Cognitive design of products for engineering and vibromechanics by criterion of minimization labor input of their manufacturing

V. P. Grahov1 , N. L. Taranuha2 , K. V. Pavlov3 , A. S. Shirobokov4

1, 2, 3, 4Kalashnikov Izhevsk State Technical University, Izhevsk, Russia

1Corresponding author

Vibroengineering PROCEDIA, Vol. 9, 2016, p. 83-88.
Received 1 October 2016; accepted 4 October 2016; published 9 October 2016

Copyright © 2016 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract.

The basis of the algorithm for determining the labor input are user-configured according to the parameters of its real production. It is shown that in the early stages of designing the designer can minimize the expected cost of the product by changing the design solutions, its head by a reporting engine will evaluate the range of materials and assortments and will issue guidelines to reduce it, and the technology and setters will calculate the final demand for materials and labor. Developed labor regulation system, built on the theory of fuzzy decision trees.

Keywords: cognitive design of products of vibromechanics, labor regulation system on the theory of fuzzy decision trees, fuzzy inference with the genetic algorithm training system.

1. Introduction

The ability to quickly assess the cost of the designed products at an early stage will allow to optimize material requirements needed for the production of products, and will even allow to optimize even before creation of the first pilot products in the available ranges a product design.

The problem of estimation of the cost of production of separate parts, where it is not a precise calculation of material consumption norms and standards of operational time, namely the evaluation of the first approximation.

The basis of the algorithm for determining the labor input are user-configured according to the parameters of its real production [3]. This lays the material parameters, the actual processing of the individual elements of geometry and cost parameters of auxiliary operations. All cost characteristics tied to specific units of available equipment and tools and specific assortments. Furthermore, we define the auxiliary and preparatory operations. Finally, here adjusted cost of operations not related to the transformation of the mold material, such as coloration, control, heat treatment, etc. Any cost parameters can be used for single parts, manufactured at the same time the party or to the entire quantity of manufactured parts, and they can be assigned automatically or interactively. Cost of items will be calculated according to the template settings and according to the actual part geometry. Will also be added the costs of setting up the equipment and any additional operations and costs referred to as a template are required for use.

So, the solution offers a wide range of tools for the analysis of future product costs. And they can be used together and separately. For example, in the early stages of designing the designer can minimize the expected cost of the product by changing the design solutions, its head by a reporting engine will evaluate the range of materials and assortments and will issue guidelines to reduce it, and the technology and setters will calculate the final demand for materials and labor.

2. The calculation of labor costs with the use of an information system based on fuzzy decision trees

2.1. Database

Consider the range of the production of basic components reducers - toothed gears. Each gear is characterized by several features: D – outer diameter; d – the inner diameter of the hole; H – thickness; h – height of the teeth; Pz – type teeth; Pm – the type of material used; Pc – type of coating.

Characteristic properties and costs of production cost are shown in Table 1 for a sample of 120 parts. This table constitute the main content of the database.

Table 1. Characteristic properties and costs of production cost

Cost
D
d
H
h
P z
P m
P c
Cost
D
d
H
h
P z
P m
P c
1
2
3
4
5
6
7
8
0.406
240
35
26
28
1
2
1
0.127
25
8
5
4
1
4
1
0.594
116
20
14
14
4
1
3
0.509
93
17
11
11
4
2
1
0.585
155
24
18
18
3
1
3
0.457
118
20
14
14
3
1
2
0.128
65
13
9
8
1
1
1
0.342
42
10
6
6
5
1
1
1.083
225
33
25
26
5
1
1
0.806
254
37
27
29
2
4
1
1.12
215
32
24
25
5
2
1
1.127
199
30
22
23
5
3
1
1.11
173
27
19
20
5
4
2
0.241
65
13
9
8
2
2
1
1.225
190
29
21
22
5
4
3
0.592
231
34
25
27
2
2
1
1.417
248
36
27
29
5
3
3
0.861
243
35
26
28
2
4
3
0.147
29
9
5
4
2
2
1
0.961
148
24
17
17
5
4
1
0.798
220
33
24
25
2
4
3
0.183
60
13
8
8
1
3
1
0.396
37
10
6
5
5
4
2
0.476
173
27
19
20
1
4
2
0.594
197
30
22
23
2
2
3
1.015
217
32
24
25
4
3
1
0.634
199
30
22
23
2
3
2
0.867
195
29
22
23
3
4
2
0.618
267
38
29
31
1
4
1
0.765
274
39
29
31
2
3
1
0.586
179
27
20
21
2
3
2
0.348
46
11
7
6
4
2
3
1.168
227
33
25
26
4
4
2
0.75
152
24
17
18
3
4
3
0.784
146
23
17
17
5
1
1
0.318
109
19
13
13
1
3
3
0.763
134
22
15
16
4
4
1
0.868
218
32
24
25
4
1
1
0.972
178
27
20
21
5
2
1
1.227
253
37
27
29
4
3
3
0.529
183
28
20
21
1
4
3
0.489
197
30
22
23
2
1
2
0.736
242
35
26
28
3
1
1
0.579
95
17
12
12
5
1
1
0.904
169
26
19
20
5
1
2
0.838
160
25
18
19
5
1
1
1.542
257
37
28
30
5
4
3
0.263
92
17
11
11
1
3
2
0.623
270
39
29
31
2
1
2
0.291
96
17
12
12
1
3
3
0.394
231
34
25
27
1
1
3
0.295
211
31
23
24
1
1
1
0.612
165
26
19
19
3
2
1
0.412
51
11
7
7
4
4
2
1.117
224
33
24
26
5
1
2
0.745
178
27
20
21
3
3
2
0.616
224
33
24
26
2
2
2
0.778
110
19
13
13
5
4
1
0.828
150
24
17
18
4
4
1
0.106
48
11
7
6
1
1
1
0.265
33
9
5
5
4
2
1
0.585
193
29
21
22
2
3
1
0.382
141
23
16
17
2
1
2
0.712
116
20
14
14
5
2
1
0.646
238
35
26
27
2
2
2
0.983
189
29
21
22
4
4
1
1.061
254
37
27
29
4
2
1
0.582
144
23
16
17
2
4
3
0.545
227
33
25
26
2
1
2
0.786
162
25
18
19
4
2
2
1.242
246
36
27
28
5
2
1
1.015
173
27
19
20
5
3
1
0.463
130
21
15
15
2
3
2
0.494
142
23
16
17
3
1
1
0.992
183
28
20
21
4
4
2
0.755
162
25
18
19
4
1
3
0.745
159
25
18
19
4
2
1
1.155
234
34
25
27
4
4
1
0.684
127
21
15
15
4
3
1
0.628
107
18
13
13
4
3
2
0.526
265
38
29
30
1
2
3
0.502
249
36
27
29
1
2
3
0.71
141
23
16
17
3
4
3
0.279
196
30
22
23
1
1
1
0.509
128
21
15
15
3
1
3
0.458
128
21
15
15
3
1
1
0.302
142
23
16
17
1
2
2
0.797
157
25
18
18
4
3
1

2.2. Pre-processing of the input data

Presented in Table 1 data is analyzed to identify correlations between variables by principal component. The user receives a graph on the screen of the spectrum of the eigenvalues, such as Fig. 1.

The Fig. 1 shows that significant are the first four ingredients. Therefore, the user can reduce the number of input variables to 4.

Fig. 1. The spectrum of eigenvalues

 The spectrum of eigenvalues

2.3. Construction of tree and base of rule

Using the above algorithm builds the appropriate decision tree. For the number of classes corresponding to the output variable on a sample of 84 items (70 %-th of sample) constructed a decision tree for all input properties (Fig. 2).

The variables Xi correspond to the properties of D, d, H, h, Pz, Pm, Pc.

These rules can be entered in the knowledge base and used for forecasting labor products were not part of the training set. Comparison of predicted and actual work is represented in Fig. 3. When comparing the value of labor costs given in the range [0, 1].

Fig. 2. The decision tree corresponding to the full set of Table 4.1 properties

 The decision tree corresponding  to the full set of Table 4.1 properties

Fig. 3. Comparison of predicted and actual work

 Comparison of predicted and actual work

This tree contains 17 units and corresponds to the following set of nine rules:

0 if X[4] >= 1.80 AND X[2] >= 17.60 AND X[1] >= 27.00 AND X[0] >= 253.80 then Y = 1

1 if X[0] >= 74.80 AND X[2] >= 17.60 AND X[1] >= 27.00 AND X[0] < 253.80 AND X[4] >= 4.40 then Y = 2

2 if X[0] >= 74.80 AND X[4] >= 1.80 AND X[2] >= 17.60 AND X[1] >= 27.00 AND X[0] < 253.80 AND X[4] < 4.40 then Y = 1

3 if X[0] >= 74.80 AND X[4] >= 1.80 AND X[2] >= 17.60 AND X[1] < 27.00 then Y = 1

4 if X[0] >= 74.80 AND X[2] < 17.60 AND X[4] >= 2.60 AND X[5] >= 3.40 then Y = 1

5 if X[0] >= 74.80 AND X[2] < 17.60 AND X[4] >= 2.60 AND X[5] < 3.40 then Y = 0

6 if X[0] >= 74.80 AND X[4] >= 1.80 AND X[2] < 17.60 AND X[4] < 2.60 then Y = 0

7 if X[0] >= 74.80 AND X[4] < 1.80 then Y = 0

8 if X[0] < 74.80 then Y = 0.

The correlation coefficient between forecast and actual values was 0.75. The mean forecast error was 7.4 %.

A decision tree can be reset by the use of compression of input data by the method of principal components.

Table 2 shows the results of calculation of the eigenvalues and the corresponding eigenvectors input from the Table 1.

The first four components are formed on the basis of the following relations:

(1)
y 1 = 0.4981 D + 0.4979 d + 0.4980 H + 0.4980 h - 0.0594 P z - 0.0298 P m + 0.0604 P c ,
(2)
y 2 = - 0.0316 D - 0.0316 d - 0.0340 H - 0.0312 h - 0.5041 P z
            + 0.0403 P m + 0.7612 P c ,
(3)
y 3 = 0.0306 D + 0.0331 d + 0.024 H + 0.031 h + 0.6507 P z + 0.7562 P m + 0.0355 P c ,
(4)
y 4 = - 0.013 D - 0.0139 d - 0.0069 H - 0.0078 h + 0.5648 P z - 0.5146 P m + 0.6447 P c ,

Table 2. The results of calculations of the eigenvalues and the corresponding eigenvectors

No
1
2
3
4
5
6
7
λ
4.0208
1.1452
1.0603
0.771
0.0013
0.0012
0.0003
0.4981
–0.0316
0.0306
–0.013
–0.1159
–0.027
0.8577
0.4979
–0.0316
0.0331
–0.0139
–0.5346
–0.5641
–0.3818
w
0.498
–0.034
0.024
–0.0069
0.8199
–0.2074
–0.1871
0.498
–0.0312
0.031
–0.0078
–0.1687
0.7987
–0.2892
–0.0594
–0.5041
0.6507
0.5648
0.0008
–0.0017
0.0014
–0.0298
0.403
0.7562
–0.5146
0.0084
0.0013
–0.0014
0.0604
0.7612
0.0355
0.6447
–0.0012
–0.0028
0.0012

Fig. 4. A decision tree was built on four main components

 A decision tree was built  on four main components

Fig. 5. Comparison of predicted and actual work by using principal component analysis

 Comparison of predicted and actual work  by using principal component analysis

Now as an input variable Xi are the components y1, y2, y3, y4. The corresponding tree shown in Fig. 4.

From a comparison of fig. 2 and 4 shows that the tree has a less complex structure and the number of sites decreased from 17 to 13. The tree corresponds to the following rules:

0 if X[0] >= –0.08 AND X[2] >= 0.79 then Y = 2

1 if X[2] >= –1.11 AND X[0] >= –0.08 AND X[2] < 0.79 AND X[1] >= –1.30 then Y = 1

2 if X[2] >= –1.11 AND X[0] >= –0.08 AND X[2] < 0.79 AND X[1] < –1.30 then Y = 2

3 if X[0] >= -2.33 AND X[0] < –0.08 AND X[2] >= 1.26 then Y= 1

4 if X[0] >= -2.33 AND X[2] >= –1.11 AND X[0] < -0.08 AND X[2] < 1.26 then Y = 0

5 if X[0] >= –2.33 AND X[2] < –1.11 then Y = 0

6 if X[0] < –2.33 then Y = 0.

The number of rules has also been reduced from 9 to 7. With a smaller number of rules has increased the quality of the forecast. Fig. 5 shows a comparison of projected and actual work.

The correlation coefficient between forecast and actual values increased to 0.833, and the mean-square prediction error decreased to 5.2 %.

As you can see, a trained information system based on using decision trees fuzzy inference copes well with the estimate of labor costs in value terms.

3. Software for the development of systems of fuzzy logic

Currently, fuzzy logic systems are widely used to control various technical systems and production process [4, 5]. In this regard, the number of software products that provide design of fuzzy systems and modeling of them, is sufficiently large. Regarding evolutionary algorithms, the software designed for their design, in wide use have. This is due to the fact that evolutionary algorithms cannot be used in general – by using configuration they require a specific situation [6].

Most software products provide the ability to design systems, fuzzy logic, based on the following stages:

1) editing of the input variables;

2) partition the domain of input variables at several intervals and each interval mapping its linguistic meaning (e.g., “low”, “medium”, “high”);

3) definition of the type of membership functions and parameters of membership functions for each linguistic variable;

4) partition of determining the output variable at several intervals, each interval mapping of linguistic meaning, definition of the type and parameters of membership functions for each output variable;

5) reference knowledge base as a production model. As productions parcels used linguistic values of the input variables are taken as prisoner’s linguistic values of the output variable;

6) defuzzification method definition output variable. Types defuzzification may vary depending on the particular software product. Basic techniques – method of the first peak, the method of the central peak, centroid method;

7) view fuzzy system in action.

Stages 2, 3 and 4 constitute the process of fuzzification (reduction to fuzziness).

A significant software product is the Matlab programming environment developed by Mathworks. Matlab is the language of mathematical data processing and provides a great number of libraries, including both purely mathematical functions and tools to design and study the properties of control systems, digital signal processing, neural networks, image processing, fuzzy logic, and even electrical and power circuits.

Matlab medium of its functionality far exceeds other packages of mathematical data processing. Tools for working with fuzzy logic in using Matlab collected in Fuzzy Logic Toolbox software package. Main features of the package: the construction of fuzzy inference systems (expert systems, regulators, approximators dependencies); Construction of adaptive fuzzy systems (hybrid neural networks); interactive dynamic simulation in Simulink package. The package allows you to work in GUI mode or in command line mode

Development of systems of fuzzy logic in the GUI mode, the program allows for Fuzzy Inference System Editor (FIS Editor) – editor-fuzzy inference system, part of the package Fuzzy Logic Toolbox Matlab programming environment. This editor allows you to carry out all stages of the design standard fuzzy systems described at the beginning of this section. In the Matlab environment supports the creation of fuzzy systems of two models: Mamdani and Sugeno.

As methods of defuzzification methods are used (Fig. 6) of the first peak (lom), the average maximum (mom), the last peak (som), the centroid (centroid), as well as any defuzzification functions, user-designed.

Easy to work with fuzzy logic systems in Matlab environment due to the presence of additional means of mass visual design, providing the modeling of fuzzy systems and facilitate the development of fuzzy systems at its various stages [1, 2].

These tools include: Membership Function Editor – editor of the membership functions, allows an fuzzification variables, choosing membership functions and their parameters in interactive mode; Rule Editor – rules editor; Rule Viewer – visualizer rules allow you to see the process of getting the result of fuzzy inference system according to various inputs; Surface Viewer – visualizer response surface; Clustering – clustering software; ANFIS Editor – editor of hybrid systems, generates and training models fuzzy Sugeno.

The essence of the editor is to generate a hybrid neural network. This neural network simulates the operation of a fuzzy logic system. In it a number of the neurons responsible for the fuzzification of the input parameters, a number of – of the rules, a number of – for the defuzzification of the output variable. From the values of the weighting factors such neural network can uniquely restore the system of fuzzy logic. These construction principles allow the use in teaching methods of fuzzy system, identical methods of training of artificial neural networks.

Fig. 6. Options defuzzification in Matlab package

Options defuzzification in Matlab package

4. Conclusions

Use effective approach to creating an automated method of valuation, which is a generalization of the method of analogies. This valuation method is based on the construction of fuzzy decision trees, establishing depending complexity of labor in terms of value, and the parameters of the trees turn different for each of the object and take into account factors that are not related to the complexity of products, but the impact on labor intensity: the equipment used, qualification of workers, conditions labor and other indicators of organizational and technical level of production. It was found that this method provides high accuracy and adaptability.

Created labor regulation system, built on the theory of fuzzy decision trees, in which the generation of the rules and the selection of the parameters of membership functions are carried out in dynamic process of learning from the available data. Since the fuzzy learning system makes use of genetic optimization algorithms, such a system is a genetic fuzzy system or adaptive fuzzy inference system with genetic algorithm training.

References

  1. Senilov M. A., Paklin N. B. Interpretation of geophysical data on the basis of adaptive model of an indistinct conclusion. Information Technologies in Science, Education, Telecommunications and Business: Materials of 31 International Conferences, The Crimea, Yalta, Journal Advances of Modern Science, Vol. 5, 2004, p. 81-84. [Search CrossRef]
  2. Senilov M. A., Petrov A. N. Improvement of quality of modeling of interpretation of geophysical data with the help of the spectral analysis. Computer Modelling, Works of the 5th International Scientific and Technical Conference, 2004, p. 118-120. [Search CrossRef]
  3. Hollnagel E., Woods D. D. Joint Cognitive Systems: Foundations of Cognitive Systems Engineering. Taylor & Francis, 2005. [Search CrossRef]
  4. Casillas J., Cordon O., del Jesus M. J., Herrera F. Genetic Tuning of Fuzzy Rule Deep Structures for Linguistic Modeling. Technical Report DECSAI-010102, Department of Computer Science and A.I., University of Granada, 2001. [Search CrossRef]
  5. Rojas I., Pomares H., Ortega J., Prieto A. Self-organized fuzzy system generation from training examples. IEEE Transactions on Fuzzy Systems, Vol. 8, 2000, p. 23-26. [Search CrossRef]
  6. Burrough P. A., van Gaans P. F. M., MacMillan R. A. High-resolution landform classification using fuzzy k-means. Fuzzy Sets and Systems, Vol. 113, Issue 1, 2000, p. 37-52. [Search CrossRef]