ANFIS Prediction of the Physical Properties of Degradable Plastic

Rosma Mohd Dom, Syamsiah Abu Bakar, Ajab Bai Akbarally and Wan Hasamudin Wan Hassan

1Faculty of Computer & Mathematical Sciences, UniversityTechnology MARA (UiTM), Malaysia 2Department of Computing,Biomass Technology Centre, Engineering & Processing Division, MPOB,

Malaysia

Abstract. ANFIS is a fuzzy inference system implemented in the framework of neural networks. This

paper presents the use of ANFIS to deduce the various combinations of polyethylene (PE) with oil palm

biomass (OPB), palm oil (PO) and starch needed in the production of degradable plastic with different

physical properties namely density, melt flow index and melting point. Experiments on the production of

different characteristics of degradable plastic are normally conducted in the labs. ANFIS simulation provides

a good alternative method for determining the physical properties of the degradable plastic. The finding

shows that ANFIS demonstrates high prediction accuracy as reflected by the small root mean square error

(RMSE) value and high correlation coefficient (r) and coefficient of determination (R2) values. ANFIS

prediction results are found to be compatible to linear regression estimations.

Keywords: ANFIS, Degradable Plastics, Physical Properties.

1. Introduction

Experiments on the production of different characteristics of degradable plastics are normally conducted

in the labs. Lab research can be very costly and time consuming. Alternatively, researchers are looking into

other methods of studying the properties of plastics produced by using computer application models. In our

study presented in this paper, the physical properties of degradable plastics are predicted based on

compositions of oil palm biomass, polyethylene , palm oil and starch modelled using ANFIS (Adaptive

Neuro-Fuzzy Inference System).

ANFIS is a hybrid between fuzzy and neural networks in which fuzzy inference is combined with the

pattern classification ability of neural networks. Application of fuzzy techniques in polymer studies is rather

new but becoming more popular. An example on the use of fuzzy approach in polymer study is the fuzzy

optimization of the flow rate of a plastic extruder process [1]. Artificial Neural Network (ANN) on the other

hand is a data-driven black- box model capable of solving highly non-linear complex problems. The ability

of artificial neural network to capture the relationship between input and output variables enables researchers

to solve large scale complex problems [2]. ANN are adjusted or trained so that a particular input leads to a

specific target output. The knowledge is stored in an opaque fashion thus the outputs of an ANN model are

difficult to interpret. The fusion of Artificial Neural Networks (ANN) and Fuzzy Inference Systems (FIS)

produces ANFIS architecture [3]. Fuzzy inference is used in this study to formulate the mapping from a

given set of input variables to an output using fuzzy logic. The output here refers to the physical properties of

degradable plastics namely the density, melt flow index and melting point. The primary mechanism to

formulate the mapping is a list of if- then statement called rules.

This study is motivated by the environmental problems caused directly or indirectly by the production

and use of plastic in the industry due to the lack of knowledge concerning the environment and consumers’

behaviour. Identifying the suitable composition of polyethylene with other gelling agents and filler in the

production of degradable plastics is essential in producing environmental friendly plastics. The objectives of

this study are:

to develop a computer application model ANFIS that can be used to find the suitable combination of

oil palm biomass, polyethylene, palm oil and starch in producing degradable plastics with different

physical characteristics.

rosma@tmsk.uitm.edu.my, nur_syam05@yahoo.com, ajab@tmsk.uitm.edu.my, wanhaswh@mpob.gov.my

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to assess the ability of ANFIS in predicting the density, melt flow index and melting point of degradable plastics by comparison with Linear Regression prediction results.

This study focuses on the development of a data- driven ANFIS using a real dataset obtained from the Malaysian Palm Oil Board laboratories. This method will help polymer researchers obtain more reliable and understandable results for the physical properties of degradable plastics produced given different combinations of various input variables. The proposed computer application prediction tool ANFIS is not to replace the conventional lab experiments or substitute the traditional statistical modelling techniques; instead it is to strengthen the present system by providing a simple simulation tool which can be useful in studying the input-output relationship governing the degradable plastic production using biomass components.

2. Development of ANFIS and Linear Regression Models for the Prediction of Physical Properties of Degradable Plastics. Biomass from the oil palm industries in Malaysia is a source of raw materials for the production of

degradable plastic. The Malaysian Palm Oil Board uses the natural fibre of oil palm biomass for the formulation of degradable plastics together with polyethylene and palm oil. Research and development on the usage of oil palm biomass in polymer industry are essential in this country.

Fuzzy systems and Artificial Neural Networks are computer application approaches that have been widely applied in various domains [4, 5]. The expressiveness of fuzzy if-then rules using linguistic variables can be combined with the learning capability of neural networks to produce Fuzzy Neural Network models [3]. The input attributes of the developed ANFIS system are the ingredients needed to produce degradable plastics namely the oil palm biomass, polyethylene, palm oil and starch. The outputs are the physical properties of degradable plastics measured in terms of Melt Flow Index (g/10min), Melting Point (oC) and Density (g/cm3). These imprecise attributes are called fuzzy linguistic variables and expressed as fuzzy linguistic labels such as Low (A1), Medium (A2) and High (A3).The research methodology undertaken is summarized in Fig.1.

Fig. 1: Summary of the research methodology.

The ANFIS model under consideration is a multi-input single-output (MISO) system with four inputs and one output. The data were obtained from the Malaysian Palm Oil Board laboratories. Due to small sample size, a commonly used re-sampling technique bootstrapping was introduced to the data set. The data was bootstrapped for 10 times before being split into training and checking data sets. For comparison

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purposes, linear regression models were also developed using similar inputs that were used in ANFIS. ANFIS and linear regression prediction accuracies are measured using the Root Mean Square Error (RMSE).

The ANFIS structure generated in this study utilizes fuzzy clustering of the input and output data sets as well as the bell-shape membership function. Thus the number of rules is equal to the number of output clusters. In order to minimize the over fitting of the model developed, the complete data set was split into a training (50%) and testing data set (50%). The ANFIS model was first trained using the training data set followed by validation process using the remaining data. The errors associated with the training and checking processes are recorded. ANFIS training was found to converge after training with 100 epochs as shown in Fig.2. RMSE for both the training and testing of ANFIS are very small which reflects the ability of ANFIS to capture the essential components of underlying dynamics governing the relationships between the input and the output variables [6]. Fig.3 shows the architecture of 4-input one-output ANFIS structure. The computation of membership functions (MFs) parameters is facilitated by a gradient descent vector.

Fig. 2: ANFIS training converges after 100 epochs. Fig.3: ANFIS architecture for a four input single-output Sugeno

fuzzy model.

ANFIS parameters are adjusted as to reduce the error measure defined by the sum of the squared difference between the actual and desired output. The root mean square error (RMSE) is calculated using

RMSE = 2

1

1 ( )N

t tt

A FN =

−∑ (1)

where and are actual and fitted values, respectively and N is the number of training or testing sample [7].

The parameters associated with MF’s will change through the learning process of ANN. The output of the th node is given in Eq. (2). Layer 1: Every node in this layer is an adaptive node with a node function

1 ( ), 1, 2Ai AiO m iμ= =

1 ( ), 1, 2Bi BiO n jμ= = (2) where m and n are the inputs to node i and A1,….i are the linguistic labels such as average, good, excellent associated with this node. 1

AiO is the membership grade of fuzzy set A1,….i and it denotes the degree to which the given inputs or satisfies the quantifier . The membership grade can be calculated using Eq.(3)

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1( ) , 1, 21 ( ) i

Aibi

i

x ix ca

μ = =−+ (3)

where , ,i i ia b c is the parameter set of a bell-shape figure. Parameters in this layer are referred as premise parameters [3].

Layer 2: Every node in this layer is a fixed node and the output is the product of all the incoming signals presented by Eq. (4).

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2 ( ) ( )ij ij A i B jO w m nμ μ= = i, j=1, 2 (4)

Each node of output represents the firing strength of a rule. Layer 3: Every node in this layer is fixed. The nodes in this layer normalizes the weight functions by

calculating the ratio of the th rule’s firing strength to the sum of all rules’ firing strengths using Eq.(5). _

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11 12 21 22

ijijij

wO w

w w w w= =

+ + + i, j=1, 2 (5)

Layer 4: The nodes in this layer are adaptive nodes. The output of this layer are represented as _ _

4 ( )ij ijij ij ij ij ijO w f w p x q y r= = + +

for i, j=1, 2 (6)where iw is a normalized firing strengths from Layer 3 and { , ,...... ,i i i iP q m r ) are the parameter sets referred as consequent parameters.

Layer 5: The single node in this layer labelled ∑ computes the overall output. The output is calculated using Eq.(7).

5 21 i ji j i i jO w f

−

== ∑

2 21 1 ( )iji j ij ij ijw p x q y r

−

= == ∑ ∑ + + (7)Fuzzy reasoning which is made up of fuzzy if-then rules together with fuzzy membership functions is the

main feature of fuzzy inference systems [3] Fuzzy reasoning derives conclusions from the set of rules which are either data driven or provided by experts [6]. Fig. 4 shows the reasoning procedure for a first order Sugeno fuzzy model. Each rule has a crisp output and the overall output is a weighted average. For example; ‘If OPB is High and PE is Low and PO is Medium and Starch is Low THEN the MFI will be Medium is a complete rule defining the relations of input and output linguistic variables.

(a) (b)

Fig.4: (a) Fuzzy reasoning procedure for Sugeno model of physical properties of degradable plastics (b) If-Then rules

derived by ANFIS.

The rule set given below illustrates the reasoning mechanism and the corresponding equivalent ANFIS architecture where the nodes of the same layer have similar functions. Rule 1: If OPB is A2 and PO is A3 and PE is A3and Starch is A2Then f1= p1OPB + q1PO + r1PE + s1Starch + t1

Rule 2: If OPB is A2 and PO is A2 and PE is A2 and Starch is A3 Then f2= p2OPB+ q2PO + r2PE + s2Starch + t2 ...... Rule n: If OPB is A1 and PO is A2 and PE is A3 and Starch is A3 Then fn= pnOPB + qnPO + rnPE + snStarch + tn

3. Findings and Analysis Initially the training data set was used to develop ANFIS models with 2-input, 3-input and 4-input. The

models were run for 1000 epochs before the best models are identified based on the smallest RMSE values.

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Next, the testing data set are fed into the trained ANFIS models. ANFIS outputs are recorded and the error is calculated by comparing ANFIS predicted values with the actual lab values. Similar training data sets are used to generate linear regression equations which are then tested on similar testing data set as used for ANFIS. Linear regression outputs are recorded and the error is also calculated by comparing linear regression predicted values with the actual lab values. All ANFIS and linear regression predicted outputs on the physical properties of degradable plastics are recorded and analyzed. Tables 1 tabulates the RMSE values for the prediction of Melting Point, Melt Flow Index and Density of degradable plastics for 2-input, 3-input and 4-input predictor sets respectively using ANFIS.

The best predictor set are determined based on the smallest RMSE values. The findings indicate that the combination of polyethylene and oil palm biomass is found to be the best 2-input predictor while polyethylene, palm oil and oil palm biomass is found to be the best 3-input predictor. The results showed that ANFIS model prediction has very low RMSE values which indicate high prediction accuracies in predicting the physical properties of degradable plastics.

Table 1: RMSE values of ANFIS models for the prediction of Melt Flow Index, Melting Point and Density.

INPUT RMSE

Melt Flow Index RMSE

Melting point RMSE Density

Train Test Train Test Train Test PE+OPB 0.0050 0.0049 0.0991 0.1519 0.0056 0.0055 PE +PO 0.0259 0.0239 0.3581 0.3359 0.0279 0.0266

PE+STARCH 0.0144 0.0157 0.5764 0.5545 0.0117 0.0123 OPB+ PO 0.0348 0.0342 0.2905 0.3109 0.0409 0.0385

OPB+STARCH 0.0155 0.0187 0.4799 0.5120 0.0134 0.0139 PO +STARCH 0.0197 0.0183 0.4754 0.5168 0.0177 0.0176 PE+OPB+PO 0.0030 0.0030 0.0820 0.1344 0.0043 0.0044

PE+OPB +STRACH 0.0030 0.0030 0.0820 0.1343 0.0043 0.0044

PE+PO +STARCH 0.0030 0.0030 0.1089 0.1639 0.0043 0.0044 OPB+PO

+STARCH 0.0030 0.0030 0.0820 0.1344 0.0043 0.0044 PE+OPB+PO

+STARCH 0.0030 0.0030 0.0820 0.1344 0.0043 0.0044 Table 2 shows ANFIS and linear regression predicted results for several combinations of input sets that

generated different physical characteristics of degradable plastics. Other combinations could also be predicted using the developed ANFIS model to suit the needs of the polymer industry in producing degradable plastics. ANFIS prediction outputs are found to be compatible to linear regression estimations.

Table 2: Melt Flow Index, Melting Point and Density of degradable plastics produced by different combinations of input variables as predicted by ANFIS and Linear Regression (LR) models.

INPUT % of each INPUT

Melt Flow Index

(g/10min) Melting Point

(oC) Density (g/cm3)

ANFIS LR ANFIS LR ANFIS LR PE + OPB 85%+15% 0.09 0.08 131 130 0.896 0.92

100%+0% 0.08 0.10 129 130 0.951 0.92 PE+OPB+PO 70%+20%+10

% 0.13 0.13

129 129

0.944 0.90

90%+0%+10% 0.45 0.16 133 129 1.030 0.90 PE+OPB+PE+Starc

h 60%+25% +10%+5% 0.08 0.16 134 128 0.747 0.89 65%+5%

+10%+20% 0.62 0.29 109 126 0.480 0.84

4. Conclusions In this paper we had described the development of a data driven ANFIS model using real data set

obtained from the Malaysian Palm Oil Board. The developed ANFIS is a soft computing approach utilizing a feed-forward multilayer neural network for fuzzy modeling. ANFIS demonstrates good prediction performance and transparency in explaining the relationship among the input and output variables understudied which is essential in prediction modeling [8]. Though statistical models have long been used in studying and predicting patterns governing predictor and predicted output relationships, this study had shown that ANFIS models are highly robust and compatible. ANFIS models are found to have good

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prediction ability in predicting the physical properties ofANFIS for the prediction of physical properties of degradable plastics is recommended.

5. Acknowledgment The authors would like to thank Universiti Teknologi MARA, Malaysia and The Ministry of Higher

Education of Malaysia for providing the research Grant (Grant No. FRGS/1/10/TK/UiTM/02/09).

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