Influence of dynamic elementary processor structure in the flank wear parameter filtration.

Brezak, Danko ; Majetic, Dubravko ; Udiljak, Toma 等

1. INTRODUCTION

Tool wear regulation, as one of the most important elements of machining process control, is basically unfeasible without highly precise and robust estimation of tool wear parameter. In order to decrease influence of estimation error on the oscillations of control variable and overall model performance, a neural network filter is proposed (Brezak et al., 2006). Its influence on the control loop dynamic was analyzed using Koren--Lenz flank wear model (Koren & Lenz, 1972). Radial Basis Function neural network (RBFNN) was utilized as a controller and simulated flank wear parameter values were additionally added with the white noise.

The filter is configured in the form of Modified Dynamic Neural Network (MDNN) which is based on Dynamic Multilayer Perceptron Network (DMLP) presented in Ayoubi et al., 1995. This type of network is characterized with dynamic neuron model, the so-called Dynamic Elementary Processor (DEP), structured as an Auto Regressive Moving Average filter and build into the network hidden layer. In different to DMLP network, in MDNN network Gaussian activation functions are used and the structure is simplified by omitting the output layer activation function. Furthermore, in this extended research, different forms (FIR and IIR) of DEP structure have been analyzed.

Detail descriptions of all elements of simulated tool wear regulation model (TWR) are given in Brezak et al., 2006. In this paper, only brief introduction to MDNN filter mathematical model is presented, together with the results of different DEP unit structures in the combination with several MDNN configurations.

2. MDNN FILTER STRUCTURE

The input (net) and output (y) at time instant n of the jth hidden layer neuron are defined as

[net.sub.j] (n) = [I.summation over (i=1) [v.sub.ji] [Z.sub.i], j = 1, ..., J, (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

where i is the number of network input vectors, [Z.sub.i] are input vector elements, are input layer weights, [[sigma].sub.j] is width and [t.sub.j] is a position of Gauss activation function. Filter output, i.e. activation function input, [[bar.y].sub.j] is modified and defined, as

[[bar.y].sub.j] (n) = [L.summation over (l=0)] [b.sub.lj] [net.sub.j](n-l) - [M.summation over (m=1)] [a.sub.mj] [[bar.y].sub.j] (n - m), (3)

where a and b are filter coefficients. Network kth output is

[O.sub.k] (n) = [J.summation over (j=1)] [y.sub.j] (n) [w.sub.kj] (n), k = 1,2, ..., K,, (4)

where [w.sub.kj] are output layer weights. Learning parameters are adapted using Resilient Back-Propagation with Weight-Backtracking method (Riedmiller & Braun, 1993 and Igel & Husken, 2000).

3. SIMULATION RESULTS

Altogether 6 MDNN configurations (3-2-1, 3-5-1, 3-8-1, 52-1, 5-5-1, 5-8-1) have been analyzed in the combination with 15 different filter (DEP) structures (L=[0, 2, 3, 4, 6], M=[2, 4, 6]). Analyzes were performed on 7 tests generated using different cutting conditions ([a.sub.p] =2.5 mm, f=0.35 mm/rev, [v.sub.c] = [125, 155, 185, 205, 225, 245, 265] m/min and two sets of estimation error (e = [+ or -] 0.05 mm and e = [+ or -] 0.1 mm). The learning and testing results were quantified with well-known normalized root mean square error (NRMSE). All types of filter structures were trained in 10000 steps. NRMSE learning index was within the interval [0.064 - 0.108] for e = [+ or -] 0.05 mm and [0.093-0.191] for e = [+ or -] 0.1 mm. For every MDNN configuration the best filter structure was selected (Table 1.) and mean NRMSE values of all tests are shown in Fig. 1.

[FIGURE 1 OMITTED]

It can be noticed that the fifth combination of DEP structure and MDNN configuration accomplished the best results for both interval of estimation error. Quality of the outputs obtained using this combination is additionally quantified by analyzing the representation of tested samples in different [DELTA]VB intervals defined in Table 2. The results of the best and worst tests for both intervals of estimation error are presented in Fig. 2 and Fig. 3. They reveal the fact that, in the worst situation that occurred in Test 3 for e = [+ or -] 0.1 mm, more than 90% of the samples were filtered within the interval [absolute value of AVB] = [0, 0.03] mm.

Influence of the remained estimation error in the filtered signal can be additionally attenuated by the controller providing quality TWR model outputs (Fig. 4.).

[FIGURE 4 OMITTED]

4. CONCLUSION

In this work, results of additional analyzes of different DEP unit structures, i.e. MDNN filter configurations used in the previously proposed tool wear regulation model are briefly presented. The filter have been analyzed in the situations of different flank wear process dynamics showing the best performance in the case of DEP unit build in the form of FIR filter (L=0, M [not equal to] 0) rather than originally suggested IIR filter (L [not equal to] 0, M [not equal to] 0). These analyzes have also confirmed that filtered tool wear parameter in the kth step should be determined on the basis of estimated values from the previous 4 steps and the last one. Structures with higher number of input neurons did not achieved better performance. Also, their usage is limited by the fact that they have higher reaction time in the cases of sudden augmentation of tool wear rate when quick adaptation of control variable is usually very important.

In the future research, previously developed flank wear regulation model modified with MDNN filter structure presented in this paper will be analyzed using mini milling machine based on open architecture control system.

5. REFERENCES

Ayoubi, M.; Schefer, M. & Sinsel, S. (1995). Dynamic neural units for nonlinear dynamic systems identification, Lecture Notes in Computer Science, Vol.930, pp.1045-1051, ISSN 0302-9743

Brezak, D.; Majetic, D.; Udiljak, T.; Novakovic, B. & Kasac, J. (2006). Adaptive control model for maintaining tool wear rate in the predefined cutting time, Proceedings of the 17th International DAAAM Symposium, Katalinic, B. (Ed.), pp. 63-64, ISBN 3-901509-57-7, Vienna, November, 2006, DAAAM International, Vienna, Austria

Igel, C., Husken, M., 2000, Improving the RPROP Learning Algorithm, Proceedings of the Second International Symposium on Neural Computation, NC2000, pp. 115-121, ISBN 3-906454-21-5, Berlin, Germany, May 2000, ICSC Academic Press

Koren, Y. & Lenz, E. (1972). Mathematical model for the Flank Wear while Turning Steel with Carbide Tools, CIRP Proceedings on Manufacturing Systems, pp.127-139

Riedmiller, M. & Braun, H. (1993). A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm, Proceedings of the IEEE International Conference on Neural Networks (ICNN), pp. 586-591, ISBN 0-7803-0999-5, San Francisco, CA, March, 1993

Tab. 1. Best filter structures
for MDNN configurations

No. MDNN DEP
 config. struct.

 1 3-2-1 L=2; M=4
 2 3-5-1 L=3; M=6
 3 3-8-1 L=0; M=6
 4 5-2-1 L=0; M=2
 5 5-5-1 L=0; M=6
 6 5-8-1 L=0; M=4

Tab. 2. Intervals of flank wear
parameter deviation

Group [DELTA]VB, mm

 G1 [0, 0.01]
 G2 (0.01, 0.02]
 G3 (0.02, 0.03]
 G4 (0.03, 0.04]
 G5 (0.04, 0.05]
 G6 (0.05, 0.07]
 G7 (0.07, 0.1]

Fig 2. Samples distribution for the best and the worst test
(e = [+ or -] 0.05 mm)

TEST 1

 Before nitration After nitration

G1 39.9% 94.2%
G2 33.8% 7.2%
G3 16.7% 0.4%
G4 8.4% 0%
G5 1.1% 0%

TEST 7

G1 35.9% 67.2%
G2 34.4% 29.7%
G3 15.6% 1.6%
G4 14.1% 0%
G5 1.6% 0%

Note: Table made from bar graph.

Fig 3. Samples distribution for the best and the worst test
(e = [+ or 0] 0.1 mm)

TEST 7

 Before nitration After nitration

G1 21.9% 54.7%
G2 20.3% 28.1%
G3 18.7% 15.6%
G4 14.1% 0%
G5 7.8% 0%
G6 12.5% 0%
G7 4.7% 1.6%

TEST 3

G1 19.5% 49.6%
G2 19.5% 30.9%
G3 14.6% 9.7%
G4 15.4% 4.9%
G5 6.5% 3.2%
G6 15.4% 1.6%
G7 8.9% 0%

Note: Table made from bar graph.