Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Plateau principle wikipedia , lookup
Computer simulation wikipedia , lookup
Corecursion wikipedia , lookup
Network science wikipedia , lookup
Machine learning wikipedia , lookup
Central pattern generator wikipedia , lookup
Pattern recognition wikipedia , lookup
Application of Artificial Neural Network in Fluid Mechanics Teaching Evaluation System ZHU Changjun, ZHOU Jihong College of Urban Construction Hebei University of Engineering, Handan Hebei 056038 [email protected] Abstract: Based on the neural network method, a neural network model for comprehensive evaluation of teaching levels in fluid mechanics is built because the classic statistics method and static model can not meet the demand of precision to the nonlinear and uncertain system.. The structure of the neural network model is described. The model is trained with fifty samples and tested with twenty samples. The test results agree well with the actual situation, showing that the model is effective in evaluating the teaching levels. Keywords: neural network; teaching evaluation; fluid mechanics 1. Introduction The artificial neural network model is an intellectual discipline that rose rapidly in the eighties. It is one non-linear system that simulates human brain structure and encourage behavior at the same time. It has been successfully applied to many fields. In recent years, the artificial neural network has been used to evaluate teaching level, and has achieved better results. Higher education has been the hot spot which people pay attention. In recent years, the Ministry of Education has carried on the level appraisal every year to several dozens universities, so right evaluation of teaching quality is also the topic which has been studied in recent years. During the evaluation of teaching level, because the factors affecting teaching level are more and the affecting degree is different, it is difficult to express the measure result using mathematical expression which belongs to the nonlinear problem. According to the characters, a neural network model for teaching evaluation system is built. 2. Principle of neural network After the first simple neural network developed by McCulloch and Pitts (1943), many types of ANN have been proposed. The neural network model with multi-hierarchic structure which is based on back-propagation (BP) arithmetic, the most widely used ANN in hydrologic modeling, is used in this study. The BP network has all the functions of the neural network and its unique advantages such as the good mapping ability of processing the rainfall-runoff partitioning with more flexibility. In addition, its network model contains a highly parallel inter-connection structure, fast self-learning and handling ability of self-adaptation, which provide foundations for the application in hydrology, especially in rainfall-runoff modeling using the incomplete material. Therefore, the BP neural network is a popular choice in the field of hydrology with various complex physical processes. In recent years, neural network has been widely applied to the teaching evaluation , in which BP network is commonly used . The model created in this paper is a BP neural network with three-layer network (Figure1), 505 Figure 1. Three-layer BP network structure In the Figure 1, p is input of neuron. Each layer has its own weight matrix W , its bias vector b , a net input vector n , and an output vector a . W is an S × R matrix, and a and b are vectors of length S respectively. The superscripts of symbols identify the layers. Also shown in Figure 1 are R 1 2 input, S neurons in the first layer, and S neurons in the second layer. Different layers can have different numbers of neurons. The outputs of layers one and two are the inputs for layers two and three. 1 Thus layer 2 can be viewed as a one-layer network with R = S inputs, S = S 1 2 1 1 2 neurons, and 2 an S × S weight matrix W . The input of layer 2 is a , and the output is a . The other layer also can be drawn using same abbreviated notation. First, the output of the network will be computed.In the hidden and output layers, the net input to unit I is of the form: s i = ∑ w ji y i + θ i (1) Several types of transfer functions are used; however, the most frequently used is the sigmoid function. This transfer function is usually a steadily increasing S-shaped curve. The sigmoid function is continuous, differentiable everywhere, and monotonically increasing. In this study, two S-shaped transfer functions in a MATLAB neural network toolbox were used: the tansig function and logsig function. The two functions are of the form: 2 −1 1 + e − 2n 1 tan sig (n ) = 1 + e −n tan sig (n ) = (2) (3) These accumulated inputs are then transformed to the neuron output. This output is generally distributed to various connection pathways to provide inputs to the other neurons; each of these connection pathways. 3. Teaching evaluation model Though neural network can be seen as one kind of “black box” model, the process of building the model is as complex as other model. During the building the model, the main contents should be considered as follows: type of neural network, data pre-process, training sample, input pattern, network topology, parameter estimation, model examination. It is a very important work to choose the model structure. One good structure can reduce the training times and improve learning precision. 3.1 Data pre-processing Data pre-processing is an important initial work. The process includes training sample's size, criterion unitizing transforms (unification replacement), the statistical property research, spatial 506 information processing as well as singular value processing and so on. Before the data is processed, the data should be divided into two groups: training sample and examining sample. There are several types of preprocessing methods. All the training data are rescaled to a specific range (e.g., [-1, 1] or [0, 1]). However, the BP model is based on the gradient descent algorithm and the transfer function which determines the relationship between inputs and outputs of a node and a network has an asymptotic nature. When the extreme values of discharge are utilized, the gradient of the transfer function will approximate to zero, consequently, leading to slow the training down. The next issue is the division of the data into the training and testing data set. The training data set is presented repeatedly to the network until the weight values are determined while the testing data set is used for the final evaluation of the BP model performance. Sometimes to overcome the problem of overfiting or to determine the stopping point of the training process, the validation set is also required. The testing data set is used for both validation and testing in this study. Although there are no general solutions to the selection of the training and testing set which may affect the performance of the BP model, both the training and testing sets representative of the evaluation system data should be carefully evaluated in the decision making. 3.2 Neuron determination of input layer According to the indicator system, the main index affecting teaching quality is 12 (table.1),so the number of input layer can be adopted as 12. the determination of input pattern is the key for the successful neural network model. If the input neurons are more, the structure of model is more complex and training period is long. Otherwise, it is difficult to get the nonlinear relationship. First-level target Teaching manner Course content Teaching method Teaching effect Table.1 comprehensive evaluation indicators of fluid mechanics Number Second-level target 1 Prepare and plan of a lesson 2 Teaching style and patience 3 Corrects students' papers and Question/answer 4 Foundation and specialization 5 Innovation and comprehension 6 Emphasis 7 Performance and velocity of language 8 Blackboard writing 9 Teaching way 10 Theory test 11 Experiment skill 12 Practice 3.3The number of hidden layers and nodes ANNs perform complicated nonlinear mapping between input and output variables through the hidden nodes in the hidden layer. It can capture the pattern in the data. So the hidden layer and nodes play very important roles in the network architecture. Most studies indicate that a single hidden layer network tends to be used to the modeling problem and if the number of hidden nodes is enough, we can obtain any desired accuracy. However, other studies demonstrated the benefits of an ANN comprised of two hidden layers . In the recognizance of these studies, a single hidden layer is used in this study. The number of hidden nodes has comparatively great difficulty in determining. The neuron selection in the hidden layer affects the precise calculation and learning efficiency for the whole BP network, up till now, there are still no unified ways to identify the number of the hidden layer neuron, which is at the stage of research and exploration. If a small number of the hidden layer neurons are chosen, the self-adaptability of the BP neural network will be reduced, thus the training results are not ideal. However, if the large number is chosen, it is generally believed that the time for network training will be greatly increased, and some meaningless information in training data will be remembered, thus it will reduce precise calculation in a sense. The most common way in determining the number of hidden 507 nodes is by using experiments or by trial-and-error. Thus in this study the more appropriate number of the hidden layer neuron is fixed for six through testing and comparing. Therefore, the chosen configuration for the BP model is 12–6–1: eight inputs, six hidden neurons in one hidden layer and one output. 3.4 learning rate In ANNs, the gradient descent algorithm is called learning rate which determine the speed of the learning phase. Thus the learning rate is crucial for the BP learning algorithm. The learning rate can be very different in different applications. If the value chosen is excessively large, a divergence will occur; if the value chosen is excessively small, the learning will be inefficient. A number of recent publications have proposed new adaptive methods which are commonly based on a trial-and-error heuristic where global learning rates are adjusted according to the error rates to improve the learning rate. They are fundamentally different from the traditional adaptive methods which include an additional momentum parameter for automatically improving the original gradient descent. In this study, we adopted a traditional method. Since there are few systematic ways of selecting the learning rate and momentum simultaneously, the ‘‘best’’ values of these learning parameters are usually chosen through experimentations. As the learning rate and momentum can take on any value between 0 and 1, it is actually impossible to do an exhaustive search to find the best combinations of these training parameters. For better performance in our experiments, we use a small learning rate of 0.13 and the associated momentum factor of 0.95 in the training. 4. Results number 1 2 3 4 5 6 7 8 9 10 ANN 0.991 0.812 0.596 0.421 0.811 0.798 0.610 0.989 0.799 0.603 Table2 testing result Expert’s value 1.0 0.8 0.6 0.4 0.8 0.8 0.6 1.0 0.8 0.6 Grade Excellent Good Medium Pass Good Good Medium Excellent Good Medium 5. Conclusions Neural network is adopted to the evaluation of the “fluid mechanics” course, which victory the subjective factors of experts. The results are effective and objective. But the neural network method has its own disadvantages. The number and quality of learning sample can affect the study performance. the choice of the layer numbers and hidden neurons also affect the study ability and study efficiency. For all this, the neural network can be seen as an excellent method to evaluate the teaching quality. References [1] Zhang heng. Application of artificial neural network in electrical engineering teaching evaluation system. Journal of wuhan university of science and engineering, 2007,20(3):110-112. [2] Martin T.Hagan, Howard B.Demuth, Mark H.Beale, Neural network design. Beijing China Machine Press,2004,239-255. [3] Han Liqun. Neural network model of teaching quality evaluation system. Journal of Beijing institute of light industry,2000,18(2):34-38. : 508