Improving of turning process efficiency by using hybrid ANFIS-ants system.

Zuperl, U. ; Cus, F.

1. Introduction

The selection of optimal cutting parameters is a very important issue for every machining process in order to enhance the quality of machining products, to reduce the machining costs and to increase the production rate. Do to machining costs of Numerical Control machines (NC), there is an economic need to operate NC machines as efficiently as possible in order to obtain the required pay back. In workshop practice, cutting parameters are selected from machining databases or specialized handbooks, but they don't consider economic aspects of machining. The cutting conditions set by such practices are too far from optimal work. Therefore, a mathematical approach has received much attention as a method for obtaining optimised machining parameters. For the optimisation of a machining process, either the minimum production time or the maximum profit rate is used as the objective function subject to the constraints. Optimization of cutting parameters is a difficult work (Cus & Balic, 2000), where the following aspects are required: knowledge of machining; empirical equations relating the tool life, forces, power, surface finish, etc., to develop realistic constrains; specification of machine tool capabilities; development of an effective optimization criterion; and knowledge of mathematical and numerical optimization techniques. Optimization of machining parameters is complicated when a lot of constraints are included, so it is difficult for the nondeterministic methods to solve this problem. Conventional optimization techniques are useful for specific optimization problems and leaned to find local optimal solution. Consequently, non-traditional techniques were used in the optimization problem. Researchers (Liu & Wang, 1999) have done comparative analysis of conventional and non-conventional optimization techniques for CNC turning process. The optimization problem in turning has been solved by genetic Algorithms (GA), Tabu search (TS), simulated annealing (SA) and particle swarm optimisation (PSO) to obtain more accurate results by (Milfelner et al., 2004). (Zuperl et al., 2007) have described the multi objective technique of optimization of cutting conditions for turning process by means of the neural networks and particle swarm optimization (PSO), taking into consideration the technological, economic and organizational limitations. Further genetic GA and simulated annealing techniques have been applied to solve the continuous machining profile problem (Milfelner et al., 2004). They have shown that GA approach outperforms the simulated annealing based approach. In this paper, a multi-objective optimization method, based on combination of ANFIS and ACO evolutionary algorithms, is proposed to obtain the optimal parameters in turning processes. The advantage with this approach is that it can be used for solving a diverse spectre of complex optimisation problems. This paper also compares the results of ANFIS-ant colony algorithm with the GA and simulated annealing (SA). The results exhibit the efficiency of the ACO over other methods.

2. Problem Formulation

The objective of this optimization machining model is to determine the optimal machining parameters including cutting speed, feed rate and depth of cut in order to minimize the operation cost and to maximize production rate (represented by manufacturing time ([T.sub.p]) and cutting quality ([R.sub.a]).

[C.sub.p] = [T.sub.p]*([C.sub.t]/T + [C.sub.l] + [C.sub.0]) (1)

where [C.sub.t], [C.sub.l] and [C.sub.0] are the tool cost, the labour cost and the overhead cost respectively; T is tool life. The objectives used in this work are determined according to (Zuperl & Cus, 2003). In order to ensure the evaluation of mutual influences and the effects between the objectives and to be able to obtain an overall survey of the manufacturer's value system the multi-attribute function of the manufacturer (y) is determined. The cutting parameter optimization problem is formulated as the following multi-objective optimization problem: min [T.sub.p] (v, f, a), min [C.sub.p] (v, f, a), min [R.sub.a] (v, f, a).

y = 0,42*[e.sub.(-0,22Tp)] + 0,17*[e.sub.(-0,26Ra)] + 0,05/(1 + 1,22*[T.sub.p]*[C.sub.p]*[R.sub.a]) (2)

A multiattribute value function is defined as a real-valued function that assigns a real value to each multiattribute alternative, such that more preferable alternative is associated with a larger value index than less preferable alternative.

The following limitations are taken into account: Permissible range of cutting conditions: [v.sub.min] [less than or equal to] v [less than or equal to] [v.sub.max], [f.sub.min] [less than or equal to] f [less than or equal to] [f.sub.max], [a.sub.min] [less than or equal to] a [less than or equal to] [a.sub.max]; Implied li from the tool characteristics and the machine capacity; The limitations of the power and cutting force are equal to: P(v, f, a) [less than or equal to] [P.sub.max], F(v, f, a) [less than or equal to] [F.sub.max].

The proposed approach consists of two steps. First, experimental data are prepared to train and test ANFIS system to represent the objective functiony (y). Finally, an ACO algorithm is utilized to obtain the optimal objective value. Figure 1 shows the flowchart of the approach.

3. ANFIS Modelling of Objective Function

First step uses an adaptive neuro fuzzy inference system (ANFIS) to model the response (manufacturer's implicit multiattribute) function (y). The variables of this problem are velocity, feed rate and depth of cut, which can have any continuous value subject to the limits available. The ANFIS system needs three inputs for three parameters: cutting speed (v), feedrate (f) and depth of cutting (a). The output from the system is a real value (y). The relationship between the cutting parameters and manufacturer objective function is first captured via a neural network and is subsequently reflected in linguistic form with the help of a fuzzy logic based algorithm. Algorithm uses training examples as input and constructs the fuzzy if-then rules and the membership functions of the fuzzy sets involved in these rules as output. Figure 2 shows the fuzzy rule architecture of ANFIS when triangular membership function is adopted.

[FIGURE 1 OMITTED]

The architectures shown in Figure 2 consist of 32 fuzzy rules. During training in ANFIS, 140 sets of experimental data were used to conduct 400 cycles of training. ANFIS has proved to be an excellent universal approximator of non-linear functions. If it is capable to represent the manufacturer's implicit multiattribute function. Using a given input/output data set, the ANFIS method constructs a fuzzy inference system (FIS) whose membership function parameters are tuned using either a backpropagation algorithm alone, or in combination with a least squares type of method. This allows fuzzy systems to learn from the data they are modeling. FIS Structure is a network-type structure similar to that of a neural network, which maps inputs through input membership functions and associated parameters, and then through output membership functions and associated parameters to outputs. ANFIS applies two techniques in updating parameters. For premise parameters that define membership functions, ANFIS employs gradient descent to fine-tune them. For consequent parameters that define the coefficients of each output equations, ANFIS uses the least-squares method to identify them. This approach is thus called Hybrid Learning method since it combines the gradient descent method and the least-squares method.

ANFIS modeling process starts by:

1. Obtaining a data set (input-output data pairs) and dividing it into training and checking data sets.

2. Finding the initial premise parameters for the membership functions by equally spacing each of the membership functions

3. Determining a threshold value for the error between the actual and desired output.

4. Finding the consequent parameters by using the least-squares method.

5. Calculating an error for each data pair. If this error is larger than the threshold value, update the premise parameters using the gradient decent method as the following ([Q.sub.next]=[Q.sub.nov]+[[eta].sub.d], where Q is a parameter that minimizes the error, [eta] the learning rate, and d is a direction vector).

6. The process is terminated when the error becomes less than the threshold value. Then the checking data set is used to compare the model with actual system. A lower threshold value is used if the model does not represent the system.

[FIGURE 2 OMITTED]

After training the estimator, its performance was tested under various cutting conditions. Test data sets collected from a wide range of cutting conditions in turning were applied to the estimator for evaluating objective function (y). The performance of this method turned out to be satisfactory for estimating of objective function (y), within a 2% mean percentage error. Once a multi-attribute value function is assessed and validated the ANFIS is used to decipher the manufacturer's overall preference and the multi-objective optimization problem will be reduced to a single objective maximization problem. (max(y)=?)

4. Ant Colony Optimization (ACO)

Special insects like ants, termites, and bees that live in a colony are capable of solving their daily complex life problems. These behaviours which are seen in a special group of insects are called swarm intelligence. Swarm intelligence techniques focus on the group's behaviour and study the decartelized reactions of group agents with each other and with the environment. The swarm intelligence system includes a mixture of simple local behaviours for creating a complicated general behaviour and there is no central control in it. Ants have the ability to deposit pheromone on the ground and to follow, in probability, pheromone previously deposited by other ants. By depositing this chemical substance, the ants leave a trace on their paths. By detecting this trace, the other ants of the colony can follow the path discovered by other ants to find food. For finding the shortest way to get food, these ants can always follow the pheromone trails. The first ACO algorithm, called ant system (AS) has been applied to the travelling salesman problem (TSP). (Dorigo, 1996) proposed an ant colony optimization methodology for machining parameters optimization in a multi-pass turning model, which originally was developed by (Vijayakumar et al.,

2002).

4.1 Ant Colony Algorithm

An ACO utilizes bi-level procedures which include local and global searches. Local search ants select a local trail I with a probability [P.sub.i](t) = [[tau].sub.i](t)/[SIGMA][[tau].sub.k](t), where i is the region index and [t.sub.i](k) is the pheromone trail on region i at time t. After selecting the destination, the ant moves through a short distance ([DELTA](T,R) = R(1 - [r.sup.10(1-T)]), where R is maximum search radius, r is a random number from [0,1], T is the total number of iterations of the algorithm.

A global search is done sequentially by crossover and mutation operations. The subsequent values of the variables of the child are set to the corresponding value of a randomly chosen parent with a crossover probability ([P.sub.c]). Mutation operation adds or subtracts a value to/from each variable with mutation probability ([P.sub.m]). The mutation step size is the same as the above distance [DELTA](T, R). Performing an ACO, ants are repeatedly sent to trail solutions in order to optimize the objective value.

The total number of ants (denoted by A) is set as half the total number of trail solutions (denoted by S). The number of global ants (denoted by G) and the number of local ants (denoted by L) are set as 80% and 20% of the total number of ants, respectively.

The ACO algorithm:

Step 1. Set parameter values including: S, A, [rho], [[tau].sub.0], [P.sub.c], [P.sub.m], T, R, and bounds of each control factor.

Step 2. Create S trail solutions (v, f, a). Estimate the objective value of the trail solutions through the ANFIS model (y).

Step 3. Set the initial pheromone value of all trails.

Step 4. Repeat steps 6-9 until the stopping criteria has reached.

Step 5. Send L ants to the selected trail solutions for local search.

Step 6. If the solution is improved, move the ants to the new solution and update the pheromone value.

Step 7. Send G ants to global trails and generate their offspring by crossover and mutation.

Step 8. Evaporate pheromone for all trails.

5. Results and Discussion

The ant colony optimization method combined with ANFIS prediction system was tested on the CNC lathe Gf02. the work piece material is mild steel (ck45) and the tool material has a carbide tip. The task is to find optimum cutting conditions for the process of turning with minimal costs. Proposed ACO approach was compared with three non-traditional techniques (GA, SA and PSO). The results obtained from four techniques are given below in Table 1. All the parameters and constraint sets are the same in all four cases. There is a total of 4 constraints.

Cutting forces and their influence on the economics of machining is summarized according to investigation of (Milfelner et al., 2004). The proposed model is run on a PC 586 compatible computer using the Matlab language. The results revelled that the proposed method significantly outperforms the GA and SA approach. The proposed approach found an optimal solution of 12.461 for as low as 1-18 runs the genetic-based approach require as much as 1-500 runs to find an solution of 14.661. This means that the proposed approach has 16.02% improvement over the solution found by GA approach and 23.08% over SA approach. Moreover, the simulated annealing approach (SA/PS) of also generated an inferior solution of 17.24 for as much as 901-1000 runs which means that the optimal solution of ACO algorithm has an improvement of 23.6%. It is observed that PSO has outperformed all other algorithms. Next ACO, SA and GA are ranked according to costs obtained from algorithms. The costs obtained and optimum machining conditions are shown in Table 1.

6. Conclusion

In this work, non-conventional optimization techniques ACO has been studied for the optimization of machining parameters in turning operations. The ACO algorithm is completely generalized and problem independent so that it can be easily modified to optimize this turning operation under various economic criteria. The algorithm can also be extended to other machining problems such as milling operations and threading operations.

DOI: 10.2507/daaam.scibook.2009.25

7. References

Cus, F. & Balic, J. (2000). Selection of cutting conditions and tool flow in flexible manufacturing system. The international journal for manufacturing science & technology, Vol. 2, 101-106, ISSN 0736-5845

Dorigo, E. (1996). The ant system: Optimization by a colony of cooperating agents. IEEE Transaction on Systems, Man and Cybernetics, Vol. 26, 1-13, ISSN 211-3441

Liu, Y. & Wang, C. (1999). Neural Network based Adaptive Control and Optimisation in the Milling Process. International Journal of Advanced Manufacturing Technology, Vol. 15, 791-795, ISSN 301-082

Milfelner, M.; Zuperl, U. & Cus, F. (2004). Optimisation of cutting parameters in high speed milling process by GA. Int. j. simul. model., Vol. 3, 121-131, ISSN 1726-4529

Vijayakumar, K.; Prabhaharan, P.; Asokan, R. & Saravanan, M. (2002). Optimization of multi-pass turning operations using ant colony system. International Journal of Machine Tools and Manufacture, Vol. 3, 633-639, ISSN 0736-5845

Zuperl, U. & Cus, F. (2003). Optimization of cutting conditions during cutting by using neural networks. Robot. comput.-integr. manuf, Vol. 19, 189-199

Zuperl, U.; Cus, F. & Gecevska, V. (2007). Optimization of the characteristic parameters in milling using the PSO evolution technique, Stroj. vestn, Vol. 53, 354-368, ISSN 0039-2480

Authors' data: Dr. Sc. Zuperl, U[ros]; Univ. Prof. Cus, F[ranc], University of Maribor, Faculty of mechanical engineering, Smetanova 17, 2000 Maribor, Slovenia, uros.zuperl@uni-mb.si, franc.cus@uni-mb.si.

This Publication has to be referred as: Zuperl, U[ros] & Cus, F[ranc] (2009). Improving of Turning Process Efficiency by Using Hybrid ANFIS-Ants System, Chapter 25 in DAAAM International Scientific Book 2009, pp. 233-240, B. Katalinic (Ed.), Published by DAAAM International, ISBN 978-3-901509-69-8, ISSN 1726-9687, Vienna, Austria

Tab. 1. Comparison of results for ANFIS-ACO, GA and PSO approach

No.   Algorithm            Constraint set                    Runs
                           tool-life;
1     PSO (Zuperl          cutting force-power; surface      1-25
      et al., 2007)        roughness;                        1-150
                           tool-life;
2     Proposed ANFIS-ACO   cutting force-power; surface      1-25
                           roughness;                        1-150
3     SA                   tool-life; cutting force-power;   1-1000
                           surface roughness;                1-1400
                           tool-life;
4     GA                   cutting force-power; surface      1-150
                           roughness;                        1-500

                                    Optimum solution

No.   Algorithm            [v.sub.opt] [m/m in]  [f.sub.opt] [mm/rev]

1     PSO (Zuperl          101.2                 0.231
      et al., 2007)        103.3                 0.217

2     Proposed ANFIS-ACO   95.19                 0.3793
                           97.43                 0.2934
3     SA                   112.8                 0.194
                           108.4                 0.221

4     GA                   102.1                 0.039
                           98.12                 0.313

                                 Optimum solution

No.   Algorithm            [a.sub.opt] [mm]   [C.sub.p] [$]

1     PSO (Zuperl          0.44               12.46
      et al., 2007)        0.51               12.23

2     Proposed ANFIS-ACO   0.84               12.42
                           0.89               12.31
3     SA                   0.46               16.15
                           0.41               16.17

4     GA                   1.268 0.612        18.39
                                              14.66

                           Average
                           optimiz.
No.   Algorithm            time [s]

1     PSO (Zuperl           3
      et al., 2007)         7

2     Proposed ANFIS-ACO    2
                            6
3     SA                   12
                           11

4     GA                    7
                            9