A Presentation on Adaptive Neuro-Fuzzy Inference System using Particle Swarm Optimization and it’s Application By Sumanta Kundu (En.R.No. 10532011) System Modeling & Control Under the guidance of Dr.M.J.Nigam

OUTLINES Introduction. Neural Network. Fuzzy Logic. Adaptive Neuro-Fuzzy Inference System. Particle Swarm Optimization Technique. Simulation results. Conclusions.

INTRODUCTION The Adaptive Neuro-Fuzzy Inference System combines the concept of Fuzzy logic and Neural network to form a hybrid intelligent system that enhances the ability to automatically learn and adapt. The Particle Swarm Optimization algorithm used to get the optimal values and parameters of our ANFIS model.

NEURAL NETWORK A Neural network can be described as a system composed of many simple processing elements operating in parallel . The function of NN is determined by network structure, connection strengths and the processing performed at computing elements or nodes. It resembles the brain in two respects: 1. Knowledge is acquired by the network through a learning process. 2. Interneuron connection strengths known as synaptic weights are used to store the knowledge.

NEURAL NETWORK ARCHITECTURE Single Layer Architecture: It has one input layer and one output layer. The assigned weight matrix is Here Wij Denotes the weight between j th source to the i th neuron

NEURAL NETWORK ARCHITECTURE Multiple Layer Architecture Here each single layer is connected in cascade form. Each layer has it’s own weight matrix , bias vector , input vector , output vector.

LEARNING Learning of NN means to find the best value of weights and bias inputs by an iterative procedure with some sets of sample data. Two forms of learning procedures are: Supervised Learning. Unsupervised Learning.

BACK PROPAGATION IN NEURAL NETWORK Back Propagation learns by iteratively processing a set Of training data (samples). For each sample, weights are modified to minimize the error between network’s classification and actual classification. The steps involved in back propagation are: Initialize the weights and biases. Feed the training sample. Propagate the inputs forward; The net input has been computed and so as the output of each unit in the hidden and output layers. Back propagate the error. Update weights and biases to reflect the propagated errors. Terminating conditions.

APPLICATION OF NEURAL NETWORK Useful in the identification and control of dynamic systems. Optical character recognition. Voice recognition. Industrial process control. Customer research. Risk management.

FUZZY LOGIC Fuzzy logic is introduced by Lotfi Zadeh in 1960’s. It is a superset of Boolean or Crisp logic. Decision making with its ability to work from approximate data and find precise solutions. Modeling of complex systems using a higher level of abstraction originating from expertise knowledge.

MODEL OF FUZZY LOGIC CONTROLLER

ADVANTAGES Fuzzy logic reduces the design development cycle. It simplifies design complexity. It simplifies implementation. It improves control performance Easy extension of the base of knowledge through the addition of new rules. Robustness in relation of the possible disturbances in the system.

DISADVANTAGES Highly dependent on expertise knowledge. Not robust in relation to topological changes. Incapable to generalize.

ADAPTIVE NEURO-FUZZY PRINCIPLE Finding the membership functions and rules is not easy task. This deficiency demands learning algorithm. Neural Network has efficient learning algorithm. The combined Neuro-Fuzzy principle has the advantage of both.

ARCHITECTURE OF ANFIS MODEL

ARCHITECTURE OF ANFIS MODEL The common rule set for two if then rules can be expressed as: Rule 1: if x is A1 and y is B1 , then z1=p1x+q1y+r1 Rule 2: if x is A2 and y is B2 , then z2=p2x+q2y+r2 Layer 1: Oi = µAi(x), i = 1, 2 Oi = µBi(y), i = 3, 4 Layer 2: Oi2 = w i= µAi(x). µBi(y) , i=1,2 Layer 3:      ARCHITECTURE OF ANFIS MODEL

Layer 4: Layer 5: ARCHITECTURE OF ANFIS MODEL

PARTICLE SWARM OPTIMIZATION TECHNIQUE Population based optimization method. No gradient information is required. Particles changes their position in a hyperspace until terminating conditions are reached.

PSO ALGORITHM Particles are put into the d-dimensional search space with randomly chosen velocities and positions. The velocity of each particle, adjusted according to its own flying experience and the other particle’s flying experience. the i-th particle is represented as xi = (xi,1 ,xi,2 ,…, xi,d) in the d-dimensional space. The best previous position of the i-th particle is recorded and represented as: Pbesti = (Pbesti,1, Pbesti,2,..., Pbesti,d)

The index of best particle in the group is gbestd. The velocity of particle i is vi=(vi,1 ,vi,2 ,……… vi,d). The modified velocity   The modified position Here i=1,2,…..n; m=1,2,……,d; The fitness function PSO ALGORITHM

APPLICATION OF PSO TECHNIQUE Model selection is the task of picking the model that best describe a data set. Task assignment is one of the core steps of effectively exploit the capabilities of distributed or parallel computing system. Adjustment of weights in Neural Network.

SPEED CONTROL OF DC MOTOR Mathematical model of dc motor ………..(1) ………….(2) ……………(3)

MODEL OF DC MOTOR IN SIMULINK

ADAPTIVE NEURO-FUZZY CONTROLLER The output of ANFIS controller changes according to error and change of error. The Sugeno type fuzzy rule is if e is Ai and de is Bi then z = f(e, de) Fig: ANFIS controller architecture

ADAPTIVE NEURO-FUZZY CONTROLLER Layer 1: Layer 2: Layer 3: Layer 4: ADAPTIVE NEURO-FUZZY CONTROLLER

ADAPTIVE NEURO-FUZZY CONTROLLER Layer 5:

MEMBERSHIP FUNCTIONS OF ANFIS CONTROLLER Input variable “e” Input variable “de”

SPEED RESPONSE OF ANFIS CONTROLLER

ANFIS CONTROLLER WITH PSO It gives the optimal range of ‘universe of discourse’ for ‘e’ and ‘de’. It defines the optimal range of each membership functions.

THE OPTIMAL MEMBERSHIP FUNCTIONS Input variable ‘e’ Input variable ‘de’

SPEED RESPONSE OF ANFIS CONTROLLER WITH PSO

From the above comparison, the ANFIS controller with PSO is CONCLUSIONS The problem of finding proper membership functions and rules can be overcome by introducing ANFIS controller. The optimal value of universe of discourse and range of each membership functions are obtained with the help of PSO technique. Results ANFIS controller ANFIS controller with PSO Rise time[sec] 0.00301 0.00285 Overshoot[%] Steady State error[%] From the above comparison, the ANFIS controller with PSO is best from other two.