Response Surface Method Model Research Articles

A response surface methodology for the use of MIL‐101 as a catalyst for the one‐step synthesis of lactide

Lactide is a vital monomer for producing high molecular weight polylactic acid (PLA) through ring‐opening polymerization. This study synthesized crude lactide from L‐lactic acid with MIL‐101 as the catalyst. MIL‐101 is a metal‐based catalyst with organic ligands (MOF) that was prepared by reacting Cr(NO3)3.9H2O with terephthalic acid (BDC). The formation of MIL‐101 was confirmed from Fourier‐transform infrared (FTIR) analysis. The role of MIL‐101 and the effect of temperature, time, and MIL‐101 loading, as well as their interactions in the conversion of lactic acid to crude lactide, were then investigated using the response surface method (RSM). Crude lactide was analyzed using 1H‐nuclear magnetic resonance (NMR) spectroscopy to confirm the presence of lactide. The RSM results indicated that the highest conversion of 22.84% can be obtained using a temperature of 175 °C, 1.5% w/w MIL‐101 loading, and a reaction time of 5 h. The RSM model showed that the interaction of MIL‐101 loading and reaction time strongly affected the conversion of lactic acid to lactide, with a P‐value of 0.0021 and an F‐value of 50.45. In contrast, the interaction of catalyst loading and temperature did not significantly affect the conversion of lactic acid to lactide, with a P‐value of 0.2565 and an F‐value of 1.75.

A combination of the particle swarm optimization-artificial neurons network algorithm and response surface method to optimize energy consumption and cost during milling of the 2017A alloy

This research aims to predict the cost and energy consumption associated with pocket and groove machining using the hybrid particle swarm optimization-artificial neurons network (PSO-ANN) algorithm and the response surface method (RSM). A parametric study was conducted to determine the best predictions by adjusting the swarm population size (pop) and the number of neurons (n) in the hidden layer. The results showed that machining strategies and sequences can have a significant impact on energy consumption, reaching a difference of 99.25% between the minimum and maximum values. The cost ( Ctot) and energy consumption ( Etot) values with the PSO-ANN algorithm increased significantly by 99.99% and 92.41%, respectively, compared to the RSM model. The minimum mean square error values for Etot and Ctot with the PSO-ANN models are 3.0499 × 10−5 and 4.6296 × 10−10, respectively. This study highlights the potential of the hybrid PSO-ANN algorithm for multi-criteria prediction and highlights the potential for improved machining of 2017A alloy.

The entropy method integrated RSM model to evaluate hole geometries in electrochemical blind hole drilling

ABSTRACTThe electrochemical drilling (ECD) process enables the machining of conductive materials with a wide range of hardness, yield strength, and brittleness. In this study, the ECD experiments have been conducted on blind hole drilling in high-speed steel material using a tailor-made ECD machine. The hole geometries (cross-sectional profiles) at different machining parameters have been examined for the hole depth consistency (HDC), hole cross-sectional area (HCAC) and the hole profile length (HPLC) evaluation (response; output) metrics introduced. The relationships between the hole geometry evaluation metrics and machining parameters are obtained using the response surface method (RSM). Using the Entropy method, an optimisation model is also proposed to combine multiple responses into a single objective function. The effectiveness of the Entropy method is compared with the Analytical Hierarchical Process (AHP). The comparison showed that the Entropy model provides more robust and convenient results than the AHP approach.

Optimal pretreatment of plantain peel waste valorization for biogas production: Insights into neural network modeling and kinetic analysis

This work proposed a model for the substrate treatment stage of biogas production process in an anaerobic digestion system. Adaptive neuro-fuzzy inference system (ANFIS), response surface method (RSM), and artificial neural network (ANN) were comparatively used in the simulation and modeling of the treatment process for improved biogas yield. Waste plantain peels were pretreated and used as substrate. FTIR and SEM results revealed that the pretreatment improved the substrate's desirable qualities. The amount of biogas yield was controlled by time, NaOH concentration, and temperature of the substrate pretreatment. Optimum pretreatment conditions obtained were a temperature of 102.7 °C, time of 31.7 min and NaOH concentration of 0.125 N. RSM, ANN, and ANFIS modeling techniques were proficient in simulating the biogas production, as evidenced by high R2values of 0.9281, 0.9850, and 0.9852, respectively. Furthermore, the values of the calculated error terms such as RMSE (RSM = 0.04799, ANN = 0.00969, and ANFIS = 0.00587) and HYBRID (RSM = 18.556, ANN = 0.803, and ANFIS = 0.0447) were low, indicating a satisfactory correlation between experimental and predicted values. Scrubbing of the biogas with caustic soda and activated charcoal increased the methane content to 94 %. The kinetics of the cumulative biogas yield were best fit with the Logistics and Modified Logistics models. The low C/N ratio in addition to the presence of potassium, nitrogen, and phosphorus suggested that the spent plantain peel slurry can be utilized as an agricultural fertilizer in crop production. The observations of this study therefore recommends the pre-treatment of biodigestion substrates as a key means to enhance beneficiation of methane production.

Optimization of ciprofloxacin removal by response surface methodology using activated carbon from Burmese grape obtained from Vietnam

Activated carbon is produced from Burmese grapes using NaOH as the activator under microwave irradiation. Through scanning electron microscopy, Fourier-transform infrared spectroscopy, X-ray diffraction analysis, and Brunauer–Emmett–Teller analysis methods, the activated carbon material is found to have a rough and uneven surface with the formation of pores, an amorphous structure, and possesses hydroxy, C–H, carbonyl, alkene, and ether functional groups. The surface area (478.5 m2 g−1) and pore size (about 3.4 nm) are calculated from the adsorption N2 equation. The adsorption mechanism of activated carbon is evaluated and follows a pseudo-first-order kinetic model (large single adsorption) and the Langmuir isotherm model (physical interaction). The factors affecting ciprofloxacin adsorption using activated carbon derived from Burmese grapes are also evaluated and optimized by the response surface method model based on influencing factors including the contact time, the solution pH, the antibiotic concentration, and the material dosage. The optimal parameters are as follows: pH = 6.26, concentration = 58.9 mg L−1, content = 0.15 g L−1, time = 54 min. Under optimal conditions, the adsorption capacity predicted from the model is 191.33 mg g−1 with an efficiency of 41.35%.

Optimized Material Removal and Tool Wear Rates in Milling API 5ST TS-90 Alloy: AI-Driven Optimization and Modelling with ANN, ANFIS, and RSM

One of the performance measures and responses in manufacturing is the optimization of the Material Removal Rate (MRR) and Tool Wear Rate (TWR). This study used the response surface method (RSM) and AI-based models of artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFISs) to model and optimize the MRR and TWR for milling API 5ST TS-90 alloys. A ZX6350C milling machine was used to conduct twenty (20) experimental runs using a 10 mm HSS end-mill cutter. The experiment was designed using Central Composite Design (CCD) in Design Expert 14 software. RSM, ANN, and ANFIS models were applied in the predictive modelling of the milling process with a coefficient of determination above 0.85. Comparatively, ANFIS and RSM were marginally better than ANN in the predicted MRR for the milling process. The ANFIS and RSM were slightly better than ANN in the predicted TWR for the milling operation. Generally, ANFIS showed a better predictive capability than RSM and ANN for both MRR and TWR. The optimum process milling parameters for the alloy were a 720-rpm spindle speed, 24 mm/min feed rate and 0.979 mm depth of cut to achieve an optimized predicted MRR of 1272.163 mm3/min and TWR of 0.781 mm/min. The optimum milling process was validated at the suggested experimental conditions by carrying out the milling experiment at those conditions, and the results of 1270.05 mm3/min for MRR and 0.77 mm/min for TWR showed a close correlation between the predicted and validated optimum. The optimum milling parameters from this study would enhance production at reduced tooling costs associated with tool wear.

Study on the multi-factors interaction of annular pulsating heat pipe based on response surface method and temperature curve analysis

Pulsating heat pipe enable rapid heat transfer over long distances and is suited for solar collector applications. However, there is no pulsating heat pipe specially designed for evacuated solar collector, which leads to a large contact thermal resistance between the heat pipe and the evacuated pipe. In this paper, a new structure of annular pulsating heat pipe (APHP) was designed. In order to efficiently optimize the operation parameters and understand the interaction of factors, the three-factors three-levels Box-Behnken Design (BBD) model of response surface method (RSM) was used to establish the optimization program, and the accuracy was tested by analysis of variance. The significance and interaction of factors (heat transfer distance, cooling water temperature and cooling water flow rate) on the heat transfer performance were analyzed according to the temperature oscillation curve. The results show that heat transfer distance has a much more significant effect on the heat transfer capacity than the cooling water temperature and cooling water flow rate. Furthermore, over long heat transfer distance, adjusting the cooling water temperature has a greater impact on the heat transfer performance. While over short heat transfer distance, adjusting the cooling water flow rate has a greater impact. The optimal working condition predicted by RSM model is 375 mm heat transfer distance, 15 °C cooling water temperature and 1.0 L/min cooling water flow rate. The actual average heat flow obtained from experiment was 99.47 W, with an error of only 2.04% from the predicted value. This paper illustrates the feasibility and efficiency of the response surface method for studying the heat transfer performance of PHP. The significance and interaction analysis of factors can provide guidance for the practical application.

A highly accurate model for prediction of thermal conductivity of carbon-based nano-enhanced PCMs using an artificial neural network

Nano-PCMs, which contain nanostructured materials, can enhance the low thermal conductivity of phase change materials (PCMs). It is crucial to predict the precise thermal conductivity of nano-PCM to assess the heat transfer during phase change procedures such as melting and solidification. In this study, artificial neural network (ANN) and response surface method (RSM) were used to develop a model for predicting the thermal conductivity of carbon-based nano-enhanced phase change materials (NEPCMs) using 482 experimental samples collected from various datasets. The carbon-based nano-particles were SWCNTs, MWCNTs, graphite, graphene, and (CNFs). Six input parameters were considered with varying temperature, mass fractions, sizes, thermal conductivities of PCMs and nano-particles, and the phase of PCM. The ANN was designed using a multi-layered feed-forward structure and Levenberg–Marquardt back-propagation algorithm with one hidden layer consisting of eight neurons. The transfer function was varied to achieve optimal performance. It was revealed that the predictive capacity of the ANN model is greater than that of the RSM model based on their corresponding the coefficient of determination (R2) and root mean square error (RMSE) values. The developed ANN achieved a R2 value of 0.99, while the RSM method model achieved an R2 value of 0.79.

Understanding and modelling the aquafeed extrusion process for Atlantic salmon feed with an empirical model

An empirical model was applied to quantitatively model the effects of extrusion variables and recipe compositions on quality of feed pellets. Lab extrusion trials were performed with an Atlantic salmon feed recipe with using a central component design (CCD). Comparing with a coated commercial feed made with the same recipe, the lab extrusion pellets had similar bulk density, hardness, and durability properties. A Response Surface Method (RSM) was also used to regress the extrusion trial data and compared with the empirical model results. The respective Absolute Average Deviation (AAD %) values of the empirical model and RSM regression were 4.1 % and 1.8 % for pellet bulk density, 7.4 % and 4.9 % for pellet hardness, 10.4 % and 10.0 % for pellet oil absorption, 13.7 % and 8.3 % for pellet water stability, and 11.3 % and 5.5 % for pellet durability. Using the model coefficients obtained from the extrusion results, the empirical model can partly extrapolate the pellet qualities of an additional extruded recipe, which has a slightly adjusted wheat gluten and wheat. The model performance was evaluated based on. R2, RSME (root-mean-square deviation), AAD % of the empirical model was better than the RSM model to predict the effects of extrusion variables on pellet quality parameters. The effects of the extrusion process variables and recipe composition on pellet quality parameters are predicted by the empirical model. Its demonstrates that the empirical model is a new method to understand extrusion trial results in different extrusion systems and recipes without changing its mathematical form of expression, which gives a common reference to compare an extruded recipe in different systems and has practical engineering applications.

Modeling and optimization of the corrosion resistance of Cr-free and Cr-based chemical conversion coatings on nickel foil by artificial neural network and response surface method

Chemical conversion treatment is one of the most powerful methods to prevent the corrosion of metals. However, determining the optimal addition amount of various active ingredients for the enhancement of corrosion resistance requires a large number of repeated experiments, which is very time-consuming and is also not helpful for figuring out the interactions between active ingredients. In the present study, Cr-free conversion coatings (CFCC) and Cr-based conversion coatings (CCC) were prepared on nickel foil and characterized by scanning electron microscopy and X-ray photoelectron spectroscopy to determine their morphology and composition of them. The corrosion resistance of conversion coatings was measured by salt spray test and further investigated using the response surface method (RSM) and artificial neural network (ANN) approach. The constructed models displayed high predictive accuracy, and the coefficient of correlation value of the RSM-CFCC, ANN-CFCC, RSM-CCC, and ANN-CCC models is 0.9441, 0.9513, 0.9535 and 0.9564, respectively. This comparative study recommends the ANN model best fits the experimental data for both CFCC and CCC. By using the ANN outputs, satisfactory results can be estimated with superior accuracy and efficiency while the RSM model can describe the interactions between factors.

Construction of response surface model for photoacoustic-based H2S measurement system and significance analysis of multiple influential factors

Herein we first introduce the relationship between the photoacoustic (PA) signals’ intensity of hydrogen sulfide (H2S) versus multiple parameters of optical path conditions, following by the construction of response surface method (RSM)-based models of the PA signals’ intensity versus the distance l1 from the laser head to the convex lens, the distance l2 from the convex lens to the PA cell (PAC), and the distance l3 from the geometric center line of the light beam to the acoustic sensor. After that, we perform the significance analysis. The results show that the RSM model with a third-order configuration is relatively preferred. The distances l1, l2 and l3 all have significant influences on the PA signals’ intensity. Additionally, we ameliorated the performance of the full third-order model by removing the non-significant terms.

Alkali-activated slag backfill grout materials optimization: statistical RSM modelling and NSGA-II performance control

Optimizing the performance of alkali-activated slag backfill grout (ASBG) is crucial for engineering applications. Fluidity and 28 d unconfined compressive strength (28 d UCS) are the two most important performances and multi-objective optimization is existed. In this research, the response surface method (RSM) for experiment design and model regression, non-dominated sorting genetic algorithm II (NSGA-II) for optimization, and entropy-based Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for decision-making were implemented. The strength formation mechanism of the optimal ASBG was investigated via microstructure evolution. The results show that the quadratic RSM models for fluidity and 28 d UCS exhibit excellent predictive fitting capabilities, with the determination coefficients of 0.9713 and 0.9588 respectively. NSGA-II coupled with entropy-based TOPSIS determined the optimal mix proportion with water-binder ratio of 0.877, binder-sand ratio of 1.000 and alkali dosage of 4.138%. The porosities at 1–28 d decrease from 10.06% to 2.62%. And the mode of microstructure evolution can be divided into two stages according to the probability distribution index and fractal dimension. In early stage, probability distribution index and fractal dimension decreased from 0.9974 to 0.4833 and 1.2498 to 1.2022. This indicated that the number of the small pores decreased and the pore boundary transformed into the softer one as the irregular plate-like GGBS dissolved. In the later stage, probability distribution index and fractal dimension increased from 0.4833 to 1.4732 and 1.2022 to 1.3273, indicating a relatively denser microstructure with fewer large pores formed.

Prediction of Sediment Yields Using a Data-Driven Radial M5 Tree Model

Reliable estimations of sediment yields are very important for investigations of river morphology and water resources management. Nowadays, soft computing methods are very helpful and famous regarding the accurate estimation of sediment loads. The present study checked the applicability of the radial M5 tree (RM5Tree) model to accurately estimate sediment yields using daily inputs of the snow cover fraction, air temperature, evapotranspiration and effective rainfall, in addition to the flow, in the Gilgit River, Upper Indus Basin (UIB) tributary, Pakistan. The results of the RM5Tree model were compared with support vector regression (SVR), artificial neural network (ANN), multivariate adaptive regression spline (MARS), M5Tree, sediment rating curve (SRC) and response surface method (RSM) models. The resulting accuracy of the models was assessed using Pearson’s correlation coefficient (R2), the root-mean-square error (RMSE) and the mean absolute percentage error (MAPE). The prediction accuracy of the RM5Tree model during the testing period was superior to the ANN, MARS, SVR, M5Tree, RSM and SRC models with the R2, RMSE and MAPE being 0.72, 0.51 tons/day and 11.99%, respectively. The RM5Tree model predicted suspended sediment peaks better, with 84.10% relative accuracy, in comparison to the MARS, ANN, SVR, M5Tree, RSM and SRC models, with 80.62, 77.86, 81.90, 80.20, 74.58 and 62.49% relative accuracies, respectively.

Fast design of catalyst layer with optimal electrical-thermal-water performance for proton exchange membrane fuel cells

The catalyst layer (CL) is the core component in determining the electrical-thermal-water performance and cost of proton exchange membrane fuel cell (PEMFC). Systemic analysis and rapid prediction tools are required to improve the design efficiency of CL. In this study, a 3D multi-phase model integrated with the multi-level agglomerate model for CL is developed to describe the heat and mass transfer processes inside PEMFC. Moreover, a research framework combining the response surface method (RSM) and artificial neural network (ANN) model is proposed to conduct a quantitative analysis, and further a rapid and accurate prediction. With the help of this research framework, the effects of CL composition on the electrical-thermal-water performance of PEMFC are investigated. The results show that the mass of platinum, the mass of carbon, and the volume fraction of dry ionomer has a significant impact on the electrical-thermal-water performance. At the selected points, the sensitivity of the decision variables is ranked: volume fraction of dry ionomer > mass of platinum > mass of carbon > agglomerate radius. In particular, the sensitivity of the volume fraction of dry ionomer is over 50% at these points. Besides, the comparison results show that the ANN model could implement a more rapid and accurate prediction than the RSM model based on the same sample set. This in-depth study is beneficial to provide feasible guidance for high-performance CL design.

Characterization of biodiesel based on plastic pyrolysis oil (PPO) and coconut oil: Performance and emission analysis using RSM-ANN approach

The work presents comparative study of the production and characterisation of sustainable biodiesel fuel made from waste plastics and virgin coconut oil. For characterisation, various chemical tests were performed, including Fourier Transform Infrared (FTIR) spectroscopy, Thermogravimetric analysis (TGA), and Gas chromatography–mass spectrometry (GCMS). The emissions and performance of this fuel were investigated to determine whether it could be utilised in diesel engines without modification. RSM (response surface method) was used to design the experiments. ANN (artificial neural network) was used to model the relationship between the input and output parameters. It was seen that, 20 % hybrid blend with diesel showed a better output (33 %) than 10 % and 30 % blend. For 75 % of load, a value of 0.12 % (minimum) CO emission was obtained for the same blend with diesel fuel. Low proportion levels blends (10 %) have less amount of oxygen content, hence reduced in NOx (400 ppm). The ANN and RSM models were found to be fitting correctly with the experimental readings, with R2 ratios varying from 90 % to 93.5 %, respectively. The outcomes demonstrated that RSM and ANN were excellent modelling techniques with good accuracy. In addition, ANN's prediction performance (R2 = 0.9978 for BTE) was somewhat better than RSM's (R2 = 0.960 for BTE).

Study of seat-to-head vertical vibration transmissibility of commercial vehicle seat system through response surface method modeling and Genetic Algorithm

Low-frequency vibration is a significant hazard to commercial vehicle drivers. Research on how to reduce seat vibration and improve human comfort in a seating system through seat design optimization is important. The novelty of this paper is to study the sensitivity analysis of seat design parameters and their interaction effects and optimize seat design for the minimum vibration transmission to human drivers. The uniqueness of this paper is the identification of the system parameters from the measured vibration acceleration data rather than from the material test.The purpose of this paper is to develop a prediction model of vibration transmissibility from input design parameters using the response surface method modeling. The statistical significance of the RSM model will be validated by analysis of variance. The design parameters will be optimized through the RSM modeling and Genetic Algorithm.The method can enhance the vibration isolation performance of the existing vehicle seat suspension system with reduced cost and without additional parts and energy consumption and make the design change and optimization of the seat suspension system simple and easy to be implemented. According to the research results, the vibration transmissibility ratio of the optimized seat system is reduced by about 10%.

Correlation development and parametric investigation for thermal–hydraulic characteristics of flying-wing fin

The present study investigates thermal–hydraulic characteristics and structural parameters of the flying-wing fins. 165 cases based on the response surface method (RSM), considering 6 geometric parameters, are carried out. Firstly, the correlations of the flying-wing fin's heat transfer (j-factor) and flow friction (f-factor) are proposed using numerical simulations. The maximum deviations of the correlation with j-factor and f-factor are 8.53 % and 9.51 %, respectively. Secondly, the effects of geometric parameters are investigated respectively using the RSM model in detail at Re of 3000. The j-factor and f-factor are positively correlated with fin pitch (Fp) and amplitude (A) while negatively correlated with wavelength (L) and fin height (Fh). The j-factor and f-factor rise and subsequently drop as the inclined angle (θ) increases. Evaluating the thermal performance shows that the optimum θ is 80°. The f-factor has a turning point at the angle of 75°. Regarding the effects between parameters, the lower f-factor can be obtained at large Fp when the fin is short while at small Fp when the fin is tall. The A and Fh change the trend of θ on j-factor and f-factor. Eventually, optimized geometrical parameters of the flying-wing fin are obtained by the desirability approach at Re = 3000.

Measuring Total Filtration Efficiency of Surgical and Community Face Masks: Impact of Mask Design Features

Surgical and community face masks are used worldwide to reduce the transmission of respiratory infections in indoor environments. Performance parameters for these loose-fitting devices are mainly focused on material filtering efficiency, while, differently from face respirators, there are no standards methods for measuring the fraction of air leaking at the face seal. This study quantifies the total filtration efficiency (TFE), a parameter based both on filter efficiency and air leakage, of 50 face mask models with the aim of understanding the role of several mask design features on TFE performance. An instrumented head form equipped with sensors for measuring volumetric airflow and differential pressure was used to simulate the air exhalation from the mouth of a person wearing a face mask. A Response Surface Method (RSM) was used to model the TFE experimental data. Results showed that TFE values ranged over a wide interval (from 5 % to 73 %), with better values at higher flowrates. A significant positive correlation was found between TFE and filter breathability. The presence of a nosepiece showed to increase the TFE on average from 4 % to 6 %, according to the flowrate. Significant improvements were associated only to nosepieces incorporating a metallic wire. The RSM model evidenced that the increase in the number of the filter layers, and the use of a meltblown layer, result in higher TFE only when a nosepiece is in place. Differently, the benefit of the nosepiece is less marked for masks made of highly breathable filters. To improve overall mask performance, the design of loose-fitting face masks should carefully compromise between breathability and filtration efficiency of the filter materials. The addition of a metallic nosepiece help improving the TFE by limiting the air leaking at the face seal.

RSM models approach for optimization of the mechanical properties of electroless Ni-B-nanodiamond coating: An experimental and molecular dynamic simulation study

This report explores the effects of electroless Ni-B-nanodiamond plating bath parameters for optimization of the hardness and deposition rate based on response surface method (RSM). Quadratic models were developed and found to be mathematically appropriate for the optimization. The nanodiamonds (ND) and optimized coating were characterized using XPS, DLS, FIB-SEM, GDOES, microhardness, and nanoindentation. The results of the molecular dynamic simulation show low adsorption energy of borohydride on nanodiamonds surface is not favourable for borohydride dehydrogenation, therefore the boron content of the coating decreases when ND are added. Raman spectroscopy, SEM, and EDS analysis carried out on different zones of the surface after scratch test show nanodiamonds undergo graphitization and micro-cracking which block crack propagation at lower load. In addition, ND improves formation of the tribolayer at higher loads. The Raman spectroscopy results after indentation tests show the possibility of SP3 to SP2 phase transformation for nanodiamonds. The molecular dynamic simulation results confirm that phase transformation through monitoring the changes in nanodiamonds interatomic potential and interatomic distances. It is believed that the volume expansion caused by this phase transformation increases the toughness of coating.

Numerical-experimental study of die geometry in the constrained groove pressing of 6061 aluminum sheets

Nowadays, in line with the need of different industries to the materials with high strength to weight ratio, researchers have drawn attention to the processes of severe plastic deformation. The constrained groove pressing (CGP) is one of the most effective methods of severe plastic deformation to produce high-strength sheet metal using two dies with different shapes (grooved and flat). Despite the advantages of CGP in creating high accumulative plastic strain, this process leads to non-uniformity in mechanical properties of the sheet. This non-uniformity is one of the limitations of the CGP process which is considered in this study. Experimental and numerical studies were performed to investigate CGP process on 6061 aluminum alloy sheet up to two complete passes and the mechanical properties of the sheets were studied. Hardness testing was conducted on the worked material and the increase in the hardness of tested material in both longitudinal and thickness directions were observed. Also, it was shown that the non-uniformity in hardness distribution is correlated to the non-uniformity in the strain distribution. So, validated numerical model was used to develop the response surface method (RSM) and consequently to investigate the effect of geometric parameters in the grooved die on the strain uniformity. Finally, die geometry was optimized using the developed RSM model to produce a sample with more uniformity in strain and hardness distribution.