Fuzzy Logic Applications for Performance-Based Design

Fuzzy Logic Applications for Performance-Based Design

Ferhat Pakdamar (Gebze Technical University, Turkey)
DOI: 10.4018/978-1-5225-2089-4.ch009
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Abstract

In this chapter, it is expressed how performance based design criteria are modeled with fuzzy logic and why it needs to be modeled with fuzzy logic. Firstly, a brief information is given about current theories and techniques such as Fuzzy Logic, Chaos, Fractal Geometry, Artificial Neural Networks; and it is mentioned about advantages of applying these techniques to the problems. Then graphical inference deduction technique is expressed by giving a summary info about Fuzzy Set Theory, membership functions, clustering, rule-based systems and defuzzification. Then the divergence of performance based design criteria is set forth by making curvature evaluations for various regulations on a column section as a structure element. Finally, it is shown in detail how to use the fuzzy set theory for solution of this disharmony by using the clustering technique on a univariate sample first and then on a multivariate sample.
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Introduction

Today, there are various techniques and theories that most of scientist are not familiar with and these are being developed to simplify operations and/or easing the life by effectively applying on all of the science branches. Names of some of these techniques can be defined according to their relevant science branch: Physics – Quantum, Mathematics – Chaos, Geometry – Fractal, Classical Logic – Fuzzy Logic; Neural Networks and Genetic Algorithm must be also added.

For example; progression of Physics towards quantum was in early of 20th century. It was specified that laws described for macro objects were not functional in micro sizes. Even if concept of quantum occurred with the studies made upon blackbody radiation by Max Planck (1900), the theory was grounded by Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg and Erwin Schrödinger.

Meeting of Mathematics with Chaos became by Edward Norton Lorenz. Edward Lorenz, who was a meteorologist, was working upon weather forecasting with his computer in 1963. In one of his studies again, Lorenz entered the number of 0,506127 as starting data in his calculation. In the next study, Lorenz considered that entering the number of 0,506127 as 0,506 would not affect the system, because he thought that the change he made was a small change. In mathematically it was so… But Lorenz shocked with the obtained results. This small change he made caused the system to give hugely different results. Lorenz thought that his computer was broken but calculations he made again and again were telling the opposite. So indeed, this change he made in his computer which was as unimportant as a flapping of a bird led system to totally differentiate. In March of 1963, Lorenz published this phenomenon he discovered on Atmospheric Sciences Magazine and he used the term of “Butterfly Effect” for the first time. Thus, “Butterfly Effect” took its place in public and scientific language.

The term of Fractal was derived from the word of “fractus” in Latin which means fragmented or broken. Fractal is the common name of complex geometrical shapes that show the characteristic of auto-simulation mostly. Even if first mathematical studies done by Karl Weierstrass in 1861, the concept of fractal proposed for the first time by Polish mathematician Benoit B. Mandelbrot in 1975 led a new geometry system creating important effect not only on mathematics but also on various areas such as physical chemistry, physiology and fluid mechanics (Mandelbrot, 1983). Expressing objects about nature with this geometry system became easier compared to Euclidean geometry.

John Holland, a psychology and computer science expert in Michigan University, is the person who made first studies about Genetic algorithms (Holland, 1975). Holland working for machine learning, considered to carry out genetic process of creatures in computer environment by being impressed by evolution theory of Darwin. He saw that successful (able to learn) new individuals can be created by undergoing a community in genetic processes such as reproduction, pairing and mutation, instead of developing the learning ability of only one mechanical structure. He did his studies by looking at natural selection and genetic evolution to find the search and optimum. During the process, he modelled computer software in problems of finding optimum and machine learning by taking example that individual adapts to environment and becomes more suitable. Genetic Algorithms (or shortly GA) is the name of the method that he developed after publishing of his book in 1975 that he explained the results of his studies.

Artificial Neural Networks (ANN) is a data processing technology which works to try to copy the data processing system of neurons and brain in human nervous system. It is based on a basis of processing data in parallel and creating a network just like the human nervous system. This parallel data processing technique provides scientist very important opportunities such as able to derive data, learn, discover and a speed. Warren McCulloch and Pitts (1943) created a computational model for neural networks based on mathematics and algorithms called threshold logic.

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