Multi-response Problem Research Articles

Experimental investigation and multi response optimization of turning process parameters for Inconel 718 using TOPSIS approach

Multi response problems are the more frequent in optimization process and Taguchi technique developed for optimizing single response problem finds inappropriate for multi response optimization process. The optimum solutions are arrived in single response optimization process when the process terminates but in a multi response problems there can be finite number of optimal solutions are arrived during the optimization process. Multi objective optimization called Non-dominated Sorting Genetic Algorithm (NSGA-II) is used in this research work to obtain non-dominated solutions. However from these set of finite number of optimized solutions, it is always advisable to arrive a single solution. Multi criteria decision making, MCDM is used in this work. MCDM is an extraordinary technique which is used to select the optimum set of given finite numbers of alternatives. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) with Analytical Hierarchy Process (AHP) is a familiar method of MCDM technique method, which solves the decision making problem. Machining of Inconel 718 using carbide cutting tool with multi objective functions is carried out in this work. The mathematical models are obtained and NSGA-II are used to develop a set of non-dominated solutions for multi objective functions. Single solution is obtained using MCDM is used to evaluate and rank the machining conditions and gives a single solution from the set of optimized solution arrived using NSGA-II.

Designing a Hybrid Model of Data Envelopment Analysis with Taguchi Approach to Optimize Multiple Response Banks Performance

Many organizations (including banks) have a multi-step process and their operations are a continuous process in successive periods. The Taguchi method is an efficient way to optimize a single quality response. However, in practice most products / processes have more than one qualitative response. Recently, the multi-answer question in the Taguchi method has attracted considerable research attention. Therefore, this study presents an efficient approach to multi-response problem solving in Taguchi method using hybrid data envelopment analysis (DEA) model. Each experiment is discussed in the Taguchi Orthogonal Array (OA) as a decision unit (DMU) with multiple input and / or output response sets. Each DMU is evaluated by a hybrid model. The sequential DUM productivity value is then used to decide the optimal factor levels for the multi-response problem. The computational results showed that the proposed approach provides the most anticipated improvement in PCA, DEA (DEAR) and other available techniques. The suggestion may be of great help to managers in solving multi-response problems in production programs in the Taguchi method. Many organizations (including banks) have a multi-step process and their operations are a continuous process in successive periods. The Taguchi method is an efficient way to optimize a single quality response. However, in practice most products / processes have more than one qualitative response. Recently, the multi-answer question in the Taguchi method has attracted considerable research attention. Therefore, this study presents an efficient approach to multi-response problem solving in Taguchi method using hybrid data envelopment analysis (DEA) model. Each experiment is discussed in the Taguchi Orthogonal Array (OA) as a decision unit (DMU) with multiple input and / or output response sets. Each DMU is evaluated by a hybrid model. The sequential DUM productivity value is then used to decide the optimal factor levels for the multi-response problem. The computational results showed that the proposed approach provides the most anticipated improvement in PCA, DEA (DEAR) and other available techniques. The suggestion may be of great help to managers in solving multi-response problems in production programs in the Taguchi method.

Central Composite Experimental Designs for Multiple Responses With Different Models

ABSTRACTCentral composite designs (CCDs) are widely accepted and used experimental designs for fitting second-order polynomial models in response surface methods. However, these designs are based only on the number of explanatory variables being investigated. In a multiresponse problem where prior information is available in the form of a screening experiment or previous process knowledge, investigators often know which factors will be used in the estimation of each response. This work presents an alternative design based on CCDs that allows main effects to be aliased for factors that are not related to the same response. This results in fewer required runs than current designs, saving investigators both time and money, by taking this prior information into account. R-package “DoE.multi.response” is included as a supplement for constructing these designs.

Integration of RSM with Grey based Taguchi Method for optimization of pulsed TIG welding process parameters

Abstract This research paper focused on process parameters optimization of Tungsten Inert Gas (TIG). Taguchi method is very effective and efficient to solve the process parameter optimization problem to the find optimum processing parameter, but it is found that the traditional Taguchi method is not sufficient to solve the problem with multi response problem to get optimum results and to meet the global challenges of the manufacturer as it is impractical to obtain more than one optimal processing parameter through Taguchi. In order to survive in the global market it is necessary to used advanced and modified optimization techniques. To intensify the efficiency of Taguchi method, it is absolutely necessary to integrate it with the other optimization approach. However, it is important to integrated Taguchi method with Grey Retion Analysis (GRA) to solve multi response optimizaton promblem futher Taguchi method is integrated with Response Surface Methodology (RSM) to determine optimum value of each parameters. Using orthogonal array L9 experiments were performed. Experimental data are used to obtain signal to noise ratio by using Minitab18 and then response surface plot is developed to obtain optimum level for every input parameter. Further, the process is integrated with RSM to developed mathematical model by using design expert 11 statistical software through full-factorial central composite design (CCD). RSM is a useful statistical tool for process optimization to obtain the required quality of weld. The Surface plot obtained from Design Expert Software 11 represent that the actual value of response i.e. depth of penetration (DOP) and width of penetration (WOP) versus the predicted value of response are close to each other. The higher value of DOP and WOP represents higher strength; analysis of variance (ANOVA) gives the highest value of F-ratio of welding speed in DOP and WOP, this result obtained from RSM showed that welding speed is the most influencing parameter which affects response characteristics.

Performance evaluation in CNC turning of AA6063-T6 alloy using WASPAS approach

PurposeSurface roughness and vibration during machining are inevitable which critically affect the product quality characteristics. This paper aims to suggest the implementation of a multi-objective optimization technique to obtain the favorable parametric conditions which lead to minimum tool vibration and surface roughness of 6063-T6 aluminum alloy in computer numerically controlled (CNC) turning.Design/methodology/approachThe case study has been accomplished according to response surface methodology RSM’s Box–Behnken design (BBD) matrix using Titanium Nitride-coated Tungsten Carbide insert in a dry environment. As the experimental results are quite nonlinear, a second-order regression model has been developed for the responses (surface roughness and tool vibration) in terms of input cutting parameters (spindle speed, feed rate and depth of cut). The goodness of fit of the models has also been verified with analysis of variance (ANOVA) results.FindingsThe significance efficacy of input parameters on surface roughness and tool vibrations has been illustrated through multi-objective overlaid 3D surface plots and contour plots. Finally, parametric optimization has been performed to get the desired response values under the umbrella of weighted aggregate sum product assessment (WASPAS) method and verified confidently with confirmatory test results.Originality/valueThe results of this study reveals that hybrid RSM with WASPAS method can be readily applicable to optimize multi-response problems in the manufacturing field with higher confidence.

A novel robust multivariate regression approach to optimize multiple surfaces

Response surface methodology involves relationships between different variables, specifically experimental inputs as controllable factors, and a response or responses by incorporating uncontrollable factors named nuisance. In order to optimize these response surfaces, we should have accurate response models. A common approach to estimate a response surface is the ordinary least squares (OLS) method. Since OLS is very sensitive to outliers, some robust approaches have been discussed in the literature. Most problems face with more than one response which are mostly correlated, that are called multi-response problem. This paper presents a new approach which takes the benefits of robust multivariate regression to cope with the mentioned difficulties. After estimating accurate response surfaces, optimization phase should be applied in order to have proper combination of variables and optimum solutions. Global criterion method of multi-objective optimization has also been used to reach a compromise solution which improves all response variables simultaneously. Finally, the proposed approach is described analytically by a numerical example.

Optimization of Process Productivity for Multi Phase Carbon Nanotubes (CNT) Reinforced Nanocomposites Using Taguchi-Fuzzy Model

The present work is focused on the processing and machining of multiphase carbon nanotubes reinforced nanocomposites. In this work the author has performed electric discharge machining on multiphase carbon nanotubes reinforced nanocomposites. Optimal combination of different process parameters have been decided determined for maximum material removal rate and minimum tool wear rate which results the improvement in productivity of the complete process. In this study four different process parameters (Peak current, gap voltage, pulse on time and duty cycle) are used and the most significant parameter is illustrated. In the present work, the factor material removal rate has been considered as productivity measure. The goal is to determine the best process condition for maximizing material removal rate and simultaneously for minimizing the tool wear rate values, which may be considered as multi-response optimization problem. Taguchi method is a well known optimization technique used for optimizing the single objective function. Consequently the conversion process of objective functions invites ambiguity, uncertainly etc. into the computation. These implications always arises the need to correlate various responses. Hence to overcome these implications a fuzzy reasoning of multiple performance characteristics has been developed. This results in the transformation of multi performance characteristics in single multi-performance characteristics (Productivity) and can be optimized using Taguchi method. Using Taguchi’s design of experiment methodology optimal combination of process parameters will be obtained for various performance measures. Process productivity Optimize using the Fuzzy logic approach and the optimal results were also validated.

Machining of fluidic channels on borosilicate glass using grinding-aided electrochemical discharge engraving (G-ECDE) and process optimization

Electrochemical discharge machining (ECDM) has already been identified as a novel process for machining advanced ceramics and glass. The major limitations of this process are high overcut of the machined channels and the difficulty in controlling the roughness of the channel. This paper presents a novel technique which uses diamond-impregnated engraving tool as the tool electrode for machining accurate and smooth channels on borosilicate glass using ECDM. This technique can be called as grinding-aided electrochemical discharge engraving (G-ECDE). The new method utilizes both the grinding action of diamond grits and the thermal and chemical effects of ECDM for material removal. Preliminary experiments are performed using Placket–Burman design with center points to study the effect of machining parameters like voltage, electrolyte concentration, pulse-on time, tool rotational speed and tool feed rate on channel overcut and surface roughness of the channel. With the significant factors identified from the preliminary experiment, the main experiment was performed using a widely used response surface design called Box–Behnken design to develop second-order response models for surface roughness and channel overcut. Response surface plots are used to identify the effect of parameters and their interactions on the responses. Technique for order preference by similarity to ideal solution (TOPSIS) is used to optimize this multi-response problem. The optimum factor levels obtained from TOPSIS are a medium feed of 2 mm/min, a low voltage of 80 V, a medium pulse-on time of 0.0011 s and a low concentration of 2 M which produced channels with a surface roughness of 0.872 μm and overcut of 0.293 mm. From the microscopic images of machined channels, material removal mechanisms of G-ECDE are confirmed to be a combination of thermal melting due to electrochemical discharges, grinding action of diamond grits and high-temperature chemical etching action of the electrolyte. The performance of G-ECDE is compared with die-sinking ECDM and electrochemical discharge milling for producing channels and found that G-ECDE is the most suitable process to produce fluidic channel on glass which is free from recast layer and heat-affected zone. The results obtained from this study proved the potential of G-ECDE in producing smooth, accurate and complex fluidic channels on the glass.

Optimisation of machining parameters on milling of GFRP composites by desirability function analysis using Taguchi method

Milling of GFRP composite materials is a rather complex task owing to its heterogeneity and the number of problems, such as surface delamination, which appear during the machining process, associated with the characteristics of the material and the cutting parameters. Optimization of machining parameters is an important step in machining. This paper presents a new approach for optimizing the machining parameters on milling glass-fibre reinforced plastic (GFRP) composites. Optimization of machining parameters was done by an analysis called desirability function analysis (DFA), which is a useful tool for optimizing multi-response problems. In this work, based on Taguchi’s L27 orthogonal array, milling experiments were conducted for GFRP composite plates using solid carbide end mills with different helix angles. The machining parameters such as, spindle speed, feed rate, helix angle and fibre orientation angle are optimized by multi-response considerations namely surface roughness, delamination factor and machining force. A composite desirability value is obtained for the multi-responses using individual desirability values from the desirability function analysis. Based on composite desirability value, the optimum levels of parameters have been identified, and significant contribution of parameters is determined by analysis of variance.Keywords: GFRP composites; Taguchi; Desirability function analysis; ANOVA; Solid carbide end mill

A robust posterior preference multi-response optimization approach in multistage processes

ABSTRACTNowadays, many manufacturing and service systems provide products and services to their customers in several consecutive stages of operations, in each of which one or more quality characteristics of interest are monitored. In these environments, the final quality in the last stage not only depends on the quality of the task performed in that stage but also is dependent on the quality of the products and services in intermediate stages as well as the design parameters in each stage. In this paper, a novel methodology based on the posterior preference approach is proposed to robustly optimize these multistage processes. In this methodology, a multi-response surface optimization problem is solved in order to find preferred solutions among different non dominated solutions (NDSs) according to decision maker's preference. In addition, as the intermediate response variables (quality characteristics) may act as covariates in the next stages, a robust multi-response estimation method is applied to extract the relationships between the outputs and inputs of each stage. NDSs are generated by the ϵ-constraint method. The robust preferred solutions are selected considering some newly defined conformance criteria. The applicability of the proposed approach is illustrated by a numerical example at the end.

Role of multi-response principal component analysis in reliability-based robust design optimization: an application to commercial vehicle design

The Taguchi method is a widely used conventional approach for robust design that combines experimental design with quality loss functions. However, this method can be only used in a single-response problem. In this study, we propose the use of principal component analysis (PCA) to consider multi-response problems in the Taguchi method and to investigate the influence factor of a cab suspension system. We compute the normalized quality loss for each response and perform PCA to calculate the multi-response performance index. In this study, control factors with three level combinations and noise factors with random sampling from each normal distribution are considered. Additionally, we applied multi-objective reliability based robust design optimization (RBRDO) to accommodate design uncertainties and its data scattering based on rational probabilistic approaches. This is used to develop the reliability assessment and reliability based design optimization and corresponds to an integrated method that accounts for the design robustness in the objective function and reliability in the constraints.

Parametric Optimization of E-Jet Based Micro Manufacturing System through Hybrid Taguchi Methodology

Electrohydrodynamic inkjet (E-Jet) printing is a non-contact mask less additive fabrication technology to print wide variety of functional materials in micro/nano scale. The material wastage in this manufacturing technology is almost avoided, which is the upmost importance while patterning highly expensive material. The printing performance depends on several process operational variables like applied voltage, stand-off height, nozzle diameter, applied pressure etc. By tuning these process variables through optimization route improved printing performance can be achieved. In this present study, an attempt has been made to optimize the printing performance characteristics namely, printed droplet diameter and ejection frequency with the help of Weighted Principle Component Analysis (WPCA) coupled with Taguchi methodology. Applied voltage between the nozzle and the substrate, applied pressure to the ink chamber, and the nozzle stand-off height taken as process parameters which are to be tuned. WPCA convert the multi-response problem into single objective problem, thus enabling the employability of Taguchi’s robust design approach and also the correlation among the responses if exists well taken care of. The study proposes favorable operational condition of the process and also highlighted the features of the proposed synergistic combination of WPCA with Taguchi method for predicting the optimal setting of process parameters.

Multi-quality Response Optimization of Wire EDM for Ni-75 using PCA based Utility theory

WEDM is a stochastic process in which large numbers of control parameters are involved. It is very critical to select the right combination of these parameters to maximize MRR and minimize surface roughness and overcut. To manufacture quality products at minimum cost, optimization is one of the methods that can be applied to achieve best manufacturing conditions. The aim of this study is the application of PCA based utility theory for multi-quality response optimization while WEDM of Nimonic-75 alloy. The control parameters selected for the study are on-time, off-time, discharge voltage, discharge current, wire feed rate and wire tension. Experiments were designed by applying Taguchi’s L27 orthogonal arrangement. PCA based utility theory was used to convert the multi-response problem into a single objective function (overall utility index). The optimal settings of control parameters were found as: On time = 114 μs, Off-time = 51μs, Discharge voltage = 20 volts, Discharge current = 200 Amp, Wire feed rate = 5 m/min and Wire tension = 2 gram.

Application of utility concept approach for multi-response optimisation of wire electrical discharge machining during profile cutting of Inconel-625

This research study investigates the effects of machining factors such as on pulse-on time, pulse-off time, servo voltage, peak current, wire feed rate and wire tension on kerf widths at different locations on the profile, i.e., at straight cut, at an angle 90°, 70° and 30° along with surface roughness, overcut, MRR and surface topography of the machined surface while WEDM of Inconel-625. Taguchi's L27 orthogonal design was applied for the planning of experiments. The utility concept was used to translate the multi-response problem into a single equivalent response called overall utility index. Pulse on time was observed as the prime factor affecting the overall utility index. Surface topography of the machined samples shows craters, debris deposited on the machined surface and micro-cracks. This paper reports machining of the complex profile on Inconel-625 and optimisation of machining factors which will be helpful for the manufacturing industries to manufacture complex patterns.

Worst-case Responses Estimate Impact on Pareto Front

For a reasoned decision-making in multiresponse problems, it is important to investigate how consistent the Pareto Frontier is to responses estimation uncertainty. To investigate the impact of this uncertainty source on the Pareto frontier, solutions achieved from the worst and mean responses estimate were generated and compared. Results are displayed graphically and a metric is used to select an optimal solution.

Optimization of Multi-response Problems with Continuous Functional Responses by considering dispersion effects

In some processes, quality of a product should be characterized by functional relationships between response variables and a signal factor. Hence the traditional methods cannot be used to find the optimum solution. In this paper, we propose a method which considers two different dispersion effects, i.e. in domain and between replicates variations in the functional responses. Besides, we propose an integral based measure to find the deviation from t

A multiresponse model for reliability‐based simulation optimization in systems subjected to random external stresses

AbstractSystems with multiple output characteristics are very difficult to optimize, especially where outputs are interrelated and some external factors affect their performance. In many systems, some correlations and/or conflicts exist between performance measures. Multiple response optimization is a mathematical‐statistical technique that helps experts improve all the system's outputs, simultaneously. The present work aims to derive a stress‐strength reliability measure for multiresponse problems, so the strength criteria of a system are optimized against external stresses. To achieve this purpose, multivariate normal‐normal stress‐strength models are developed and applied for optimization of (s, S) inventory systems in which demands and lead times are random. At the end, a numerical example is also studied to illustrate the efficacy of the proposed approach.

Parametric optimization for performance and emissions of DI diesel engine with Mahua biodiesel along with Diethyl ether as an additive

ABSTRACTIn this work an attempt is made to optimize the performance and emission characteristics of a direct-injection diesel engine fuelled with Mahua methyl ester and Diethyl ether as an additive, with two input parameters (load and fuel) and for nine response parameters (exhaust gas temperature, brake specific fuel consumption and brake thermal efficiency, and emissions of hydrocarbons, carbon monoxide, carbon dioxide, oxygen, nitrogen oxides and smoke). In order to find out the optimal response, a set of experiments was conducted. Grey relational analysis was applied to the experimental results to determine the optimal combination of load and fuel, by converting the multiresponse problem into the single response problem with the help of grey relational grade. Signal-to-noise ratio and grey relational grade are used as a performance index, and a combination of input parameters were predicted. Finally, for validation, response surface methodology is used to obtain a desirability approach which is used in turn to find the optimal combinations. It was observed that Mahua methyl ester +10% Diethyl ether as the fuel at 30 kg load is an optimal solution.

Optimization of problems with multivariate multiple functional responses: A case study in air quality

ABSTRACTOptimization of multi-response problems is a popular subject in the literature. However, the problem becomes complicated when the responses are functional due to the existence of signal factors. In this article, we have proposed a combined index to optimize multivariate multiple functional responses by considering functional specification limits and a target. The relation among the responses and controllable factors is characterized by polynomial equations to consider the curvature of the response functions. The validity of the proposed method is checked by a simulation example. To show the applicability of the proposed method, a real case about Tehran air quality is analyzed. Latitude and longitude are considered to be signal factors, and different pollutant values are responses of the experiment. Government policies in each time interval are considered as controllable factors. Finally, an optimization algorithm is used to find the best decisions for government policies.

Multi-response optimization of post-fire performance of strain hardening cementitious composite

This paper presents results of an experimental program conducted to optimize the post-fire performance of Strain Hardening Cementititous Composites (SHCC) using Taguchi approach with utility concept. The experiments were first undertaken by determining nine SHCC mixes using a standard L9 (34) orthogonal array of four parameters and each parameter with three levels. The four parameters of SHCC mixes included fly-ash/binder ratio, sand/binder ratio, water/binder ratio and fiber proportions. The responses of SHCC to be optimized were tensile strain capacity, compressive strength and post-fire compressive strength after subjected to 200 °C, 400 °C, 600 °C and 800 °C of isothermal heating. Utility concept was introduced to simplify the multi-response problem into mono-response question together with Taguchi method. The role of different parameters on the composite responses of SHCC was examined. Furthermore, an optimal SHCC mix to maximize multi-responses was determined based on statistical analysis and validated by additional confirmation tests.