The mechanical properties of the composite were first determined experimentally. The experimental results were subsequently used as input data to train and test the neural network model developed in this study. The procedures and materials used to obtain the experimental data are presented in this section.
Materials and equipment
Collection and preparation of date palm wood flour/LDPE composite
The date palm wood was obtained from Nnamdi Azikiwe University Awka, permanent site, Anambra State, Nigeria. The shells were sun-dried in the open air to a moisture content of about 8%, crushed and ground. The ground wood was sieved using a mechanical sieve of size 150, 212, 250 and 300 μm. The date palm wood flour is shown in Figure 1. The sieved wood was dried in a laboratory oven at 105°C to a final moisture content of 3% to 4% and stored in plastic bags for further compounding.
Collection and preparation of recycled low-density polyethylene
The recycled low-density polyethylene (LDPE) plastic container was obtained from the refuse bin. The plastic was washed and sun-dried to remove dirt. The (LDPE) materials were cut to small sizes to enable the crushing machine to accept the material after drying.
Methodology
The date palm wood flour constitutes the filler for the composite. The date palm wood flour of different weight percent was filled with the remaining percentage being LDPE. The particle sizes of 150, 212, 250 and 300 μm were used to examine the size effect of date palm wood flour as filler in the properties of LDPE, respectively. These particle sizes were examined to find the one which gives the best properties on the LDPE. The date palm wood of each of the flours was filled at 2%, 4%, 6%, 8%, 10%, 12%, 14%, 16%, 18%, 20%, 22%, 24%, 26%, 28% and 30% by weight of the filler content, respectively.
The filler and polyethylene were mixed at different percentage compositions of the flour. The density of the LDPE was 0.91 g/cm3. The mixing of the recycled LDPE and date palm wood flour was done using a single screw extruder with serial number 811613 manufactured by Dongyang Fuqiang Electrical Industry Co., Ltd, China. The diameter of the screw was 25 mm, and the ratio of length to diameter was 3.6. Since the melting point of LDPE is 115°C, the temperature of the screw extruder was set at 130°C to 140°C during the compounding process to ensure that the melt flow index of at least 9.0 g/10 min is achieved for successful mixing. Melt compounding was chosen because dry blending of the material before loading the mould could result in an uneven mix due to the considerable differences in particle size, morphology and specific gravity of the two materials. Each of the mixture was injection-moulded using an injection moulding machine. The composites which were produced were allowed to cool at room temperature. Prior to mechanical tests, the composites were conditioned at 65% relative humidity and at room temperature of 23°C.
Testing of tensile specimen properties
The tensile test was carried out using a universal tensile machine (ENERPAC model No PUJ1200E) in accordance with ASTM D638 (ASTM 2013a). The test was performed at a cross-head speed of 5 mm/min.
The dimensions of tensile test specimen size for ASTM used were 3 mm × 12.5 mm × 60 mm. The specimen was placed in the grips of the machine and pulled until there was failure. The ultimate tensile strength, elongation and modulus were determined. Figure 2a shows the setup for the tensile test.
Testing of flexural specimen properties
The equipment used for this was a universal testing machine, ENERPAC model No PUJ1200E, located at Standard Organization of Nigeria, Enugu State. The test was performed under the room temperature.
The dimension of flexural test specimen size for ASTM D790 (ASTM 2013b) used was 3 mm × 40 mm × 140 mm. The length of support span was 100 mm, the specimen lied on a support span, and the load was supplied to centre of the sample. The test was stopped when failure occurred. The flexural strength and modulus were determined. Figure 2b shows the setup for the flexural test.
Testing of Izod notch impact specimen
The equipment used for this test was an impact tester machine manufactured by Samuel Devison Ltd, Leeds, England (model number LS102 DE) located at Standard Organization of Nigeria, Enugu State.
The dimension of Izod impact testing specimen size for ASTM D256 (ASTM 2013c) used was 3 mm × 10 mm × 55 mm. The specimen was clamped into the machine. The pendulum from the impact tester was released and allowed to strike through the specimen. The Izod notched impact energy absorbed was determined.
Neural networks
As has been previously mentioned, the origin of artificial neurons (ANNs) is based on the work of McCulloch and Pitts in 1943 (McCulloch and Pitts 1943). Artificial neurons are building blocks for artificial neural networks. We shall discuss here the structure artificial neurons and neural network used in this research.
Artificial neurons
Artificial neural networks make use of artificial neurons. ANNs simulate the manner of operation of natural neurons in the human body. The basic unit of operation of an ANN is the neuron shown in Figure 3.
In a typical neuron shown in Figure 3, the input to the neuron x
i
is multiplied by a weighting function W
i
to generate the transformed input W
i
x
i
. The transformed inputs are summed to obtain the summed input. The summed input constitutes the variables to the activation/transfer function, g, which generates the output a
i
. The output of the transfer function is compared to a threshold value. If the output is greater than the threshold value, the neuron is activated and signal is transferred to the neuron output; alternatively, if it is less, the signal is blocked.
Given an input vector X = (x
1, x
2, … x
n
), the activations of the input units are set to (a
1, a
2, … a
n
) = (x
1, x
2, … x
n
) and the network computes to
$$ I{n}_i={\displaystyle \sum_{j=1}^n{W}_{j,i}{a}_j} $$
(1)
$$ {a}_i=g\left(I{n}_i\right). $$
(2)
The transfer function could be a threshold transfer function, a sin function, a sigmoid function, hyperbolic tangent function, etc. Differentiable transfer functions are preferred. Similarly, non-linear transfer functions perform better than linear transfer function. Bearing these in mind, in this particular application, we chose the sigmoid function. The sigmoid activation function is given by the equation
$$ {a}_i=g\left(I{n}_i\right)=\frac{1}{1-{e}^{-I{n}_i}}\kern0.5em . $$
(3)
Training the network (learning) could be a supervised or unsupervised training. In supervised training, the network is provided with the inputs and appropriate outputs; hence, the network is trained with a set of examples in a specified manner. In unsupervised/adaptive learning, the network is provided with inputs but not the outputs. In this present application, we used the supervised learning; hence, the appropriate network architecture is the feedforward architecture.
The feedforward network architecture
As has been mentioned, the developed neural network models are feedforward multiplayer perceptron networks (MLP). The hidden units as previously noted use the sigmoid activation function. The network model is shown in Figure 4.
In the feedforward network shown in Figure 4, the output of the network is compared with the desired output. The difference between the output and the desired output is known as the error, E. ANNs learn by trying to minimize this error. The learning process uses optimisation algorithms such as the Levenberg-Marquardt algorithm, gradient descent algorithm, genetic algorithm or some other natural optimisation algorithm. These algorithms work by adjusting the weights, W
i
, such that the error, E, is minimized. Most ANNs use the simple gradient descent optimisation algorithm. In this work, we used this algorithm. Hence, the learning process uses the sum of squares error criterion E to measure the effectiveness of the learning algorithm.
$$ E=\frac{1}{2}{\mathrm{Err}}^2\equiv \frac{1}{2}{\left(y-{h}_W(x)\right)}^2 $$
(4)
Here
y = Y = the true/experimental value
$$ \widehat{Y}={h}_W(x) $$
(5)
h
W
(x) is the output of the perceptron.
The ANN for predicting the mechanical properties of date palm fibre/polymer composite
Recall that our application is for the prediction of the mechanical properties of polymer composite, and we used supervised learning. Hence, 70% of the data was used for training, while 30% was used for testing and validation. The maximum number of epoch was set to 1,000. The epoch was set to 1,000 not for any theoretical reasons but to ensure that there is sufficient number of iterations during the learning process. Also, learning was fast at this level, and the optimum performance was obtained in all cases when the epoch was less than 50. The ANN training was done using the Levenberg-Marquardt algorithm which performed better than others.
Single network architecture was used in the study. The network architecture consists of a single input unit, one hidden layer with two hidden units (nodes) and one output unit. We used the sigmoid transfer function in the all the processing units in the hidden layer. The network structure is shown in Figure 5. The input X to the neural network is the filler content in percent.
The network design was based on the fact that a typical back-propagation network has an input layer, an output layer, and at least one hidden layer (Anderson and McNeill 1992). There is no theoretical limit on the number of hidden layers, but typically there is just one or two (Anderson and McNeill 1992). Some work has been done which indicates that a maximum of four layers (three hidden layers and one output layer) are required to solve problems of any complexity (Anderson and McNeill 1992). According to one of the rules of designing typical back-propagation networks, if the process being modelled is separable into multiple stages, then additional hidden layer(s) may be required (Anderson and McNeill 1992). Bearing these in mind, we limited the number of hidden layers in our network to one.
The input-output relationship being modelled is univariate which is quite simple, unlike complex multivariate relationships. Anderson and McNeill (1992) stated that one of the rules of designing typical back-propagation networks is that as the complexity in the relationship between the input data and the desired output increases, the number of the processing elements in the hidden layer should increase. Based on the rule for determining the upper bound of processing elements in the hidden layer (Anderson and McNeill 1992), we chose a scaling factor of 2. This choice is based on the fact that our training data is not noisy with an exact relationship of the input to the output. Consequently, we determined the upper bound of the processing units in the hidden layer to be three. Hence, in accordance with this rule, we chose two processing elements in our hidden layer instead of three or more. Moreover, when we increased the processing elements to more than two, we did not obtain any improvement in our results. Also, when the number of elements was reduced to one, the results obtained were poorer than when the elements were two. Hence, for better efficiency and model parsimony, we stuck to two processing elements.