### Time Manufacturing Prediction: Preprocess Model in

### Time Manufacturing Prediction: Preprocess Model in

### Neuro Fuzzy Expert System

### Neuro Fuzzy Expert System

### Ing. Sergio Gallo, Teresa Murino, ph.d., Prof. LiberatinaC. Santillo

### Ing. Sergio Gallo, Teresa Murino, ph.d., Prof. LiberatinaC. Santillo

### Università degli Studi di Napoli Federico II

### Università degli Studi di Napoli Federico II

### Facoltà di Ingegneria

### Facoltà di Ingegneria

### Dipartimento di Progettazione e Gestione Industriale -

### Dipartimento di Progettazione e Gestione Industriale - Sezione Impianti Industriali

### Sezione Impianti Industriali

### Phone: + 39 – 081 – 7682334; Fax + 39 –081 -5937324

### Phone: + 39 – 081 – 7682334; Fax + 39 –081 -5937324

### sergallo@unina.it – murino@unina.it - santillo@unina.it

### sergallo@unina.it – murino@unina.it - santillo@unina.it

### ABSTRACT:

### ABSTRACT:

It is well known that an efficient time manufacturing prevision is a It is well known that an efficient time manufacturing prevision is a key-factor in today's global market.key-factor in today's global market. In particular, the growing interest in job-shop model arises from the nIn particular, the growing interest in job-shop model arises from the need of an efficient management of eed of an efficient management of Mixed ModelMixed Model Assembly Cell and Flexible Manufacturing System. Due to the complexity of prevision problems, a neuro-fuzzy Expert Assembly Cell and Flexible Manufacturing System. Due to the complexity of prevision problems, a neuro-fuzzy Expert System has been widely proposed.

System has been widely proposed.

Recently the hybridisation of Fuzzy Logic with self-learning procedure have received concrete performance increase by Recently the hybridisation of Fuzzy Logic with self-learning procedure have received concrete performance increase by the continuos increasing of the computational power of available computers, but the difficulties connecting whit high the continuos increasing of the computational power of available computers, but the difficulties connecting whit high number of entries still exist.

number of entries still exist. This paper presents a p

This paper presents a pre-learning re-learning procedure to overpass the procedure to overpass the complexity of entries domain. In pcomplexity of entries domain. In particular the model isarticular the model is tested in a mechanical manufacturing operative

tested in a mechanical manufacturing operative contest.contest.

KEYWORD: Time manufacturing, Flexible Manufacturing System, Neuro-Fuzzy Expert

KEYWORD: Time manufacturing, Flexible Manufacturing System, Neuro-Fuzzy Expert SystemSystem

### INTRODUCTION

### INTRODUCTION

The development of Fuzzy Inference System characterised by a large number of input variables (more than five or six), The development of Fuzzy Inference System characterised by a large number of input variables (more than five or six), appears very difficult especially in knowledge engineering in order to specify the real input variables, the relative appears very difficult especially in knowledge engineering in order to specify the real input variables, the relative relations, such as the consequent complexity of the knowledge base. [1][3][4]

relations, such as the consequent complexity of the knowledge base. [1][3][4]

As matter of fact, the absence of standard methods for transforming human experience in knowledge base (rules and As matter of fact, the absence of standard methods for transforming human experience in knowledge base (rules and database) of Expert System and effective methods for tuning the membership functions such as minimising the output database) of Expert System and effective methods for tuning the membership functions such as minimising the output error measure or maximising performance index, influences the results of Fuzzy System. [3][6

error measure or maximising performance index, influences the results of Fuzzy System. [3][6÷÷8]8]

Particularly, many difficulties appear during the knowledge building the system if skilled people and experts are not Particularly, many difficulties appear during the knowledge building the system if skilled people and experts are not available. Lot of rules correspondent to the number of input variables and to the fuzzy set used, that involves the available. Lot of rules correspondent to the number of input variables and to the fuzzy set used, that involves the definition of rules often redundant and sometimes impossible combinations of fuzzy set from the logical and physical definition of rules often redundant and sometimes impossible combinations of fuzzy set from the logical and physical point of view. Then low system precision and long times of elaboration.

point of view. Then low system precision and long times of elaboration.

The problem is simplified cashiering the opportune rules or combinations, but in this case is necessary the availability The problem is simplified cashiering the opportune rules or combinations, but in this case is necessary the availability and the collaboration of an expert with consequent expansion of the times for a correct development. Generally, the and the collaboration of an expert with consequent expansion of the times for a correct development. Generally, the discrimination among the rules, renders hard maintenance of knowledge base system. In fact, the adjournment discrimination among the rules, renders hard maintenance of knowledge base system. In fact, the adjournment performed from different planners, often involves the writing of rules that could be redundant or in contrast with the performed from different planners, often involves the writing of rules that could be redundant or in contrast with the previous rules.

previous rules.

In any case, also arranging experienced people, in operational very booming contexts characterised by an elevated In any case, also arranging experienced people, in operational very booming contexts characterised by an elevated numbers of variables, times and results of fuzzy inference process appear unlikely preventable. [6

numbers of variables, times and results of fuzzy inference process appear unlikely preventable. [6÷÷9]9]

In addition the Neural Networks of classical types, results complex to develop when they are processing a large number In addition the Neural Networks of classical types, results complex to develop when they are processing a large number of signals related to the high numbers of variables. The main problem is the complexity of hidden layer that result in a of signals related to the high numbers of variables. The main problem is the complexity of hidden layer that result in a high number of examples strictly depending from variables, layers and nodes. Especially if an adequate capability of high number of examples strictly depending from variables, layers and nodes. Especially if an adequate capability of generalisation is needed. [2][12][13]

In this situation, the phase of learning will be realised by adequate numbers of examples and by number of varying and In this situation, the phase of learning will be realised by adequate numbers of examples and by number of varying and from the number of levels and nodes.

from the number of levels and nodes.

Unfortunately, in industrial activity, the main difficulty is the availability of information, often incomplete or Unfortunately, in industrial activity, the main difficulty is the availability of information, often incomplete or discriminating, and in each case times of development, relative to an optimal realisation of the neural structure will be discriminating, and in each case times of development, relative to an optimal realisation of the neural structure will be elevated.

elevated.

The small number of

The small number of examples, the choice examples, the choice of the self-learning algorithm of the self-learning algorithm and the determination and the determination of the architecture,of the architecture, affect the abilities of generalisation of the net, and the utilisation of pure neural networks, in the operational context affect the abilities of generalisation of the net, and the utilisation of pure neural networks, in the operational context appears particularly binding. [2][12][13]

appears particularly binding. [2][12][13]

The present work proposes a hybrid procedure that get from the effect synergy of the previous techniques a sensible The present work proposes a hybrid procedure that get from the effect synergy of the previous techniques a sensible increase of the throughputs of Expert System.

increase of the throughputs of Expert System.

The proposed methodology, overpassing the difficulties to manage an elevated number of variables, answers to the The proposed methodology, overpassing the difficulties to manage an elevated number of variables, answers to the characteristics of simplicity, objectivity and flexibility of the system, and also a small time of development and characteristics of simplicity, objectivity and flexibility of the system, and also a small time of development and realisation. This model is based on a technique of pre-processing the input vector.

realisation. This model is based on a technique of pre-processing the input vector.

PROPOSED METHODOLOGY PROPOSED METHODOLOGY

When the fuzzy inference system is supported by the self-learning algorithm it achieves a hybrid mode to the definition When the fuzzy inference system is supported by the self-learning algorithm it achieves a hybrid mode to the definition of the if-then rules, also in absence of experts about the problem domain. [12

of the if-then rules, also in absence of experts about the problem domain. [12÷÷18][20]18][20]

In fact, showing the patterns of data, and using the adequate instructions, the net can identify the fuzzy set and tuning In fact, showing the patterns of data, and using the adequate instructions, the net can identify the fuzzy set and tuning the membership functions, and using the opportune defuzzification model allows the self-organisation of the neural the membership functions, and using the opportune defuzzification model allows the self-organisation of the neural structure prearranging the hidden layers, generally composed of fixed nodes characterised by weights and known structure prearranging the hidden layers, generally composed of fixed nodes characterised by weights and known connections. [12

connections. [12÷÷18][20]18][20]

The methodology presents itself particularly proper to the rebuilding of bonds in phenomena characterised from The methodology presents itself particularly proper to the rebuilding of bonds in phenomena characterised from strongly non-linear bonds when information or experts are not available.

strongly non-linear bonds when information or experts are not available.

Additionally, the knowledge base of the Expert System is corporate from database and being separate from the Additionally, the knowledge base of the Expert System is corporate from database and being separate from the inference system, it is easy the adjournment of the system using new

inference system, it is easy the adjournment of the system using new data without break into the inferential ability of data without break into the inferential ability of thethe algorithm. [12

algorithm. [12÷÷18][20]18][20]

The automatic generation of the rules, could realise, in case of high numbers of entries, complex if-then structures, and The automatic generation of the rules, could realise, in case of high numbers of entries, complex if-then structures, and therefore would miss the simplicity and objec

therefore would miss the simplicity and objectivity of the hybrid system. The proposed methodology tivity of the hybrid system. The proposed methodology is originated fromis originated from some concepts of the Mathematical Analysis.

some concepts of the Mathematical Analysis.

Human reasoning, consists of modelling across the expert system, the functional links existing between the input Human reasoning, consists of modelling across the expert system, the functional links existing between the input variables domain and the output one. (Figure 1). Particularly considering the functional link y= F (P) that correlates the variables domain and the output one. (Figure 1). Particularly considering the functional link y= F (P) that correlates the input vector P(x

input vector P(x11,x,x22,..,x,..,xNN) defined in entering domain X) defined in entering domain X N N

, with the domain of the only

, with the domain of the only output variableY (see Fig.1)output variableY (see Fig.1)

F(P) F(P) X XNN YY Fig.1 Fig.1

In order to reconsider the function F(P) utilising Composite Functions Theorem the function F(P) could be written as In order to reconsider the function F(P) utilising Composite Functions Theorem the function F(P) could be written as F(P)= g[f(P)], [19] reducing the problem of the determination of the only function unknown F, to the determination of F(P)= g[f(P)], [19] reducing the problem of the determination of the only function unknown F, to the determination of the two functions components; respectively internal component function f and external component function g. (Figure the two functions components; respectively internal component function f and external component function g. (Figure 2).

g(f g(f 11(x(x11,x,x22,…,x,…,xPP)) X XNN g(f g(f 22(x(x11,x,x22,…,x,…,xQQ)) YY ……….. ……….. g(f g(f k k (x(x11,x,x22,…,x,…,xRR)) ∀ ∀P,Q,RP,Q,R<<NN

Fig.2 - Composite Functions Theorem Fig.2 - Composite Functions Theorem

Successively, using human experience to approximate the internal components such as number, form, etc, ANFIS Successively, using human experience to approximate the internal components such as number, form, etc, ANFIS (Adaptive Network based Fuzzy Inference System) will provide to adapt the proposed link and adjust the error done (Adaptive Network based Fuzzy Inference System) will provide to adapt the proposed link and adjust the error done using the human approximation. [12][13]

using the human approximation. [12][13]

This pre-processing model allows starting from N input variables, trough the Composite Functions Theorem, to have This pre-processing model allows starting from N input variables, trough the Composite Functions Theorem, to have K

K<< N input variables, where K is the new number of internal components fixed in number N input variables, where K is the new number of internal components fixed in number and form. (Fig.2 – Fig.3)and form. (Fig.2 – Fig.3) The present paper proposes a fast methodology to design, develop and implement an expert system with many inputs The present paper proposes a fast methodology to design, develop and implement an expert system with many inputs which presents acceptable processing-data times through neuro-fuzzy principles. The proposed methodology has been which presents acceptable processing-data times through neuro-fuzzy principles. The proposed methodology has been tested in designing, developing and implementing an expert system for fast estimate of

tested in designing, developing and implementing an expert system for fast estimate of processing times processing times on lathes of on lathes of mechanical components.

CASE STUDY CASE STUDY

The pre-processing methodology has been tested in an important Italian firm that, using flexible production cells, The pre-processing methodology has been tested in an important Italian firm that, using flexible production cells, produces aeronautical and auto components on order.

produces aeronautical and auto components on order.

Generally, in the operational context of a firm that manufactures batches of mechanical products, is very important the Generally, in the operational context of a firm that manufactures batches of mechanical products, is very important the ability of estimate the production costs of components, parts and complex apparels with industrial reliability, in quickly ability of estimate the production costs of components, parts and complex apparels with industrial reliability, in quickly times and with criterions of objective evaluations.

times and with criterions of objective evaluations.

input 1 input 1 input

input 2 2 Nodo Nodo 11 …… …… input P input P input P+1 input P+1 input

input P+2 P+2 Nodo Nodo 22 ……. ……. input Q input Q ANFIS Output ANFIS Output input Q+1 input Q+1 input

input Q+2 Q+2 Nodo 3Nodo 3 ……. ……. input R input R input R+1 input R+1 input

input R+2 R+2 Nodo Nodo 44 ……

…… input N input N

Fig.3 –

Fig.3 –Pre-processingPre-processingmodelmodel

The timeliness and reliability in the respect of the costs of production are actually the key of the success in the The timeliness and reliability in the respect of the costs of production are actually the key of the success in the acquisition of new programs of production.

acquisition of new programs of production.

At this time the characteristics of timeliness, reliability an

At this time the characteristics of timeliness, reliability and objectivity, are not achievable in an d objectivity, are not achievable in an acceptable way usingacceptable way using the usual operational based on the evaluation of "experience." We tend often to privilege the timeliness, but we obtain a the usual operational based on the evaluation of "experience." We tend often to privilege the timeliness, but we obtain a reliability loss. In other cases, if we aim to

reliability loss. In other cases, if we aim to the reliability of the estimation that involves an analytical rigid the reliability of the estimation that involves an analytical rigid evaluation, inevaluation, in addiction of congruent times of answer. One of the most evident limits of the estimation process, it is the "subjectivity" addiction of congruent times of answer. One of the most evident limits of the estimation process, it is the "subjectivity" of the analysis tied to the specific experience of the analyst, that makes not transferable and perishable the evaluation. of the analysis tied to the specific experience of the analyst, that makes not transferable and perishable the evaluation. This research proposes an Expert System (ES) of estimation and the comparison with the "conventional" model, to the This research proposes an Expert System (ES) of estimation and the comparison with the "conventional" model, to the purpose of audit the implementation, in terms of availability, precision and objectivity of the evaluation, that they could purpose of audit the implementation, in terms of availability, precision and objectivity of the evaluation, that they could be achieve

be achieve using using these systhese systems.tems.

This study consists of the evaluation of lathes process in circular symmetry pieces, noted that in the field of the This study consists of the evaluation of lathes process in circular symmetry pieces, noted that in the field of the removals processing, lathes constitutes the more frequent operation and the processing time represents the principal removals processing, lathes constitutes the more frequent operation and the processing time represents the principal share of the time cycle in the modern flexible cell.

share of the time cycle in the modern flexible cell.

The logic of evaluation follows from the experience of the analyst, and consists to analyse the problem not considering The logic of evaluation follows from the experience of the analyst, and consists to analyse the problem not considering simultaneously all the variables, but clustering variables group according to the reasoning structured showed in figure 4. simultaneously all the variables, but clustering variables group according to the reasoning structured showed in figure 4. First, the expert analyses the homogeneous groups of entry variables, then esteems the value of the intermediary First, the expert analyses the homogeneous groups of entry variables, then esteems the value of the intermediary correspondent variables basing himself on experience rules, and afterward, correlates the intermediary variables up to correspondent variables basing himself on experience rules, and afterward, correlates the intermediary variables up to arrive at to the last level of aggregation that furnishes the exit variable. The input variables are from the indicators that arrive at to the last level of aggregation that furnishes the exit variable. The input variables are from the indicators that originate from the exterior of the process (tailored to the customer) and from the inland (state and availability of the originate from the exterior of the process (tailored to the customer) and from the inland (state and availability of the resources).

Input4= Profilo esterno Input4= Profilo esterno

del finito del finito Input5 = Sbilanciamento Input5 = Sbilanciamento (statico e dinamico) (statico e dinamico) Input3 = Numero Input3 = Numero diametri est. diametri est.

Input6 = Possibilità presa Input6 = Possibilità presa

mandrino mandrino Input1 = Somma quote Input1 = Somma quote

filettate filettate

Input7 = Lung. tot. Max int. Input7 = Lung. tot. Max int. Lung. tot. Max est. Lung. tot. Max est. Input8 = Num. Diametri Int. Input8 = Num. Diametri Int. Input9 = Lung. tot. Max int. Input9 = Lung. tot. Max int. Diametro min. int. Diametro min. int. Input10 = Num. cavità int. Input10 = Num. cavità int.

Input26 = Num. gole est. Input26 = Num. gole est. Input27 = Num. gole int. Input27 = Num. gole int. Input28 = Num. tolleranze di Input28 = Num. tolleranze di

orientamento e orientamento e posizione posizione Input29 = Num. tolleranze di Input29 = Num. tolleranze di forma o filettature forma o filettature a passo fine a passo fine Input30 = Area 'vuoti' interni Input30 = Area 'vuoti' interni

Area del finito 'pieno' Area del finito 'pieno' Input11 = Volume da asportare Input11 = Volume da asportare

a taglio interrotto a taglio interrotto

Input16

Input16 = = Lung. Lung. grezzogrezzo Diam. Diam.

Input12 = Sigma di resistenza Input12 = Sigma di resistenza Input 13 = Presenza di Input 13 = Presenza di

trattamenti termici trattamenti termici Input14 = Provenienza del Input14 = Provenienza del

grezzo grezzo

Input18 = Caratteristiche del Input18 = Caratteristiche del

Tornio Tornio

Input15 = Potenza al mandrino Input15 = Potenza al mandrino

Input17 = Sezione min. Input17 = Sezione min.

resistente resistente

Input19 = Num. di tolleranze Input19 = Num. di tolleranze di quota indicate est. di quota indicate est. Input20 = Num. di tolleranze Input20 = Num. di tolleranze di quota indicate int. di quota indicate int. Input21 = Valore min. toller. Input21 = Valore min. toller.

di quota di quota

Input23 = Num. gole con toller. Input23 = Num. gole con toller.

Input24 = Materiale Input24 = Materiale

grezzo grezzo Input22 = Valore min. toller.

Input22 = Valore min. toller. geometrica geometrica

Input25 = Area gole Input25 = Area gole

Input31 = Massa tot. di Input31 = Massa tot. di

metallo da asportare metallo da asportare Input0 = Tipologia pezzo

Input0 = Tipologia pezzo (standard o speciale) (standard o speciale) Geometria Geometria esterna esterna 1 1 Input2 = Lunghezza max

Input2 = Lunghezza max esterna esterna Geometria Geometria interna interna 2 2 Percorso Utensile Percorso Utensile 1 1 Singolarità di Singolarità di forma forma 4 4 Caratteristiche Caratteristiche del Materiale del Materiale 3 3 Vibrazioni Vibrazioni 4 4 Sezione media Sezione media truciolo truciolo 2 2 Usura media Usura media tagliente utensile tagliente utensile 1 1 Velocità Velocità approssimativa approssimativa di taglio di taglio 2 2 Caratteristiche Caratteristiche funzionali richieste funzionali richieste 5 5 Numero Numero approssimativo di approssimativo di passate passate 3 3 Capacità di Capacità di asportazione asportazione unitaria unitaria Tempo di Tempo di lavorazione lavorazione Fig 4

These parameters are called

These parameters are called direct variablesdirect variables, respondent to specific applications of peculiarity, simplicity and, respondent to specific applications of peculiarity, simplicity and objectivity. The following level, is corporate from the opportune aggregation of the

objectivity. The following level, is corporate from the opportune aggregation of the direct variablesdirect variables and it has beenand it has been decided level of the

decided level of the secondary quantitiessecondary quantities. The following level of the united variables is called the. The following level of the united variables is called the primary quantities. primary quantities. (Fig.4)

(Fig.4)

The passage from the

The passage from the direct variablesdirect variables to theto the primary quantities, primary quantities, is a phase strongly subjective because tied to theis a phase strongly subjective because tied to the intimate patrimony of experience and chord of the experienced technologist. Schematically the modes of aggregation intimate patrimony of experience and chord of the experienced technologist. Schematically the modes of aggregation implicate:

implicate:

Ø

Ø The evaluation of the applications to which the piece has destined, to recognise the parts that necessitate of moreThe evaluation of the applications to which the piece has destined, to recognise the parts that necessitate of more precise processing dilating the time

precise processing dilating the time manufacturing.manufacturing.

Ø

Ø The evaluation of the The evaluation of the processing difficulties processing difficulties of the peculiar form of the peculiar form or material of the por material of the piece, and iece, and then use it of then use it of distinctive devices, facility or methodology of work that satisfy the technical and economic requisite of the process. distinctive devices, facility or methodology of work that satisfy the technical and economic requisite of the process.

Ø

Ø The graphic analysis of the component and morphological comparison of the product pieces with already realisedThe graphic analysis of the component and morphological comparison of the product pieces with already realised to show the similarities that facilitate evaluation

to show the similarities that facilitate evaluation

Then, only a strongly subjective comparison and optimisation process of the indicators, we can find the

Then, only a strongly subjective comparison and optimisation process of the indicators, we can find the primary primary quantities

quantities(( path tool, cutting speed, number of passing, removal bulk path tool, cutting speed, number of passing, removal bulk ). After reckoning these quantities we will furnish). After reckoning these quantities we will furnish the quantity of removal material for hour (ability of hourly removal), and dividing the bulk of removal material with the quantity of removal material for hour (ability of hourly removal), and dividing the bulk of removal material with this quantities we will furnish the processing time.

this quantities we will furnish the processing time.

The purpose to develop the Expert System, using the pre-processing methodology, we make some technological The purpose to develop the Expert System, using the pre-processing methodology, we make some technological opportune hypotheses, that the problem dominion answers to the hypotheses of composed functions Theorem. [19] At opportune hypotheses, that the problem dominion answers to the hypotheses of composed functions Theorem. [19] At first, to the goal of audit the definition hypotheses, and then consider the

first, to the goal of audit the definition hypotheses, and then consider the direct variablesdirect variables domain constituted fromdomain constituted from disjointed subsets whose union constitutes the dominion of the input variables (Fig.4- Fig.5), is necessary free from the disjointed subsets whose union constitutes the dominion of the input variables (Fig.4- Fig.5), is necessary free from the strictly dependence of the technological indicators of

strictly dependence of the technological indicators of processing.processing.

On first step, using the firm experiences, chosen only four formal entry variables (

On first step, using the firm experiences, chosen only four formal entry variables ( path tool, cutting speed, number of path tool, cutting speed, number of passing, removal bulk

passing, removal bulk ), that will represent the real variable "handled" by the model, correspondent to the four functions), that will represent the real variable "handled" by the model, correspondent to the four functions [fk]. That represents a vector with 31 relative components related to the 31

[fk]. That represents a vector with 31 relative components related to the 31 direct variablesdirect variables(Fig 2- Fig.5(Fig 2- Fig.5÷÷Fig.7).Fig.7).

After we have characterised the subsets to correlate these parameters to the

After we have characterised the subsets to correlate these parameters to the exit domain (time processing), the followingexit domain (time processing), the following passage is the way to determine the internal component functions ([fk]) that complete the pre-learning phase. In other passage is the way to determine the internal component functions ([fk]) that complete the pre-learning phase. In other words it consents,

words it consents, "suggesting" bonds between the input variables, to restrict the number of the elaborate variable"suggesting" bonds between the input variables, to restrict the number of the elaborate variable across the neuro-fuzzy structure.

across the neuro-fuzzy structure.

Path tool Path tool X

X⊆⊆⊆⊆RR3131 Cutting speedCutting speed ANFIS ANFIS TimeTime

Number of passing Number of passing Removal bulk Removal bulk

Fig.5- Transforming

Fig.5- Transforming31 direct variables31 direct variables toto4 formal entries4 formal entries

The functional dependence ([fk]), between the formal entering variables (

The functional dependence ([fk]), between the formal entering variables ( path tool, cutting speed, number of passing, path tool, cutting speed, number of passing, removal bulk)

removal bulk) and the real entering variables (and the real entering variables (direct variablesdirect variables) have been formulate hypothesising a bond “simply”) have been formulate hypothesising a bond “simply” linear with coefficients +1 or- 1, depending on effect of the advised variable on the formal [fk], respectively of the linear with coefficients +1 or- 1, depending on effect of the advised variable on the formal [fk], respectively of the increasing or decreasing type. In analytical terms, the described phase has characterised from a matrixes product whose increasing or decreasing type. In analytical terms, the described phase has characterised from a matrixes product whose execution is automated by a formal layer of fixed nodes, up stream of the input layer, called

execution is automated by a formal layer of fixed nodes, up stream of the input layer, called pre-learning pre-learninglayer (Fig.6).layer (Fig.6). The matrixes are corporate from digital data representative of the values engaged from the

The matrixes are corporate from digital data representative of the values engaged from the direct variablesdirect variablesin about 110in about 110 orders realised from the firm. Relatively to each order have been recorded the correspondent time processing also, to orders realised from the firm. Relatively to each order have been recorded the correspondent time processing also, to asses the result of the mode across the comparison between the values esteemed from the model (result of the learning) asses the result of the mode across the comparison between the values esteemed from the model (result of the learning) and the real correspondent values.

Summarising the hypotheses of ES is: Summarising the hypotheses of ES is:

Ø

Ø Setting interdependence of some technological ties, formulating a simplified corporate model only from someSetting interdependence of some technological ties, formulating a simplified corporate model only from some lathes time prevision indicators (path tool, cutting speed, number of passing, removal bulk)

lathes time prevision indicators (path tool, cutting speed, number of passing, removal bulk)

Ø

Ø Correlate these indicators betweenCorrelate these indicators between direct variablesdirect variables by means of simple relations ([fk]) that with the opportuneby means of simple relations ([fk]) that with the opportune coefficients point out the effects (increase-decrease), then place on top the functional bonds.

coefficients point out the effects (increase-decrease), then place on top the functional bonds.

Also if determining the functional links without any experimental check could appear a substantial forcing, in the phase Also if determining the functional links without any experimental check could appear a substantial forcing, in the phase of engineering the input domain using firm experiences and the quality of result, legitimate the reasoning of the of engineering the input domain using firm experiences and the quality of result, legitimate the reasoning of the pre-processing mode. processing mode. f f 11(X(X11) = ) = f f 11(x(x11,x,x22,x,x33,x,x44,x,x55,x,x66,x,x77,x,x88,x,x99,x,x1010) ) == +1x+1x11+1x+1x22+1x+1x33+1x+1x44+1x+1x55+1x+1x66+1x+1x77+1x+1x88+1x+1x99+1x+1x1010 f f 22(X(X22) = ) = f f 22(x(x1111,x,x1212,x,x1313,x,x1414,x,x1515,x,x1616,x,x1717,x,x1818) ) == -1x-1x1111-1x-1x1212-1x-1x1313-1x-1x1414+1x+1x1515-16x-16x1616-1x-1x1717+1x+1x1818 f f 33(X(X33) =f ) =f 33(x(x1919,x,x2020,x,x2121,x,x2222,x,x2323,x,x2424,x,x2525,x,x2626,x,x2727,x,x2828,x,x2929,x,x3030,)=,)= +1x +1x1919+1x+1x2020+1x+1x2121+1x+1x2222+1x+1x2323+1x+1x2424+1x+1x2525+1x+1x2626+1x+1x2727+1x+1x2828+1x+1x2929+1x+1x3030 f f 44(X(X44) = ) = f f 44(x(x3131) =) = +1x+1x3131 f f 11(X(X11)) f

f 22(X(X22)) Direct variablesDirect variables

f

f 33(X(X33)) == (x) (x) ** Transferring MatrixTransferring Matrix

f f 44(X(X44))

input 1 input 1 input

input 2 2 Nodo Nodo 11 …… …… input P input P input P+1 input P+1 input

input P+2 P+2 Nodo Nodo 22 …….

……. input

input Q Q ………

….

…. ANFIS ANFIS OutputOutput

…. …. Nodo Nodo KK …. …. Input N Input N Fig.6

Input1 = Somma quote filettate Input1 = Somma quote filettate Input2

Input2 = Lunghezza = Lunghezza esterna massesterna massimaima Input3

Input3 = Numero = Numero di diametri di diametri esterniesterni Input4

Input4 = Profilo = Profilo esterno del esterno del finitofinito Input5

Input5 = Sbilanciamento = Sbilanciamento (statico e d(statico e dinanamicoinanamico Path ToolPath Tool Input6

Input6 = = Possibilità Possibilità presa presa mandrinomandrino Input7

Input7 = L.tot.max interna = L.tot.max interna / L.tot.max es/ L.tot.max esternaterna (primary quanties(primary quanties)) Input8

Input8 = = Numero Numero Diametri Diametri interniinterni Input9

Input9 = L.tot.max inte= L.tot.max interna / Diametro rna / Diametro min. internomin. interno Imput10

Imput10 = Nume= Numero Cavità ro Cavità interneinterne ((direct variablesdirect variables))

Input11

Input11 = Volume = Volume asportato a tagasportato a taglio interrottolio interrotto Input12

Input12 = Sigma = Sigma di resistenzdi resistenzaa Input13

Input13 = Presenza = Presenza di trattamenti termicdi trattamenti termicii Input14

Input14 = Provenienza = Provenienza del grezzodel grezzo Cutting SpeedCutting Speed Input15

Input15 = Ca= Caratteristiche deratteristiche del torniol tornio Input16

Input16 = Potenza = Potenza al mandrinoal mandrino (primary quanties)(primary quanties) Input17

Input17 = Lunghezza = Lunghezza / Diametro / Diametro (grezzo)(grezzo) Input18

Input18 = Sez.R= Sez.Resistente esistente minimaminima ((direct variablesdirect variables))

Processing Processing Input19

Input19 = N.di tolleranze di = N.di tolleranze di quota indicate (est.)quota indicate (est.) timetime Input20

Input20 = N.di tolleranze = N.di tolleranze di quota indicate di quota indicate (int.)(int.) Input21

Input21 = Valore min. = Valore min. tolleranza di tolleranza di quotaquota Input22

Input22 = Valore = Valore min tolleranza gmin tolleranza geometricaeometrica Input23

Input23 = Numero = Numero gole con gole con tolleranzatolleranza Input24

Input24 = = MaterialeMateriale Input25

Input25 = Area oc= Area occupata da cupata da golegole Number of passingNumber of passing Input26

Input26 = N.g= N.gole eole esternesterne Input27

Input27 = N= N.gole .gole interneinterne (primary quanties)(primary quanties) Input28

Input28 = N. di toll. di orie= N. di toll. di orientamento e posizionentamento e posizione Input29

Input29 = N. di toll.di forma = N. di toll.di forma o filettatture a passo o filettatture a passo finefine Input30

Input30 = Area vuoti interni / = Area vuoti interni / Area del finito pienoArea del finito pieno ((direct variablesdirect variables))

Input31 =

Input31 = Removal BulkRemoval Bulk

Fig.7 – Flow chart of "SE" knowledge Fig.7 – Flow chart of "SE" knowledge

In order to understand the new methodology of aggregation and optimisation of input variables, showed in figure 7, it is In order to understand the new methodology of aggregation and optimisation of input variables, showed in figure 7, it is necessary an example.

Referring, for simplicity, to the

Referring, for simplicity, to the path tool path toolto implement, it has seen like the morphological characteristics of the pieceto implement, it has seen like the morphological characteristics of the piece that also contributes to the determination of the

that also contributes to the determination of the cutting speed cutting speed , but the experiences of the firm have highlighted that, but the experiences of the firm have highlighted that often in high precision mec

often in high precision mechanics, not being neceshanics, not being necessary distinctive attention sary distinctive attention to contain flickers and unbato contain flickers and unbalance of thelance of the pieces, is possible to refer only to right indicators in the determination of the

pieces, is possible to refer only to right indicators in the determination of the path tool path tool, extrapolating that is from the, extrapolating that is from the direct variables

direct variablesdomain articulate subsets of elements. Then, to realise the opportune partitions of the entry, dominion,domain articulate subsets of elements. Then, to realise the opportune partitions of the entry, dominion, the training data set has been built given to the neural network only commodities that they don't necessitate of the training data set has been built given to the neural network only commodities that they don't necessitate of complexes tighten tools. These elements have bee

complexes tighten tools. These elements have been characterised and represented in the groups of indicators showed n characterised and represented in the groups of indicators showed inin figure 7

figure 7

Next step in pre-processing, for example, determinated entering domain of

Next step in pre-processing, for example, determinated entering domain of path tool path tool, referring to input2 (fig.7), the, referring to input2 (fig.7), the practical experience allowed to approximate linear function link between this input and

practical experience allowed to approximate linear function link between this input and path tool, then we assignpath tool, then we assign proportional constant to 1.

proportional constant to 1.

For other groups of indicators, for example Input12 (Sigma di resistenza- Fig.7), this observation arises in lathes For other groups of indicators, for example Input12 (Sigma di resistenza- Fig.7), this observation arises in lathes operation, if increase the mechanical properties of the piece we need often to reduce cutting speed than we assign operation, if increase the mechanical properties of the piece we need often to reduce cutting speed than we assign constant to -1. Using these reasonings conduct to the definition of a matrix (Fig.8) called of "transferring" where each constant to -1. Using these reasonings conduct to the definition of a matrix (Fig.8) called of "transferring" where each row vectors is composed of the prevoius selected linear constants and that realise the metamorphosis from the 31 row vectors is composed of the prevoius selected linear constants and that realise the metamorphosis from the 31 entering variables to the 4 real entering variables

entering variables to the 4 real entering variables. Practically the four internal . Practically the four internal functions are representative of the fourfunctions are representative of the four constituent equations the linear system of fig.6 (see also the figure 2), and comes realised across the pre-learning layer. constituent equations the linear system of fig.6 (see also the figure 2), and comes realised across the pre-learning layer. The parameters of the fixed nodes of this layer represents the linear relative constants to the elaborate function, and all The parameters of the fixed nodes of this layer represents the linear relative constants to the elaborate function, and all the mode has been automated by the MatLab system. The training matrix elaboration originates from this initial layer the mode has been automated by the MatLab system. The training matrix elaboration originates from this initial layer and it also generates the checking data set. The results of the elaboration have

and it also generates the checking data set. The results of the elaboration have presented in next figure.presented in next figure.

CONCLUSION CONCLUSION

The listing of the Matlab program that realises the exposed mode is: The listing of the Matlab program that realises the exposed mode is:

%*******CARICA DATI DI INGRESSO*********************** %*******CARICA DATI DI INGRESSO*********************** load dati; load dati; load tempi; load tempi; load mas; load mas; load cost; load cost; % ******ATTIVA NE

% ******ATTIVA NEURONE URONE FORMALE DI IFORMALE DI INGRESSO**********NGRESSO********** inform = cost*dati; inform = cost*dati; in = [inform mas]; in = [inform mas]; in1 = (1:90,:); in1 = (1:90,:); in2 = (91,109,:); in2 = (91,109,:); tempi1 = (1:90,:); tempi1 = (1:90,:); tempi2 = (91,109,:); tempi2 = (91,109,:); trnData = [in1 tempi1] trnData = [in1 tempi1] chkData = [in2 tempi2] chkData = [in2 tempi2] NumMFs = 3;

NumMFs = 3;

MfType = ' gbellmf '; MfType = ' gbellmf ';

%*****GENERA MATRICE ANFIS*************************** %*****GENERA MATRICE ANFIS*************************** Fismat = genfis1(trnData,NumMFs,MfType);

Fismat = genfis1(trnData,NumMFs,MfType);

[Fismat1, trnError, StepSize, Fismat2, chkError] = ... [Fismat1, trnError, StepSize, Fismat2, chkError] = ...

anfis(trnData, Fismat, [250;0;0.1;0.9;1.1], [], chkData); anfis(trnData, Fismat, [250;0;0.1;0.9;1.1], [], chkData); %*****GENERA ANFIS

%*****GENERA ANFIS OUTPUT******************************OUTPUT****************************** trnOut = evalfis(in1, Fismat1);

trnOut = evalfis(in1, Fismat1);

Use of MatLab, for this algorithm, is justified from the capability of realising the analytical operations connected with Use of MatLab, for this algorithm, is justified from the capability of realising the analytical operations connected with the pre-learning phase and afterward it uses the ANFIS modes (Adaptive Network [based] Fuzzy Inference System) the pre-learning phase and afterward it uses the ANFIS modes (Adaptive Network [based] Fuzzy Inference System) contained in the toolbox Fuzzy Logic and Neural Network, in an only environment, avoiding complex handling and contained in the toolbox Fuzzy Logic and Neural Network, in an only environment, avoiding complex handling and transfers of the data.

### Fig.8

### Fig.8

The operation of the program has been set on 90 training drawing of piece already produced by the firm and checked The operation of the program has been set on 90 training drawing of piece already produced by the firm and checked with 20 drawing piece. The answers of the Root Mean Square Error is showed in Fig.8 and we have compared it to the with 20 drawing piece. The answers of the Root Mean Square Error is showed in Fig.8 and we have compared it to the effective processing time to the ANFIS output in Fig.9. In terms of the mean error (deliberate like average of the error effective processing time to the ANFIS output in Fig.9. In terms of the mean error (deliberate like average of the error percent in each of the 110 examples) a mean error has been obtained, on the training time about of the 5% while on the percent in each of the 110 examples) a mean error has been obtained, on the training time about of the 5% while on the checking data about of the 24%. This result, legitimate the operational capability of the pre-process reasoning and can checking data about of the 24%. This result, legitimate the operational capability of the pre-process reasoning and can be acceptable for some kinds of order, or for reference budgets, because the use of such kind of expert system doesn't be acceptable for some kinds of order, or for reference budgets, because the use of such kind of expert system doesn't require specialised manpower and we have had

require specialised manpower and we have had very small data processing.very small data processing.

Fig.9 Fig.9

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