ANN pred.  Experimental result  ANN pred.  Experimental result  ANN pred.  Experimental result  
1  0.18640  0.1840  0.1979  0.202  0.2130  0.2127 
2  0.2142  0.2137  0.1499  0.1525  0.1640  0.1621 
3  0.2031  0.2050  0.1279  0.1255  0.1168  0.12 
Training data set for testing ANN model and comparison results of predicted and measured dimensions of microgroove
Sl. no.  Responses (mm)  

Upper width  Lower width  Depth  
ANN pred.  Experimental result  ANN pred.  Experimental result  ANN pred.  Experimental result  
1  0.1958  0.1967  0.1341  0.1390  0.1601  0.1600 
2  0.2215  0.2210  0.1534  0.1550  0.1932  0.2000 
3  0.2163  0.2154  0.1715  0.1910  0.1667  0.1680 
4  0.1206  0.1930  0.1262  0.1280  0.1524  0.1620 
5  0.2327  0.2330  0.1931  0.2005  0.2323  0.2343 
6  0.2131  0.2490  0.1515  0.1620  0.1688  0.2090 
7  0.2003  0.2210  0.1468  0.1355  0.1669  0.1650 
8  0.2003  0.2054  0.1534  0.1565  0.1758  0.1760 
9  0.2073  0.2062  0.1479  0.1495  0.1522  0.1420 
10  0.2003  0.1950  0.1468  0.1350  0.1609  0.1640 
11  0.2035  0.1853  0.1297  0.1295  0.1636  0.1640 
12  0.1789  0.1792  0.1348  0.1295  0.1517  0.1495 
13  0.2131  0.1915  0.1516  0.1365  0.1819  0.1850 
14  0.209  0.2090  0.1292  0.1265  0.1898  0.1893 
15  0.2039  0.2040  0.1114  0.1135  0.1605  0.1590 
16  0.1957  0.1956  0.1242  0.1255  0.1407  0.1367 
17  0.1918  0.1915  0.1714  0.1745  0.1946  0.1937 
18  0.1996  0.1996  0.1659  0.1700  0.1685  0.1630 
19  0.2003  0.2060  0.1468  0.1430  0.1669  0.1550 
20  0.2024  0.1995  0.1569  0.1470  0.1305  0.1420 
21  0.2003  0.1992  0.1468  0.1420  0.1669  0.1427 
22  0.2124  0.2040  0.1371  0.1440  0.1336  0.1327 
23  0.2371  0.2370  0.1396  0.1425  0.2295  0.2280 
24  0.2316  0.2316  0.1853  0.1735  0.1909  0.1832 
25  0.1937  0.1940  0.194  0.1700  0.2058  0.2057 
26  0.2035  0.1907  0.1234  0.1190  0.1229  0.1170 
27  0.215  0.2160  0.1589  0.1535  0.127  0.1260 
28  0.2151  0.2125  0.1861  0.2091  0.1698  0.1700 
29  0.2003  0.2067  0.1468  0.1630  0.1669  0.1683 
Optimization using genetic algorithm
The following points give a generic view of how GAs operate (Krimpenis et al. 2014): (1) a population of individuals (solutions) is created that consists of random individuals (initialization); (2) a function or a model (objective function) measures individual performance and determines their ability to survive and reproduce; (3) individuals are ranked (ranking) and the best/fittest individuals (according to a fitness function, which is an objective function transformation) are chosen (selection operator) to mate in pairs (crossover operator) and thus create new individuals and hence a whole new population. Every new individual (offspring) carries genetic characteristics from both parents. Slight mutation (mutation operator) occurs from generation to generation with given probability. Other population diversion operators, such as inversion, may be applied to the offspring; (4) in order to satisfy the criteria of the objective function, increasing competition among individuals leads to “survival of the fittest.” This way, one generation after the other tends to have better genetic material (or characteristics) that help them survive. Individuals with best characteristics constitute the best solution to the problem; (5) this process continues in a repetitive manner until convergence criteria are met, i.e., the chromosomes have the best fitness or potential (optimum) solution for a specific problem is obtained. Immediately after the new generation is created, it is further assessed and checked through experimentation for the conformability and agreement (Shaik and Srinivas 2017).
Dimensional deviations of microgroove under GAbased optimum parametric conditions
Optimum process parameters  Targeted output (mm)  Dimensional deviations (mm)  

Lamp current  Pulse frequency  Pulse width  Air pressure  Cutting speed  Upper width  Lower width  Depth  Upper width deviation  Lower width deviation  Depth deviation 
19.5 Amp  4 kHz  6%  1.2 kgf/cm^{2}  24 mm/s  0.2  0.2  0.2  − 0.0278  0.0102  − 0.0308 
Comparison results of ANN prediction, GAbased optimization and actual experimentally observed dimensional deviations of microgroove on Al_{2}O_{3}
Method  Optimal process parameters  Upper width deviation (UWD)  Lower width deviation (LWD)  Depth deviation (DD)  Average error (%)  

X _{1}  X _{2}  X _{3}  X _{4}  X _{5}  Pred.  Exp.  Err. (%)  Pred.  Exp.  Err. (%)  Pred.  Exp.  Err. (%)  
ANN prediction in accordance with GA process parameters  1.2  19.5  4  6  24  − 0.025  − 0.0261  4.21  0.0098  0.011  9.916  − 0.0276  − 0.0301  8.31  7.47 
Optimization result based on GA  − 0.0278  − 0.0261  6.5  0.0102  0.011  7.27  − 0.0308  − 0.0301  2.33  5.37 
Conclusions

Experimentations have been successfully conducted using central composite design of RSM. The results are used to develop the mathematical model. The quadratic (secondorder) mathematical model proposed for various dimensional deviations of microgroove using RSM is not only capable of achieving precise required dimension of microgrooves on aluminum oxide but also useful for predicting new experiments. The models are found to be adequate and statistically significant because of their higher R^{2} value (89.1% for UWD, 91.7% for LWD, and 89.4% in case of DD), and Pvalue is lower than 0.05.

The experimental results are used to develop a multilayer feedforward back propagation. The performance of predictive ANN model based on 5883 architecture gave the minimum error (MSE = 0.000099) and presented highly promising confidence with percentage of error less than 3% while compared with experimental result data sets.

Optimization employing GA technique shows the optimal setting of process parameters in microgrooving operation of aluminum oxide by Nd:YAG laser treatment at lamp current of 19.5 Amp, pulse frequency of 4 kHz, pulse width 6%, cutting speed of 24 mm/s and air pressure of 1.2 kgf/cm^{2} with estimated minimal deviation of upper width − 0.0278 mm, lower width of 0.0102 mm and depth of − 0.0308 mm. The experimental result for the optimal setting shows that there is a considerable improvement in the laser microgrooving process.

The present research based on GA, ANN and statistically multiregression analysis (RSM) has demonstrated the ability to optimize and to accurately model the dimensional deviations of microgroove through advances in computer technology.

The proposed multiple approaches (experimental, evolutional, statistic and stochastic) present reliable methodologies to improve laser microgrooving process, and they can be employed in realtime process monitoring, model predictive control and optimization in several machining processes.

The outcome of the present research in the area of pulsed Nd:YAG laser micromachining of engineering ceramics can be effectively utilized by manufacturing engineers for the investigation and prediction of Nd:YAG laser process parametric settings for micromachining and microfabrication of different ceramic materials with intricate shape geometries.

The present research study of pulsed Nd:YAG laser microgrooving operation on aluminum oxide ceramic will be useful as technological guidelines for further research in the area of laser microgrooving process of structural ceramics.

This work will open up (1) future scope to study the cut surface quality with integrity for utilizing laser microgrooving more effectively and (2) challenging possibilities for exploring effective applications of laser technology for microgrooving of advanced ceramics in the field of highprecision microengineering.
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