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.

Materials Selection of Thermoplastic Matrices of Natural Fibre Composites for Cyclist Helmet Using an Integration of DMAIC Approach in Six Sigma Method Together with Grey Relational Analysis Approach

Natural fibre reinforced polymer composite(NFRPC)materials are gaining popularity in the modern world due to their eco-friendliness,lightweight nature,life-cycle superiority,biodegradability,low cost,and noble mechanical properties.Due to the wide variety of materials available that have comparable attributes and satisfy the requirements of the product design specification,material selection has become a crucial component of design for engineers.This paper discusses the study’s findings in choosing the suitable thermoplastic matrices of Natural Fibre Composites for Cyclist Helmet utilising the DMAIC,and GRA approaches.The results are based on integrating two decision methods implemented utilising two distinct decision-making approaches:qualitative and quantitative.This study suggested thermoplastic polyethylene as a particularly ideal matrix in composite cyclist helmets during the selection process for the best thermoplastic matrices material using the 6σtechnique,with the decision based on the highest performance,the lightest weight,and the most environmentally friendly criteria.The DMAIC and GRA approach significantly influenced the material selection process by offering different tools for each phase.In the future study,selection technique may have been more exhaustive if more information from other factors had been added.

Multi-Criteria Group Decision-Making Method Based on an Improved Single-Valued Neutrosophic Hamacher Weighted Average Operator and Grey Relational Analysis

This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.

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.

ESTIMATION METHOD FOR AIRCRAFT SIMILARITY BASED ON FUZZY THEORY AND GREY INCIDENCE ANALYSIS

An estimation method for aircraft similarity based on fuzzy theory and grey incidence analysis is presented. This estimation method is made up of the triangular fuzzy transforming model of linguistic variables and the method of grey incidence analysis. Nine feature attributes of aircraft are selected to estimate the similarity between the new aircraft and the existing aircraft. A new aircraft X and other six existing aircrafts are taken as examples. Analyses show that similarity estimation results obtained from the method are in accordance with practice.

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.

Grey Correlation Analysis of Physiological Traits Related to Drought Tolerance in Pennisetum sp.

The drought resistance of Pennisetum sp. was analyzed under different drought stress conditions simulated by various concentrations of PEG-6000. Changesofa series of indexes such as chlorophyll content, water content, relative electrical conductivity of osmotic solution, MDA content, proline content, soluble polysaccharide content and soluble protein content in the leaves were measured.The correlation of these indexes with the drought resistance of Pennisetum sp. was an- alyzed by the method of grey correlation analysis. The results showed that the chlorophyll, water content, relative electrical conductivity and soluble protein con- tentexhibited obvious negative correlation with the stress concentration, which de- creasedfollowing the increase of PEG-6000 concentration. The soluble polysaccha- ride contentshowed an increasing trend,the MDA content showed a rise at first fol- lowed by a declinetrend, while the prolinecontent was just opposite to MDA. The changes of the 3 indexes showed obvious positive correlation with thestress con- centration. The correlation of these indexes with the drought resistance of Pennise- tum sp. were ranked as follows： leaf water content （0.980 8）, chlorophyll content （0.967 9）, MDA content （0.876 0）, soluble polysaccharide content （0.839 5）, soluble protein content（0.827 5）, relative electrical conductivity of osmotic solution（0.670 8）, and proline content（0.571 3）.

Application of Grey Relational Analysis in Regional Water Environment Assessment——Taking Jin River Basin as An Example

According to the data from four water monitoring stations at Meihewan, Shimawan, Tanwan and Jinbin, the water environment at the downstream basin of Jin River was evaluated through grey reIational analysis in this study. The resuIts showed that the water environment was severeIy contaminated by phosphorus, am-monia nitrogen and permanganate.

Analysis of Driving Factors of Grain Output in Henan Province Based on Grey Correlation Model

Henan Province is an important grain production base, whose stable production is related to the economic development and social stability significantly. To summarize the primary factors of grain producing, we used grey correlation analysis method to analyze 10 correlative factors such as grain yield, grain yield per unit area, effective irrigated area, rural employed persons, grain planting area, consumption of chemical fertilizer in 25 years. The results showed order of synthetic degree of incidence: effective irrigated area>rural electricity consumption>consumption of chemical fertilizer>disaster crop area>grain yield per unit of area>total power of agricultural machinery>afflicted crop area>grain planting area>number of the rural employed persons. Finally, according to synthetic degree of incidence between influential factors and total grain output respectively, a series of measures and the suggestions was proposed for grain production in Henan Province, which will also provide the scientific basis and help for the government correct decision-making.

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.

HIERARCHIC GREY QUASI-PREFERRED ANALYSIS MODEL AND ITS APPLICATION

The grey quasi-preferred analysis (GQPA) is one of important methods for realizing system analysis to conquer the limitations of the existing GQPA model, without any considerations to the difference of the different behavioral factor′s importance. It could not be used to analyze the complex system with multi-hierarchy correlation factors, the weighted synthetic method for calculating abstract incidence degrees between the system beha-vioral characteristics and correlative factors in different hierarchies is given out,and the hierarchic grey quasi-preferred analysis (HGQPA) model is established. The effectiveness of the HGQPA model is tested by the scientific-technical system of Jiangsu Province. The depth and the range of the application of GQPA are developed, and the HGQPA model is regarded as a new approach to systemically analyze the complex systems with multi-hierarchy correlation factors.

Effects of Nitrogen, Phosphate and Potassium Fertilizers on Soft Rot of Konjac Based on Grey Correlation Analysis

[Objective] The effects of different application amounts of nitrogen, phos-phate and potassium fertilizers on soft rot of konjac were investigated in this study. [Method] The grey correlation analysis was adopted to evaluate the correlation be-tween the application amount of nitrogen, phosphate and potassium fertilizers and the occurrence of soft rot of konjac. [Result] The excessive application of nitrogen fertilizer would induce the occurrence of soft rot of konjac, but the application of potassium fertilizer had a good control effect on soft rot. [Conclusion] The applica-tion amount of nitrogen fertilizer should be control ed reasonably in the planting of konjac, but the application amount of phosphate and potassium fertilizer could be in-creased to some extent, reducing the occurrence of soft rot of konjac.

Research on the Agriculture Production Structure in Shandong Province Based on the Grey Relational Dynamic Analysis

In accordance with grey relational dynamic analysis, overall structure and inner structure of agriculture were analyzed and the grey relational sequence inte- grals were concluded of Shandong agriculture during 2003-2014. Besides, the re- search analyzed the contributions by specific agricultural sectors and Shandong a- gricultural structure from natural endowments, policy, and agricultural modernization. Finally, the development countermeasures and suggestions were proposed.

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 multivariate grey incidence degree based on principal component analysis

To overcome the too fine-grained granularity problem of multivariate grey incidence analysis and to explore the comprehensive incidence analysis model, three multivariate grey incidences degree models based on principal component analysis （PCA） are proposed. Firstly, the PCA method is introduced to extract the feature sequences of a behavioral matrix. Then, the grey incidence analysis between two behavioral matrices is transformed into the similarity and nearness measure between their feature sequences. Based on the classic grey incidence analysis theory, absolute and relative incidence degree models for feature sequences are constructed, and a comprehensive grey incidence model is proposed. Furthermore, the properties of models are researched. It proves that the proposed models satisfy the properties of translation invariance, multiple transformation invariance, and axioms of the grey incidence analysis, respectively. Finally, a case is studied. The results illustrate that the model is effective than other multivariate grey incidence analysis models.

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.

Study of a Comprehensive Assessment Method for Coal Mine Safety Based on a Hierarchical Grey Analysis

Coal mine safety is a complex system, which is controlled by a number of interrelated factors and is difficult to estimate. This paper proposes an index system of safety assessment based on correlated factors involved in coal mining and a comprehensive evaluation model that combines the advantages of the AHP and a grey clustering method to guarantee the accuracy and objectivity of weight coefficients. First, we confirmed the weight of every index using the AHP, then did a general safety assessment by means of a grey clustering method. This model analyses the status of mining safety both qualitatively and quantitatively. It keeps management and technical groups informed of the situation of the coal production line in real time, which aids in making correct decisions based on practical safety issues. A case study in the application of the model is presented. The results show that the method is applicable and realistic with regard to the core of a coal mine's safety management. Consequently, the safe production of a mine and the awareness of advanced safe production management is accelerated.

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.