# Experiment and Modeling on Macro Fiber Composite Stress-Induced Actuation Function Degradation
## 4 Predictive Modeling of Stress Induced MFC Actuation Function Degradation  
The degradation of material performance is always accompanied by some form of material nonlinear mechanical behavior, hence the macroscopic appearance of degradation will also be nonlinear. The radial basis function (RBF) neural network model can approach any non-linear functions [16], and this feature is used for modeling the degradation paths based on known degradation data. In order to obtain a prediction model for the actuation function degenerate degree prediction of the MFC actuator undergoing cyclic load, the RBF neural network learning algorithm is adopted. The established actuation function degradation prediction model of the MFC actuator can be used to predict the actuation function index \(A\) of the MFC actuator for arbitrary given stress amplitude and cycles of cyclic load within concerned stress amplitude range. The RBF radial basis function neural network is a forward network composed of three layers [17]. The first layer is the input layer composed of input nodes. The second layer is hidden layer, the neurons number of which needs to be determined. The third layer is the output layer, it is the response of the input layer, and the number of the output nodes is determined according to the dimensions of our output data. The key to establish this RBF neural network model is to determine the distributed parameters spread and the number of hidden layer nodes \(mn\). The larger the spread is, the smoother the fitted curve will be, but the fitting accuracy will be reduced. The smaller the spread is, the higher the curve fitting accuracy will be, but the prediction ability of new data will get lower. The number of neurons in the hidden layer, \(mn\), is not the more the better. Simply pursuing the fitting accuracy, too many neurons will also lead to over fitting. Generally the number of neurons in the hidden layer  
Figure 9: Actuating function index \(A\) of MFC actuator versus loading cycles. can be determined according to the empirical formula \(mn=\sqrt{mn_{p}+mn_{T}}+n\), in which \(mn\), \(mn_{p}\), \(mn_{T}\) are the numbers of neurons in the hidden layer, input layer and output layer, respectively, and \(n\) is any integer between 1 and 10. The main procedure of establishing the prediction model using the RBF neural network learning algorithm is summarized as follows: Firstly, normalize the input and output, which are the cycles of the given stress amplitude cyclic load and the corresponding measured actuation function index \(A\)\((\sigma,N)\), and then use these data to train the neural network, and calculate the square sum of the fitting error, the square sum of the prediction error and the sum of the total error. The distribution parameter of the neural network and the number of neurons in the hidden layer are adjusted to get the highest fitting accuracy for describing the actuation functional degenerate curve. Finally, the prediction model will be established with the settled parameters. In order to demonstrate the feasibility of the above-mentioned procedure, the measured data of 12 MPa, 18 MPa and 30 MPa are used as the training samples to train the prediction model of the RBF neural network. The modeling process was implemented in MATLAB by using the \"newrb\" function. When the number of neurons in the hidden layer, \(mn=25\), and the distribution parameter of neural network spread = 0.5731, the neural network model has the highest accuracy for describing the measured actuation function degradation of the MFC actuator. Table 2 shows the model parameters of the RBF neural network model for the actuation function degradation prediction of the MFC actuator. The established model has been used to predict the degradation curve for the actuation function degradation of the MFC actuator undergoing the cyclic load with the stress amplitude of 24 MPa.