Prediction of Fatigue Life of Fiber Glass Reinforced Composite (FGRC) using Artificial Neural Network

M.S


I. Typical of rotor blades fatigue; loads
The load on the rotor blade is in two extreme ways. This is illustrate in Figure 1, which first, shows the applications of composite materials (bicycles, cars, airplanes, helicopters, bridges, wind turbines), with the No. of load cycles that experienced; during the life of structure, and on the vertical, the degree of variations in load cycles. Rotor blades of Wind turbine are subjected to a wide No. of loads during; their lifetime of twenty years. Prediction of the No.; of load cycles were up to or cycles [1]. Second, high variability are showed by this loads. The variation; of loads on rotor blades is a result of the random nature of the wind. This is in spite of the fact, that there is indeed regular component of fatigue; loading.

II. Materials of Rotor blade
Typically, rotor blade is constructed from fiberreinforced polymer, because of its high stiffness, ratio of high (stiffness to density) and good toughness of fracture [2]. Typically, continuous fiberglass composite is used, although designer is moving toward employing fiberglass because of its stiffer fiber and is slowly becoming available for wind industries. In this case, the materials used in wind turbine, relative to composite of aerospace, is characterize by relatively coarsely. The fibers are contained in polymer matrix, which provide a resistance to the compression load, but mainly serve to fix and align the fibers geometrically. Wide of blades are made from polyester but epoxy is also used. Both densities; are the same but better performance of fatigue is attributed to composite with the epoxy matrix, enable of lighter design. Moreover, the advantage of epoxy is the absence the vapor of toxic styrene during manufacturing. Essentially, each blade is made with resin.

III. The Aim of the work
The aim of the present research is to optimize life predictions of composite under variable stress loads. Ultimately, this research aims to optimize life prediction guidelines by enhancement the fatigue life prediction that obtained by the traditional approaches using linear, power law and quadratic polynomial regression in comparison with ANN techniques that considered as an accurate and reliable method IV. Fatigue of composite Before the fatigue; has been treated generally, so an introduction of fatigue life must be given. Fatigue loads; are represented by a waveform, typically sinusoidal, cyclic load. The characteristic of this waveform is given in Figure  2, in terms of the quantity S and N. Typically; stresses are used for homogeneous material, while strain is preferred for composite. For (N), the No. of cycles to failures is used. In addition, half cycle to failure, No. of load sequence to failure, or No. of cycles to predefined stiffness, may be used. The result of fatigue experiments is often plotted in (S-N) diagrams, as shown in Figure 2. In general, fatigue characteristics are calculated by the slope of the (S-N) curve. The flat S-N curve (small slop) often is considered; to represent main fatigue characteristics over the steep S-N curve. The fatigue behavior can be appraised, depend upon; the location of the intersect with the abscissa. Knowledge of the damage mechanisms and their progression is to understand the fatigue behavior of composite materials, these damage mechanisms are abundant, they occur at many unpredictable locations throughout the laminate. There are five major damage mechanisms: cracking of matrix, breaking of fiber, crack coupling, beginning of delamination and growth of delamination. Figure 3 shows the state of damage versus percent1 of life for three phase's progression of damage. Phase I, cracking of matrix; Phase II, fracture of fiber, crack coupling and beginning of delamination; Phase III, growth of delamination and final fracture1 [4].

I. Fabricatingcmold
The mold was manufactured from two steel plates in the workshop. It has dimensions of 30*30 cm 2 area with thickness of 3mm as shown in Figure 4, with some weights to make the fibers tighten and strung.

II. Fatigue test Specimen
The specimens are cut out of 30*30 cm 2 panels and the cut edge is polished in two stages in order to remove the flaws and the additional fibers and to obtain surfaces. Emery papers of grade 434 and 1000 were used for this purpose. According to ASTM D 3479/D 3479M-96, standard test method, the specimens are prepared for fatigue of composite materials [5]. Suitable dimension for fatigue specimens to satisfy the section the machine that suited for flat plate specimens. Figure 5 shows the geometry of the specimens with its dimension, Figure 6 shows the fatigue specimens.

III. Fatigue test procedure
Fatigue test is a procedure type of cyclic bending2 loading. The aim of the fatigue test is to produce S-N curve (applied stress versus No. of cycles to failure) for each fatigue test specimen. For this test, the AVERY Fatigue Testing Machine Type-7305 is designed to apply loads with or without initial static loads, as shown in Figure 7. The grip is provided for the cyclic load where3 the load is applied on one4 end of the fatigue specimen by an oscillating1 spindle by a connection means such as a crank, connecting rod and double eccentric attached. The eccentric attachment can be adjusted to provide the necessary range of bending angle. At the opposite end of the specimen, the applied load is measured by means of a Torsion Dynamometer. The angle of twist can be registered by horizontal rod on a Dial gage. The relationship between the reading of dial gage and the imposed torque by using the calibration curves. From the applied torque and the deflection angle, the applied stress can be calculated. In order to record the number of cycles, a revolution counter is fitted to the motor. The cycling rate is 1420 rpm (24 Hz). The test machine is adjusted at stress ratio R=-1 refers to that the cyclic bending load stress means tension-compression stress. Each set of specimens have been tested by changing the moment each time and recording the number of cycle to failure".

IV. Artificial Neural Network (ANN)
The history of AI (Artificial Intelligence) is begun in 1956 as a term by John McCarthy first academic conference (Dartmouth). After five years, Alan Turing gave a proposal about the machines that can be able to simulate the human brain and can3 do intelligent things [6]. AI becomes important area of research in many fields; "engineering, science, education, medicine, business, accounting, finance, marketing, economics and stock market" [7]. The intelligent machines are nearly similar to the humans brain and it follow that one could achieve AI by simulating the function of the humans brains on the computer. The artificial neural network can be characterized by several features: "large number of simple neuron-like processing elements; large number of weighted connections between the elements in which the weights on the connections encode the networks knowledge; highly parallel; distributed control and emphasis on learning internal representations automatically" [8]. An input of neural network determines the net input signals to neuron that coming from the inputs with activation functions that calculate the activation; level of the neuron as a function of its summation input signals and (perhaps) of its previous situation. The output signals are emitted through output of the neuron [9].

V. Feed Forward Back Propagation Neural
Network (FFNN) [10] FFNN is one of the most popular structures in ANNs, which are widely used to solve many complex problems by creating a relationship between input and output. In many applications, BPNN widely used method for FFNN learning because it has good advantage with simple implementation. The structure of BBNN is shown in Figure 8 where the output of neuron is input to the next neuron multiplied by its weights [11].
The input values converted to output values by calculation of activation functions, which is sigmoid activation, function because it is differentiable: Where is a constant parameter, and is the input to the activation function [12]. BPNN is widely used in diverse applications like performance evaluation, location selection, prediction and optimization. a 1 = f 1 (IW 1,1 ×p+b 1 ) (2) a 2 =f 2 (LW 2,1 ×a 1 +b 2 ) (3)

VI. Generalized Regression Neural Network (GRNN)
GRNN has a certain characteristics which are used to solve a complex problem because it is fast learning and good approximate with a large number of training data. It consist of three layers, in other research four layers; input, pattern, summing and output layer as shown in figure (9). Normal distribution function is the probability density function that is used in GRNN [14].
Where: is distance and ( ( ) ( ), is the mean input and is the smoothness parameter (can be arbitrarily chosen to. ) and t is the number of alteration

VII. Radial Basis Function Neural Network (RBFNN)
RBFNN can be used as a replacement of many networks that have flexibility transfer function (sigmoid activation function) and it is considered as powerful method for regression and approximation. It consists of three layers; input, hidden that has the nonlinear (RBF) and output layer with linear activation function; as shown in Figure 10. The technique of (RBF) provides better generalization ability to avoid unnecessary lengthy calculations. The (RBF) represented as: ( ) ‖ ‖ (5) Where: is the mean value of the data, is the distance of the data from the mean value and is the input data.

VIII. Design of ANN
The ANN consists of elements that are analogue to the neuron in the brain. The processing contains of many computational1 elements that are arranged in layer. Several advantages of ANN including the ability to learn compared to the conventional techniques. For designing the ANN models, the first step is the characterize of the problems that have to be solved, this will calculate the selection of suitable topology of the network. Next step is to identify the input data which can be binary or real values input. In the last step, determination of the input1, hidden and output layers to give a best performance. "To evaluate the performance of each models, the performance criteria formula are defined as: Where and are observed and predicted values respectively.
Is the number of input data". In ANN, all records of different orientation are used. 75% of records are training, 10% are cross validation and 15% are testing. Three steps are (7) used in each network; first with one input parameter (stress load), second with two parameters (stress load and angle of orientation) and third with three input parameters (stress load, angle of orientation and thickness of ply) in (FFNN1, 2, 3), (GRNN1, 2, 3) and (RBNN1, 2, 3) respectively.

I. Prediction of fatigue life (FGRC) using Artificial Neural Network (ANN)
Many mathematical models are discussed in the previous section in order to predict the fatigue life of different orientations of (FGRC) using traditional models (linear, power law, quadratic polynomial regression models). Very efficient tool is used which are (ANN) in order to approximate the output of the networks to the experimental results. ANN is used in many architectures for prediction of fatigue life. In ANN, all records of different orientations are used. 75% of records are training, 10% are cross validation, and 15% are testing.

II. Prediction of fatigue life using feed forward neural network (FFNN)
FFNNs are used to predict the fatigue life of (FGRC) of all orientations with many models. These networks work with hyperbolic (logsigmoid) activation function in three strategies: Firstly, one parameter, which is stress load, as an input variable to the network and one output, which is No. of cycles to failure, as an output variable of the network (FFNN1). Secondly, two parameters, which are stress load and angle of orientation, as an input variables to the network and one output, which is No. of cycles to failure, as an output variable of the network (FFNN2). Thirdly, three parameters, which are stress, angle of orientation and the thickness of the ply, as the input to the network and one output, which is No. of cycles to failure, as an output variable of the network (FFNN3).

III. Prediction of fatigue life using Generalized Regression Neural Network (GRNN)
Fatigue life of (FGRC) has been predicted by using Generalized Regression Neural network (GRNN) with many models, and it works with three strategies: Firstly, one parameter, it is stress load, as an input variable to the network and one output, which is No. of cycles to failure, as an output variable of the network. Secondly, two parameters, they are stress load and angle of orientation, as the input to the network and one parameter, which No. of cycles to failure, as the output of the network. Thirdly, three parameters, they are stress load, angle of orientation and thickness of ply, as the input to the network and one parameter; it is the No. of cycles, as the output of the network. The test results of (GRNN 1, 2, 3) are listed in Tables 8, 9 and 10 respectively.  The fatigue life of both experimental number of cycles and the output of the (RBNN1, 2, 3) are shown respectively in Figures 18, 19 and 20.

IV. Prediction of fatigue life using Radial Basis Neural Network (RBNN)
Fatigue life of (FGRC) has been predicted by using Radial Basis Neural Network (RBNN) with many models, and it works with three strategies: Firstly, stress load is the input variable to the network and the No. of cycles is the output of the network. Secondly, stress load and angle of orientation as the input parameters to the network and number of cycles as the output parameter of the network. Thirdly, three inputs, they are stress load, angle of orientation and thickness of ply, to the network and one output, which is the number of cycles, of the network. The test results of (RBNN1, 2, 3) are listed in Tables 11, 12 and 13 respectively.   ANNs are used for the prediction and optimization of fatigue life of (FGRC) and found more accurate than conventional mathematical methods (as illustrated in appendix-A) because there is more than one input to the networks. The results of (RBNN3) with three input parameters give more accuracy than (FFNN3) and (GRNN3).

Conclusions
ANNs are accurate and efficient method for prediction and optimization of the fatigue life of (FGRC). More parameters give more details about the materials, so one, two and three parameters are individual to three networks: (FFNN1, 2, 3), (GRNN1, 2, 3) and (RBNN1, 2, 3). In general, (RBNN) model gives best and more accurate results than (FFNN) and (GRNN).

Suggestions of Future work
Recommendations for future work are including in following: 1-Study the prediction of fatigue life of (FGRC) with unidirectional angle of fibers at ( ), ( ), ( ) and ( ) plies using Artificial Intelligence. 2-Study the prediction of fatigue life of (FGRC) with different type of layers.
3-Study of fatigue life with other parameters like; Different Stress ratio (R), different degrees of temperature and number of layers.
Using many soft computing methods for prediction and optimization, like; recurrent network, Probabilistic neural network, Neurogenetic algorithm and Neuro-fuzzy algorithm, to compare the results for optimal prediction of fatigue life.