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Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Lakhmi C. Jain; N.M. Martin CRC Press, CRC Press LLC ISBN: 0849398045 Pub Date: 11/01/98 |
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Koji Shimojima
Material Processing Department
National Research Institute of Nagoya
Japan
Toshio Fukuda
Department of Micro System Engineering
Nagoya University
Japan
In this chapter, we introduce a hierarchical control system for an unsupervised Radial Basis Function (RBF) fuzzy system. This hierarchical control system has the skill database, which controls fuzzy controllers acquired through the unsupervised learning process based on Genetic Algorithms. Thus, the control system can use the acquired fuzzy controller effectively and it leads to reducing the iteration time for a new target. The effectiveness of the proposed method is shown using the simulations of the cart-pole problem.
In recent years, intelligent techniques such as fuzzy logic, fuzzy reasoning, and fuzzy modeling are used in many fields including engineering, medical, and social sciences. Some fuzzy control systems can be seen in home appliances, transportation systems, and manufacturing systems. We also successfully applied the fuzzy inference for the sensor integration system [1-3].
The fuzzy system has a characteristic to represent human knowledge or experiences using fuzzy rules; however, the fuzzy systems have some problems. In most fuzzy systems, the shape of membership functions of the antecedent and the consequent and fuzzy rules are determined using trial and error by operators. It is time consuming. The problem is more serious when the fuzzy logic is applied to a complex system.
In order to solve this problem, some self-tuning methods have been proposed such as Fuzzy Neural Network [4,5] using back propagation algorithm [6], fuzzy learning using the Radial Basis Function (RBF) [7,8], Genetic Algorithm (GA) for deciding the shapes of membership functions and fuzzy rules [9,10], and the gradient descent method [11].
These methods can learn faster than neural networks; however, the operator must determine the number and shapes of membership functions before learning. The learning ability and accuracy of approximation are related to the number or shape of membership functions. Fuzzy inference with more membership functions and fuzzy rules have higher learning ability, however, these may include some redundant or unlearned rules. The number of rules is the product of the number of membership functions for each input, and these increase with increase of the input dimension; therefore, operators need to pay attention when deciding the structure of the fuzzy systems.
The fuzzy inference based on the RBF that adds a new rule for the maximal error point through the learning process has been proposed. In this method, fuzzy rules depend on the learning data set. If the learning data is biased, there are some unlearned areas or redundant fuzzy rules. Furthermore, this method does not delete a fuzzy rule, instead it adds new fuzzy rules; therefore it poses a problem because addition of fuzzy rules causes problems in the calculation time and memories.
To solve these problems, we proposed a new type of self-tuning fuzzy inference [12]. The membership function of the antecedent is expressed by the RBF. The supervised/unsupervised learning algorithms are based on the genetic algorithm, and the supervised learning also utilizes the gradient descent method to tune the shape and position of membership functions and the consequent values. However, these systems do not use previous learning results effectively. Therefore, if the systems handle a new task, the systems need additional learning for the new task. The GA based learning takes a long time to learning.
In this chapter, we propose the hierarchical control system with unsupervised learning based on skill knowledge database. In this system, the skill knowledge database manages fuzzy controllers acquired through previous learning process as skills. Therefore the system can use previous learning results for control/learning a new task. The effectiveness of this system is shown through some simulation results.
Several researchers have proposed automatic design (self-tuning) methods. Most of them focused on tuning membership functions. For example, neural networks are used as membership values generator, fuzzy systems are treated as networks, and back-propagation techniques are used to adjust the shapes of membership functions. However, these tuning methods are weak, because the convergence of tuning depends on the initial conditions such as the number and shapes of membership function, and sometimes it converges to a local minimum.
We have proposed a new method for auto-tuning and optimization of the structure of the fuzzy model. The GA is one of the optimization methods using a stochastic search algorithm based on the biological evolution process. However, the GA is a coarse searching and not the best method to find the optimal value.
We have proposed a fuzzy system based on RBF and its tuning method based on the GA [12]. The tuning algorithm not only tunes the shapes of membership functions and the consequent value, but also optimizes the number of membership functions and the number of rules.
First, we present the equations of the fuzzy system between input and output variables. The fitness value μj of the rules and the output value Yp are expressed by Equations (1) and (2),
where i is the input variable number, j is the fuzzy rules number, and p is the data sets number.
The shapes of the membership functions are expressed by RBF with a dead zone c that is useful for reducing the membership functions and fuzzy rules. The membership function in the i-th input value and the j-th fuzzy rule is expressed by:
where a, b, c are the coefficients that decide the shape of membership functions shown in Figure 1.
Figure 1 Membership function based on RBF.
To encode the information of membership functions, we use 31 bits memory for every membership function: each coefficient a, b, c used 10 bits; 1 bit is used as a flag of the membership functions validity. The consequent part is encoded into 16 bits memory in the case of unsupervised learning. Equations (5), (6), and (7) are used to decode the chromosome into the parameters of membership functions (see Figs. 1 and 2) in both unsupervised and supervised learning methods. Equation (8) is used to decode the value for the consequent parts in case of the unsupervised learning.
Figure 2 Coding scheme.
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