Performance Comparison of Artificial Neural Network ... - IEEE Xplore

Performance Comparison of Artificial Neural Network and Expert System in Prediction of Flow Stress Asif Iqbal School of Mechanical Engineering Dalian University of Technology Dalian 116024, P.R. China [email protected]

Abstract— Modeling of various manufacturing processes, including force and power requirements, depends on accurate estimation of a material’s flow stress. The paper presents a mutual comparison between rule-based expert system and artificial neural network in predicting flow stress of a commonly used type of steel. The prediction processes take microstructure, applied temperature, strain, and strain rate as process parameters. The prediction results of both the systems show a good deal of match with the actual values. Keywords— fuzzy reasoning; rule-based system; properties estimation; AISI 4340

I.

INTRODUCTION

Flow stress is the stress required to sustain plastic deformation at a particular value of strain [1]. Prediction of flow stress is important for modeling plastic deformation process and for having estimate of force and power requirements during various forming and machining processes. Flow stress of a material is dependent on its microstructure (quantified by hardness), temperature, strain, and strain rate. Unlike elastic deformation, there is no analytical model for exact determination of stress in plastic range. Some approximation methods like power law and saturation models have been put forward, which considerably lack prediction accuracy [2]. Researchers have also worked out some advanced empirical models by considering the effects of strain hardening, visco-plasticity, and thermal softening. The commonly-accepted empirical model is Johnson-Cook (J-C) model [3], which has been widely applied in approximating flow stress [4]. Its revised form has been presented by Rule et al, with claim of improvement in flow stress approximation for some ductile materials being worked at high strain rates [5]. Due to high degree of complexity involved in the empirical and numerical modeling, flow stress prediction seems to be a hot area for application of Artificial Intelligence (AI) tools. Of all such methods, artificial neural networks (ANN) have been widely applied. Among the earlier papers, [6] presented application of back-propagation ANN for prediction of flow stress of a medium-carbon-steel under conditions of constant strain rate and temperature. Anijdan et al reported the

c 978-1-4673-6322-8/13/$31.00 2013 IEEE

application of ANN for the prediction of flow stress of 304 stainless steel [7]. The combination of ANN and genetic algorithm (GA) was used to for optimization of flow stress in 304 stainless steel under cold and warm compression. In another paper, ANN was utilized to model and simulate the flow stress for AA5083 with regard to dynamic strain ageing [8]. The effect of microstructure (or hardness) was not considered. Yang et al have addressed the design of genetic algorithms in developing a hybrid ANN model for aluminum alloy flow stress prediction [9]. Once again, the effect of materials’ microstructure was not considered. Phaniraj et al have modeled the flow stress for plain carbon steels using ANN and employing carbon equivalent as the fourth input parameter [10]. Prediction errors ranging from 2 to 60% have been reported. In a recent paper, an ANN approach, employing the same three input parameters, has been applied for predicting flow stress in the isothermal compression of as-cast TC21 titanium alloy [11]. A maximum prediction error of 4.6% has been reported. The author was unable to find any paper that focuses a comprehensive application of expert system for prediction of flow stress. Moreover, as is clear from the literature survey, only three input parameters (strain, strain rate, and temperature) have been used by most of the ANN models, without considering effect of microstructure or temper condition of the material. These observations came out to be the basic motivation for undertaking the current research work. In this paper, two distinct AI methods, artificial neural network and rule-based expert system (employing fuzzy reasoning), have been utilized and mutually compared in modeling flow stress of a high strength low alloy steel, AISI 4340, by employing strain, strain rate, temperature, and material temper (hardness) as input parameters. AISI 4340 is a nickel-chromium-molybdenum based heat-treatable steel, which is usually quenched and tempered. II.

EXPERIMENTAL FLOW STRESS DATA

Experimental data related to high-rate and high-temperature plastic deformation of AISI 4340 were collected from the previously published papers.

555

Fig. 2. Flow stress data for 32HRc temper of AISI 4340 [12] Fig. 1. Flow stress data for 30HRc temper of AISI 4340 [3]

(a)

(b)

(c)

(d)

Fig. 3. Flow stress data for 38HRc temper of AISI 4340: (a–c) [13]; (d) [14]

(a)

(b)

Fig. 4. Flow stress data for 45HRc temper of AISI 4340 [15]

556

2013 IEEE 8th Conference on Industrial Electronics and Applications (ICIEA)

(a)

(b)

Fig. 5. Flow stress data for 49HRc temper of AISI 4340 [15]

Figs. 1, 2, 3, 4, and 5 present the actual flow stress data for 30, 32, 38, 45, and 49HRc tempers, respectively [3, 12–15]. From the study of the plots provided in the Figs. 1–5, it can be easily observed that increase in material hardness, strain rate, or strain causes increase in flow stress, while the effect of temperature is opposite. A total of 166 data sets were collected from the previous papers, of which, 143 were used to train the intelligent systems and the remaining 23 for simulation and testing. III.

THE ARTIFICIAL NEURAL NETWORK

Firstly, a feed-forward back-propagation ANN was developed to predict the flow stress. This type of network is the most widely used and applied configuration. The ANN consisted of four neurons in the input layer (one each for hardness, temperature, strain rate, and strain) and one in the output layer (for predicted flow stress). The topology regarding number of hidden layers and number of neurons in each hidden layer was finalized after a series of trial-and-error efforts. Numerous network topologies, with count of hidden layers ranging from 1 to 3 and count of neurons per hidden layer ranging from 3 to 50, were tested for best training

performance. The minimum Mean Squared Error (MSE) of 0.158MPa, when trained with 143 data sets, was obtained with a 4-25-15-1 topology. The ANN was trained by LevenbergMarquardt back-propagation algorithm and the tangentsigmoidal function was used as input-output transfer function throughout the network. The training phase was completed in 15 epochs, consuming merely 2 seconds of a 2.7GHz system with 1GB of RAM and 32-bit operating system. Fig. 6 presents the topology of the network. In order to judge the system’s prediction performance a measure, “Prediction Error (PE)” has been formulated as follows: (1) where: n = number of data sets used for testing ı = actual value of flow stress ısys = flow stress predicted by the intelligent system

Fig. 6. The ANN topology, consisting of 2 hidden layers


557

TABLE I. S/No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hardness (HRc) 30 30 30 30 32 38 38 38 38 38 38 38 38 38 38 38 38 45 45 45 45 49 49

Temperature (K) 298 500 735 735 422 373 298 573 773 298 573 873 1173 1373 773 973 1373 173 373 173 298 298 173

Strain rate (per sec) 570 604 650 650 0.002 0.0002 500 500 500 1500 1500 1500 1500 1500 2500 2500 2500 0.0001 0.0001 1000 1000 0.0001 1000 PEANN

SIMULATION AND TESTING OF THE ANN Strain 0.055 0.020 0.007 0.132 0.082 0.057 0.024 0.067 0.056 0.110 0.143 0.156 0.102 0.074 0.114 0.217 0.194 0.1 0.025 0.06 0.044 0.197 0.047

The developed ANN was simulated and the generated results were tested for prediction accuracy against 23 data sets. Table I presents the detail. The table shows that the prediction error incurred by this method is 20.35MPa. The actual flow stress, related to the testing data, is in the range of 215–1790MPa with an average value of 1052MPa. The prediction error is merely the 1.93% of the average value. This analysis clearly suggests that the presented ANN has produced exceedingly acceptable prediction results. IV.

THE EXPERT SYSTEM

A rule-based expert system, employing fuzzy reasoning, was developed as the second intelligent system to predict flow stress of the material. As determining flow stress is a complex process involving high degree of impreciseness, the situation calls for application of fuzzy logic in development of the prediction rules. Manual development of a rule-base based on the knowledge contained by 143 data sets seems to be an immensely laborious task. Therefore, a self-development algorithm, as described comprehensively in [16], for automatic development of fuzzy sets (for input and output variables) and prediction rules, was utilized for the said purpose. Five triangular fuzzy sets were developed for hardness and ten each for temperature, strain rate, and strain. Twenty five triangular sets were developed for the only output variable, the flow stress. The detail is as follows:

ı (MPa) 1058.7 843.3 741.5 880.6 1017 1147.3 1337.8 1108.4 744.3 1530.6 1191.6 592.6 343.8 215.7 823.1 622.4 265.3 1702.4 1403.1 1692.2 1499 1658 1790

ıANN (MPa) 1073.3 838.1 694.4 883.5 1006.4 1147.7 1358.0 1114.5 768.8 1544.9 1190.4 592.8 353.5 217.3 835.5 614.3 264.2 1710.0 1308.6 1653.8 1570.0 1705.9 1763.5

|ıANN – ı| (MPa) 14.6 5.1 47.1 2.8 10.6 0.4 20.2 6.1 24.5 14.4 1.2 0.2 9.7 1.5 12.4 8.2 1.1 10.0 94.4 38.2 71.0 47.9 26.5 20.35 MPa

Hardness (HRc): S1: (26.2 1) (30 1) (32 0); S2: (30 0) (32 1) (38 0); S3: (32 0) (38 1) (45 0); S4: (38 0) (45 1) (49 0); S5: (45 0) (49 1) (52.8 1) Temperature (K): S1: (53 1) (173 1) (298 0); S2: (173 0) (298 1) (373 0); S3: (298 0) (373 1) (500 0); S4: (373 0) (500 1) (573 0); S5: (500 0) (573 1) (735 0); S6: (573 0) (735 1) (773 0); S7: (735 0) (773 1) (973 0); S8: (773 0) (973 1) (1173 0); S9: (973 0) (1173 1) (1373 0); S10: (1173 0) (1373 1) (1493 1) Strain rate (sec–1): S1: (0 1) (0.0001 1) (0.0002 0); S2: (0.0001 0) (0.0002 1) (0.002 0); S3: (0.0002 0) (0.002 1) (500 0); S4: (0.002 0) (500 1) (570 0); S5: (500 0) (570 1) (604 0); S6: (570 0) (604 1) (650 0); S7: (604 0) (650 1) (1000 0); S8: (650 0) (1000 1) (1500 0); S9: (1000 0) (1500 1) (2500 0); S10: (1500 0) (2500 1) (2750 1) Strain: S1: (0 1) (0 1) (0.002 0); S2: (0 0) (0.002 1) (0.01 0); S3: (0.002 0) (0.01 1) (0.014 0); S4: (0.01 0) (0.014 1) (0.03 0); S5: (0.014 0) (0.03 1) (0.035 0); S6: (0.03 0) (0.035 1) (0.05 0); S7: (0.035 0) (0.05 1) (0.052 0); S8: (0.05 0) (0.052 1) (0.15 0); S9: (0.052 0) (0.15 1) (0.2 0); S10: (0.15 0) (0.2 1) (0.8162 1) Flow stress (MPa): S1: (136.756 1) (231.3 1) (258.5 0); S2: (231.3 0) (258.5 1) (300 0); S3: (258.5 0) (300 1) (370.7 0); S4: (300 0) (370.7 1) (481.3 0); S5: (370.7 0) (481.3 1) (520.4 0); S6: (481.3 0)

558


(520.4 1) (568.4 0); S7: (520.4 0) (568.4 1) (648.7 0); S8: (568.4 0) (648.7 1) (683.7 0); S9: (648.7 0) (683.7 1) (709.6 0); S10: (683.7 0) (709.6 1) (723.9 0); S11: (709.6 0) (723.9 1) (758.5 0); S12: (723.9 0) (758.5 1) (826 0); S13: (758.5 0) TABLE II. Rule No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

Hard S1 S1 S1 S1 S1 S1 S1 S1 S1 S1 S1 S1 S1 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3

Antecedents Temp Str. rate S2 S5 S2 S5 S2 S5 S2 S5 S2 S5 S4 S6 S4 S6 S4 S6 S4 S6 S6 S7 S6 S7 S6 S7 S6 S7 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S3 S2 S3 S2 S3 S2 S3 S2 S2 S4 S2 S4 S2 S4 S2 S4 S2 S4 S5 S4 S5 S4 S5 S4 S5 S4 S7 S4 S7 S4 S7 S4 S7 S4 S2 S9 S2 S9 S2 S9 S2 S9 S5 S9 S5 S9 S5 S9 S5 S9 S7 S9 S7 S9 S7 S9 S9 S9 S9 S9 S9 S9 S9 S9 S10 S9 S10 S9 S10 S9 S10 S9 S7 S10 S7 S10 S7 S10

Strain S2 S4 S5 S8 S9 S1 S3 S8 S9 S2 S5 S8 S9 S4 S8 S10 S4 S6 S8 S10 S4 S6 S9 S10 S1 S3 S6 S7 S8 S1 S4 S6 S7 S1 S4 S6 S8 S1 S6 S8 S9 S1 S6 S8 S9 S1 S6 S9 S1 S6 S8 S10 S1 S6 S9 S10 S2 S9 S10

(826 1) (879.7 0); S14: (826 0) (879.7 1) (940 0); S15: (879.7 0) (940 1) (969.8 0); S16: (940 0) (969.8 1) (1082.1 0); S17: (969.8 0) (1082.1 1) (1236.7 0);

THE FUZZY RULE-BASE

Consequent F. stress S13 S14 & S15 S16 S17 S18 S10 S13 S15 S16 & S17 S8 S12 & S13 S13 S14 S17 S19 S25 S16 & S17 S17 S18 S22 & S23 S16 & S17 S17 S18 S22 S17 S19 S20 & S21 S21 S21 & S22 S14 S16 S17 S17 S8 S10 S11 S12 S17 & S18 S20 & S21 S21 S22 S14 & S15 S17 S17 & S18 S18 S5 S7 S7 S3 S3 S3 & S4 S4 S1 S1 S1 S1 S9 S13 S14

Rule No. 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118

Hard S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S3 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S4 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S5 S2 S2 S2 S2 S2 S2 S2

Antecedents Temp Str. rate S8 S10 S8 S10 S8 S10 S8 S10 S9 S10 S9 S10 S9 S10 S9 S10 S10 S10 S10 S10 S10 S10 S10 S10 S1 S1 S1 S1 S3 S1 S3 S1 S3 S1 S3 S1 S1 S8 S1 S8 S1 S8 S1 S8 S2 S8 S2 S8 S2 S8 S2 S8 S3 S8 S3 S8 S3 S8 S3 S8 S3 S8 S1 S1 S1 S1 S1 S1 S1 S1 S2 S1 S2 S1 S2 S1 S3 S1 S3 S1 S3 S1 S1 S8 S1 S8 S1 S8 S2 S8 S2 S8 S2 S8 S2 S8 S3 S8 S3 S8 S3 S8 S3 S8 S2 S3 S2 S3 S3 S3 S5 S3 S5 S3 S5 S3 S5 S3

Strain S2 S8 S9 S10 S2 S8 S9 S10 S2 S8 S9 S10 S1 S8 S1 S7 S8 S10 S1 S3 S4 S6 S1 S3 S5 S8 S1 S3 S5 S6 S8 S1 S7 S9 S10 S1 S7 S9 S1 S7 S9 S1 S3 S5 S1 S3 S5 S7 S1 S3 S5 S8 S8 S1 S1 S1 S9 S1 S9


Consequent F. stress S6 S7 S7 & S8 S8 S3 & S4 S4 S4 S4 S1 S2 S2 S2 S20 & S21 S23 S19 S21 S21 S21 & S22 S22 S22 & S23 S22 S22 & S23 S21 S21 & S22 S20 & S21 S21 & S22 S20 S20 S20 S20 S21 S22 S24 S24 & S25 S24 & S25 S20 & S21 S23 S23 S20 S22 & S23 S23 S22 & S23 S23 S23 & S24 S22 S23 S23 S23 & S24 S21 S22 S22 & S23 S23 S17 S13 & S14 S13 S12 & S13 S17 & S18 S12 S16 & S17

559

(a)

(b) Fig. 7. Triangular fuzzy sets for: (a) hardness and (b) temperature

TABLE III. Hardness (HRc)

S/No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

30 30 30 30 32 38 38 38 38 38 38 38 38 38 38 38 38 45 45 45 45 49 49

Temperature (K) 298 500 735 735 422 373 298 573 773 298 573 873 1173 1373 773 973 1373 173 373 173 298 298 173 PERBS

SIMULATION AND TESTING OF THE RULE-BASED SYSTEM (RBS)

Strain rate (per sec) 570 604 650 650 0.002 0.0002 500 500 500 1500 1500 1500 1500 1500 2500 2500 2500 0.0001 0.0001 1000 1000 0.0001 1000

Strain 0.055 0.020 0.007 0.132 0.082 0.057 0.024 0.067 0.056 0.110 0.143 0.156 0.102 0.074 0.114 0.217 0.194 0.1 0.025 0.06 0.044 0.197 0.047

S18: (1082.1 0) (1236.7 1) (1256.6 0); S19: (1236.7 0) (1256.6 1) (1368 0); S20: (1256.6 0) (1368 1) (1469 0); S21: (1368 0) (1469 1) (1560.8 0); S22: (1469 0) (1560.8 1) (1678 0); S23:

560

ı (MPa) 1058.7 843.3 741.5 880.6 1017 1147.3 1337.8 1108.4 744.3 1530.6 1191.6 592.6 343.8 215.7 823.1 622.4 265.3 1702.4 1403.1 1692.2 1499 1658 1790

ıES (MPa) 1093.21 828.5 792.25 881.96 1013.9 1153.82 1333.4 1095.47 769.48 1528.33 1193.41 580.96 335.35 196.12 826.52 633.6 263.33 1671.34 1462.35 1762.86 1514.9 1744.4 1758.2 22.04 MPa

|ıES – ı| (MPa) 34.6 14.8 50.7 1.3 3.1 6.6 4.4 13.0 25.2 2.2 1.9 11.7 8.4 19.6 3.4 11.2 2.0 28.7 59.3 70.9 15.9 86.4 31.8

(1560.8 0) (1678 1) (1778 0); S24: (1678 0) (1778 1) (1820.1 0); S25: (1778 0) (1820.1 1) (1884.84 1)


For the purpose of clarity, Fig. 7 presents the fuzzy sets of hardness and temperature in graphical form. Moreover, 118 fuzzy rules, for the prediction of flow stress of AISI 4340, were developed automatically. Table 2 presents the detail. For clarity, rule number 1 can be interpreted as follows:

[2]

W.F. Hosford, Mechanical Behaviour of Materials, 2nd ed., Cambridge University Press, Cambridge, 2009

[3]

IF Hardness is S1 and Temperature is S2 and Strain Rate is S5 and Strain is S2 THEN Flow Stress is S13.

[4]

G.R. Johnson and W.H. Cook, “Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures”, Eng. Fract. Mech. vol. 21(1), pp. 31–48, 1985 L. Daridon, O. Oussouaddi, and S. Ahzi, “Influence of the material constitutive models on the adiabatic shear band spacing: MTS, power law and Johnson–Cook models”, Int. J Solids & Struct., vol. 41, pp. 3109–3124, 2004 W.K. Rule and S.E. Jones, “A revised form for the Johnson-Cook strength model”, Int. J Impact Eng., vol. 21(8), pp. 609–624, 1998 K.P. Rao, K.P and Y.K.D.V. Prasad, “Neural network approach to flow stress evaluation in hot deformation”, J Mater. Proc. Technol., vol. 53, pp. 552–566, 1995 S.H.M. Anijdan, H.R. Madaah-Hosseini, and A. Bahrami, “Flow stress optimization for 304 stainless steel under cold and warm compression by artificial neural network and genetic algorithm”, Mater. & Design, vol. 28(2), pp. 609–615, 2007 H. Sheikh and S. Serajzadeh, “Estimation of flow stress behavior of AA5083 using artificial neural networks with regard to dynamic strain ageing effect”, J Mater. Proc. Technol., vol. 196, pp. 115–119, 2008 Y.Y. Yang, D.A. Linkens, and M. Mahfouf, “Genetic algorithms and hybrid neural network modelling for aluminium stress—strain prediction”, Proc. IMechE, Part 1: J Syst. & Control. Eng., vol. 217(1), pp. 7–21, 2003 M.P. Phaniraj and A.K. Lahiri, “The applicability of neural network model to predict flow stress for carbon steels”, J Mater. Proc. Technol., vol. 141, pp. 219–227, 2003 Y. Zhu, W. Zeng, Y. Sun, F. Feng, and Y. Zhou, “Artificial neural network approach to predict the flow stress in the isothermal compression of as-cast TC21 titanium alloy”, Comp. Mater. Sci., vol. 50(5), pp. 1785–1790, 2011 W.F. Brown, H. Mindlin, and C.Y. Ho, Aerospace Structural Metals Handbook: vol. 1, Purdue University, West Lafayette, IN., 1996 W-S. Lee and G-W. Yeh, “The plastic deformation behaviour of AISI 4340 alloy steel subjected to high temperature and high strain rate loading conditions”, J Mater. Proc. Technol., vol. 71, pp. 224–234, 1997 F.R. Larson and J. Nunes, “Low temperature flow and fracture tension properties of heat treated SAE 4340 steel”. Trans. ASM, vol. 53, 663– 682, 1961 Y.C. Chi, S. Lee, K. Cho, and J. Duffy, “The effect of tempering and test temperature on the dynamic fracture initiation behaviour of an AISI 4340 VAR steel”, Mat. Sci. & Eng. A, vol. 114, pp. 105–126, 1989 A. Iqbal, N.U. Dar, N. He, M.M.I. Hammouda, and L. Li, “Selfdeveloping fuzzy expert system: A novel learning approach, fitting for manufacturing domain”, J Intell. Manuf., vol. 21, pp. 761–776, 2010 K. Hashmi, I.D. Graham, B. Mills, “Data selection for turning carbon steel using a fuzzy logic approach”, J. Mater. Proc. Technol., vol. 135, pp. 44–58, 2003

In some of the rules, the consequent part consists of combination of two fuzzy sets in the form “Sx & Sy”. This term can be interpreted as the union of fuzzy sets Sx and Sy. A production expert system shell, Fuzzy CLIPS (C language integrated production systems), was used for simulation of the fuzzy rule-base on the 23 experimental data sets. In the simulation, the max-min inference method was used for yielding aggregation of the fuzzy rules. The detail of this strategy can be studied from the paper [17]. Table III presents the simulation and testing results. The prediction error in this case is 22.04MPa, which comes out to be 2.09% of the average value (1052MPa) of the flow stress data used in table III. The error value is again highly acceptable, though it is slightly more than that produced by the ANN (1.93%). But it is worth comparing that the expert system was developed just once, while the ANN topology was amended many a times, following trial-and-error approach, for improvement in the training results.

[5] [6]

[7]

[8]

[9]

[10]

[11]

V.

CONCLUSIONS

The paper has put forward an artificial intelligence approach for prediction of flow stress of a commonly used steel type. Two intelligent systems, artificial neural network and fuzzy expert system were developed and compared for prediction accuracy. In comparison to most of the previously published work, this paper has also worked on the effect of microstructure, in addition to those of temperature, strain rate, and strain in predicting flow stress. Both the systems came up with acceptable prediction results and their mutual difference in prediction error is merely 0.16%. The prediction errors (1.93% and 2.09%) are significantly lower than those reported by the other researchers. REFERENCES [1]

M.P. Groover, Fundamentals of Modern Manufacturing; Materials, Processes, and Systems, 3rd ed., John Wiley & Sons, Inc., Hoboken, NJ, 2007

[12] [13]

[14]

[15]

[16]

[17]


561