Simplifying the powder metallurgy manufacturing process using soft computing tools

Accepted Manuscript Title: SIMPLIFYING THE POWDER METALLURGY MANUFACTURING PROCESS USING SOFT COMPUTING TOOLS Author: P. Radha G. Chandrasekaran N. Selvakumar PII: DOI: Reference:

S1568-4946(14)00572-9 http://dx.doi.org/doi:10.1016/j.asoc.2014.11.011 ASOC 2611

To appear in:

Applied Soft Computing

Received date: Revised date: Accepted date:

10-2-2014 20-10-2014 14-11-2014

Please cite this article as: SIMPLIFYING THE POWDER METALLURGY MANUFACTURING PROCESS USING SOFT COMPUTING TOOLS, Applied Soft Computing Journal (2014), http://dx.doi.org/10.1016/j.asoc.2014.11.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

SIMPLIFYING THE POWDER METALLURGY MANUFACTURING PROCESS USING SOFT COMPUTING TOOLS P.Radha+*, G.Chandrasekaran*, N.Selvakumar#

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*Department of Computer Applications, #Department of Mechanical Engineering, Mepco Schlenk Engineering College, Virudhunagar–District, Pin: 626 005, Tamilnadu, India. + Corresponding author: e mail: [email protected], Phone: +91 4562 235453 Abstract

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The tools of soft computing will aid the knowledge mining in predicting and classifying the properties of various parameters while designing the composite preforms in the manufacturing of

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Powder Metallurgy (P/M) Lab. In this paper, an integrated PRNET (PCA-Radial basis functional neural NET) model is proposed in different versions to select the relevant parameters for preparing composite preforms and to predict the deformation and strain hardening properties of

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Al-Fe composites. It reveals that the predictability of this model has been increased by 67.89% relatively from the conventional models. A new PR-filter is proposed by slightly modifying the

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conventional filters of RBFNN, which improves the power of PRNET even though raw data are

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highly non-linear, interrelated and noisy. Moreover, fixing the range of input parameters for classifying the properties of composite preforms can be automated by the Fuzzy logic. These

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types of models will avoid expensive experimentation and risky environment while preparing sintered composite preforms. Thus the manufacturing process of composites in P/M Lab will be simplified with minimum energy by the support of these soft-computing tools.

Key words:

Soft computing; Computational Intelligence; Knowledge Mining; Powder

Metallurgy; Composite preforms;

1.0 Introduction Soft computing models have been studied in recent years, with an objective of achieving human like performance in many fields of knowledge engineering. These tools are being successfully applied in material design, improvement and selection as well as in the control of the processes in materials fabrication. Many researchers have attempted to use soft computing tool like neural network for various applications in manufacturing such as, tool wear, TTT 1 Page 1 of 43

diagram prediction, optimization of powder packing density, Powder Metallurgy (P/M) process modelling, turning force prediction and on-line monitoring etc., [1-3]. The life cycle of P/M process needs a different sequence of operations with various machines to manufacture the composite preforms as a steel manufacturing process [4]. Figure 1 exhibits the various stages like

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blending, mechanical alloying, cmpacting, sintering, prforms and inspecting the products, involved in powder metallurgy process. In P/M laboratory, the needed metal powders are mixed

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in different ratios ,compressed and sintered to prepare powders to prepare composite preforms (pre-designed forms), which will be used as models to manufacture various products such as

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aircraft parts, aluminium coins and snowing machinery parts etc. Using Soft computing models, the various deformation and strain hardening characteristics of preforms are mined before

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preparing the material parts. The deformation characteristics like axial strain (z), hoop strain (), conventional hoop strain (’), strain factor (S), Poisson’s ratio (), new Poisson’s ratio (), axial stress (z), hoop stress (), hydrostatic stress (m) and strain hardening characteristics like

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instantaneous strain hardening exponent (ni) and instantaneous strength coefficient (ki) of these manufactured composite preforms will be varied with respect to the proportions of input

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lubricant (L).

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parameters like compaction load (P), aspect ratio (A), fractional density (D), iron content (C) and

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Fig. 1 Life cycle of powder metallurgy process While applying hard computing methods, the P/M process needs three critical stages: selection of relevant input parameters, fixing the range of input parameters and predicting the various characteristics of composite preforms. In this work, the soft computing tools are applied for simplifying the manufacturing process of Al-Fe composite preforms. The section 2.0 covers the literature survey of related work. The role of hard computing in conventional process and soft computing techniques in knowledge mining are described in the Sections 3.1 and 3.2 respectively. The purpose of the soft computing tools for each stage of this work is mentioned in the Chapter 4. The design and implementation details were described in the Chapter 5 along with the need of the pre-processing. The results are analyzed and reported in the Chapter 6. 2 Page 2 of 43

2.0 Literature survey The knowledge oriented models described in this paper were not developed by any researcher in the field of powder metallurgy. But anyway, the survey was done over the related

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problems of this work in three aspects: Data level, architecture level and an efficiency of an intelligent algorithm. Data cleaning is a major step in the knowledge discovery process [5]. Our

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intelligent/soft computing algorithms will take more time complexity if we apply dirty data to the knowledge mining. In the related work, the properties of raw data were not analyzed in detail.

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Data transformation (normalization) and data reduction (fixing the range of parameters and selecting the relevant subset selection) are two major issues in data cleaning. The raw data was handled without using these mining techniques in the previous work while predicting various

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parameters [3, 6-19]. Also the data discretization was not applied to fix the range of input parameters for supporting data reduction in the previous work. Moreover, the survey done on the

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previous research, which reveals that the pre-processing steps like data cleaning, normalization and data reduction were not carried out for handling non-linear, interrelated, noisy and null data.

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In this paper, the systematic strategy is prescribed to handle this kind of data. The initial research for the computation of data was started in the year 2003 [20] to

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predict the properties of the properties of composite preforms without applying soft computing models. It took more resources and time. The researchers had to conduct the experiments,

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physically for each sample in the Laboratory. Later, the statistical methods were applied. The following observations were made over statistical method like multiple regression analysis:  Polynomial regression can be applied only for single input and single output parameters.  Too complex for statistical methods because numerous variables are involved and nonlinearity of the relationship between the varieties of parameters [21].  Statistical methods will be suitable only, when the number of variables is small and when their effects can be described by simple relationships [8].  Regression analyses are not particularly suited to modelling due to substantial gap present in the data [20].  In some cases, multiple regression yields better results, but it can be limited to predicting the single output. So it is not applicable to multi-dimensional data.

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Then the soft computing based tools were used. In the architecture level, most of the related work for this work had predicted only few linear parameters (even a single parameter) from more inputs using the Neural Network tool [2, 6-7, 9, 15-19, 22-27]. Only a few researchers had applied the soft computing tools in simulating the preform other than Al-Fe composites,

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where the number of outputs is less than or equal to the number of inputs [11, 14, 24-25, 28-31]. By trial and error, the architecture was fixed. The objective of this work is to predict more

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outputs from optimal inputs.

While developing the intelligent models, the generality should be measured to

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recognize the independent test samples. The capacity of architecture, number of training samples and network convergence determines the generality of the model. Fox example, if the hidden layer size is more than the number of training samples, then the network will converge quickly.

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But the network generalization will be very poor. This kind of problem called overfitting was reported in the related work [32], where various generalization tools were utilized to avoid

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overfitting. But the network was unable to predict the outputs for null parameters. Also the system accuracy was evaluated using the biased measure like correlated coefficient instead of the

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unbiased measure like Average Absolute Relative Error (AARE) percentage. Hence the objective of the proposed model is to improve the generality in terms of AARE% and also to handle the

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null entries in data for an analysis.

The intelligence of an algorithm was not analyzed in terms of system accuracy and

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convergence (training completion) in the related work [12-13]. The previously developed models took more epochs like 175 [11], 251 [12], 1322 [13], 160 [14], 4541 (55hours) [15], 130 [17], and 1537695 [18] even for predicting few linear outputs with limited training samples. The previous research used the conventional filters to find the activation functions. Hence the proposed work aims to find the suitable filter to improve the training time.

3.0 Role of hard computing in conventional P/M process The life cycle of P/M covers various stages as shown in Figure 1. The role of hard computing method under the different stages of the manufacturing process of P/M Lab is described as given below: 3.1 Life cycle of P/M process

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3.1.1 Metal powder preparation process Generally a product is identified for manufacturing using P/M process; the selection of material and process parameters requires inputs from a number of experts in the field. Unlike wrought products, design specifications determine the process parameters and type of powder to

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be used in producing a P/M part [1]. In the initial stage of the manufacturing process, numerous variables are used in hard computing model to predict the output. It is difficult to apply different

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permutations of input parameters in mixing powders and to select the most relevant input combination, since each input combination will give different results. While using hard

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computing model, it is very critical to select the needed input combination of the required product. This work will be automated with the help of soft computing tool in P/M Lab to select

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the proper input combination of metal powders.

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3.1.2 Blending and mechanical alloying process

In the next stage of P/M process, the needed metal powders are mixed in different ratios

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using ball-milling equipment as shown in Fig.2(a) to prepare powders in homogeneous form is frequently used to improve various material properties and to prepare advanced materials that are

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different or impossible to be obtained by traditional techniques. With respect to the product type in production, the proper range of input parameters should be applied. The blending and

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mechanical alloying process may need repeated experiments due to the wrong range of powder mixture, for the inexperienced users. The intelligent oriented models like soft computing will aid the blending and mechanical alloying process, in fixing the ratios of various input parameters in preparing the powder mixture.

3.1.2 Compression and sintering process The die set assembly as shown in Fig.2 (b) is used to compress the above powder mixture and sintered (heated) to get the required shapes of preforms. In this work, atomized aluminium powder of–150 m size was obtained from M/s. The Metal Powder Company Limited, Madurai, Tamilnadu, India. The aluminium powder was analyzed and was found to be of purity greater than 99.68% have been used throughout the experiment. The aluminium powder was used for 5 Page 5 of 43

preparing compacts of different height to diameter ratios (aspect ratio). The initial aspect ratios were 0.50, 0.75 and 1.00. Compacts of above initial aspect ratios were prepared from the aforesaid powder on a compacting pressure of 1005, 1555, 2055, 2155 and 280 5 MPa in a universal testing machine having capacity of 1.0 MN with various initial compaction densities

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of 80, 85, 88, 90 and 92 % of the theoretical density. Molybdenum disulphide (MoS2) was used to lubricate the punch, die and the butt, when preparing the compacts. The sintering was carried

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in an electric muffle furnace at 52010C for a holding period of one hour. The measurements such as height, diameters and densities were carried out before and after each of deformations.

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During the axial compression tests, the die set was well lubricated by MoS2, which created a situation for almost ideal deformation. In general, each compact was subjected to compressive

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loading in steps of 0.01 MN until the appearance of visible cracks on the free surface. Immediately after the completion of each step of loading, the height, the contact diameters (at the top and bottom), the bulged diameter and the density were measured for each of the deformed

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compacts, the density measurements were carried using the Archimedes principle [20]. The aluminium (Al) and iron (Fe) powders are mixed in different ratios with

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molybdenum disulphide (MoS2) as die surface lubricant in order to prepare green compacts. This powder mixture is loaded into the die set assembly and then to universal testing machine as

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shown in Fig.2(b). As the compaction load (L) increases, the density of the powder mixture

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increases and hence the height of the preform (h0) will decrease. After the completion of sintering of green compacts, it is ready for inspection, which is named as preforms. The load, P is applied over the preform with an increment of 5 kN. If the load increases, the deformation and strain hardening properties of the preform also increases proportionally. The minimum and maximum aspect ratio of preform (A) is 0.4645 and 1.0539 respectively, and this also depends on compaction load and weight of powder used for compaction. Similarly, the minimum and maximum values for fractional density (D) are 0.82 and 0.99 respectively. The output parameters representing the characteristics of preforms increases if the fractional density increases, but after certain limit it will decrease. Using, hard computing methods, it is difficult to find the association between input and output parameters. Hence the need occurs to apply Soft computing models to simplify this work.

Fig.2(a) Ball milling equipment

Fig.2(b) Compaction process 6 Page 6 of 43

3.1.3 Hard computing model for inspection process At the end of the manufacturing process, the properties of developing preforms are studied before shifting the preforms to the production process of material parts. While applying

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hard computing (deterministic) model, it has to implement the Ludwik equations [20] completely to predict the deformation and strain hardening properties.

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Deformation characteristics:

 Using the initial height of preform (h0) and height after the deformation (hf), the axial    

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h  z  ln 0  hf

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strain can be calculated as given below:

(1)



 2 D B 2  DC 2    ln 2 3DO 

  

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 Hoop strain is calculated with a contact and bulged diameter of the samples. (2)

where D0 is an Initial diameter of the preform, Db is a Bulged diameter of the preform

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and

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Dc is a Contact diameter of the preform after deformation.  Conventional hoop strain is calculated without bulged diameter of the sample. (3)

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D   '  ln c   D0 

 Strain factor using axial strain z and hoop strain  is defined as

S  e z 

(4)

 Poisson’s ratio based on contact diameter () is calculated as below:



 ' z

(5)

 Poisson’s ratio () based on contact & bulged diameter is calculated as below:



 2 z

(6)

 Axial stress is mechanical stress defined for rotationally-symmetric objects being the result of deformation acting longitudinally (axially), with load P as given below: 7 Page 7 of 43

z 

4P Dc2

(7)

 Hoop stress based on bulged and contact diameter can be derived as         z  1    Where   d  d z

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(8)

 is the slope between hoop strain () and axial strain (z). 1     z  3

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M 

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 Meanwhile, the hydrostatic stress (M) can be calculated using the relationship:

Strain hardening characteristics:

(9)

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The properties ni and ki are derived using the difference between the mth and (m-1)th rows of axial strain and axial stress parameters as given below:

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   ln  m    m 1  ni      ln  m     m 1 

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 Instantaneous strain hardening exponent

(10)

 Instantaneous strength coefficient

 m   m1   mn   mn 1 

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(11)

Since the hard computing model adopts sequential computation, it takes more time and effort. As raw-data collected from the P/M Lab are interrelated, noisy and highly non-linear as given below, these are not suitable to parallel processing. Hence, it is advisable to use soft computing based model which can tolerate imprecision, uncertainty, partial truth and approximation to simplify the manufacturing process of preforms [21]. Interrelated data The certain output parameters should be fed as input to derive the other set of output parameters. As mentioned in the mathematical representation, the output parameters are given as derived from other output parameters as given below:

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Output parameters

Needed output parameters to act as inputs Not having this type of input

4,6

1,2

5

1,3

8

1,2,7

9

7,8 9

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10,11

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1,2,3,7 (Linear parameters)

Noisy data

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While measuring the parameters of raw-data using physical instruments in P/M Lab, it is possible to have the variation between the measured (actual) data and expected data. The unwanted data may affect the system accuracy.

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Empty data

It is possible to have certain rows of the parameter may be empty (Table 1). In the raw database

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Table 1, the empty cell of ni and ki parameters will be derived from the difference between two subsequent previous two rows of known column value as per the Eqn. (10 & 11). In each experimental data set, for the every first row, there is no previous row value. It is not applicable

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to find the difference between the mth and (m-1)th rows of strain and stress parameters. Hence,

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nearly 42 rows are made as empty for the parameters ni and ki.

Table 1 Raw data of preforms derived from lab experiments

Highly non-linear data

More parameters have a non-linear relationship with each other. Fig.3(a) shows the linear relationship between axial strain and hoop strain. But Fig.3(b) shows the non-linear relationship between variation of stress (axial, hoop and hydrostatic stress) and axial strain.

Fig. 3 (a) Linear relationship between axial strain and hoop strain

Fig. 3 (b) Non-linear relationship between various stresses and axial strain

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3.2 Soft computing methods in proposed model The experiments conducted physically in P/M Lab as given in Sec. 3.1, need costly equipments. In order to provide security to the people working in P/M Lab and by considering the drawbacks behind the hard computing models as given in Sec. 3.1, the proposed work will be

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implemented by the soft-computing tools. Fig.4 shows that the proposed model based on soft computing will reduce the complexity rather than the conventional hard computing model in

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terms of time, manpower and other resources using the components mentioned in Fig.5. The tool of soft-computing, Neural Network (NN) has major contribution in prediction oriented problems

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[21]. As per the existing models adopted in the previous research [6-9] with NN, there is no more efficient neural network design in the powder metallurgy field to select the relevant input features (meaningful parameters) in predicting the properties of composite preforms.

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Many input features are involved in designing the soft-computing model and these parameters (features) can be selected only by the experience of technicians in the powder

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metallurgy Lab. And also, for each set of combination, these earlier models gave different results. To overcome this problem, a mathematical procedure, Principal Component Analysis (PCA) is

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integrated with NN to build PRNET model to select the most relevant input features, since it is a powerful tool to convert a set of observations of possibly correlated variables into a set of values

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of linear uncorrelated variables called principal components. It reduces the dimension of input and improves the efficiency of the system [33]. In implementing NN, Radial basic Functional

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Neural Network based model is preferred, since it offers a powerful framework for representing non-linear mappings from several inputs to one or more outputs [34]. In this work, different categories of PRNET models are proposed and also a new filter of type PR filter is proposed by slightly modifying the components of conventional filters of RBFNN to improve the power of PRNET even though raw data are highly nonlinear, interrelated, null and noisy. Also the Fuzzy logic of soft computing tool will be used to fix the range of parameters used in designing preforms, since it will be helpful to make a clear quality distinction among the product lots [35]. The following section 4.0 describes in detail about the components involved in the proposed model.

Fig.4 Overview of the proposed model

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Fig.5 Architecture of the proposed soft computing model

4..0 Role of Soft Computing tools in P/M process In recent years a considerable research effort is being gone into the development of soft

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computing for data analysis, function approximation, sensor processing and control of material properties. Significantly, their ability to perform complex nonlinear mappings can be used for

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approximating multiple input and multiple output relationships. The modelling problem in P/M process can be thought of as a continuous non-linear mapping from ‘n’ dimensional space to ‘m’

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dimensional space. The soft computing based models have significant contribution in simplifying

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the various processes involved in the manufacturing of composite preforms as given below:

4.1 Prediction tool 4.1.1 RBFNN

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A fundamental aspect of Neural networks (NN) is to use simple processing elements that are essentially models of neurons in the brain. These elements are then connected together in a

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well-structured fashion, although the strength and nature of each of the connecting links dictate the overall operational characteristics of the total network. Neural networks operate by

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simulating the ability of biological neural systems to perform complex decision making tasks without any prior programming. They are feed-forward networks consisting of three layers

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namely input, hidden and output layer as given in Fig.6. The hidden layer has kernel neurons and an output layer has linear neurons [36]. The connection between input and hidden layer does not use the weighted sum of inputs. The output of the hidden layer represents basis functions, which are determined by the distance between the network input and the centre of the basis function. As the input moves away from a given centre, the neuron output drops off rapidly to zero. The output layer of RBFNN is linear and produces a weighted sum of the outputs of the hidden layer. The neurons in the RBFNN have localized receptive fields because they only respond to inputs that are close to their centres. Construction of radial basis function neural networks involves selection of radial basis function centroid, radius (width or scale), and number of radial basis function (RBF) units in the hidden layer [37]. RBFNN’s are commonly following a hybrid procedure in two stages. In the first stage, from the available training samples the centers are selected and radial functions are 11 Page 11 of 43

computed without a target in unsupervised mode. The second stage operates in supervised mode, where the weights are computed using the target values of training samples.

Fig. 6 RBFNN Model

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4.1.2 Algorithm

In the proposed RBFNN model, the exact interpolation, called NADP (Neuron At every

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Data Point) is preferred for training the Network, because this technique maps every point in the input pattern to the output layer. The given Q amount of training samples is considered as centers

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in this method. Formally, the exact interpolation of Q data points in a multi-dimension space require all the D dimensional input patterns x k = { xik , i= 1, 2… D} to be mapped onto the

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corresponding target output yk where D is the size of the input layer. The goal is to find the f function such that  k

k

 1 ....... Q

(12)

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f (x k )  y

This approach requires Q amount of radial basis functions. The algorithm given below is used to interpolate the source data exactly:

Initialize the free parameters like the spread factor, number and values of centers, the

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I. II.

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type of radial basis function and weight values between hidden and output layer. The kth training pattern with D amount of features is applied to input layer X, whose size

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is equal to D .Then each input (xi ; i=1,2,..D) node of kth pattern sends the input data to the hidden layer. III.

th

At hidden layer, the distance between the input layer X and the j center point 

is j

calculated by the formula: || X-

IV.



j

||=

i D jQ

 i 1

j 1

( x i, j 



j ,i

)

2

(13)

The activation of hidden unit () is determined by the distance between the input vector and centers using any one of the RBFNN filters  as given in Sec. 4.1.3. (14)

 j ( X )  f (||    j ||)

 is a Q x Q matrix computed entirely from the data points X

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  (|| X1 1||)...... (|| X1Q ||)        (|| X Q 1||)...... (|| X Q  Q ||)    V.

(15)

The activation of the output unit is determined by a dot product between the hidden

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activation vector and weight vector. For convenience an additional basis function  0 with a constant activation value of ‘1’ can be used with weight W0 to improve the accuracy of

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the network. Finally the value of kth output neuron is calculated by: Q

y k   W jk  j (  )  W 0 0

VI.

(16)

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j 1

The above steps (I-V) belong to the training procedure. At the end of training, the weight vector is used to test the generality of network with independent test samples. The functions and target vector T of

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Weight may be computed in terms of known  supervised learning as below:

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The unknown term ‘W’ required for the network recognition can be calculated by: Wb   1T

(17)

While testing the independent input samples, Wb is separated as W and Wo to derive the

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VII.

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Eqn. (17) can be derived easily since  been symmetric, that is Y   T W  W

output value Y using the Eqn. (16).

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4.1.3 Proposed filters in RBFNN

As per the algorithm of RBFNN in Sec. 4.1.2, the deviation between the input nodes and RBF centers are calculated and it applies to filters of RBFNN to derive the output of hidden layer as per Eqn. (14). The RBFNN supports the possible conventional filters as given below: Gaussian function  (r )  exp  r   2 2

 2 

Cubic function

(18)

 (r )  r 3

(19) Linear function

 (r )  r

(20)

Multi Quadric function  ( r )  r 2   2

(21)

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Gaussian kernel has almost exclusively been used as basic function of the cluster centers of RNFNN in most of its applications. This work proposes PR filter as given in Eqn. (22) by slightly modifying the parts from the above conventions filters. r2 2 2

(22)

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PR Filter

 (r ) 

4.1.4. Reduction tool for input parameters

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Principal Component Analysis (PCA) involves a mathematical procedure that transforms a number of (possibly) correlated variables into a (smaller) number of uncorrelated variables

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called principal components. The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible. It helps to discover or to reduce the dimensionality of the data

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set and to identify new meaningful underlying variables. Vijay Manikandan Janakiraman et al [9] used PCA as a pre-processing step to reduce the input dimension, thereby reducing the memory

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requirements of the models and to reduce the cross-validation time required to identify optimal model hyper-parameters. Jing Zhou et al., [34] applied the PCA to acquire main features of measured data for quick and accurate fault detection and identification in health monitoring.

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The raw data set has more number of input parameters in the form of P, Ho, Hf, Do, Dc,

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DB,  ,  , iron content and lubricant. While using with more input parameters, the network complexity increases in architecture and it will turn in increasing the training time. Also, each

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input pattern will give different results. Hence the selection of relevant input features is the main issue in designing the architecture of neural networks. Using the working experience in P/M Lab, the input layer size may be decided. There is no assurance to select the unique optimal selection among the available input features. The PCA tool helps in identifying meaningful parameters and reducing the dimension of the input space, which in turn reduces the architecture and training time. Also, this provides the unique path for deciding the possible input features in P/M Lab.

4.2 Fixing tool for a range of input parameters (Data Discretization) Fuzzy logic (F/L) is a form of many-valued logic or probabilistic logic and it deals with reasoning that is approximate rather than fixed and exact. Compared to traditional binary sets (where variables may take on true or false values) fuzzy logic variables may have a truth value that ranges in degree between 0 and 1. Fuzzy logic has been extended to handle the concept of 14 Page 14 of 43

partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific functions. Fuzzy set, therefore, provides a powerful computational paradigm for extending the capability of binary logic in ways that enables a much better representation of knowledge in

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materials engineering [21]. This is because fuzzy logic facilitates the expression of continuous by way of assigning a numerical grade of membership.

cr

The multi-value attribute of F/L allows intermediate values to be defined between conventional binary evaluation points, such as the degree of presence or absence of a material

us

constituent of a composite. This facilitates the intuitive assignment of numerical values in obtaining exact solutions even when vague or imprecise concepts are used to describe material properties. Qian Zhang et al [39] successfully applied F/L to the industrial problems of predicting

an

machining induced residual stresses for aerospace alloy components as well as modelling the mechanical properties of heat-treated alloy steels. Yuanfei Han et al, [40] applied strain rate,

M

deformation temperature and the strain as input parameters and flow stress as output parameter using ANFIS model. Hence, the application of fuzzy logic will be helpful in P/M Lab. for

d

classifying the properties of composites into various levels like low, medium, high and very high level. The knowledge of this classification will be useful for the technicians working in the P/M

Ac ce p

te

Lab to fix the range of input parameters while mixing various powders for preparing composites.

5.0 Design and Implementation

The dirty data will slow down the mining algorithm. Hence the following strategies were adopted to convert the dirty data into clean data. 5.1 Data Preprocessing 5.1.1 Data Cleaning

The highly non-linear parameters (ni and ki) representing the strain hardening properties have more incomplete entries (empty cells). The following issues were tried to substitute the values for these null parameters. 1. The empty cells may be omitted completely from the raw database. 2. The empty cells may be substituted strictly by zero. 3. The empty cells may be substituted by the mean of the parameter

15 Page 15 of 43

The first method is logically incorrect, since it affects the originality of the raw data. The second method is not adequate since the conflict may occur between the original raw value (zero) and substituted value (zero). Among the above methods, third strategy is felt as a suitable 0.23 and parameter ki is substituted by its mean value 222.5365. 5.1.2 Data Normalization/ De-normalization

ip t

method than the other two methods. In this case the empty cell of ni is substituted by the mean

cr

The raw data reported in Table 1, has an irregular range of values in the input and output parameters. Some are having the values below 1.0 and some are having valueeedis greater than

us

or equal to 1.0. This kind of distribution will slow down the learning period and generalization of the system. Hence, the source data collected from P/M Lab is normalized to enhance the learning period of system. Before applying the soft computing tools, the raw data x is mapped as

N max  N min  max x  min x 

(23)

M

X n  N min  ( X  min x )

an

normalized data xn between 0 and 1, as given below:

where the minx and maxx are the minimum and maximum value of x respectively. Further, the

d

Nmin and Nmax are the minimum and maximum value of normalized data respectively. Since the

Xn 

X

 min x  max x  min x 

te

Nmin is zero and Nmax is one, the above equation is reduced to: (24)

Ac ce p

At the end of successful learning, to recognize the independent test samples, the post processing (De-normalization) is applied as given below to convert the normalized data into raw data. X= (Xn+ minx) (maxx - minx)

(25)

In order to verify the de-normalized output while predicting the properties of composite preforms, the error is derived between the expected and actual value of the system. This error is measured in the form of correlation coefficient (R) and Average Absolute Relative Error (AARE) percentage as given in Eqn. (26). The AARE% is used mostly in this paper since it is an unbiased term to measure the error accurately. AARE % 

Absoluteraw  data  network  output  X 100 raw  data

(26)

Also the reduction process mentioned in the section 4.2, applies normalization with respect to the mean and standard deviation for a certain case. 16 Page 16 of 43

5.2 Soft computing model Design The raw data with 463 samples are collected as per the procedure stated in the section 1.2.2. The raw data is pre-processed using the procedures of Sec. 5.1.1 and 5.1.2. The raw data with 21 parameters is divided into two data sets, namely: training (350 samples) and testing (113

ip t

samples). Among 21 parameters, 10 parameters are considered as input and remaining 11 parameters are named as output parameters to represent the deformation and strain hardening

cr

properties of composite preforms. The network structure is fixed as x—350— 11, where the size of input layer x will be determined by the reduction process. The mining algorithm Sec. 4.1.2 is

us

used to train the samples. The weight vector for this algorithm is initialized as random values between zero and one. The pure linear filter is selected for mapping input and output data and PR

an

filter is used for mapping the input data of the hidden layer.

5.3 Implementing the soft computing models

M

The programming language C++ and the software package MATLAB 2010 were used to implement this work. MATLAB is a high-level technical computing language and interactive

d

environment for algorithm development, data visualization, data analysis, and numeric computation. Using the MATLAB product, we can solve technical computing problems faster

te

than with traditional programming languages such as C, C++, and Pascal. For implementing a Neural network, the object-oriented classes, namely input neuron,

Ac ce p

hidden neuron, output neuron and friend class namely ‘back’ were developed in C++. Each class has the necessary private data members to represent activation value, out value, error and weight information of each kind of neuron and also sufficient public member functions. The output neuron object includes additionally the desired or target value specified by the user. The friend class is a backbone of an entire architecture to map input to output. The data files were used to retrieve the information for the network and to transfer the network simulated results. In the client program, three objects such as train object, validate object and test object were created to test the network training, validation and testing. Fuzzy code was developed using MATLAB.

17 Page 17 of 43

6.0 Results and discussions 6.1 Effect of NN Prediction tool Among the samples collected from P/M Lab, 350 are used as training samples and 113 independent samples are used as testing samples. The hidden layer size is 350, since this model

ip t

uses NADP method as discussed in Sec. 4.1.2, where all training samples are used as hidden neuron/centers. The output layer has 11 nodes representing the equations (1-11). The PR filter as

cr

mentioned in Sec. 4.1.3 is used for improving the accuracy of network output.

Case 1: Using the working experience in P/M Lab, the number of input nodes is decided. This

us

kind of RBFNN model based on knowledge of P/M Lab determines 5 input nodes, namely load, aspect ratio, iron content, lubricant and the fractional density. The testing is done with

an

independent test samples and errors of output nodes are calculated. The optimal spread factor  value is chosen as 2.0 in this case. As given in Fig.7, the maximum and minimum error is 16.741% and 0.847% respectively in this method. Only 4 parameters have the error value less

M

than 5%. The average of the sum of the AARE error % for all parameters is 7.24%. This term is high since most of the output parameters are non-linear, interrelated and noisy data. Table 2

te

d

summaries the outcome of various Models described in 6.1 and 6.2

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Fig.7 Comparison of PRNET Model based on Lab Knowledge and conventional RBFNN Case 2: To enhance the output performance, the number of input nodes is increased from 5 to 10 to cover all the input variables used in mathematical representations of hard computing model of Sec.3. Table 2 shows that this approach gives the average error as 4.02 %. Still the hydrostatic stress of deformation and strain hardening properties are greater than 6 %.

Table 2 Average of Sum of AARE% of all parameters of various models

The above two cases have drawbacks. In the first case, the neural network designer should have the prominent knowledge in selecting the most relevant features for predicting the properties of composites. In the second case, the need occurs to take care of all the independent variables arise from the mathematical model, which gives the effect of hard computing model scenario. The results of neural network will vary with respect to the input combination. Hence, 18 Page 18 of 43

the neural network should be trained in trial and error basis with different combinations of input pattern. It is very different to define the correct combination of input variables, which will be solved by PCA.

ip t

6.2 Effect of feature reduction tool

PCA makes some transformation over the source data. It is applied along with RBFNN to

cr

enhance the output of prediction tool. This kind of integrated model is developed in different approaches and the outcome is shown in Fig.8.

us

RBF-PCA-type-1:

All source variables P, Ho, Hf, Do, Dc, DB,  ,  , fractional density and lubricant are

an

applied to PCA, which reduces the number input features from 10 to 5. These selected five features are normalized in terms of mean y and standard deviation y given below: =

x  x    yx   y 



(27)

M

Xn

In this case, the normalized data are expected with y as zero and y as one. Then, the

d

normalized inputs are considered as input nodes for RBFNN, which gives the average of

RBF-PCA-type-2:

te

AARE% over 11 output parameters is 3.26%.

Ac ce p

In this type, all the raw data are pre-processed by PCA and the resultant seven parameters are normalized using Eqn. (27). The average error in all parameters is computed as 3.19% RBF-PCA-type-3:

In this method, all the parameters are normalized using the Eqn. (24) then applied to PCA to reduce the features from 20 to 10 and average of error of all parameters is 1.48%. RBF-PCA-type-4:

Finally, this method tries to select 12 features from 20 variables, which gives the average AARE% over 11 parameters is 1.29%. After training the network, the output is compared with experimental data, whose partial result is given in Tables 3 (a-c) and Fig. 9 reports the R between the experimental data and PRNET output for eleven output parameters. From Fig.7, it is noted that the PRNET models give good accuracy in deformation and strain hardening properties due to the selection of meaningful input features compared to the conventional models of section 3.1. Also, it seems that the PRNET selection with limited input features is the best one, than the 19 Page 19 of 43

selection through the working experience of P/M Lab. The PRNET model provides best guidelines in selecting the relevant input features and it gives more accuracy in predicting the output parameters even with missing entries. This model will be helpful in selecting the relevant input features for the inexperienced persons working in P/M lab. The good accuracy is known as

ip t

1.29 by the RBF-PCA-type-4 and accuracy due to the exclusion of PCA is 4.02. The deviation between these two values is measured in terms of AARE% as 67.89%. Table 4 shows the power

cr

of PR filter in improving the predictability of PRNET, where the new filter effect is compared with conventional filter types like Gaussian, Cubic, linear and multi-quadric specified in Eqns.

us

(18-21).

an

Fig.8 Effect of various PCA Models

Fig.9 Correlation coefficient (R) for PRNET Model

M

Table 3(a) Partial experimental output, Network output data with error value for the output parameters 1, 2, 3 and 4

d

Table 3(b) Partial experimental output, Network output data with error value for the output parameters 5, 6, 7 and 8

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Table 3(c) Partial experimental output, Network output data with error value for the

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output parameters 9, 10 and 11

Table 4 Comparison with various filters

6.3 Effect of input range fixing tool The fuzzy logic can model the non-linear functions of arbitrary complexity. Fuzzy logic gives approximation solution while neural network gives exact solutions. The fuzzy inference system shown in Fig.10 with interrelated variables is used to enhance reasoning in classifying the properties of composites. This system adapts major three input variables, namely load, aspect ratio and fractional density and 11 output parameters. As per the input given, it will give classify the properties of composites.

20 Page 20 of 43

Member function: The input parameters, load, aspect ratio and fractional density uses triangular-shaped membership function. The triangular curve is a function of a vector, x, and depends on three scalar parameters a, b, and c as given below:

ip t

  x  a, c  x   f ( x, a, b, c) = max min , ,0   ba cb  

(28)

cr

The parameters a and c locate the "feet" of the triangle and the parameter b locates the peak. i) Load:

us

The minimum and maximum values for load are 5 and 120 respectively in the collected raw data. The membership value is categorized into low, medium and high levels as given below: -4

Medium

20

40

40

64.5 110

64.5

120

M

High

5

an

Membership value = Low

ii) Aspect ratio:

d

The minimum and maximum values for aspect ratio are 0.4645 and 1.0539 respectively

0.2287

0.4645

0.7003

Medium

0.5243

0.7000

0.9000

High

0.8181

1.0540

2.0000

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Membership value = Low

te

in the collected raw data. The level of classification depends on this input as given below:

iii) Fractional density:

The minimum and maximum values for fractional density are 0.82 and 0.99 respectively in the collected data. Until a certain limit of fractional density, the output parameters increases afterwards their value decreases. As given in Fig. 10 (b), it is represented as additional classification “very high”. Membership value =

Low

0.7467

0.8147

0.8557

Medium

0.8097

0.8677

0.8707

High

0.8670

0.8967

0.9400

Very high

0.9401

0.9890

1.0700

21 Page 21 of 43

Eleven output parameters of Fuzzy Inference System (FIS) use the trapezoidal function whose curve is a function of a vector, x, and depends on four scalar parameters a, b, c, and d, as given by:

ip t

  x  a, d  x   f ( x, a, b, c, d ) = max min ,1, ,0   ba d c   

(29)

cr

The parameters a and d locate the "feet" of the trapezoid and the parameters b and c locate the "shoulders." FIS model classifies the input data into low, medium, high and very high

us

using the inference rules as given below: Inference rules:

an

 If load increases the deformation and strain hardening properties increases.  The aspect ratio value is directly proportional to the deformation and strain hardening properties.

M

 The output parameter increases if the fractional density increases. But after certain limit it will decrease.

te

d

The above constraints are implemented in FIS by:

1. If (Load is Low) or (Aspect ratio is Low) or (Fractional_density is Low) then (output1

Ac ce p

is Low)(output2 is Low)(output3 is Low)(output4 is Low)(output5 is Low)(output6 is Low)(output7 is Low)(output8 is Low)(output9 is Low)(output10 is Low)(output11 is Low)

2 If (Load is Medium) or (Aspect ratio is Medium) or (Fractional_density is Medium) then (output1 is Medium)(output2 is Medium)(output3 is Medium)(output4 is Medium)(output5 is Medium)(output6 is Medium)(output7 is Medium)(output8 is Medium)(output9 is Medium)(output10 is Medium)(output11 is Medium) 3. If (Load is High) or (Aspect ratio is High) or (Fractional_density is High) then (output1 is High)(output2 is High)(output3 is High)(output4 is High)(output5 is High)(output6 is High)(output7 is High)(output8 is High)(output9 is High)(output10 is High)(output11 is High)

22 Page 22 of 43

4. If (Fractional_density is Very_High) then (output1 is Low)(output2 is Low)(output3 is Low)(output4 is Low)(output5 is Low)(output6 is Low)(output7 is Low)(output8 is Low)(output9 is Low)(output10 is Low)(output11 is Low) Case 1: 0.3;

45

0.8;

classifies the output into low, medium and high level as follows: 0.0958

0.0911

cr

Low level: 0.0461

1.0664

0.0580

0.0591 33.9198 17.8077

4.0654

0.0568

0.1950

1.2800

0.2450

0.2500 94.3787 68.2840 13.1544

0.2400

0.3436

1.4933

0.4317

0.4405 154.7674 118.6460 22.2283

us

118.8190 Medium level: 0.4050

0.3850

an

502.2000 0.6784

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High level: 0.7136

119 1.08] and FIS

ip t

Load and aspect ratio are given in the form [5

d

884.8562

0.4229

Case 2:

te

The load, aspect ratio and fractional density are given as input in the low, medium and high level in the range [5 0.3 0.82; 45 0.8 0.9; 119 1.08 0.99], and FIS classifies all outputs with Low: 0.0958

Ac ce p

respective to their level. 0.0911

0.0461

1.0664

0.0580

0.0591 33.9198 17.8077

4.0654

0.0568

0.1950

1.2800

0.2450

0.2500 94.3785 68.2834 13.1542

0.2400

0.3439

1.4936

0.4320

0.4409 154.8721 118.7335 22.2441

0.4232

118.8190 Medium: 0.4050

0.3850

502.2000 High: 0.7142

0.6789

885.5222

23 Page 23 of 43

Case 3: The fractional density for the “very high level” is tested at 0.98 and FIS classifies all outputs with low level. Low: 0.0943

0.0478

1.0687

0.0600

0.0612 34.5797 18.3583

123.0026

0.0588

cr

Fig.10 (a) FIS model

4.1645

ip t

0.0992

us

Fig.10 (b) Member function for fractional density

From the above analysis, it proves that the load should be between 5- 40, aspect ratio

an

between 0.2287 and 0.7003 and fractional density between 0.7467 and 0.8557 to classify as low level properties of preforms. The load should be 20 - 64.5, aspect ratio between 0.5243 - 0.9000

M

and fractional density between 0.8097 - 0.8707 to classify the medium level. To classify higher level properties of composite preforms, the load must in the range 64.5– 120, aspect ratio must be

te

7.0 Conclusions

d

0.8181 - 2.0 and fractional density must be in the range as 0.8670 - 0.9400.

The conclusions that can be derived from this soft computing modelling for this analysis are as

Ac ce p

given below:

 PRNET developed in this work is capable of identifying the most meaningful parameters for RBFNN training and predicting deformation and strain hardening properties of Al-Fe composite preforms used in manufacturing divisions of the P/M Lab with proposed PR filter.

 Its predictability has increased by 67.89% relative from the conventional model even though the existence of highly non- linear interrelated and noisy raw data.  Fuzzy logic helps to decide the range of input parameters for classifying the various properties of composite preforms.  These Knowledge Based Systems developed using Soft computing tools will provide accurate and timely advice relating to the design and manufacture of powder metallurgy parts, even though the raw data are interrelated, non-linear, noisy and empty entries. 24 Page 24 of 43

 They not only avoid expensive experiments, but also evade handling unsafe materials that cause severe damage to the environment.  In future, this kind of soft computing models will be helpful for researchers to predict the

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characteristics of any kind of powder materials even for the nano composite preforms.

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process, International journal of Computational Materials Science, 50(7) (2011)

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cr

ip t

2273–2279.

29 Page 29 of 43

List of Tables: Table 1

Raw data of preforms derived from Lab Experiments

Table 2

Average of sum of AARE% of all parameters of various models

Table 3(a)

Partial experimental output, Network output data with error value for the output

Table 3(b)

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parameters 1, 2, 3 and 4.

Partial experimental output, Network output data with error value for the output

parameters 9 10 and 11. Comparison with PR filter

an

Table 4

Partial experimental output, Network output data with error value for the output

us

Table 3(c)

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parameters 5, 6, 7 and 8.

List of Figures:

Life cycle of powder metallurgy process

Fig.2(a)

Ball milling equipment

Fig.2 (b)

Compaction process

Fig.3 (a)

Linear relationship between hoop strain and axial strain

Fig.3 (b)

Non-linear relationship between various stresses and axial strain

Fig.4

Overview of the proposed model

Fig.5

Architecture of proposed soft computing model

Fig.7

d

te

Ac ce p

Fig.6

M

Fig. 1

RBFNN model

Comparison of PRNET model based on lab knowledge and conventional RBFNN

Fig.8 Fig.9

Effect of various PCA models Correlation coefficient (R) for PRNET Model

Fig.10(a)

FIS Model

Fig.10(b)

Member function for fractional density

30 Page 30 of 43

Table 1 Raw data of preforms derived from lab experiments Load

Hf

DC

 z   

  

'

e  z  





 z   m

ni --

ki

mm

5

9.42 20.31 20.31 0.92 0.00 0.00 0.00

1.00

0.00 0.00 15.41 7.68 2.57

10

9.39 20.32 20.32 0.93 0.00 0.00 0.00

1.00

0.00 0.00 30.86 16.72 4.71 0.41 867.55

15

9.33 20.35 20.35 0.93 0.01 0.00 0.00

1.01

0.01 0.00 46.14 27.43 6.24 0.34 336.57

20

9.28 20.39 20.39 0.94 0.02 0.01 0.00

1.01

0.02 0.01 61.24 38.41 7.61 0.22 250.26

7

19.18 20.33 20.33 0.90 0.00 0.00 0.00

1.00

0.00 0.00 21.56 11.30 3.42

15

19.03 20.36 20.37 0.91 0.01 0.00 0.00

1.01

0.00 0.00 46.06 26.12 6.65 0.42 736.07

20

18.70 20.50 20.55 0.91 0.03 0.02 0.01

1.02

0.33 0.13 60.57 39.99 6.86 0.30 172.88

25

18.17 20.73 20.80 0.92 0.06 0.04 0.02

1.04

0.33 0.30 74.10 50.75 7.78 0.29 171.80

5

9.81 20.38 20.38 0.89 0.00 0.00 0.00

1.00

0.00 0.00 15.33 2.17 1.39

10

9.77 20.39 20.39 0.89 0.01 0.00 0.00

1.01

0.00 0.00 30.63 6.31 2.11 0.45 1004.43

16

9.70 20.46 20.46 0.90 0.01 0.00 0.00

1.01

0.00 0.00 48.69 12.01 4.23 0.34 920.13

20

9.65 20.47 20.47 0.90 0.02 0.01 0.01

1.01

0.25 0.20 60.80 17.12 6.56 0.26 818.72

us

cr

ip t

N

--

--

--

--

--

an

mm

 f    th

d

M

mm

DB

1

Name of the Model

Ac ce p

No.

te

Table 2 Average sum of AARE% of all parameters of various models

Feature selection by

Feature

Average of Sum of

Reduction

AARE% of all parameters

working 5 (Without reduction)

7.24

All features without PCA

10 (Without reduction)

4.02

RBF-PCA-type 1

5 from 10

3.26

RBF-PCA-type 2

7 from 20

3.19

5

RBF-PCA-type 3

10 from 20

1.48

6

RBF-PCA-type 4

12 from 20

1.29

experience in P/M Lab

2 3 4

31 Page 31 of 43

Table 3(a) Partial experimental output, Network output data with error value for the output parameters 1, 2, 3 and 4 z

No.

’



S

N/w/o

Err.

E/o

N/w/o

Err.

E/o

N/w/o

Err.

E/o

N/w/o

Err.

1.

0.280

0.275

0.005

0.240

0.240

0.000

0.120

0.115

0.005

1.180

1.179

0.001

2.

0.400

0.399

0.001

0.350

0.352

0.002

0.180

0.169

0.011

1.260

1.259

0.001

3.

0.520

0.508

0.012

0.460

0.455

0.005

0.230

0.219

0.011

1.340

1.336

0.004

4.

0.610

0.596

0.014

0.550

0.546

0.004

0.280

0.268

0.012

1.390

1.390

0.000

5.

0.000

0.007

0.007

0.000

0.000

0.000

0.000

-0.001

0.001

1.000

1.000

0.000

6.

0.020

0.023

0.003

0.010

0.013

0.003

0.010

0.009

0.001

1.020

1.021

0.001

7.

0.080

0.085

0.005

0.070

0.062

0.008

0.030

0.001

1.050

1.053

0.003

us

cr

ip t

E/o

an

0.031

Table 3(b) Partial experimental output, Network output data with error value for the

N/w/o

M

output parameters 5, 6, 7 and 8

Err.

E/o

N/w/o

Err.

E/o

N/w/o

Err.

0.003 0.410

0.409

0.001

109.3

112.1

2.753

80.6

82.2

1.604

0.440

0.000 0.420

0.419

0.001

119.5

123.6

4.105

88.9

91.5

2.648

0.440

0.443

0.003 0.420

0.423

0.003

127.5

133.4

5.846

95.2

99.1

3.901

4.

0.450

0.454

0.004 0.440

0.443

0.003

133.3

139.2

5.927

100.5

104.1

3.911

5.

0.000

0.000

0.000 0.000

0.000

0.000

30.8

30.6

0.153

17.0

17.5

0.474

6.

0.300

0.295

0.005 0.200

0.200

0.000

60.7

61.2

0.473

37.2

38.5

1.321

7.

0.400

0.406

0.006 0.380

0.376

0.004

87.1

86.5

0.514

60.1

59.9

0.171



N/w/o

Err.

1.

0.430

0.433

2.

0.440

3.

E/o

Ac ce p

te

E/o

d



No.

z



32 Page 32 of 43

Table 3(c) Partial experimental output, Network output data with error value for the output parameters 9, 10 and 11 M

No.

ni

ki

N/w/o

Err.

E/o

N/w/o

Err.

E/o

N/w/o

Err.

1.

9.570

9.944

0.374

0.260

0.259

0.001

152.1

156.0

3.9

E/o –

2.

10.200

10.722

0.522

0.250

0.249

0.001

150.0

155.1

5.0

Experimental

3.

10.790

11.474

0.684

0.270

0.264

0.006

152.0

159.4

7.4

output

4.

10.940

11.702

0.762

0.270

0.262

0.008

152.2

159.5

7.2

N/w/o –

5.

4.610

4.397

0.213

0.000

0.000

0.000

0.000

0.4

0.4

Network output

6.

7.840

7.556

0.284

0.480

0.472

0.008

365.7

373.0

7.2

Err. – Error

7.

9.000

8.896

0.104

0.290

0.291

0.001

178.8

179.0

0.2

value

an

us

cr

ip t

E/o

Cubic filter

Linear filter

Multi-Quadric

PR-filter

2.50655487

4.90519074

1.59421334

1.59529722

0.35863006

4.1194719

3.14385519

2.69209456

2.69232382

0.21944013

3.2789044

6.95255399

2.18443059

2.1586816

1.79040972

0.16211602

0.11507286

0.11846953

0.11840352

0.00215818

0.4399215

0.40942078

0.48882992

0.48917313

0.00454538

0.72819369

0.34182823

0.74511733

0.74505787

0.00324028

0.61730141

0.64043972

0.65428924

0.65433548

0.23573105

1.20444932

4.49642293

1.33864274

1.33979699

0.2242156

2.67468405

3.30662465

2.23094876

2.23294407

0.151513

1.26876441

0.32016891

0.84783869

0.84903742

0.00546739

1.42188243

1.15617863

1.31824147

1.31831844

0.01655852

Ac ce p

te

d

Gaussian Filter

M

Table 4 Comparison with various filters

33 Page 33 of 43

ip t cr us an M d te Ac ce p

Fig. 1 Life cycle of powder metallurgy process

34 Page 34 of 43

ip t cr us an

Ac ce p

te

d

M

Fig. 2(a) Ball milling equipment

Fig.2(b) Compaction process

35 Page 35 of 43

0.30

ip t

HOOP STRAIN

0.20

Initial fractional density: 0.89 Al-2%Fe Composite Lubricant : Graphite Aspect ratio: 0.50 0.75 1.00

0.00 0.00

us

cr

0.10

0.20

AXIAL STRAIN

0.30

an

0.10

M

Fig. 3 (a) Linear relationship between hoop strain and axial strain

150

d

Aluminium preform Lubricant: MoS2 Aspect ratio: 1.00

te

50

0

Ac ce p

STRESSES,MPa

100

0.0

0.1

0.2

AXIAL STRAIN 0.3

0.4

0.5

0.6

0.7

Axial stress

-50

Hoop stress Hydrostatic stress

-100

-150

Fig. 3 (b) Non-linear relationship between various stresses and axial strain

36 Page 36 of 43

ip t

Conventional model (High complexity)

us

cr

Experimental results

an

Proposed model PRNET (less complexity)

Properties -Analysis

M

Fig.4 Overview of the proposed model PCA

Raw data

te

d

Normalized data

Ac ce p

Classification of composite preforms

Prediction of properties of composites Optimal Features/ Parameters

Process control Neural Networks

Fuzzy Data

Fig.5 Architecture of the proposed soft computing model 37 Page 37 of 43

ip t cr us

Ac ce p

te

d

M

an

Fig. 6 RBFNN odel

Fig.7 Comparison of PRNET model based on Lab Knowledge and conventional RBFNN

38 Page 38 of 43

ip t cr us an

Ac ce p

te

d

M

Fig.8 Effect of various PCA Models

39 Page 39 of 43

40

Page 40 of 43

d

te

Ac ce p us

an

M

cr

ip t

Fig. 9 Correlation coefficient R for various outputs (a) z (b)  (c) ’ (d)S (e) 

ip t

(f)  (g) z (h)  (i) M

te

d

M

an

us

cr

(j) ni (k) ki

Ac ce p

Fig.10 (a) FIS Model

Fig.10 (b) Member function for fractional density

41 Page 41 of 43

SIMPLIFYING THE POWDER METALLURGY MANUFACTURING PROCESS USING SOFT COMPUTING TOOLS

cr

ip t

P.Radha *, G.Chandrasekaran*, N.Selvakumar# *Department of Computer Applications, #Department of Mechanical Engineering, Mepco Schlenk Engineering College, Virudhunagar–District, Pin: 626 005, Tamilnadu, India. + Corresponding author: e mail: [email protected], Phone: +91 4562 235453 . GRAPHICAL ABSTRACT

M

Prediction of properties of composites Optimal Features/ Parameters

te

d

Classification of composite preforms

an

Raw data

us

PCA

Normalized data

Ac ce p

Process control

Neural Networks

Fuzzy Data

42 Page 42 of 43

SIMPLIFYING THE POWDER METALLURGY MANUFACTURING PROCESS USING SOFT COMPUTING TOOLS

ip t

P.Radha *, G.Chandrasekaran*, N.Selvakumar# *Department of Computer Applications, #Department of Mechanical Engineering, Mepco Schlenk Engineering College, Virudhunagar–District, Pin: 626 005, Tamilnadu, India. + Corresponding author: e mail: [email protected], Phone: +91 4562 235453

cr

Highlights:

Ac ce p

te

d

M

an

us

 This soft computing based model act as an expert in manufacturing of composites.  Capable to select the range of parameters for predicting their properties.  It will avoid expensive experimentation.

43 Page 43 of 43