An intelligent hybrid approach for industrial quality control combining neural networks, fuzzy logic and fractal theory

doi:10.1016/j.ins.2006.07.022

Information Sciences

Volume 177, Issue 7, 1 April 2007, Pages 1543-1557

https://doi.org/10.1016/j.ins.2006.07.022 Get rights and content

Abstract

The application of type-2 fuzzy logic to the problem of automated quality control in sound speaker manufacturing is presented in this paper. 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, by applying type-2 fuzzy logic, an intelligent system for automated quality control in sound speaker manufacturing is developed. 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 produced by good sound speakers. The fractal dimension is used as a measure of the complexity of the sound signal.

Introduction

In this paper, we present the use of an intelligent hybrid approach, combining type-2 fuzzy logic and neural networks, to the problem of quality control in the manufacturing of sound speakers. The quality control of the speakers was done manually by checking the quality of sound achieved after production [4]. A human expert evaluated the quality of sound of the speakers to decide if production quality was achieved. Of course, this manual inspection of the speakers was time consuming and occasionally resulted in errors in quality evaluation [8]. For this reason, it was necessary to consider automating the quality control of the sound speakers using intelligent techniques and fractal theory. The problem of measuring the quality of the sound speakers can be outlined 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 with some appropriate metric.
(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, otherwise it is of bad quality.

The first part of the problem was solved by using a multimedia kit that enables us to extract the sound signal as a file, which basically contains 108,000 points over a period of time of 3 s (this is the time required for testing). We can consider that the sound signal is expressed as a time series [3], which captures the basic characteristics of the speaker. The second part of the problem was addressed by using a neuro-fuzzy approach to train a fuzzy model with the data coming from the good quality speakers [9]. We used a neural network [6] to obtain a Sugeno fuzzy system [22] with the time series of the ideal speakers. In this case, a neural network [5], [17], [21] 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 [13], 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.

Section snippets

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.

To understand how speakers work, the first thing you need to do is understand how sound

Type-2 fuzzy logic systems

Fuzzy logic systems are comprised of rules. Quite often, the knowledge that is used to build these rules is uncertain. Such uncertainty leads to rules whose antecedents or consequents are uncertain, which translates into uncertain antecedent or consequent membership functions [7], [29]. Type-1 fuzzy systems [6], whose membership functions are type-1 fuzzy sets, are unable to directly handle such uncertainties [15]. We describe briefly in this section, type-2 fuzzy systems, in which the

Description of the problem

The basic problem consists in the identification of sound signal quality. Of course, this requires a comparison between the real measured sound signal and the ideal good sound signal. We need to be able to accept speakers, which have a sound signal that do not differ much from the ideal signals. We show in Fig. 6 the form of the sound signal for a good speaker (of a specific type). The measured signal contains about 108,000 points in about 3 s. We need to compare any other measured signal with

Fractal dimension of an object

Recently, considerable progress has been made in understanding the complexity of an object through the application of fractal concepts [8] and dynamic scaling theory [18]. For example, financial time series show scaled properties suggesting a fractal structure [1], [2]. The fractal dimension of a geometrical object can be defined as follows: $d = \lim_{r \to 0} [\ln N (r)] / [\ln (1 / r)]$ where N(r) is the number of boxes covering the object and r is the size of the box. An approximation to the fractal dimension can

Experimental results

In this section, we describe the experimental results obtained with the intelligent system for the automated quality control. The intelligent system uses a fuzzy rule base to determine automatically the quality of sound of speakers. We used a neural network to adapt the parameters of the fuzzy system using real data. We used the time series of 108,000 points generated by a good sound speaker (which covers a period of 3 s) as training data in the neural network. We then use the measured data of

Conclusions

We described in this paper the application of fuzzy logic to the problem of automating the quality control of sound speakers during manufacturing in a real plant. Type-2 fuzzy logic was used for the fuzzy rules of quality evaluation because human experts have uncertainty in membership function specification. We have implemented an intelligent system for quality control in MATLAB language using the new approach. We also use the fractal dimension as a measure of geometrical complexity of the

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An intelligent hybrid approach for industrial quality control combining neural networks, fuzzy logic and fractal theory

Abstract

Introduction

Section snippets

Basic concepts of sound speakers

Type-2 fuzzy logic systems

Description of the problem

Fractal dimension of an object

Experimental results

Conclusions

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Information Sciences

Information Sciences

Information Sciences

Information Sciences

Soft Computing for Control of Non-linear Dynamical Systems

Hybrid intelligent systems for time series prediction using neural networks, fuzzy logic and fractal theory

IEEE Transactions on Neural Networks

Soft Computing and Fractal Theory for Intelligent Manufacturing

The Loudspeaker Cookbook

Adaptive Filter Theory

Neuro-Fuzzy and Soft Computing

Operations on Type-2 fuzzy sets

Fuzzy Sets and Systems

The Fractal Geometry of Nature