CHAPTER 6 NEURAL NETWORK BASED SURFACE ROUGHNESS ESTIMATION

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1 CHAPTER 6 NEURAL NETWORK BASED SURFACE ROUGHNESS ESTIMATION 6.1. KNOWLEDGE REPRESENTATION The function of any representation scheme is to capture the essential features of a problem domain and make that information accessible to a problem-solving procedure. It is obvious that a representation language must allow the programmer to express the knowledge needed for a problem solution. Intelligent activity, in either human or machine, is achieved through the use of: 1. Symbol patterns to represent significant aspects of a problem domain. 2. Operation on these patterns to generate potential solutions to problems. 3. Search to select a solution from among these possibilities. Abstraction, the representation of only that information needed for a given purpose, is an essential tool for managing complexity. It is also important that the resulting programs be computationally efficient. Expressiveness and efficiency are major dimensions for evaluating knowledge representation languages. Many highly expressive representations are too inefficient for use in certain classes of problems. Sometimes, expressiveness must be sacrificed to improve efficiency. This must be done without limiting the representation s ability to capture essential problemsolving knowledge. Optimizing the trade-off between efficiency and expressiveness is a major task for designers of intelligent systems and is the focus of this thesis. 101

2 Knowledge representation languages are also tools for helping humans solve problems. As such, a representation should provide a natural framework for expressing problem-solving knowledge and in this context ANN is used as the representation tool. 6.2 DESIGN ISSUES IN ANN LEARNING Before a neural network is trained to learn a classification task, the following design issues must be considered. 1. The number of nodes in the input layer should be determined. Assign an input node to each numerical or binary input variable. If the input variable is categorical, either create one node for each categorical value or encode the K-ray variable using [log 2 k] input nodes. 2. The number of node in the output layer should be established. For two-class problem, it is sufficient to use single output node. For k - class problem, there are k output nodes. 3. The network topology (e.g., the number of hidden layers and hidden nodes, and feed-forward are recurrent network architecture) must be selected. Note that the target function representation depends on the weight of the links, the number of hidden nodes and hidden layers, biases in the nodes, and type of activation functions. Finding the right topology is not an easy task. One way to do this is to start from a fully connected network with a sufficiently large number of nodes and hidden layers, and then repeat the model-building procedure with a smaller number of nodes. This approach can be very time 102

3 consuming. Alternatively, instead of repeating the model-building procedure, some of the nodes could be removed and depict the model evaluation procedure to select the right model complexity. 4. The weights and biases need to be initialized. Random assignment is usually acceptable. 5. Training examples with missing values should be removed or replaced with most likely value REASON FOR CHOOSING ANN The general characteristics of an artificial network are; Multilayer neural networks with atleast one hidden layer are universal approximators; i.e., they can be used to approximate any target functions. Since an ANN has a very expressive hypothesis space, it is important to choose the appropriate network topology for a given problem to avoid model overfitting. 1. ANN can handle redundant features because the weights are automatically learned during the training step. The weights for redundant features tend to be very small.neural networks are quite sensitive to the presence of noise in the training data. One approach to handling noise is to use a validation set to determine the generalization error of the model. Another approach is to decrease the weight by some factor for every iteration. 103

4 2. The gradient descent method used for learning the weights of an ANN often converges to some local minimum. One way to escape from the local minimum is to add a momentum term to the weight update formula. 6.4 ESTIMATION OF SURFACE ROUGHNESS USING NEURAL NETWORK In this, the multi-layer perception neural network with back-propagation as the training algorithm is employed and the neural network is trained with the selected significant patterns for the effective prediction of surface roughness. The results obtained illustrate that the designed system is capable of estimating the surface roughness effectively. In the present work, data are processed on-line and using the neural network, R t is estimated. The data collected is pre-processed for normalization and fed to the neural network for training. Data is fed into the network through an input layer; it is processed through one or more intermediate hidden layers and finally fed out of the network through an output layer. This back-propagation learning employs gradient descent to minimize the squared error between the network output values and the target values for those 1 2 outputs E( w) = ( d k yk ) 2 k Where d k is output target vector and y k is output unit k. The activation function used in each node of hidden layer is sigmoid function 1 given by f ( x) = ( σx) 1+ e The application procedure for BPN is as follows: Step 1: Initiliaze weights (from training algorithm) 104

5 Step 2: For each input vector do steps 3-5 Step3: For I = 1,., n ; set activation of input unit, x i ; Step4: For j=1,.. p; Z n inj = Voj + i= 1 X V i ij Step5: For k=1,., m y p ink = Wok + j= 1 Z W j jk Y k = f ( y ink ) Where V oj = bias on hidden unit j Z j = Hidden unit j W ok = bias on output unit k Y k = Output unit k ANN with wavelet transform based image features In this approach the key input features collected for training the network consist of the following: (i) Energy total(e t ) (ii) Energy horizontal (E h ) (iii) Energy vertical (E v ) and 105

6 (iv) Energy diagonal (E d ) (extracted using wavelet transform) and the desired output is R t Milling operation and experimental roughness features used for training Experiments were conducted and samples of 45 milled specimens were obtained over a wide range of cutting conditions and presented to the neural network. This is shown in Appendix (Table A1.1). The network used for training is shown in Fig Fig: 6.1 ANN Model used to estimate R t (Training parameters extracted using WT) Grinding operation and experimental roughness features used for training Experiments were conducted and samples of 45 ground specimens were obtained over a wide range of cutting conditions and presented to the neural network. This is shown in Appendix (Table A1.2). The network used for training is same as used for milling (Fig. 6.1). 106

7 6.5 OBSERVATIONS The information contained in the wavelet scheme could be more significant since it retains both the spatial and time information of the image. This significant information is correlated with the surface roughness using the ANN in this work. The error curve, neural network mapping curve and the convergence plots are shown in Fig. 6.2 to Fig In figure, the x-axis denotes the range of variations of surface roughness R t about its nominal value and in this work, the variations was chosen as x [-6,6] microns i.e. the ANN was trained for R t(nominal) ± 6 microns. The results are shown for first 500 epochs. Fig. 6.2 indicates that, the neural network is able to map with the R t data with lesser error for most of the data points. However, when the data points are much closer to the nominal value, the network exhibits an increased error and therefore, the number of epochs must be increased. Accuracy of the results on increasing the epochs with weights in layer of nodes is portrayed in Fig. 6.5 to 6.7. Multilayer perceptron trained with matlab NN toolbox Error between Data and Neural Network Mapping Range of variation of Rt Fig: 6.2 Error plot between target data and neural output 107

8 Multilayer perceptron trained with matlab NN toolbox Data and Neural Network Mapping Range of variation of Rt Fig: 6.3 Mapped output points over the range of trained input data set Performance is and Goal is 0 at one epoch Training Number of epochs Fig: 6.4 Training curve for the first 500 epochs 108

9 Fig: 6.5 Predicted Result Accuracy on Increasing Epoches output snapshot. 109

10 Fig: 6.6 Predicted Result Accuracy on Increasing Epochs 110

11 Fig: 6.7 Neural Output Captured GUI 111

12 The experimental machining parameters and the estimated surface roughness values for 12 test cases are shown for milling and grinding process in table 6.1 and 6.2 respectively. The stylus R t is also indicated in the table along with the estimation error. Table 6.1 Experimental Milling parameters (WT) and surface roughness for verification tests Machining Conditions Features of image texture Stylus Vision Error Test No. V (m/s) F (m/rev) D (mm) E h E v E d E t R t (µm) R t (µm) M M M M M M M M M M M M

13 Table 6.2 Experimental grinding parameters (WT) and surface roughness for verification tests Test No. Machining conditions features of image texture Stylus Vision Error V F D E h E v E d E t R t (µm) R t (µm) (%) G G G G G G G G G G G G

14 6.6 SUMMARY The greatest advantage of ANNs is its ability to be used as an arbitrary function approximation mechanism which 'learns' from observed data is exploited in this chapter. However, using them is not so straightforward and a relatively good understanding of the underlying theory is essential. Critical issues related to ANN based applications such as, choice of model, learning algorithm, selecting and tuning an algorithm for training on unseen data, robustness, etc. were explored. Their simple implementation and the existence of mostly local dependencies exhibited in the structure makes it suitable for fast, parallel implementations in hardware. The ANN based surface roughness estimation was found to be consistent when tested with samples both for milling and grinding process. 114