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.

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.

Analysis on Fuji Apple Tree Structures and Related Factors under Different Pruning Modes

To determine the correlations between the tree structuresof Fuji apple with different pruning modes and each factor, the data about 3 tree structures which were free spindle short shoot, free spindle long shoot and slenderspindle short shoot in Xingtang County of Hebai Province were investigated, then by SPSS anal- ysis, the correlations between the taperingness and each growth factor of inserted small branch were compared. The results showed that the taperingness of central trunk of free spindle dwarf-shoot Fuji apple treeshad negative correlations with each factor of inserted small branch, while the taperingness of central trunk of free spin- dle long-shoot Fuji apple treeshad positive correlations with each factor of inserted small branch, the taperingness of central trunk of slenderspindle short-shootFuji ap- ple treeshad negative correlation with total thickness of inserted small branch, but had positive correlations with other factors. This study can provide a scientifictheo- retical basis for the pruning technology of high-density planting trees grafting by dwarfing self-rooted rootstock.

GRA BASED ANALYSIS ON FACTORS INFLUENCING CO_2 EMISSIONS IN CHINA

How to achieve the objective of reducing CO2 emissions has been an academic focus in China recently. The factors influencing CO2 emissions are the vital issue to accomplish the arduous target. Firstly, three influential factors, the energy consumption, the proportion of tertiary industry in gross domestic product （GDP）, and the degree of dependence on foreign trade, are carefully selected, since all of them have closer grey relation with China＇s COz emissions compared with others when the grey relational analysis （GRA） method is applied. The study highlights co-integration relation of these four variables using the co-integration analysis method. And then a long-term co-integration equation and a short-term error correction model of China＇s CO2 emissions are devel- oped. Finally, the comparison is exerted between the forecast value and the actual value of China＇s CO2 emissions based on error correction model. The results and the relevant statistics tests show that the pro- posed model has better explanation capability and credibility.

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.

Application of coupled analysis methods for prediction of blast-induced dominant vibration frequency

Blast-induced dominant vibration frequency （DVF） involves a complex, nonlinear and small sample system considering rock properties, blasting parameters and topography. In this study, a combination of grey relational analysis and dimensional analysis procedures for prediction of dominant vibration frequency are presented. Six factors are selected from extensive effect factor sequences based on grey relational analysis, and then a novel blast-induced dominant vibration frequency prediction is obtained by dimensional analysis. In addition, the prediction is simplified by sensitivity analysis with 195 experimental blast records. Validation is carried out for the proposed formula based on the site test database of the first- period blasting excavation in the Guangdong Lufeng Nuclear Power Plant （GLNPP）. The results show the proposed approach has a higher fitting degree and smaller mean error when compared with traditional predictions.

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.

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.

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.

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.

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.

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.

Grey Relational Analysis on the Effects of Rainfall Factors on Runoff and Sediment in the Sloping Farmland with Different Plants in the Central South of Shandong Province

[Objective] The aim was to study the main rainfall factors influencing runoff and sediment in the sloping farmland with different plants in the central south of Shandong Province.[Method] Through grey relational analysis,the effects of different rainfall factors on runoff and sediment with different plants in the central south of Shandong were studied.[Result] In the sloping farmland with different plants,the effects of rainfall factors on runoff and sediment weren’t consistent.Rainfall was the dominant influencing factor of runoff,but PI30 had the greatest influence on runoff in natural grassland.Meanwhile,rainfall intensity was the main influencing factor of sediment,but PI had the greatest influence on sediment in Astragalus adsurgens Pall.plot.The compound factor had the minimal influence on runoff and sediment in Arachis hypogaea plot and natural grassland.In A.adsurgens Pall.plot,rainfall intensity had the minimal impact on runoff,but the compound factor had the least effect on sediment.[Conclusion] The study could provide theoretical references for the comprehensive control of slope soil erosion,the optimum utilization and sustainable development of land.

CAE-Based Robust Optimization for Deep-Drawing Process of Sheet Metal Forming Using Grey Relational Analysis Method

The theory of grey systems is a new technique for performing prediction, relational analysis and decision making in many areas. The grey relational analysis was used to optimize the deep-drawing process parameters with considerations of the multiple response （the wrinkle, crack and thinning variation）. The deep-drawing parame- ters, such as the blank holding force （Fhh）, the radii of punch and die （R1.R2）, the coefficients of friction （μ1,μ2,μ3） are considered. An orthogonal array is used for the experimental design. The multiple response values are ob- tained making use of finite element analysis （FEA）. Optimal process parameters are determined by the grey rela- tional grade obtained from the grey relational analysis for multi-performance characteristics （the wrinkle, crack and the thinning）. The analysis of variance （ANOVA） for the grey relational grade is implemented. The results show that the quality of stamped parts can be improved effectively through the new approach. The grey relational analysis can be applied in sheet metal forming.

Symplectic analysis for elastic wave propagation in two-dimensional cellular structures

On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional （2D） symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures＇ configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.

Applications of gray relational analysis in gastroenterology

ABM: To introduce the basic methods of gray relational analysis (GRA) and to illustrate its applications in gastroenterology. METHODS: With the essential formulae of GRA and several typically practical examples, the procedure of GRA was introduced. Examples were drawn from the gastroenterological studies. Thus the trait of GRA could be demonstrated. RESULTS: The superiority of GRA in gastroenterological study was proved by the examples. CONCLUSION: GRA can be applied mechanically or flexibly in gastroenterology.