On Estimation of Optimal Process Parameters of the Abrasive Waterjet Machining

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1 On Estimation of Optimal Process Parameters of the Abrasive Waterjet Machining Andri Mirzal Faculty of Computing Universiti Teknologi Malaysia UTM JB, Johor Bahru, Malaysia Abstract: This paper is a commentary on the work of Zain et al. (2011a) in which they proposed the use of soft computing techniques, i.e., genetic algorithm (GA) and simulated annealing (SA), to estimate optimal process parameters of the abrasive waterjet machining. We found a fundamental problem with their work; the authors have misinterpreted the original work of Caydas and Hascalik (2008) in which the real problem is how to build predictive models for the machining process, not to optimize the model variables using the estimate model as presented by Zain et al. (2011a). In addition to this problem, the objective function to be optimized is an infinitely differentiable quadratic formula with box constraints, thus instead of using soft computing techniques, gradient methods that have better convergence property and are usually faster should be employed first. In particular, we show that the active set method outperforms GA and SA both in the machining performance and computational times (about 13 times faster than GA and 462 times faster than SA). Keywords: abrasive waterjet machining, active set method, gradient method, optimization, soft computing. 1. Introduction Scientific publications are tools to communicate and share scientific findings and progresses. With the abundant people involve in research activities, the number of scientific publications grows exponentially. One of the most challenging problems is thus how to keep up with this trend. The other problem is how to learn the necessary knowledge to produce and review scientific findings. Sometimes we are unable to properly answer these challenges. This can result in inappropriate, misleading, or erroneous papers being published in scientific journals because authors and reviewers may not have sufficient knowledge. Fortunately, the problem of papers with this kind of contents getting published can be easily fixed because science is self-correcting. Thus, journals as scientific communication tools should allow peer verifications on the published works to be published or otherwise the published papers will remain unverified and thus errors and misleading results will be spread out. This commentary is such an effort to do peer verification on the work of Zain et al. (2011a) in which they proposed the use of soft computing techniques, i.e., genetic algorithm (GA) and simulated annealing (SA), to estimate optimal process parameters of the abrasive waterjet machining based on the work of Caydas and Hascalik (2008). They also repeated the same mistake in their subsequent work (Yusup et al., 2013) in which they proposed the use of artificial bee colony to solve the same problem. 2. Abrasive waterjet machining models Abrasive waterjet (AWJ) machining is a process for material processing and machine parts fabrication by utilizing AWJ machine. AWJ is a cutting machine that uses a highly concentrated stream of water mixed with abrasive particles to cut through the materials (Caydas and Hascalik, 2008). The performance of AWJ machining is determined by the quality of processed products that is usually measured using surface roughness (Caydas and Hascalik, 2008). 1

2 In the original work (Caydas and Hascalik, 2008), the authors considered machining parameters of traverse speed (V), waterjet pressure (P), standoff distance (h), abrasive grit size (d), and abrasive flow rate (m) as the inputs and surface roughness (R a ) as the output to build two predictive models using artificial neural networks (ANN) and second-order polynomial regression respectively. The models were then trained by using 13 sets of experimental data, and performance evaluation was conducted by using the remaining 14 sets of the data as test dataset in which it was shown that the ANN model gave better prediction to the R a values than the regression analysis. Mathematically, if F is the AWJ machining process, then: ( ), and then the predictive models were built to estimate F that gives outputs as closest as possible to R a values in the test dataset. 3. The work of Zain et al. (2011a) In the work of Zain et al. (2011a), the authors misinterpreted the result of the original work by Caydas and Hascalik (2008). Instead of building a better predictive model to estimate F, they took the regression model in the original work which is an estimate to the unknown F as the true F, and then computed the values of model variables (V, P, h, d, and m) that result in more optimal R a values using two soft computing techniques: GA and SA. So under the work of Zain et al. (2011a), the problem became: ( ), where F rm is the second-order polynomial regression model from the original work (Caydas and Hascalik, 2008) that estimates F: F rm = V P h d m V P h d m Vm Pm hm dm. (1) They also introduced some constraints on the model variables that were taken from machining settings used in the original work: 50 V 150, 125 P 250, 1 H 4, 60 D 120, 0.5 M 3.5. There is no justification in using these constraints, and it is possible that the real physical constraints of the AWJ machine can be different since the above values are the machining settings for certain experiments conducted in the original work. Since F rm is just an estimate to the real process, the surface roughness values corresponding to the optimal model variables computed by GA or SA certainly are only estimates to the real values. Thus comparing these values to the surface roughness values from experiments as shown by Zain et al. (2011a) certainly is a misleading effort. Zain et al. actually has many papers that repeatedly do the similar flaw, e.g., Zain et al. (2010a), Zain et al. (2011b), Zain et al. (2010b), Zain et al. (2012a), Zain et al. (2011c), Zain et al. (2011d), and Zain et al. (2012b), so that it is necessary to do peer verification on their works. 2

3 4. Quadratic programming model As shown in the above section, the problem addressed by Zain et al. (2011a) is a quadratic programming with box constraints. And since the objective function (1) is also infinitely differentiable, some established gradient based methods in quadratic programming should be employed first to solve the problem before using soft computing techniques because the formers have better convergence property and also are usually faster than the latters. In particular, we demonstrate the use of the active set method, an established gradient based optimization method, to optimize the above problem. To use the active set method, the problem is rewritten into the standard quadratic form: ( ) where vector x contains the model variables (V, P, h, d, and m) in its entries. Therefore the lowerbound l, upperbound u, matrix A, vector b, and constant c can be written as: [ ], [ ],, [ ], and 5. Experimental results. To conduct the experiment, we used the built-in quadprog function in MATLAB. The following lines were entered into the MATLAB command prompt to get the results: options = optimset('algorithm','active-set'); [x, Ra] = quadprog(2*a,b,[],[],[],[],l,u,[],options); Ra = Ra + c; where A, b, l, u, and c correspond to the A, b, l, u, and c, x denotes the vector x, and Ra denotes the R a. The last line was used to shift the R a value because we removed the constant c in line two to compute R a. Table 1 summarizes the results and also displays the results reported by Zain et al. (2011a) for GA and SA. As shown, the active set method outperformed both GA and SA in producing minimum R a. Table 1. Summary of the results. Method R a Optimal model variables V P h d m GA [1] SA [1] Active Set

4 To get a more thorough performance comparison, certainly using only one case is insufficient and inconclusive. Therefore we created 100 equivalent problems of the same size as the problem in (1) randomly, and recorded the average computational times (in second) and investigated which method performed the best in each cases. For a fair treatment, we also used the built-in MATLAB function GA and simulannealbnd for GA and SA. Table 2 summarizes the results, and as shown the active set method was not only much faster than GA and SA (about 13 times faster than GA and 462 times faster than SA), but also offered much better solutions as it outperformed GA and SA in 92 cases out of 100 cases. Table 2. Performance comparison for 100 cases. GA SA Active Set Average comp. times #times performed the best Conclusion The process of scientific publication that traditionally involves authors, editors, and reviewers can sometimes fail in recognizing papers with misleading, inappropriate, or erroneous contents. Even though recently many efforts have been spent on identifying such papers, usually only papers with scientific misconduct contents gain some attention. Certainly, there are also papers without such contents but nonetheless contain some misleading, inappropriate, or erroneous contents. To evaluate this kind of papers and to avoid the spreading of the errors, peer verification should be allowed to be published. Peer verification thus can be considered as an additional stage in scientific publication after the papers being published. In this commentary, we provide such peer verification on the work of Zain et al. (2011a) in which we pointed out that the authors have misinterpreted the work of Caydas and Hascalik (2008). We think it is necessary to do this verification since the authors seem to not understand what is wrong with their works as they repeatedly do the similar flaw in many of their papers. We also showed that the problem is a simple quadratic programming with box constraints. Thus it would be better if standard gradient based methods were employed first before soft computing techniques because the formers have better convergence property and also usually are faster than the latters. In particular we demonstrated that the active set method outperformed GA and SA both in optimizing the objective functions and in the computational times. References (Caydas and Hascalik, 2008) Caydas, U. and Hascalik, A., A study of surface roughness in abrasive waterjet machining process using artificial neural networks and regression analysis method, Journal of Materials Processing Technology 202: , (Yusup et al., 2013) Yusup, N., Sarkheyli, A., Zain, A.M., Hashim, S.Z.M., and Ithnin, N., Estimation of optimal machining control parameters using artificial bee colony, Journal of Intelligent Manufacturing, (Zain et al., 2010a) Zain, A.M., Haron, H., and Sharif, S., Application of GA to optimize cutting conditions for minimizing surface roughness in end milling machining process, Expert Systems with Applications 37: , (Zain et al., 2010b) Zain, A.M., Haron, H., and Sharif, S., Simulated annealing to estimate the optimal cutting conditions for minimizing surface roughness in end milling Ti-6Al-4V, Machining Science and Technology 14: 43-62,

5 (Zain et al., 2011a) Zain, A.M., Haron, H., and Sharif, S., Genetic algorithm and simulated annealing to estimate optimal process parameters of the abrasive waterjet machining, Engineering with Computers 27: , (Zain et al., 2011b) Zain, A.M., Haron, H., and Sharif, S., Estimation of the minimum machining performance in the abrasive waterjet machining using integrated ANN-SA, Expert Systems with Applications 38: , (Zain et al., 2011c) Zain, A.M., Haron, H., and Sharif, S., Optimization of process parameters in the abrasive waterjet machining using integrated SA GA, Applied Soft Computing 11: , (Zain et al., 2011d) Zain, A.M., Haron, H., and Sharif, S., Integration of simulated annealing and genetic algorithm to estimate optimal solutions for minimising surface roughness in end milling Ti-6AL-4V, International Journal of Computer Integrated Manufacturing 24: , (Zain et al., 2012a) Zain, A.M., Haron, H., Qasem, S.N., and Sharif, S., Regression and ANN models for estimating minimum value of machining performance, Applied Mathematical Modelling 36: , (Zain et al., 2012b) Zain, A.M., Haron, H., and Sharif, S., Integrated ANN-GA for estimating the minimum value for machining performance, International Journal of Production Research 50: ,