Order Response Surface Model Research Articles

Prediction of effective parameters for 3D printing of poly lactic acid-carbon fibre composites using intelligent frameworks based on mechanical response

Purpose This paper aims to find the effective 3D printing process parameters based on mechanical characteristics such as tensile strength and hardness of poly lactic acid (PLA)/carbon fibre composites (CF-PLA) by implementing intelligent frameworks. Design/methodology/approach The experiment trials are conducted based on design of experiments (DoE) using Taguchi L9 orthogonal array with three factors (speed, infill % and pattern type) and three levels. The factors have been optimized by solving the regression equation which is obtained from analysis of variance (ANOVA). The contour plots are generated by response surface methodology (RSM). The influencing parameters are found by using Box–Behnken design. The second order response surface model demonstrated the optimal combination of input parameters for higher tensile strength and hardness. Findings The influencing parameters are found by using Box–Behnken design. The second order response surface model demonstrated the optimal combination of input parameters for higher tensile strength and hardness. The results obtained from RSM are also confirmed by implementing the machine learning classifiers, such as logistic regression, ridge classifier, random forest, K nearest neighbour and support vector classifier (SVC). The results show that the SVC can predict the optimized process parameters with an accuracy of 95.65%. Originality/value 3D printing parameters which are considered in this work such as pattern types for PLA/CF-PLA composites based on intelligent frameworks has not been attempted previously.

Normative database of response surface method for human trunk extension in isometric mode.

Recent studies show that asymmetric movements are important Low Back Disorders risk factors. Measuring the trunk strength and identifying the coupling effects in different postures can provide an objective tool to assess one's task capacity. This paper estimates the maximum performance capacity for isometric trunk extension and accompanying torques. Thirty males performed maximum voluntary isometric extension in 33 trunk postures on Sharif Lumbar Isometric Strength Tester device. Corresponding moments and angular positions were collected. Second-order full response surface models (RSM) were exploited to formulate the relationship between strengths and three trunk angles. The results of correlation coefficient, percent of standard estimation error and lack of fit reflected the adequacy of models. In conclusion, the main torque was the extension, but at the same time lateral bending and rotation torques were observed. For predicting these three torques in a specific posture and injury prevention, the second order RSM is a useful tool. The presented models can be used in the fields of ergonomics, occupational biomechanics and sport.

I-optimal or G-optimal: Do we have to choose?

When optimizing an experimental design for good prediction performance based on an assumed second order response surface model, it is common to focus on a single optimality criterion, either G-optimality, for best worst-case prediction precision, or I-optimality, for best average prediction precision. In this article, we illustrate how using particle swarm optimization to construct a Pareto front of non-dominated designs that balance these two criteria yields some highly desirable results. In most scenarios, there are designs that simultaneously perform well for both criteria. Seeing alternative designs that vary how they balance the performance of G- and I-efficiency provides experimenters with choices that allow selection of a better match for their study objectives. We provide an extensive repository of Pareto fronts with designs for 17 common experimental scenarios for 2 (design size N = 6 to 12), 3 (N = 10 to 16) and 4 (N = 15, 17, 20) experimental factors. These, when combined with a detailed strategy for how to efficiently analyze, assess, and select between alternatives, provide the reader with the tools to select the ideal design with a tailored balance between G- and I-optimality for their own experimental situations.

Optimization of process parameters in machining of Inconel 718 super alloy on HMT (NH22) capstan lathe using genetic algorithm subject to minimization of surface roughness

Inconel 718 has been machined on HMT (NH22) capstan lathe following central composite design of experiment to develop the response surface model. The surface roughness has been predicted using a first order regression model by varying the cutting velocity, feed and depth of cut. The student’s t test and p-values have revealed that the depth of cut as well as combined effects of feed and depth of cut are significant process parameters. The second order response surface model has been developed to account the effect of curvature in predicting the surface roughness. The response surface plots reflect that the roughness of the Inconel workpiece varies largely with the variation in depth of cut and combination of feed and depth of cut. As a test of reliability Fisher’s F-test has been conducted. The F-test revels that the response surface model converges with the observed data reliably. A python code has been generated for genetic algorithm to optimise the process parameters by minimising the surface roughness. The results of the genetic algorithm have converged with the results of the confirmation run.

Parametric optimization of electroless Ni-P-CNT coating using genetic algorithm to maximize the rate of deposition

To improve the surface property of 99% pure copper substrate Electroless Ni-P-CNT coating was deposited. The effect of the elements of the coating bath on the rate of mass deposition has been examined and discussed in this study. The first order regression equation has been developed to predict the rate of deposited mass per unit area. The Student’s t test have exhibited that the concentrations of Nickel Sulphate, Sodium hypophosphite and the carbon nanotubes (CNT) significantly affect the rate of deposition of the electroless Ni-P-CNT coating. A response order response surface model has been developed to consider the effect of curvature in predicting the response. The response surface and counter plots reveal that the variations in concentration of the individual process parameters influence the deposition rate dramatically. The F-test has confirmed that the predicted response surface equation shows an excellent fitting with the observed data. The optimum concentrations of Nickel Sulphate, Sodium hypophosphite and carbon nanotubes in the coating bath have been evaluated using genetic algorithm to maximise the rate of deposition of electroless Ni-P-CNT composite coating. The results of the genetic algorithm are consistent with the results of the confirmation run.

Investigation and Mathematical Modelling of Optimized Cutting Parameters for Surface Roughness of EN-8 Alloy Steel

The work done in this work deals with the efficacy of cutting parameters on surface of EN-8 alloy steel. For knowing the optimal effects of cutting parameters response surface methodology was practiced subjected to central composite design matrix. The motive was to introduce an interaction among input parameters, i.e., cutting speed, feed and depth of cut and output parameter, surface roughness. For this, second order response surface model was modeled. The foreseen values obtained were found to be fairly close to observed values, showed that the model could be practiced to forecast the surface roughness on EN-8 within the range of parameter studied. Contours and 3-D plots are generated to forecast the value of surface roughness. It was revealed that surface roughness decreases with increases in cutting speed and it increases with feed. However, there were found negligible or almost no implication of depth of cut on surface roughness whereas feed rate affected the surface roughness most. For lower surface roughness, the optimum values of each one were also evaluated.

Optimizing air-frying process conditions for the development of healthy fish snack using response surface methodology under correlated observations.

Air frying technique was used for the preparation of fish cutlet-a popular fish snack with low fat content, better protein content and color. The process conditions viz: temperature varying from 160 to 200°C and time varying from 5 to 15min were optimized using response surface methodology. A factorial design with 9 runs satisfying rotatability conditions under correlated errors was formulated for the experiment. The parameters of first order response surface model with interaction were estimated by generalized least square method. The optimum temperature-time combination for air-frying condition was found to be 180°C and 12min, respectively for low fat content, better protein content and colour, comparable texture profile and sensory acceptability when compared to deep fried fish cutlet samples. Air-fried fish cutlets can be a healthier protein rich snack product as an alternative to deep fat fried fish cutlets.

Statistical modelling and optimization of microhardness transition through depth of laser surface hardened AISI 1045 carbon steel

The mechanical properties of laser surface hardened material are closely related to the hardened layer. Respective study of geometrical dimension and microhardness would only result in insufficient understanding of the hardened layer. In this paper, a central composite design (CCD) is proposed, based on response surface methodology (RSM), to investigate the influences of processing parameters including laser power (LP), scanning speed (SS) and defocusing distance (DD) on the geometrical dimensions, microhardness and microhardness transition of laser surface hardened AISI 1045 carbon steel. Two-tailed Pearson correlation of selected responses was firstly undertaken to screen out unrelated ones. Second order response surface models were then developed and tested for three responses: hardened width (HW), microhardness of hardened area (MH) and hardness gradient (HG). Scanning electron microscopy(SEM) was conducted to evaluate the evolution of microstructure with three process parameters. The results indicate that three response models are capable of interpreting the hardened width, microhardness and hardness gradient with satisfactory accuracy. It is observed that the HW is only linearly determined by LP and SS, while the hardness properties (MH and HG) are both affected by all the investigated parameters significantly. The hardness of base metal can be improved from 200HV to 660HV after laser surface hardening. Quadratic correlation can be obtained when the HG is transformed inversely. Validation experiment was finally conducted for testing the generalisation of fitted regression models. As the maximum relative prediction errors for three responses are respectively 4.18%, 2.25% and −4.36%, good generalisation has been accomplished by the developed models.

Response Surface Methodology in Application of Optimal Manufacturing Process of Axial-Flow Fans Adopted by Modern Industries

Response surface methodology (RSM) is a collection of mathematical and statistical techniques that help in model building and analysis of problems in which a response (output variable) of interest is influenced by numerous factors (independent variables) with the objective of optimizing this response. It is widely used in many disciplines such as Manufacturing Industries, Engineering and Agricultural Sciences. Different types of axial flow fans are being used in manufacturing industries in cooling mechanisms where a lot of heat is produce by the machines and in semi-arid and arid areas to regulate room temperatures. Though little research has been done to ascertain the strength of axial flow fans, there was need to study the optimal specifications of fans to be manufactured by industries to produce a more efficient, strong and long lasting cooling fan. This new focus from the manufacturers represents new quality fans that significantly increase market profitability. In this study, second order response surface model was used to estimate the axial-flow fan parameters. Three experimental factors or specifications were evaluated, that is; the hole type in the fan spyder (blades), the barrel surface type onto which the “spyder” was placed, and the assembly method type for the two components. Central composite designs satisfying all the rotatability conditions were constructed. The D- and A- optimal criteria were used to evaluate the effectiveness of the design. Secondary data was used to obtained second order optimal model for manufacturing process of axial-flow fans adopted by industries. The partial derivatives of the model were used to determine the stationary points of the response surface. Contour plots were used to determine whether the stationary were at maximum, minimum or saddle points. R statistical program was used in analysis of the data.

Design of experiment in analyzing uncertainty of simulation results in accident reconstruction

In order to obtain a more accurate interval of an accident reconstruction result, two modified experiment design methods were proposed. The first is based on the orthogonal design (OD) and it is named as the orthogonal-based design (OBD), while the other is based on the uniform design (UD) and it is named as the multi-response surface-uniform design (MUD). Furthermore, some conclusions are given according to seven numerical cases: results obtained from the Latin hypercube sampling design (LHS) are the worst, while those obtained from the UD are the last but one, and all are worse than the results obtained from the OBD and the MUD. Furthermore, some conclusions about the number of simulation runs of each design of experiment (DOE) can be given: if the second order response surface model is selected, the number of simulation runs of the LHS is the same as the UD, and all are lesser than the number of simulation runs of the OBD and the MUD in most cases. As for the OBD and the MUD, the number of simulation runs of the OBD is lesser than the number of simulation runs of the MUD, but the MUD can be applied more widely than the OBD. Finally, a true vehicle-pedestrian accident case is given, Pc-Crash was used to reconstruct the accident based on all traces provided by the police, and the interval of the impact velocity of the vehicle was calculated using the OBD, results showed that the research is meaningful in practice.

Effect of Process Factors on Pervaporation Dehydration of Isopropanol

The paper aimed at studying the performances of pervaporation separation of isopropanol-water system using a Pervatech ceramic membrane at various values of feed mixture flow rate (F=1000 kg/hr), feed water mass fraction (xF=0.1-0.2), operation temperature (t=60-90 �C), permeate pressure (pP=1000-9000 Pa) and water separation degree (sW=0.9, 0.95). Membrane total flux and separation factor were predicted applying a second order response surface model with 3 factors, i.e., xF, t and pP. An algorithm for estimating the membrane surface area was presented. Membrane area increased with sW and xF and its lowest values (A=13 m2 for xF=0.1 and A=24 m2 for xF=0.2) were attained for t=60 �C and pP=9000 Pa. These findings could be applied for optimizing the process of isopropanol dehydration by pervaporation.

Application of response surface methodology for modeling and optimization of Bacillus subtilis spores inactivation by the UV/persulfate process

Stronger disinfection techniques are required to inactivate Bacillus subtilis spores as surrogate microorganisms for Cryptosporidium parvum oocysts. In this study, the effects of UV and persulfate separately and also in combination were investigated on B. subtilis spore inactivation. Central composite design and response surface methodology were used to optimize target microorganism reduction. Contact time, initial pH, and persulfate dosage were considered as input experimental variables. Based on the design of the experiments, first and second order response surface models have been developed to correspond to the output response of B. subtilis spore reduction. It can be concluded that microbial reduction by UV alone was more effective than persulfate, while the combined UV/persulfate process demonstrated the highest log reduction (4.1) under the following optimal conditions: 60 min contact time, pH = 7.8, and persulfate dosage of 30 mM. On the other hand, the optimal condition for UV treatment was a contact time of 60 min at a pH of 5.0, which led to a 3.19 log spore inactivation. Consequently, the UV/persulfate system can be introduced as an alternative disinfectant for the inactivation of B. subtilis spores.

Extrusion Process Parameters Optimization for the Aluminum Profile Extrusion of an Upper Beam on the Train Based on Response Surface Methodology

Extrusion process parameters play key roles in aluminum profile extrusion processes. In this literature, by using Box-Behnken experimental design to arrange the simulations using the ALE software HypereXtrude, Response Surface Methodology (RSM) were applied to study the simulation results and discuss the effects of five process parameters, namely billet diameter, billet preheat temperature, die temperature, container temperature, and ram speed, on the outlet velocity distribution uniformity of the profile named an Upper beam on the Train. The interactions between the five parameters also were investigated. Additionally, a second order response surface model between the extrusion process parameters and the evaluation criterion of outlet velocity uniformity was established. An optimization of the process parameters with the purpose to find the most uniform outlet velocity distribution was carried out based on the response surface model. The results show that the three parameters, namely billet diameter, ram speed and die temperature, have significant impact on the outlet velocity uniformity. And there are obvious interactions between these three parameters. After the subsequent optimizations, a more uniform outlet velocity distribution was obtained, and the final acceptable profiles were produced.

Approximated optimum condition of second order response surface model with correlated observations

In the present paper we establish an inference procedure for the eigenvalues of the model matrix of the second-order response surface model (RSM). In contrast to the classical treatment where the sample are assumed to be independently distributed, in this work we do not need such distributional simplification. The confidence region for the unknown vector of the eigenvalues is derived by means of delta method. The finite sample behavior of the convergence result is discussed by Monte Carlo Simulation. We get the approximated distribution of the pivotal quantity of the population eigenvalues as a chi-square distribution model. Next we attempt to apply the method to a real data provided by a mining industry. The data represents the percentage of cobalt (Co) observed over the exploration region.

Statistical analysis of magnetorheological ball end finishing parameters using response surface methodology

Bidisperse magnetorheological polishing fluid (BMRPF) was used to gently finish work-piece surfaces on ball end magnetorheological finishing (BEMRF) tool. BMRPF was synthesised with optimum composition obtained by vibration sample magnetometer (VSM) test and magnetorheological characterisation which gives maximum magnetisation and yield behaviour. A five-levels three-factors central composite design of experiments (DOE) was used to develop an experimental plan for investigating process parameters' effect on percentage reduction in surface roughness (%ΔRs). Response surface methodology (RSM) was used to predict profile and surface roughness. Experiments were conducted on mild steel and surface roughness before and after experiments were measured. An effective second order response surface model for %ΔRs was obtained with significant factors and their interactions. Physical interpretation of process parameters' effect on %ΔRs was analysed and optimum values were obtained. Experiment was further conducted with optimum process parameters, and %ΔRs was calculated then compared with maximum %ΔRs obtained by regression model.

Rotatable Response Surface Designs in the Presence of Differential Neighbour Effects from Adjoining Experimental Units

ABSTRACT: In RSM, it is generally assumed that the observations are independent and there is no overlap effects from the neighbouring units. But in situations where the units are placed linearly side by side, there is a chance to have overlap effects/neighbour effects from the adjoining experiments units. For example, in field experiments if a chemical spray is applied to one plot, it may spread over to the nearby plots due to wind. Hence, the response from a particular plot may be afected by effects from the adjacent plots and this efect has to be included in the model while fitting RSM. In this paper, first and second order response surface models with diferential effects from adjoining left and right neighbouring units has been considered and the conditions for the model with diferential neighbour effects to be rotatable have been obtained. Method of obtaining designs satisfying the derived conditions has been described. An illustration to show the impact of including neighbour effects in the model on the parameter estimates has also been given using a simulated data set. These designs result in more precise estimates of the parameters of the response surface model.

Response surface methodology for optimization of fermentation process parameters for improving apple wine quality

Apple wine is a fermented alcoholic beverage made from apple juice. To ensure optimal apple wine processing performance and premium final product quality, an optimized selection of various parameters for apple wine fermentation process is imperative. This study is aimed at optimizing the fermentation process based on three primary fermentation parameters, including fermentation temperature, initial pH value and inoculum volume, to improve apple wine quality using response surface methodology (RSM) coupled with central composite rotatable design method (CCRD). Based on the experimental data analysis a second order response surface model was developed to describe the relationship between fermentation temperature, initial pH value, and inoculum volume with respect to the sensory score of apple wine. The results of analysis of variance (ANOVA) showed that the model established by response surface quadratic regression was adequate for predicting apple wine quality. It was observed that the quality of apple wine was significantly influenced by fermentation temperature (p ≤ 0.01), followed by initial pH value (p ≤ 0.01) and inoculum volume (p ≤ 0.01). The temperature of 20 °C, initial pH value of 3.6 and inoculum volume of 9 % were found to be the optimal fermentation condition for ensuring premium quality of apple wine.

Modeling the Sorption of Ni2+ and Co2+ on Saprist Peat Using the Response Surface Methodology

A detailed study of the sorption of Ni2+ and Co2+ from simulated wastewater on saprist peat is presented. The significantly decomposed peat possessed a strong sorptive capacity that was maintained over a wide range of pH. With a metal concentration range of 50 to 200 mg/L, pH range of 3 to 10, peat dose of 2 to 40 g/L, and contact time of 12 to 24 h, batch experiments were conducted based on a four-factor Box-Behnken response surface design. The percentage removals of Ni2+ and Co2+ were analyzed using analysis of variance. Second order response surface models were developed with the significant factors and their interactions to predict the percentage sorption of Ni2+ and Co2+ independently. The prediction equations were verified with additional data not used in developing the equations. The study showed that the saprist peat could be a potential industrial metal adsorbent and the percentage of uptake of Ni2+ and Co2+ could be accurately predicted using the second order response surface models developed. Ni2+ uptake was greater for the two metals and reached a maximum value at just below a neutral pH and Co2+ uptake continued to increase from pH > 5, with higher uptake percentage at pH 10.

Optimum selection of machining parameters in ball end magnetorheological finishing process

Ball end magnetorheological finishing (BEMRF) tool has been used to finish mild steel work-piece surface using sintered magnetic abrasives based magnetorheological polishing (MRP) fluid. A comparative study has been done on mild steel surface with synthesised and unbounded magnetic abrasives based MRP fluid. Then percent reduction in surface roughness (%∆Ra) was calculated and compared. The response %∆Ra was found superior while finishing with synthesised MRP fluid. A detailed study with five levels and three factors central composite design of experiments (DOEs) was done to develop experimental plan. Response surface methodology (RSM) was adopted to predict the profile and %∆Ra. An effective second order response surface model was developed with significant factors and their interactions. Physical interpretation of effect of machining parameters on %∆Ra was analysed and obtained optimum values. Then experiment was conducted with optimum machining parameters and %∆Ra was calculated and compared with maximum %∆Ra obtained by regression model.

Dispersive Liquid-Liquid Microextraction with Liquid Chromatography-Tandem Mass Spectrometry for the Determination of Triazine, Neonicotinoid, Triazole and Imidazolinone Pesticides in Mineral Water Samples

Mineral water is known for its high purity. Because mineral water is produced by the infiltration of water through the soil, there is the possibility of contamination with pesticides. The aim of this study was to develop a simple, rapid and efficient method for the extraction and preconcentration of different classes of pesticides in mineral water samples by dispersive liquid-liquid microextraction (DLLME) coupled with liquid chromatography tandem mass spectrometry. To optimize the DLLME conditions for the different classes of pesticides and access the effect of variables on the extraction, a central composite design (CCD) with a five-level fractional factorial design was used for the construction of a second order response surface model (RSM). The limits of quantification were between 0.005 and 0.5 μg L-1. Correlation coefficients (r) were higher than 0.999. Recoveries ranged from 102 to 120%, with relative standard deviations between 1 and 10%. Low matrix effect for all compounds was observed. The result showed that using a mixture of acetone and acetonitrile as disperser solvent and a mixture of chloroform and monochlorobenzene as extractor solvent, it is possible to employ the traditional DLLME with chlorinated solvents to extract the multiclass pesticides from the water samples.