1. Introduction

The problem of faults and defects produced during the mechanical spinning of yarns is as old as the industry itself. In earlier times, much skill and experience were required in order to detect and remove these faults.

In this paper, an attempt is made at providing a key to enable the source of faults to be located. It is understood that only the more common defects can be covered here, since there is no end to the list of possible reasons. In any event, there is no complete replacement for skill and experience. An important point to be borne in mind is:

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that machines generally create short term variations, and

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that when ultimately drafted, these appear as long-term or count variations.

Figure 1 illustrates the types of fault in the spinning mill.

Detects in cotton spinning

2. Wavelength range of machine’s faults [1]

Table 1 (1.A and 1.B) presents a specification of machine elements and machine sets at which faults may occur, together with the dimensions and formulas related, as well as their positions at the spectrograms.

Table 1.A. Machine parts, schematic drawings and dimensions specification.

Machine part	Geometrical arrangement of the particular machine elements end sets	Specification of dimensions and other parameters
Ring spinning	df di do d D1 D2	df = front roller diameter. do = outer diameter of bobbin. di = inner diameter of bobbin. dT = traveller diameter. D1= front draft. D2= back draft. l1 = length of top apron. l2 = length of bottom apron.
	df D1 D2
Speed frame	di d df	df = front roller diameter. do = outer diameter of bobbin. di = inner diameter o bobbin. dT = traveller diameter. D1= front draft. D2= back draft. l1 = length of top apron. l2 = length of bottom apron.
Draw frame	1 2 4 5 6 7 D1 D2	1,2 = front roller diameter. 3,4,5 = middle roller diameter. 6,7= back roller diameter. D1= front draft. D2= back draft.
Comber	1 2 3 4 5 6 7 8 D1 D2	1,2 = front roller diameter. 3,4 = middle roller diameter. 5,6 = back roller diameter. 7,8 = detaching roller diameter. D1= front draft. D2= back draft.
	4
		1 = licker-in diameter.
		2= cylinder diameter.
Card	2	3 = doffer diameter.
		4 = lifting-of of flats.
	3 15	5 = calender roller diameter.

Table 1.B. Machine parts, formulations of wavelengths and positions at the spectrograms.

Machine	Source	Calculation of wave length
Ring Spinning	Front roller Middle roller Back roller Top apron Bottom apron Drawbox drive Ring traveller Empty spindle Full spindle Drafting waves	λ1=d1*π λ2=d1*π*D1 λ3=d1*π*Dtotal λ4=l1*D1 λ5=l2*D1 λ6 shorter than λ3 λ7=dT*π λ8=di*π λ9=do *π λ10~2.75*l
Speed Frame	Front roller Middle roller Back roller Top apron Bottom apron Drawbox drive Empty spindle Full spindle Drafting waves	λ1= d1 *π λ2= d1 *π*D1 λ3= d1*π*Dtotal λ4=l1*D1 λ5=l2*D1 λ6 shorter than λ3 λ7=d*π λ8=d*π λ9~3.5*l
Draw Frame II/I	Front roller Front roller Middle roller Middle roller Back roller Back roller Drawbox drive Drafting waves	λ1= d1*π λ2= d2 *π λ3= d1*π*D1 λ4,5=d*π*D1 λ6=d*π*Dtotal λ7=d*π*Dtotal λ8 shorter than λ6 λ9~4*l
Comber	Front roller Middle roller Middle roller Back roller Drawbox drive Drafting waves	λ1,2=d1,2*π λ3,5,6=d3,4,5*π*D1 λ4=d4 *π*D1 λ7,8=d*π * Dtotal λ9 shorter than λ6 λ10~4*l
Card	Licker-in Cylinder Doffer Card flats Calender rollers	Vpd Vpd ** ** 1 1 1 π πλ = Vpd Vpd ** ** 2 2 2 π πλ = Vpd Vpd ** ** 3 3 3 π πλ = 4 4 * * nl Vpl =λ πλ 5 * 5 = d

3. Genetic algorithms (GA)

A genetic algorithm (GA) is a probabilistic search and optimisation technique based on the principles of biological evolution, natural selection, and genetic recombination, simulating the survival of the fittest in a population of potential solutions of individuals. GAs are capable of globally exploring a solution space, pursuing potentially fruitful paths while also examining random points to reduce the likelihood of settling for a local optimum [Goldberg, 1989]. They are conceptually simple yet computationally powerful, making them attractive for use in complex domains, and have been demonstrated on a wide variety of problems.

GAs and evolutionary computation, which use the twin metaphors of natural evolution and survival of the fittest, derive their strength by working on populations of solutions and are therefore best exploited in a parallel computing environment.

GAs function by iteratively refining a population of encoded representations of solutions. ‘Parents’ from a population are ‘selected’ for ‘crossover’ and ‘mutation’. The ‘offspring’ form the new population. The ‘selection’ process is controlled via a fitness measure that is closely related to the optimisation objective. This generation cycle is repeated until a solution with the desirable quality is located.

GA evolution emerges from the following simple rules:

1. Initiate: Create a population of a some specific size.
2. Evaluate fitness: Calculate a fitness value for each individual in the population by evaluating how good solution the individual is to the given problem.
3. Reproduce: Let the best individuals have offspring with each others by choosing two individuals at a time. The probability for choosing an individual is weighted by the individual’s, fitness value so that the good ones in the population reproduce many time more likely than the bad ones. The offspring are created by cutting both of the two individuals at the same randomly selected point and then switching their ends, as shown in Figure 2.

1. Mutate: Choose a small, predefined percentage of the individuals randomly and randomly change one gene in each of them.
2. Copy the best individual of the last generation on one individual in the new generation to prevent possible degeneration.

By repeating these simple rules, the population evolves very fast and finds a good or the optimum solution from huge search spaces by searching only a small fraction of the search space. By searching only 10 ^-32 %–fraction of a search space, a GA can still find the optimum solution in more than 10% of the searches [2]. Of course this depends on the structure of the problem. If not the optimum, a GA generally still finds very good solutions.

The author applied the GA to the physically based jumping problem. The system learned to jump much higher than expected in only 50 generations. The population size was 400, mutations were made to 10% of the population, and only the 10 best individuals were allowed to make offspring. The fitness function used simulated the system with each string of the population, and gave a simple rating relative to how high the system jumped.

In his Siggraph 94 article [2], Karl Sims proposed a technique for creating evolving virtual creatures in a simulated physical environment. He used genetic algorithms for both, creating the bodies of the creatures as well as evolving behaviour for them. The behaviours that he created realised swimming, locomotion, jumping and following a light. The behaviours created were interesting, goal-oriented and life-like; they could not easily be predicted. The GA learns how to use the body it is given by knowing what it wants to accomplish with it (fitness evaluation). The GA basically tries everything the body is capable of, and improves the ways that lead towards the goal (better fitness value).

GAs are a very good tool for finding solutions from huge search spaces. They are good for many problems such as scheduling, DNA fragment assembly, edge colouring, minimum set-covering, ‘travelling salesman’ and other NP-hard (Non-deterministic Polynomial-time hard) problems [3]. NP-hard problems are solvable in polynomial time. Usually this means that these problems grow in complexity so fast, as a function of the order of the problem, that no matter how much the computers evolve, the problems cannot be solved with brute-force methods. An example of this is the chess search problem. With a problem branching factor of 35, the problem grows so fast as the function of the planning depth that the exponential evolving speed of computers does not help much in essentially deeper planning.

In relations to computer games, GAs embody one challenging problem. They search for solutions to a static problem, one that remains the same. The GA cannot iterate to find a maximum if the systems’ behaviour changes between generations. Thus, one cannot really make the GA learn while playing against the human user, as the human user does not act in the same way every time.

However, there are many things, game AI wise, that can be done with GAs. For an example, one can make a population of individuals with different FSM behavioural probability distributions and rate their success as a fitness value. The best ones can then reproduce as the game proceeds. This would lead the game AI to slowly improve against the particular player. The choice of the fitness function is essential to how well a GA evolves.

3.1. Genetic algorithm procedure

Figure 3 explains how the GA can be used to obtain the best chromosome which maximizes ψ (χ) .

ki

Begin

{

Assume the fitness function as ψ (χ)

ki

Create a chromosome structural as follows;

{ Generate a number of slots equal to I, which represent input vector X. Put a random value 0 or 1 in each slot.

} G=0, where G is the number of the generation.

G

Create the initial population, P of T chromosomes, P()t , where t=1 to T.

G

Evaluate the fitness function according to P()t .

While termination conditions not satisfied, Do

{ G=G+1

G

Select number of chromosomes from P()t according to the roulette wheel procedure.

Recombine between them using crossover and mutation.

G

} show the best chromosome which satisfies the conditions

} End

Figure 3. Genetic algorithmic procedure.

For extracting a rule belonging to class K, the best chromosome must be decoded as follows:

- The best chromosome is divided into N segments.

- Each segment represents one attribute, An(n=1,2,….,N), and has a corresponding bit length mn which represents their values.

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The attribute values are existed if the corresponding bits in the best chromosome equal one and vice versa.

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The operators OR and AND are used to correlate the existing values of the same attribute and

the different attributes respectively. The overall methodology of rule extraction is shown in Figure 4.

Data base fault

4. Illustrative example

The authors applied this technique in a virtual draft system simulation model [VDSS] [4]. The VDSS was given a database with 4 attributes and one output class, as shown in Table 2. The linguistic values of each attribute and the output class are summarised as follows; Fault type = A1 = (False Real) Spectrum shape = A2 = (Mechanical Draft waves) Fault category = A3 = (periodical Non periodical) Harmony = A4 = (odd even odd & even Non) Fault source = AT = (Ambient Coiling Drafting)

The encoding values of the given database are shown in Table 3. Table 4 shows the result from the expert database by using the genetic algorithm (GA).

http://www.autexrj.org/No2-2007/0161.pdf 86 Table 3. Encoded database.

Table 4. Extracted ruler from expert database.

5. Conclusion

This paper studies AI techniques for detecting the spinning fault resource. This technique involves extracting the fault resource from the expert database by using genetic algorithms. The expert

http://www.autexrj.org/No2-2007/0161.pdf 87

database consists of spectrogram specification such as fault category (periodic OR non-periodic), fault type (false OR real), spectrogram shape (mechanical OR Drafting wave), … etc.