Entropy Measurement Technique Research Articles

Optimization of machining parameters during end milling of super alloys using Grey based Taguchi method coupled with entropy measurement technique

Optimization of machining parameters during end milling of super alloys using Grey based Taguchi method coupled with entropy measurement technique

Optimization of a two degrees of freedom compliant mechanism using Taguchi method-based grey relational analysis

This paper presents a multi-response optimal design for new two degrees of freedom compliant mechanism (TDCM) by the use of the hybrid statistical optimization techniques such as Taguchi method, response surface methodology, grey relational analysis and entropy weighting measurement technique. The design parameters like various thicknesses of flexure hinges play a vital role in determining its quality characteristics of TDCM. The quality characteristics of TDCM are assessed by measuring the displacement and first natural frequency. The experimental trials are designed by the Taguchi’s L25 orthogonal array. A hybrid approach of grey-Taguchi based response surface methodology and entropy measurement is then combined to maximize both the displacement and first natural frequency simultaneously. Response surface methodology is utilized for modeling the relationship between design parameters and two responses with grey relational grade. Entropy measurement technique is employed for calculating the weight corresponding to each of quality characteristics. Analysis of variance (ANOVA) is conducted to determine the significant parameters affecting the responses. ANOVA and confirmation tests are conducted to validate the prediction accuracy and the statistical adequacy of the developed mathematical models. The experimental results were in a good agreement with the simulation results from ANSYS. The proposed methodology is expected to use for related micropositioning compliant mechanisms.

Application of entropy measurement technique in grey based Taguchi method for optimization of MIG welding process parameters

We seldom realized that without this form of metal work, many structures would cease to be in existence. A skilled journeymen welder joins metal in such a way that it is not able to be parted unless it is cut. Welding is an absolutely essential technique used in various industries like automotive industry, construction industry as well as in the aviation industry. Hence welding process parameters are required to be optimized for their responses or welding characteristics. This study incorporates entropy measurement technique based on grey Taguchi method to analyze multiple quality characteristic optimization of metal inert gas welding of low carbon steel plates. For this study, four control variables are selected current, voltage, gas flow rate and wire feed rate and analysing their effect on the four quality characteristics ultimate tensile strength, elongation %, bending strength and hardness of the weldments have been investigated in this paper. In order to optimize the multiple quality characteristic of the MIG welding, grey relational analysis coupled with entropy measurement method has been employed. Using entropy measurement method, value of weight corresponding to each quality characteristic has been assigned, so that the importance can be properly determined. Using the theory of grey relational analysis, these have been accumulated to calculate the overall grey relational grade. Signal to Noise ratio (S/N ratio) is applied to find the optimal parameter setting. To determine the contribution of MIG welding process parameters, Analysis of variance (ANOVA) on grey relational grade has been calculated. The confirmatory test also has been done for verifying the results. A foresaid methodology has been found fruitful in the cases where simultaneous optimization of huge number of responses is required.Keywords: Metal Inert Gas (MIG) Welding, Grey-Taguchi Method, Entropy Measurement Technique, Analysis of variance (ANOVA), S-N ratio.

Multi-objective Optimal Design of a 2-DOF Flexure-Based Mechanism Using Hybrid Approach of Grey-Taguchi Coupled Response Surface Methodology and Entropy Measurement

A large displacement and a high first natural frequency are two main concerns for any flexure-based positioning system. A two-degree-of-freedom (DOF) flexure-based mechanism (FBM) with a modified double-lever amplification mechanism is first designed. This study then proposes a multi-objective optimal design of the 2-DOF FBM using the hybrid approach of grey-Taguchi coupled response surface methodology and entropy measurement. The design variables of the 2-DOF FBM include the thickness of the flexure hinges and the length of lever amplification, both of which play vital roles in determining quality responses. The quality responses of the 2-DOF FBM are assessed by measuring the displacement and first natural frequency. The experimental plan is carried out using the Taguchi \({L_{25}}\) orthogonal array. An integrated approach of grey-Taguchi- based response surface methodology and entropy measurement is then applied for the multi-objective optimization of the 2-DOF FBM. To illustrate the relation between the design variables and the output responses, mathematical regression models are developed. The entropy measurement technique is applied to calculate the weight factor corresponding to each response. Then, an analysis of variance (ANOVA) is conducted to determine the significant parameters affecting the responses. In addition, the ANOVA and experimental validations are conducted to validate the statistical adequacy and the prediction accuracy of the developed mathematical models, respectively. The results reveal that the regression models have good statistical adequacy and excellent prediction accuracy. The confirmation results of the grey relational grade fall within 95 % of the confidence interval. It is strongly believed that the proposed approach has great potential for the optimal design of related flexure-based mechanisms.

A Parametric Optimization of FSW Process Using RSM Based Grey Relational Analysis Approach

Age-hardenable aluminum alloys, primarily used in the aerospace, automobile and marine industries (2xxx, 6xxx and 7xxx), can be welded using solid-state welding techniques. Friction stir welding is an emerging solid-state welding technique used to join both similar and dissimilar materials. The strength of a friction stir welded joint depends on the joining process parameters. Therefore, a combination of the statistical technique called response surface methodology (RSM) based grey relational analysis (GRA) coupled with entropy measurement technique was proposed to select the process parameters suitable for joining AA 2024 and AA 6061 aluminum alloys via friction stir welding (FSW). The significant process parameters, such as rotational speed (N), welding speed (F), axial load (P) and pin shapes (PS), were considered during the statistical experiment. The results indicate the square (SQ) pin shape plays a vital role and yields an ultimate tensile strength of 141 MPa for an elongation of 12% versus cylinder (CY) and taper (TA) pin profiles. The root cause for joint strength loss and fracture mode was analyzed using scanning electron microscopy (SEM). Severe material flow leads macro defects such as pinholes and porosity degrades the joint strength by approximately 44% for AA 2024 and 51% for AA 6061 fabricated FS-welded aluminum alloys relative to the base material. The results for this approach are useful for accurately controlling the response and optimize the process parameters

Application of Entropy Weight Technique in Grey Relational Analysis for Scheme Optimization of Sewage Treatment Plant

In this paper, an attempt has been made to apply an efficient technique, in order to solve the uncertainty of multi-objective optimization, in the field of sewage treatment plant. The traditional grey relational analysis has been extended to deal with the multi-objective optimization problems. The difficulty of traditional grey relational analysis exists in calculation of the multiple indicators and ignorance of the relationship among evaluating indicators. But there is no specific guideline for assigning these indicator weights. In this context, the present study aims to apply the entropy measurement technique in order to determine the weights of evaluating indicators, which avoids the subjectivity in the process of estimating the weights. The proposed method involves four steps, including 1) original data processing, 2) grey relational coefficients calculation, 3) indicator weight calculation, and 4) grey relation grade calculations. The previously mentioned method has been applied to optimize schemes of a sewage treatment plant. The paper demonstrates a detailed methodology of the proposed technique as well as its effectiveness and applicability.

USE OF DESIRABILITY FUNCTION AND PRINCIPAL COMPONENT ANALYSIS IN GREY-TAGUCHI APPROACH TO SOLVE CORRELATED MULTI-RESPONSE OPTIMIZATION IN SUBMERGED ARC WELDING

Submerged arc welding (SAW) is an important metal fabrication technology specially applied to join metals of large thickness in a single pass. In order to obtain an efficient joint, several process parameters of SAW need to be studied and precisely selected to improve the bead quality. Many methodologies have been proposed in the past research to address this issue. However, a good number of past works seek to optimize SAW process parameters with only one response. In practical situations, not only influence of process parameters and their interactive effects on output responses are to be critically examined but also attempt is to be made to optimize more than one response simultaneously. To this end, the present study considers four process control parameters viz. voltage (OCV), wire feed rate, traverse speed and electrode stick-out. The selected weld quality characteristics related to features of bead geometry are depth of penetration, reinforcement and bead width. An integrated approach capable of overcoming the drawbacks of traditional optimization approaches has been suggested and results thereof analyzed. The proposed approach explores Orthogonal Array (OA) experiments for adaptation to grey-Taguchi method. Principal Component Analysis (PCA) has been used to convert correlated response values into uncorrelated quality indices called principal components. Based on desirability loss, grey relational coefficients of each quality indices have been calculated. These coefficients have been further accumulated to calculate overall grey relational grade. Individual response weights have been calculated using entropy measurement technique. Finally, Taguchi method has been adopted for optimization purpose. The study finally demonstrates the robustness and flexibility of the integrated approach in solving multi-criteria optimization problem in SAW process.

Solution of Correlated Multi-Response Optimization Problem

This paper highlights an integrated approach to solve the correlated multi-response optimization problem through a case study in submerged arc welding (SAW). The proposed approach has been presented to overcome different limitations and drawbacks of existing optimization techniques available in literature. Traditional Taguchi optimization technique is based under the assumption that quality responses are independent to each other; however, this assumption may not always be valid. A common trend in the solution of a multi-objective optimization problem is to convert these multi-objectives into an equivalent single objective function. While deriving this equivalent objective function, different weightage are assigned to different responses according to their relative priority. In this regard, it seems that no specific guideline is available for assigning individual response weighs. To avoid this, Principal Component Analysis (PCA) has been adopted to eliminate correlation among individual desirability values and to calculate uncorrelated quality indices that have been aggregated to calculate overall grey relational grade. This study combines PCA, Desirability Function (DF) approach, and grey relation theory to the entropy measurement technique. Finally, the Taguchi method has been used to derive optimal process environment capable of producing desired weld quality related to bead geometry.

Parametric optimization of CNC end milling using entropy measurement technique combined with grey-Taguchi method

End milling is the most important milling operation, widely used in most of the manufacturing industries due to its capability of producing complex geometric surfaces with reasonable accuracy and surface finish. However, with the inventions of CNC milling machine, the flexibility has been adopted along with versatility in end milling process. In order to build up a bridge between quality and productivity and to achieve the same in an economic way, the present study highlights optimization of CNC end milling process parameters to provide good surface finish and high material removal rate (MRR). The surface finish of the machined surface has been identified as quality attribute whereas MRR has been treated as performance index directly related to productivity. Attempt has been made to optimize quality and productivity in a manner that these multi-criterions could be fulfilled simultaneously up to the expected level. This has invited a multi-objective optimization problem which has been solved by Taguchi method coupled with grey relational analysis. Depending on relative importance, the priority weights of individual quality and performance attributes have been estimated by entropy measurement technique. Multi-objectives related to quality and productivity has been accumulated to evaluate an equivalent single quality index (called grey relational grade); which has been optimized finally by Taguchi method. Application feasibility of the aforesaid optimization technique has been illustrated in this reporting. Keywords: CNC end milling, surface finish, material removal rate (MRR), entropy measurement technique, Taguchi method

Application of entropy measurement technique in grey based Taguchi method for solution of correlated multiple response optimization problems: A case study in welding

In the present work, an attempt has been made to apply an efficient technique, in order to solve correlated multiple response optimization problems, in the field of submerged arc welding. The traditional grey based Taguchi approach has been extended to tackle correlated multi-objective optimization problems. The Taguchi optimization technique is based on the assumption that the quality indices (i.e. responses) are independent or uncorrelated. But, in practical cases, the assumption may not be valid always. However, the common trend in the solution of multi-objective optimization problems is to initially convert these multi-objectives into an equivalent single objective function. While deriving this equivalent objective function, different priority weights are assigned to different responses, according to their relative importance. But, there is no specific guideline for assigning these response weights. In this context, the present study aims to apply the entropy measurement technique in order to calculate the relative response weights from the analysis of entropy of the entire process. Principal Component Analysis (PCA) has been adopted to eliminate correlation that exists among the responses and to convert correlated responses into uncorrelated and independent quality indices, called principal components. These have been accumulated to calculate the overall grey relational grade, using the theory of grey relational analysis. Finally, the grey based Taguchi method has been used to derive an optimal process environment capable of producing the desired weld quality. The previously mentioned method has been applied to optimize bead geometry parameters of submerged arc bead-on-plate weldment. The paper highlights a detailed methodology of the proposed technique and its effectiveness.

Application of entropy measurement technique in grey based Taguchi method for optimization of MIG welding process parameters

We seldom realized that without this form of metal work, many structures would cease to be in existence. A skilled journeymen welder joins metal in such a way that it is not able to be parted unless it is cut. Welding is an absolutely essential technique used in various industries like automotive industry, construction industry as well as in the aviation industry. Hence welding process parameters are required to be optimized for their responses or welding characteristics. This study incorporates entropy measurement technique based on grey Taguchi method to analyze multiple quality characteristic optimization of metal inert gas welding of low carbon steel plates. For this study, four control variables are selected current, voltage, gas flow rate and wire feed rate and analysing their effect on the four quality characteristics ultimate tensile strength, elongation %, bending strength and hardness of the weldments have been investigated in this paper. In order to optimize the multiple quality characteristic of the MIG welding, grey relational analysis coupled with entropy measurement method has been employed. Using entropy measurement method, value of weight corresponding to each quality characteristic has been assigned, so that the importance can be properly determined. Using the theory of grey relational analysis, these have been accumulated to calculate the overall grey relational grade. Signal to Noise ratio (S/N ratio) is applied to find the optimal parameter setting. To determine the contribution of MIG welding process parameters, Analysis of variance (ANOVA) on grey relational grade has been calculated. The confirmatory test also has been done for verifying the results. A foresaid methodology has been found fruitful in the cases where simultaneous optimization of huge number of responses is required.Keywords: Metal Inert Gas (MIG) Welding, Grey-Taguchi Method, Entropy Measurement Technique, Analysis of variance (ANOVA), S-N ratio.