STATISTICAL AND SOFTWARE APPLICATIONS IN THE

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STATISTICAL AND SOFTWARE APPLICATIONS IN THEMATERIALS SELECTIONDr. ing. Adrian Stere PARIS, Univ. Politehnica Bucharest, email: s paris@clicknet.roDr.ing. Cristian DRAGOMIRESCU, Univ. Politehnica Bucharest, email:cristian dragomirescu@yahoo.comDr. Constantin TÂRCOLEA, Univ. Politehnica Bucharest, email:constantin tarcolea@yahoo.comAbstract New materials advanced engineering design, but for making a rational selection, based onlyona few characteristics, it is necessary a systematic procedure for selecting materials and processes. A statisticalapproach is applied to the selection of materials for the new products. The choice of a material for a product isnot based on all the attributes, but on a combination of properties. The paper presents a method of reduction ofattributes to a combination of a few artificial factors. Numerical examples are exemplified in the paper.Statistical software (XLSTAT, SPSS, MINITAB, etc).facilitates the work, with greater rapidity and flexibility.Keywords: materials selection, statistics, software1. INTRODUCTIONThe choice of materials for a new product is made usually from among the knownmaterials. The present conditions impose the taking into consideration of a very largespectrum of materials, both conventional and non-conventional, their number being over100,000.A complex problem, in practice is the definition of a spectrum of properties, startingwith the general ones such as density, melting point, cost, etc., up to the most particular, forcertain classes of materials, as for example, the water absorption for polymers, the changingof properties by thermal treatment for alloys, etc. as well as the technological properties, thatcan cover as much as possible the existing range [11].2. METHODS APPLIED FOR MATERIALS SELECTION2. 1.Traditional methodsThe selection of the materials group uses the following premises:a) the taking into consideration of an ever larger spectrum of materials, defining ascomplete as possible the selection range;b) the division of materials in "equivalence classes", the classification of materials thusobtaining a significant reduction of the selection space: the initial chaoticallymultitude is reduced to smaller number of classes, the number of each class havingcommon properties, processes accompanied or not by the elimination or somematerials taken into consideration;c) the establishing of the same simple and efficient methods of selection, with thepossibility of implementing on a computer [2], [7] ,[9].93Fiabilitate si Durabilitate - Fiability & Durability Supplement No 1/ 2014Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X

The establishment of the materials selection method may be approached:-by matrix, by granting some marks and shaves [9];-graphically, by plotting (regularly bidimensionals, fig.1) that enable data visua1isation,defining some restrictions, etc.The graphical method may by approach in a determinist way [2], [9], or statistically [5], [11].The selection system may be:-unique, for example in the matrix case, resulting the hierarhisation of material group[7];-iterative, by successfully resuming the data groups of materials and basic properties,resulting a final classification with intermediate possibilities of changing the criteria.Fig.1 Ashby’s modulus density materials selection chart. [5]2. 2.Statistical methods for material selectionMultivariate Analysis is used to the analysis of data which are multivariate in thesense that each object bears the values of several characteristics of interest. In order toperform multivariate exploratory statistics, these data must be interpreted as anattributes/objects table [16].94Fiabilitate si Durabilitate - Fiability & Durability Supplement No 1/ 2014Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X

Multivariate data analysis contains two classes of methods: analyzing data andadvanced data analysis. In the first class are: Factor Analysis, Principal ComponentAnalysis (PCA), Biplot, Discriminant Analysis (DA) [13], Correspondence Analysis (CA),Multiple Correspondence Analysis (MCA), etc. The second group contains: CanonicalCorrespondenceAnalysis (CCAandpartial CCA),GeneralizedProcrusteanAnalysis(GPA), Multiple Factor Analysis (MFA), etc., for various applications, fromecology to marketing [1], [15].Factor analysis is a multivariate statistic technique to reduce data set to lowerdimensions, so that this yields to the minimum deformation of the original cloud, and thenew cloud is simpler than the original one. An example of application of this method inmaterial selection is presented in [1].Another practical example is the search for the material of the bicycle chain [12]. Onthe basis of carbon percentage, five materials such as S45C, Q235, ASTM A36, AISI 1038,C40 have been selected for bicycle chain [17]. The six analyzed properties are density (D) inkg/m3, Young’s Modulus of elasticity (YM) in GPa, Tensile strength (TS) in MPa, Yieldstrength (YS) in MPa, Hardness (BH) in HB and Elongation in % (E) (tab.1) [12].Mat./Prop.S45CQ235ATM36AlSi1038C40DTable 1. Data of material selection 830Singh and Kumar [12] developed a variant of TOPSIS for the material selection. TheTechnique for Order Preference by Similarity to Ideal Solution method (TOPSIS) wasintroduced as a decision making technique with a goal based approach for finding thealternative that is closest to the ideal solution, considering the distance of that design fromideal and non-ideal solution [3].The present paper proposes a statistical tool, PCA, for the material selection:Principal Component Analysis (PCA) is a standard technique to reduce multivariate datasets in a subspace of small dimension, in this case a bivariate one [14]. The number ofobservable attributes gives the dimension of the initial representation space of the objects[10], [16]. Instead of real attributes, the PCA uses new factors, but artificial ones, so that thesubspace yields the minimum deformations of the original cloud of data [14].95Fiabilitate si Durabilitate - Fiability & Durability Supplement No 1/ 2014Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X

Table 2. Statistical evaluation of dataTable 3.Correlation matrixA dimensional reduction example for a family of materials for sliding bearing uses theJöreskog's method [11], [15]. Jöreskog's method considers that theoretical covariance matrixof the standardized attributes, V, is factorized as a sum [15].The results of the PCA application for the materials data from table 1 are conciselypresented above, with XLSTAT 7.5.2 - Principal Component Analysis (PCA). Table 2indicates the principal statistic characteristics and table 3 presents the correlation matrix,where the big correlation coefficient (0.883) between density and yield strength is obvious,easy to explain technically.Table 4. EigenvaluesTable5. EigenvectorsEigenvalues from table 4 and fig.2 correspond to the variance explained by theprincipal components, while eigenvectors from table 5 correspond to the principalcomponents. Approximately 83% from the total variance is explained by the first two newfactors, so the selection can be followed only with these factors. A biplot allows informationof the data matrix to be displayed graphically: in fig.3 materials (observations) are displayedas points while variables (properties) are displayed either as vectors or linear axes and thelength of the lines approximates the variances of the variables.The longer the line, thehigher is the variance96Fiabilitate si Durabilitate - Fiability & Durability Supplement No 1/ 2014Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X

Fig.2.Eigenvalues bar chartFig.3.Biplot chart(here Tensile strength TS is maximal).A new statistical developmentis the artificial neural networks (ANN), a family oftechniques for numerical learning, with many nonlinear computational elements which form thenetwork nodes or neurons, linked by weighted interconnections. Part of the appeal of neuralnetworks is that when presented with noisy or incomplete data, they will produce an approximateanswer rather than one that is incorrect [10]. Software developments like SPSS facilitate theutilisation of such advanced statistical methods. The ANN methodology has been applied forselection of powder and process parameters for Powder Metallurgy (PM) part manufacture[4]. This methodology differs from the statistical modeling of mechanical properties in that itis not necessary to make assumptions regarding the form of the functions relating input andoutput variables [4].3. CONCLUSIONSThe paper offers a synthesis between the engineering experimental activity and themodern computer assisted statistical applications. The applied statistical methods carried outsome correlations, interdependences regression functions to evaluate the initial experimentalresults for. A possibility of getting down the properties range, is the taking into considerationof the correlation between the properties studying thus only the independent properties to thepossible extent. The great advantage is the consistent statistical support and the easy access tospecialized software, with extended conclusions. The continuation of the experiments willoffer the possibility to verify the inference of the mathematical assumptions.REFERENCES1. Amza, Gh., Paris, A.S., Târcolea, C. Risk and Factor Analysis, Proceedings of the 3td WSEASInternational Conference on Risk management, assessment and mitigation RIMA’10, Univ.Politehnica, Bucharest, in vol. Recent Advances in Finite Differences-Finite Elements-FiniteVolumes-Boundaries Elements, Bucharest, 2011, pp.146-15197Fiabilitate si Durabilitate - Fiability & Durability Supplement No 1/ 2014Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X

2. Ashby, M.F., Johnson, K. Materials and Design, the Art and Science of Materials Selection inProduct Design, Ed. Butterworth Heinemann, Oxford, 2002.3. Bhutia P. W, Phipon R. Application of AHP and TOPSIS method for supplier selection problem,IOSR Journal of Engineering (IOSRJEN), Volume 2, Issue 10, Oct. 2012, pp. 43-50.4. Cherian R.P., Smith L.N., Midha P.S. A neural network approach for selection of powdermetallurgy materials and process parameters Artificial Intelligence in Engineering, Volume 14, Issue1, Jan. 2000, Pages 39–445. Holloway L. Materials selection for optimal environmental impact in mechanical design, Materialsand Design 19, 1998, pp. 133-1436. Hopgood A. A. Intelligent Systems for Engineers and Scientists, CRC Press, London, 20117. Murray G. Handbook of Materials Selection for Engineering Applications, Dekker MechanicalEngineering, CRC Press, New York, 19978. Paris A.S. Statistik Anwendungen in Ingenieurwissenschaften - eine starkeInnovationsunterstützung - “Interdisciplinary approach of innovation as a progress factor”International Scientific Conference Bucharest, Romania, Dec. 2012, FILS, UPB, Ed. PrintechBucharest, 2013, pp. 15-209. Paris, A., Ionescu, S., Szel, P., Târcolea, C. Statistical approach in the selection of materials forengineering products. Scientific Seminar “Modern mechanical design” Bucharest, 18-20 sept. 1991,University Politehnica Edition, Bucharest, 1991, pp.97-106.10. Paris, A.S., Târcolea, C. PCA Applied for Equipments Selection, International Conference onManufacturing Science and Education- MSE 2011- Sibiu-Romania Proceedings of the 5th InternationalConference on Manufacturing Science and Education- MSE 2011, vol.I, Creative Thinking inEngineering and Academic Education, June 2-5, Editura Universitatii Lucian Blaga, Sibiu, 2011, pp349-35211. Paris, A.S., Târcolea C. Computer aided selection in design processes with multivariate statistics,Proceedings of the International Conference on Manufacturing Systems – ICMaS, Bucharest, Vol. 4,2009, pp.335-338.12. Singh H., Kumar R. Selection of Material for Bicycle Chain in Indian Scenario using MADMApproach, Proceedings of the World Congress on Engineering 2012 Vol III WCE 2012, July 4 - 6,2012, London, U.K.13. Târcolea C., Paris, A. S. Discriminant Analysis and Applied Regression The InternationalConference of Differential Geometry and Dynamical BSG PROCEEDINGS 18, (DGDS-2010) August2010, Bucharest, Geometry Balkan Press, pp. 221-226, 2011, pp.95-10014. Târcolea, C., Paris, A.S., Demetrescu –Târcolea, A. Statistical methods applied for materialsselection The International Conference DGDS-2008 & MENP-5 August 29 - September 02, 2008,Mangalia, Romania, Applied Sciences, Geometry Balkan Press, Vol.11, 2009, pp. 145-150.15. Târcolea, C., Paris, A.S. The Joreskog technique applied for materials design, In vol.Proceedings of the 17th International Conference on Manufacturing Systems – ICMaS13-14 nov.2008, Ed Acad. Romane, Bucharest, Romania, pp.309-31216. Târcolea, C., Paris, A, S., Voicu, P. Principal Component Analysis Applied to AgriculturalEquipments, Tarım Makinaları Bilimi Dergisi (Journal of Agricultural Machinery Science) Istanbul, 7(3), 2011, pp.305-30898Fiabilitate si Durabilitate - Fiability & Durability Supplement No 1/ 2014Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X

Multivariate Analysis is used to the analysis of data which are multivariate in the . Statistical evaluation of data Table 3.Correlation matrix A dimensional reduction example for a family of materials for sliding bearing uses the . Ashby, M.F., Johnson, K. Materials

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