Tool Wear Prediction Using Evolutionary Dynamic Fuzzy Neural (EDFNN) Network

Mahardhika Pratama , Meng Joo Er , Xiang Li , Oon Peen Gan , Richad.J.Oentaryo , San Linn , Lianyin Zhai , Imam Arifin

School of Electrical and Electronic Engineering, Nanyang Technological University (NTU), Singapore, email : MAHARDHI1@e.ntu.edu.sg , EMJER@ntu.edu.sg

Singapore Institute of Manufacturing Technology (SIMTech), Singapore, email : xli@SIMTech.a-star.edu.sg Electrical Engineering Department, Institut Teknologi Sepuluh Nopember (ITS), Indonesia, email :

arifin-i@ee.its.ac.id Abstract—In development of self-organizing fuzzy neural network, selection of optimal parameters is one of the key issues. This is especially so for a system with more than 10 parameters whereby it will be challenging for expert users to determine the optimal parameters. This paper presents a hybrid Dynamic Fuzzy Neural Network (DFNN), and Genetic Algorithm (GA) termed Evolutionary Dynamic Fuzzy Neural Network (EDFNN) for the prediction of tool wear of ball nose end milling process. GA, well known for its powerful search method, is implemented to obtain optimal parameters of DFNN, so as to circumvent the complex time varying property without prior knowledge or exhaustive trials. Degradation of machine tools in ball nose end milling process is highly non-linear and time varying. Benchmarked again original DFNN in the experimental study, EDFNN demonstrates the effectiveness and versatility of proposed algorithm which not only produces higher prediction accuracy, and faster training time, but also serves to more compact and parsimonious network structure.

Keywords: Genetic Algorithm, DFNN, tool wear prediction, ball nose end milling process.

I. INTRODUCTION Tool condition Monitoring System (TCMS), which gives information about tool condition, such as tool wear, is crucial in the high speed machining process. The TCMS is integration of sensors (to acquire the required data), a data acquisition system (to collect signals from a machining centre), data pre processing unit (to extract useful signatures from the signal) and intelligent system (it uses its intelligence to predict the tool wear based on the features of the signal). TCMS is critical since in industrial process (ball nose end milling process), there is no way to measure a tool wear subsequently during the process run. In a fully or partially automated manufacturing system the tool condition monitoring system plays an important role by providing instantaneous information. Arguably, this helps to drive the plant without any stoppage thereby increasing productivity and cost effectiveness. Not all features of signal captured by the sensors are informative to supply the information of the tool condition. In this light of this issue, many researchers use feature

extraction to obtain signal feature which is passed to the predictive algorithm. Combining those features with the cutting conditions will describe the changes in resulting surface quality and tool condition during the process [1]. In the experimental configuration, there are three sensors. They are force sensor, vibration sensor, and Acoustic Emission (AE) sensor. It should be envisaged that cutting force as one of the most informative signals in the machining process which carries substantive information about the immediate interactions between the cutter and work-piece, and should be highly contributive in analyzing the performance of the cutting process [2]. In order to forecast tool wear in milling process, the employed model should be [3]: 1) The model shows non-linear relations between the input features and tool wear. 2) Input of the model includes the cutting parameters such as spindle speed and feed rate. The theory of fuzzy sets was published by Zadeh [4,8] which is widely deployed to circumvent many engineering problems. Equipped by human like linguistic and approximate reasoning, the fuzzy system provides more attractive and transparent modeling tool. In particular, the versatility of the fuzzy logic may appear when the system is too complex to be analysed by physical based approach or the source of information is interpreted qualitatively, inexactly, or uncertainly. The fuzzy system may be viewed as one step towards a rapprochement between conventional precise mathematical model and human like decision making. Nevertheless, a classical paradigm of the fuzzy method is over dependent on the expert knowledge in order to obtain appropriate rules. It doesn’t coincide with reality which the rules may be lost their validity over time, especially in the system with various operating condition and changing characteristic. Due to those drawbacks, several scientists intend to combine fuzzy logic and Neural

This project is fully supported with A*STAR Science and Engineering Research Council (SERC) Singapore and Poland.

978-1-61284-972-0/11/$26.00 ©2011 IEEE 4739

Network to inhibit a weakness of the individual system. State of the art approach was proposed by R.J Jang with Adaptive Network Based on Fuzzy Inference System (ANFIS) [5]. When commencing learning, the ANFIS initializes a fixed number of rules. Subsequently, the rule is tuned by a hybrid learning of back propagation and least square methods. The rule or cluster is crafted by a grid partitioning technique. The major bottleneck of the grid partitioning technique is that the number of rule increases exponentially when the number of data also increases. Another drawback is that the ANFIS still operates under the fixed network structure which doesn’t coincide to handle a time varying domain. As successor of the ANFIS, many researchers proposed methods which may self generate the rules from data streams [7,9,10]. The pioneer of this work is Wu and Er [6] which established Dynamic Fuzzy Neural Network (DFNN). The DFNN starts training procedure with empty rule base. Furthermore, it might evolve the rules simultaneously. Inconsequential rules are removed by Error Reduction Ratio (ERR) to maintain the validity of rule base and the compactness of the structure. One of key issue in the DFNN is that there are ten predefined constants. These parameters are not straightforward to be chosen, and gives substantial contribution to the performance. The idea of using Genetic Algorithm (GA) in the Fuzzy Neural Network (FNN) has been proposed by several researches. One of them was devised by Farag et al [13]. Farag’s idea comprises three learning steps. First learning is used to find initial membership function of fuzzy model using self organizing learning which is analogous with statistical clustering. Moreover, the width of the Gaussian function is tuned using N-nearest-Neighbors Heuristic. Second phase determines the rules of fuzzy logic connecting consequent and premise part using maximum matching factor. Finally, Multiresolutional Genetic Algorithm (MRD-GA) is used instead of back propagation algorithm which is well known that imposes to attain a global optima value. However, Farag’s model operates under the fixed network structure. Another method was proposed by Leng et al [14] namely Self Organizing Fuzzy Neural Network Based on Genetic Algorithm (SOFNNGA). At the first, SOFNN algorithm attempts to seek an initial structure, after that, the GA is used to prune inconsequential rule in order to avoid a redundant network structure which adverse its effectivity. The selection of predefined parameters requires prior knowledge or exhaustive trials which is impractical for a complex real world engineering problem. Benefiting the GA, well known as powerful search method, is a plausible manner to alleviate this issue. The substantial spirit of this paper is fusing the GA and DFNN termed Evolutionary Dynamic Fuzzy Neural Network (EDFNN) for optimal selection of the DFNN predefined parameters. Therefore, the parameters might be automatically obtained without any prior knowledge or extensive trials. Nonetheless, the GA is also able to determine one set of global optima value which

may suit with the problem changing characteristic of the system overtime. This paper is organized as follows: Section 2 describes the fundamental concepts of EDFNN. Section 3 exposes the experimental setup. The experimental result is supplied on the Section 4. The rest of this paper exhausts some conclusions, recommendations, and future works.

II. LITERATURE REVIEW The fundamental principle of DFNN and The idea of EDFNN are described in this section. They include learning principle of DFNN, parameter optimization using Genetic Algorithm (GA).

A. Dynamic Fuzzy Neural Network (DFNN) The DFNN proposed by Wu and Er [6] is one of pioneers in self constructing fuzzy neural network. This method enables to evolve and prune its fuzzy rules exploiting the hierarchical self organizing principle, and Error Reduction Ratio (ERR) method. The ingredient concept of hierarchical self organizing learning is that, at the first time, the DFNN forms a rough but global rule base in order to seek the most troublesome position which is not able to be accommodated by existing fuzzy rules. As the value of the parameters decrease over time, a more fine grained rule base is established which may accurately capture data distribution. The DFNN is organized by five layers network, they are input layer, Membership Function (MF) layer, hidden layer, normalized layer, and output layer. The DFNN is Takagi Sugeno Kang (TSK) fuzzy type, and realized by Extended Radial Basis Function (ERBF) network (more than 3 layers, no bias considered, and output is polynomial instead of constant). Fig 1 exhibits the structure of DFNN. For simplicity, this paper only considers a Multi Input Single Output (MISO) case. However, the result will be ready to be extended for Multi Input Multi Output (MIMO) case. First layer is the input layer. It doesn’t perform any mathematical operations. It just passes an external stimulus from environment onto the next layer. The second layer is MF’s layer, it maps the crisp variable into the respective fuzzy value.

(1)

The next layer is the hidden layer or rule layer. This layer captures output features of previous layer, and combines them to get a firing strength of each rule.

(2)

The fourth layer normalizes the firing strength into the range of [0,1]. Hence, this layer is called the normalized layer.

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(3)

The last layer is output layer, it utilizes a weighted sum operation for all incoming signals, the product of the output layer is a crisp variable, the final output of the system.

(4)

(5)

(5) represents a form of TSK fuzzy type, the output is a polynomial or function instead of a constant. For Takagi Sugeno (TS) fuzzy type is shown at (6) which is a constant which is also familiarly known as singleton fuzzy type.

(6)

In the DFNN, there are two criteria to automatically generate the fuzzy rules. Those criteria are system error, and accommodation boundary. The criteria rely on two variables as follows

(7)

(8)

Fig.1. Architecture of DFNN

are predefined constants. System error implies that if the error is bigger than then the network has a big error for the current input of interest. In other words, the current input can not be handled successfully with the existing rule base, a thus new rule should be introduced.

(9)

If

(10)

Then new rule should be added or instantly adjust the winning rule (the closest rule in the Euclidean sense).

If the minimum Euclidean distance between input feature and the centers of RBF function is larger than , it is a prognosis that the network has bad coverage to cover current input datum. The current input can not be clustered. Therefore, it should either add a new rule or simply adjust width of the winner.

(11)

If

(12)

Then the new rule should be crafted.

The width and center are allocated as follows:

(13)

(14)

is overlapping factor defined priori. As foreshadowed in the previous section, This paper just discusses the case in which , and . There are three other cases which may happen respect to the aforementioned two criteria. If one of all criteria is encountered, then the DFNN produces an action accordingly. Fig 2 illustrates the a flowchart of overall algorithm of the DFNN. The consequent part of fuzzy rule is derived by the use of Least Square method.

(15)

(16)

is the target value, is calculated using (3). The pruning technology used in DFNN is called Error Reduction Ratio (ERR) in order to fire obsolete rules which is no longer contributive to the system. ERR is originally proposed by Chen et all [12] intended to seek a subset of significant regressors. For the obvious mathematical derivation of ERR the reader would be better to refer to original paper of DFNN [6]

(17)

If

(18)

Then the rule no longer provides significant contribution, it should be deleted to attain a compact and parsimonious network structure. is determined priori. refers to significance of rule . is the number of existing rules.

B. Evolutionary Dynamic Fuzzy Neural Network (EDFNN)

There are eleven parameters which need to be defined priori. The parameters directly influence the performance of the

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DFNN. Traditionally, they are determined randomly as any arbitrary values. The fundamental idea of the EDFNN is that the use of GA as a powerful search method. it’s started from generating random number of each chromosome. A population is organized from several chromosomes. A search process is held by using the genetic operators (mutation, crossover) which is intended to satisfy desired objective function. Eleven parameters of DFNN are fused into one single chromosome. Initially, these parameters are assigned random values among [0,1]. The chromosomes entering genetic operations are evaluated by using the well known Roulette Wheel method. Fitness function is computed by (19) which is a maximization case. The aim is to minimize Root Mean Square Error (RMSE), number of rules, and training time of DFNN thereby achieving a high predictive accuracy while simultaneously retaining compact and parsimonious network structure.

(19)

The eleven parameters are as following:

= max of accommodation criterion = min of accommodation criterion

= decay constant = max of output error = min of output error

= convergence constant = the width of the first rule

= overlap factor of RBF units = width updating factor. = Significance of the rules

The mutation process is dependent on a probability of mutation . Defined a value from random parameter , if

is larger than , then the mutation will take place. The mutation is undertaken for the selected gen in the chromosome by the Roulette Wheel. Furthermore, the selected gen will be randomized into value between a range of [-1,1]. The crossover operator takes place for two selected chromosomes as a parent. The crossover inherits the gen characteristic of a parent repeatedly M times:

(20)

In which is recombination rate which is a predefined parameter, is the population. The crossover swaps gen on chromosome with a fixed probability. The stopping criteria are encountered when fulfilling a convergence and optimization progress. If the chromosome has been converged then the process will be stopped accordingly. In other words, when the new chromosome is no longer changed for several consecutive times, thus the process is stopped. The second criterion is based on whereby the average fitness is no longer changed among at least four

previous generations. The optimization process will not yield a drastically far solution. Therefore, it should be ended. Determining size of population and mutation probability is a critical issue. The GA is inherently a random process, thus it needs extensive computation. There are several recommendations to select feasible parameters of GA. [14] advices to select a suitable population size and mutation probability intended to eradicate a high computational cost of the GA through choosing a sufficient number of population and mutation.

(21)

(22)

’s the number of populations, ’s mutation probability,

, ’re length of chromosome and default value of variable respectively.

Fig.2. Overall Learning scheme of DFNN

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III. EXPERIMENTAL SETUP Tool condition monitoring and prediction are crucial in the high speed machining process [15]. Achieving accurate tool wear prediction is difficult and tremendously desired, due to uncertainty, and nonlinearity of the machining process [16]. In the tool wear forecasting, the first and the most important step is a data preprocessing. The raw signal is collected trough seven channels DAQ. The first three channels are force signal in the three cutting axes (X,Y,Y) measured by dynamometer, the next three channels captures vibration signals within three axes measured by Accelerometer, the last one is AE (Acoustic Emission) signals measured by AE sensor. The signal during cutting process has to be separated. In order to distinguish them, the signal needs to be converted into frequency domain using Fast Fourier Transform (FFT). Fig 3 illustrates employed equipment during the milling process The collected data are enormous so that it has to be limited only within thirty revolutions. This phase is called revolution based separation. Not all information in the force signal are important, thus the features of the signal have to be extracted. There are sixteen features correlated with tool wear, nevertheless, there are only four features suffering a high correlation with the tool wear. [2] suggests that there are only four features that are highly important in order to predict tool wear from the force signal. They are maximum absolute force, amplitude of force, average force, amplitude ratio. This paper determines to employ these features due to sufficiency.

Fig.3. Equipments during milling process.

IV. Simulation and Discussion

Data from 2 cutters are collected, normalized and shuffled. Data dimension is 630 pairs. In this experiment, EDFNN is benchmarked again the original DFNN. The Genetic Algorithm (GA) is applied once to obtain the eleven parameters of the DFNN. The data proportion for training and testing is 90% and 10% respectively. The experiments are driven fifty times to investigate the effectiveness of the EDFNN. The parameters yielded by the GA are listed on the Table 1. The simulation results of 50 trials are listed on Table 2.

Average Percentage Error (APE) is employed to evaluate the performance of the already trained EDFNN in both of training and testing.

(23)

Sample of Root Mean Square Error (RMSE) from 50 trials is depicted by Fig 4. From table 1, the EDFNN is less accurate than the DFNN. However, training mechanism of the EDFNN is quite faster than the DFNN. Moreover, the EDFNN has smaller rule base size than the DFNN. In the previous trial, the tool wear is forecasted by the force signal. In fact, the force sensor is expensive, and has a big size property so that it is complicated to be installed. This paper also comprehensively investigates that the vibration signal can be utilized as well as an alternative of the force signal. Naturally, there are twenty one features which are extracted by the feature extraction process. The feature selection takes place in order to recognize a feature which considerably coincides with the tool wear. Eventually, this paper acquires seven features which suffer the most correlative with the tool wear, they are amplitude, energy, RMS and average power in x, y and z-axes. Data are collected from two cutters. A number of throughout data is 630 pairs. Data are normalized, and shuffled prior they are fed to EDFNN. Table 3 summarizes the consolidated performance of the EDFNN and DFNN from 50 rounds experiment. Fig 5 exhibits a sample of RMSE in one round experiment.

Fig 4. RMSE during training.

Table 2. The performance of both algorithm

Algorithm APE (%) APE (%) Rule Time(s)

EDFNN 1.17 1.13 4.9 0.56

DFNN 1.16 1.01 5.1 4

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Fig 5. RMSE during training.

Table 3. The parameters obtained by GA

Parameters Force Vibration

0.3133 0.1145

0.1484 0.0723

0.2838 0.2996

0.1423 0.8161

0.0770 0.4539

0.6190 0.4423

0.771 0.3345

0.4910 0.5867

0.9296 0.9698

0.1186 0.1664

Table 4. Comparison between EDFNN and DFNN

Algorithm APE (%) APE (%) Rule Time(s)

EDFNN 5.6 0.37 4.8 0.86

DFNN 6.64 0.4 5.2 9.96

From Table 3, the EDFNN yields a better result than the DFNN. The EDFNN has a slightly better accuracy than the DFNN. Nevertheless, a speed of training in the EDFNN is much faster than the DFNN. Nonetheless, the EDFNN produces more compact and parsimonious structure again DFNN.

Conclusions and Future Work

This paper proposes a technique to obtain the optimal predefined constants in the DFNN termed Evolutionary

Dynamic Fuzzy Neural Network (EDFNN). In the experiment, the tool wear of ball nose end milling process is forecasted. The prediction task is carried out without any prior knowledge or trial and error. The experiment result from comprehensive experiment demonstrates which the EDFNN is not only able to self finding the predefined parameters of the DFNN, but also to improve the performance of the DFNN. The EDFNN produces competitive accuracy as the DFNN. Nevertheless, the EDFNN yield faster training speed, and more compact and parsimonious structure than that DFNN. As future work, the GA would be enhanced to increase the speed of optimization process which is well known as a major bottleneck of the GA.

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