A New Approach for Quality Control of Sound Speakers Combining Type-2 Fuzzy Logic and Fractal Theory Patricia Melin and Oscar Castillo Department of Computer Science Tijuana Institute of Technology P.O. Box 4207, Chula Vista CA, 91909, USA pmelin@tectijuana.mx ocastillo@tectijuana.mx Abstract: We describe in this paper the application of type-2 fuzzy logic to the problem of automated quality control in sound speaker manufacturing. Traditional quality control has been done by manually checking the quality of sound after production. This manual checking of the speakers is time consuming and occasionally was the cause of error in quality evaluation. For this reason, we developed an intelligent system for automated quality control in sound speaker manufacturing. The intelligent system has a type-2 fuzzy rule base containing the knowledge of human experts in quality control. The parameters of the fuzzy system are tuned by applying neural networks using, as training data, a real time series of measured sounds as given by good sound speakers. We also use the fractal dimension as a measure of the complexity of the sound signal. I. INTRODUCTION We describe in this paper the application of a type-2 fuzzy logic approach to the problem of quality control in the manufacturing of sound speakers in a real plant. The quality control of the speakers was done before by manually checking the quality of sound achieved after production [4]. A human expert evaluates the quality of sound of the speakers to decide if production quality was achieved. Of course, this manual checking of the speakers is time consuming and occasionally was the cause of error in quality evaluation [8]. For this reason, it was necessary to consider automating the quality control of the sound speakers. The problem of measuring the quality of the sound speakers is as follows: 1) First, we need to extract the real sound signal of the speaker during the testing period after production 2) Second, we need to compare the real sound signal to the desired sound signal of the speaker, and measure the difference in some way 3) Third, we need to decide on the quality of the speaker based on the difference found in step 2. If the difference is small enough then the speaker can be considered of good quality, if not then is bad quality. The first part of the problem was solved by using a multimedia kit that enable us to extract the sound signal as a file, which basically contains 108000 points over a period of time of 3 seconds (this is the time required for testing). We can say that the sound signal is measured as a time series of data points [3], which has the basic characteristics of the speaker. The second part of the problem was solved by using a neuro-fuzzy approach to train a fuzzy model with the data from the good quality speakers [9]. We used a neural network [6] to obtain a Sugeno fuzzy system [14] with the time series of the ideal speakers. In this case, a neural network [5, 11, 13] is used to adapt the parameters of the fuzzy system with real data of the problem. With this fuzzy model, the time series of other speakers can be used as checking data to evaluate the total error between the real speaker and the desired one. The third part of the problem was solved by using another set of type-2 fuzzy rules [17], which basically are fuzzy expert rules to decide on the quality of the speakers based on the total checking error obtained in the previous step. Of course, in this case we needed to define type-2 membership functions for the error and quality of the product, and the Mamdani reasoning approach was used. We also use as input variable of the fuzzy system the fractal dimension of the sound signal. The fractal dimension [9] is a measure of the geometrical complexity of an object (in this case, the time series). We tested our fuzzy-fractal approach for automated quality control during production with real sound speakers with excellent results. Of course, to measure the efficiency of our intelligent system we compared the results of the fuzzy- fractal approach to the ones by real human experts. II. BASIC CONCEPTS OF SOUND SPEAKERS In any sound system, ultimate quality depends on the speakers [4]. The best recording, encoded on the most advanced storage device and played by a top-of-the-line deck and amplifier, will sound awful if the system is hooked up to poor speakers. A system's speaker is the component that takes the electronic signal stored on things like CDs, tapes and DVD's and turns it back into actual sound that we can hear. A. Sound Basics To understand how speakers work, the first thing you need to do is understand how sound works. Inside your ear is a very thin piece of skin called the eardrum. When your eardrum vibrates, your brain interprets the vibrations as sound. Rapid changes in air pressure are the most common thing to vibrate your eardrum. An object produces sound when it vibrates in air (sound can also travel through liquids and solids, but air is the transmission medium when we listen to speakers). When something vibrates, it moves the air particles around it. Those air particles in turn move the air particles around them, carrying the pulse of the vibration through the air as 0-7803-7280-8/02/$10.00 ©2002 IEEE