A Hybrid Optimization Approach of Single Point Incremental Sheet Forming of AISI 316L Stainless Steel Using Grey Relation Analysis Coupled with Principal Component Analysiss

We investigated the parametric optimization on incremental sheet forming of stainless steel using Grey Relational Analysis(GRA) coupled with Principal Component Analysis(PCA). AISI 316L stainless steel sheets were used to develop double wall angle pyramid with aid of tungsten carbide tool. GRA coupled with PCA was used to plan the experiment conditions. Control factors such as Tool Diameter(TD), Step Depth(SD), Bottom Wall Angle(BWA), Feed Rate(FR) and Spindle Speed(SS) on Top Wall Angle(TWA) and Top Wall Angle Surface Roughness(TWASR) have been studied. Wall angle increases with increasing tool diameter due to large contact area between tool and workpiece. As the step depth, feed rate and spindle speed increase,TWASR decreases with increasing tool diameter. As the step depth increasing, the hydrostatic stress is raised causing severe cracks in the deformed surface. Hence it was concluded that the proposed hybrid method was suitable for optimizing the factors and response.

Application of Grey Correlation Degree Analysis in Broad Bean Strain Screening

[Objectives] The aim was to clarify the target and approach to purifying and selecting Baoshan Touxinlv broad bean. [Methods] In 2012,5 homozygous strains were selected successfully as the material,and completely randomized block arrangement was adopted with 3 repeated trials to analyze the effects of plant height,effective length of podding branches,branch number per plant,pod number per plant,grain number per pod and 100-grain weight on the yield of each plant in the system. [Results] The results showed that the effects of the various factors on the yield of Baoshan broad beans were in the order of grain number per pod 〉 effective length of podding branches 〉 100-grain weight 〉 pod number per plant 〉 branch number per plant 〉 plant height. [Conclusions]In breeding new strains of Baoshan broad beans,under the premise of ensuring the seed nature and quality of the original variety,priority should be given to the gain number per pod and the increment of effective length of podding branches,followed by the pod number per plant,branch number per plant,plant height,which is the best way to breed new strains of Baoshan Touxinlv broad beans.

Application of Grey-correlated Spectral Region Selection in Analysis of Near-infrared Spectra

The optimal selection method of spectral region based on the grey correlation analysis was applied in the analysis of near-infrared（NIR） spectra. In order to compute ＂characteristic＂ spectral region, 160 samples of tobacco were surveyed by NIR. Next, the whole spectral region was randomly divided into six regions, and the values of association coefficients and correlation orders of different regions were computed for total sugar, reducing sugar and nicotine. Moreover, two regions that owned the largest value of association coefficient were regarded as ＂characteristic＂ spectral region of a model. Finally, the quantitative analysis models of different components were established via the partial least squares method, and the common selection methods of spectral region were compared. The simulation results indicate that the models to choose the spectral region based on grey correlation analysis are more effective than the common selection methods of spectral region, the optimized time of algorithm is shorter, the prediction precision of the models is higher and generalization ability for quantitative analysis results is stronger. This research can provide the support for the quantitative analysis models of NIR spectra and new idea for commercial analysis software of NIR. So, it has a high application value in the analysis of NIR spectra.

Grey Relevance Analysis of Major Factors of Energy-Related CO2 Emissions in Tianjin,China

Energy-related CO2 emissions from Tianjin’s production and household sectors during 2000–2012 were calculated based on the default carbon-emission coefficients provided by the Intergovernmental Panel on Climate Change.Grey relational analysis was used in this study to capture the dynamic characteristics of 12 different factors related to CO2 emissions.The results indicated that population scale and structure,industrial structure,per capita disposable income,energy consumption and structure appeared as the main drivers related to the CO2 emissions increase during the study period.Based on the research,we make the policy recommendations including optimizing the industrial structure and energy structure,improving energy efficiency and promoting low-carbon consumption.

Grey Relational Analysis between Chlorophyll a and Environmental Factors in ShaHu Lake

[Objective] The aim was to explore effects of environmental factors on the content of Chlorophyll a in ShaHu Lake.[Method] Based on the data in Shahu Lake from November in 2007 to September in 2008,the relationship between chlorophyll a and environmental factors like water temperature,pH,secchi-depth （SD）,total nitrogen,total phosphorus and potassium permanganate index was studied by grey relational analysis method.[Result] The main environmental factors affecting the content of Chlorophyll a in ShaHu Lake were in order of water temperature potassium permanganate index 〉total nitrogen 〉pH〉 total phosphorus 〉SD.[Conclusion] The research provides reference for the control of eutrophication and the reasonable development and utilization of Shahu Lake.

Insulation fault diagnosis based on group grey relational grade analysis method for power transformers

Utilising dissolved gases analysis, a new insulation fault diagnosis methodfor power transformers is proposed. This method is based on the group grey relational grade analysismethod. First, according to the fault type and grey reference sequence structure, some typicalfault samples are divided into several sets of grey reference sequences. These sets are structuredas one grey reference sequence group. Secondly, according to a new calculation method of the greyrelational coefficient, the individual relational coefficient and grade are computed. Then accordingto the given calculation method for the group grey relation grade, the group grey relational gradeis computed and the group grey relational grade matrix is structured. Finally, according to therelational sequence, the insulation fault is identified for power transformers. The results of alarge quantity of instant analyses show that the proposed method has higher diagnosis accuracy andreliability than the three-ratio method and the traditional grey relational method. It has goodclassified diagnosis ability and reliability.

Correlation, Principal Component and Grey Relation Analysis of Sweetpotato Root Biological Traits

[Objective] This study was conducted to explore the internal relationship among root biological traits of sweetpotato, as well as the regularity in their formation and differentiation. [Method] The root traits of 10 sweetpotato cultivars were measured through hydroponic culture in a greenhouse and field survey, and then their correlations were analyzed by statistical methods. [Result] The root morphological traits of sweetpotato at seedling stage such as projected area, surface area, average diameter and volume processed the highest contribution rate （80.56%） 10 d after transplanting, and the contribution rate of root average diameter reached 27.79% 20 d after transplanting. Storage root fresh weight per plant shared extremely significant positive correlations with storage root fresh weight of penultimate node and storage root fresh weight of antepenultimate node, and a significant positive corre- lation with commercial storage root number, and a significant negative correlation with storage root number of penultimate node. Among them, the correlation coeffi- cient of storage root fresh weight per plant with storage root fresh weight of antepenultimate node was the highest （0.659 5）. Fifteen days after transplanting, storage root fresh weight per plant had significant negative correlations with root projected area, surface area and volume. There was a significant positive correlation between root dry weight and storage root fresh weight per plant 25 d after transplanting. Root dry weight, volume, length, average diameter of sweetpotato seedlings had higher relational degrees with storage root fresh weight per plant. Ten and twenty days after transplanting were important time for the growth and differentiation of sweetpotato roots. In addition, node length and planting depth had certain influence on sweetpotato yield, and direct relationship existed between the seedling root biological traits and storage root yield of sweetpotato. [Conclusion] The results provide theoretical support for standard cultivation and new variety breeding of sweetpotato.

Study on effectiveness evaluation of weapon systems based on grey relational analysis and TOPSIS

To evaluate the effectiveness of weapon systems, the advantages and disadvantages of grey relational analysis and TOPSIS for multiattribute decision-making is pointed out, and an effectiveness evaluation model of weapon systems by combining grey relational analysis and TOPSIS is proposed. The model aggregates the grey relational grade and the distance to a new integrated closeness and reflects not only the trend but also the situation of the alternative. The example illuminates that the model is effective for the effectiveness evaluation of weapon systems.

Nutritional evaluation of different cultivars of potatoes(Solanum tuberosum L.) from China by grey relational analysis(GRA) and its application in potato steamed bread making

Chemical composition(moisture,protein,starch,ash,fiber,fat),vitamins(vitamin C,vitamin B1,vitamin B2),total polyphenol content,antioxidant capacity,minerals,and amino acid of 14 potato cultivars in China were evaluated.The results indicated that all parameters varied significantly among different potato cultivars.The total starch,crude protein and fat content ranged between 57.42–67.83%,10.88–14.10% and 0.10–0.73% dry weight(DW),respectively.Moreover,the consumption of potato increased remarkably the dietary intake of vitamins,K,Mn and Cu.In addition,the chemical score of amino acid varied considerably between different cultivars,which ranged from 54(Neida 3 and Neida 41) to 71(Neida 34).Grey relational analysis(GRA) indicated that Neida 26 exhibited the most comprehensive nutritional values among potato cultivars,followed by Neida 42.Different potato flours had a significant effect on the quality parameters of potato steamed bread(PSB),Neida 26 and Neida 34 were more suitable for making PSB.

Comprehensive security risk factor identification for small reservoirs with heterogeneous data based on grey relational analysis model

Identification of security risk factors for small reservoirs is the basis for implementation of early warning systems.The manner of identification of the factors for small reservoirs is of practical significance when data are incomplete.The existing grey relational models have some disadvantages in measuring the correlation between categorical data sequences.To this end,this paper introduces a new grey relational model to analyze heterogeneous data.In this study,a set of security risk factors for small reservoirs was first constructed based on theoretical analysis,and heterogeneous data of these factors were recorded as sequences.The sequences were regarded as random variables,and the information entropy and conditional entropy between sequences were measured to analyze the relational degree between risk factors.Then,a new grey relational analysis model for heterogeneous data was constructed,and a comprehensive security risk factor identification method was developed.A case study of small reservoirs in Guangxi Zhuang Autonomous Region in China shows that the model constructed in this study is applicable to security risk factor identification for small reservoirs with heterogeneous and sparse data.

Grey relational analysis on the relation between marine environmental factors and oxidation-reduction potential

The effects of marine environmental factors-temperature （T）, dissolved oxygen （DO）, salinity （S） and pH--on the oxidation-reduction potential （ORP） of natural seawater were studied in laboratory. The results show an indistinct relationship between these four factors and the ORE but they did impact the ORP. Common mathematical methods were not applicable for describing the relationship. Therefore, a grey relational analysis （GRA） method was developed. The degrees of correlation were calculated according to GILA and the values of T, pH, DO and S were 0.744, 0.710, 0.692 and 0.690, respectively. From these values, the relations of these factors to the ORP could be described and evaluated, and those of T and pH were relatively major. In general, ORP is influenced by the synergic effect of T, DO, pH and S, with no single factor having an outstanding role.

Function chain neural network prediction on heat transfer performance of oscillating heat pipe based on grey relational analysis

As for the factors affecting the heat transfer performance of complex and nonlinear oscillating heat pipe (OHP),grey relational analysis (GRA) was used to deal with the relationship between heat transfer rate of a looped copper-water OHP and charging ratio,inner diameter,inclination angel,heat input,number of turns,and the main influencing factors were defined.Then,forecasting model was obtained by using main influencing factors (such as charging ratio,interior diameter,and inclination angel) as the inputs of function chain neural network.The results show that the relative average error between the predicted and actual value is 4%,which illustrates that the function chain neural network can be applied to predict the performance of OHP accurately.

Application of grey relational analysis in sheet metal forming for multi-response quality characteristics

The theory of grey systems is a new technique for performing prediction, relational analysis and decision making in many areas. In this paper, the use of grey relational analysis for optimizing the square hole flanging process parameters with considerations of the multiple response (the average flanging height, regular flanging and maximum strain) is introduced. Various flanging parameters, such as the blank inner radius rb, blank inner width B0, are considered. An orthogonal array is used for the experimental design. Multiple response values are obtained using finite element analysis (FEA). Optimal process parameters are determined by the grey relational grade obtained from the grey relational analysis for multi-performance characteristics (flanging height, regular flanging and maximum strain). Analysis of variance (ANOVA) for the grey relational grade is implemented. The results showed good agreement with the experiment result. Grey relational analysis can be applied in multiple response optimi-zation designs.

Response surface method using grey relational analysis for decision making in weapon system selection

A proper weapon system is very important for a na- tional defense system. Generally, it means selecting the optimal weapon system among many alternatives, which is a multiple- attribute decision making （MADM） problem. This paper proposes a new mathematical model based on the response surface method （RSM） and the grey relational analysis （GRA）. RSM is used to obtain the experimental points and analyze the factors that have a significant impact on the selection results. GRA is used to an- alyze the trend relationship between alternatives and reference series. And then an RSM model is obtained, which can be used to calculate all alternatives and obtain ranking results. A real world application is introduced to illustrate the utilization of the model for the weapon selection problem. The results show that this model can be used to help decision-makers to make a quick comparison of alternatives and select a proper weapon system from multiple alternatives, which is an effective and adaptable method for solving the weapon system selection problem.

Multi-response optimization of process parameters in friction stir welded AM20 magnesium alloy by Taguchi grey relational analysis

The purpose of this paper is to optimize the process parameter to get the better mechanical properties of friction stir welded AM20 magnesium alloy using Taguchi Grey relational analysis(GRA).The considered process parameters are welding speed,tool rotation speed,shoulder diameter and plunging depth.The experiments were carried out by using Taguchi's L18 factorial design of experiment.The processes parameters were optimized and ranked the parameters based on the GRA.The percentage influence of each process parameter on the weld quality was also quantified.A validation experimental run was conducted using optimal process condition,which was obtained from the analysis,to show the improvement in mechanical properties of the joint.This study also shows the feasibility of the GRA with Taguchi technique for improvement in welding quality of magnesium alloy.

Multi objective prediction and optimization of control parameters in the milling of aluminium hybrid metal matrix composites using ANN and Taguchi-grey relational analysis

This study aims to optimize the input parameters such as mass fraction and particle size of SiC along with depth of cut,feed and cutting speed in the milling of Al5059/SiC/MoS2.The hybrid metal matrix composites are generally fabricated by reinforcing of different sizes(10,20,40 μm)of SiC with aluminium at a different levels(5%,10%& 15%)whereas the MoS2 addition is fixed as 2%.The effect of each control factor on response variables are analyzed through Taguchi S/N ratio method.Also,the most significant method for prediction of response parameters is satisfied by ANN model than the regression model.Analysis of variance(ANOVA)results envisage that mass fraction of SiC,feed rate is the most domineering factor on response variable.

GREY RELATIONAL ANALYSIS: A NEW STATISTICAL METHOD OF MULTIFACTORIAL ANALYSIS IN MEDICINE

The concept, fundamental theory, analytical steps and formulae of grey relational analysis (GRA)-a new statistical method or multifactorial analysis in the field of medicine were introduced. GRA of grouping sequence that is applied to medical study was built by the authors. An example was given to demonstrate it. The superiority of GRA was recounted briefly.

Optimization of cutting parameters with Taguchi and grey relational analysis methods in MQL-assisted face milling of AISI O2 steel

This study aims to examine the usability of environmentally harmless vegetable oil in the minimum quantity of lubrication(MQL)system in face milling of AISI O2 steel and to optimize the cutting parameters by different statistical methods.Vegetable oil was preferred as cutting fluid,and Taguchi method was used in the preparation of the test pattern.After testing with the prepared test pattern,cutting performance in all parameters has been improved according to dry conditions thanks to the MQL system.The highest tool life was obtained by using cutting parameters of 7.5 m cutting length,100 m/min cutting speed,100 mL/h MQL flow rate and 0.1 mm/tooth feed rate.Optimum cutting parameters were determined according to the Taguchi analysis,and the obtained parameters were confirmed with the verification tests.In addition,the optimum test parameter was determined by applying the gray relational analysis method.After using ANOVA analysis according to the measured surface roughness and cutting force values,the most effective cutting parameter was observed to be the feed rate.In addition,the models for surface roughness and cutting force values were obtained with precisions of 99.63%and 99.68%,respectively.Effective wear mechanisms were found to be abrasion and adhesion.

The Evaluation on Ecological Agricultural Development in Sichuan Province on the Basis of Grey Relational Analysis

By using the grey relational model,14 indexes of ecological agricultural development in Sichuan Province from 1997 to 2008 are analyzed.According to the relational degree results,the ecological agricultural development in 12 years can be divided into three stages:the first stage is from 1997 to 2000,with the shape of inverted U;the second stage is from 2001 to 2004,belonging to transition stage with slow growth rate;the third stage is from 2005 to 2008,belonging to the stage of rapid growth.It draws conclusion that per capita grain yield is an important element for evaluating ecological agricultural construction.Besides,reducing the energy consumption of per unit production,improving labor productivity and increasing agricultural science and technology application and input on agricultural infrastructure construction are the engine for developing Sichuan ecological agriculture.

Optimization of green sand mould system using Taguchi based grey relational analysis

The strength of the mould cavity in sand casting is very much significant to attain high-quality castings. Optimization of green sand process parameters plays a vital role in minimizing casting defects. In the present research work, the effect of process parameters such as AFS grain fineness number, water, molasses, bentonite, fly ash, and ramming, and their levels on the resultant mould properties were investigated and optimized using Taguchi based grey relational analysis. The Taguchi L18 orthogonal array and analysis of variance(ANOVA) were used. The quality characteristics viz., green compression strength, permeability, bulk density, mould hardness and shatter index of green sand mould were optimized using grey relational grade, based on the experiments designed using Taguchi's Design of Experiments. ANOVA analysis indicated that water content is the most influential parameter followed by bentonite, and degree of ramming that contributes to the quality characteristics. The results are confirmed by calculating confidence intervals, which lies within the interval limits. Finally, microstructure observations and X-ray diffraction analysis have been performed for the optimal sand parametric combination. Results show that presence of maximum amount of SiO_2, which might be the reason for enhancement of the physical properties of the sand.