design of neural network-based estimator for tool wear modeling in

J Intell Manuf (2008) 19:383–396DOI 10.1007/s10845-008-0090-8

Design of neural network-based estimator for tool wear modelingin hard turning

Xiaoyu Wang · Wen Wang · Yong Huang ·Nhan Nguyen · Kalmanje Krishnakumar

Received: 1 January 2007 / Accepted: 1 September 2007 / Published online: 25 January 2008© Springer Science+Business Media, LLC 2008

Abstract Hard turning with cubic boron nitride (CBN)tools has been proven to be more effective and efficient thantraditional grinding operations in machining hardened steels.However, rapid tool wear is still one of the major hurdlesaffecting the wide implementation of hard turning in indus-try. Better prediction of the CBN tool wear progression helpsto optimize cutting conditions and/or tool geometry to reducetool wear, which further helps to make hard turning a viabletechnology. The objective of this study is to design a novelbut simple neural network-based generalized optimal estima-tor for CBN tool wear prediction in hard turning. The pro-posed estimator is based on a fully forward connected neuralnetwork with cutting conditions and machining time as theinputs and tool flank wear as the output. Extended Kalmanfilter algorithm is utilized as the network training algorithm tospeed up the learning convergence. Network neuron connec-tion is optimized using a destructive optimization algorithm.Besides performance comparisons with the CBN tool wearmeasurements in hard turning, the proposed tool wear estima-tor is also evaluated against a multilayer perceptron neuralnetwork modeling approach and/or an analytical modelingapproach, and it has been proven to be faster, more accurate,and more robust. Although this neural network-based esti-mator is designed for CBN tool wear modeling in this study,

X. Wang · Y. Huang (B)Department of Mechanical Engineering, Clemson University,Clemson, SC 29634-0921, USAe-mail: [email protected]

W. WangCollege of Mechanical and Energy Engineering,Zhejiang University, Hangzhou 310027, P.R. China

N. Nguyen · K. KrishnakumarIntelligent Systems Division, NASA Ames Research Center,Moffett Field, CA 94035, USA

it is expected to be applicable to other tool wear modelingapplications.

Keywords Tool wear · Hard turning · Neural network ·Extended Kalman filter · Connectivity optimization

Introduction

The hard turning process is defined as the single point turn-ing of materials with hardness higher than 50 HRC under thesmall feed and fine depth of cut condition. It offers possiblebenefits over the process of grinding in the context of lowerequipment costs, shorter setup time, fewer process steps,greater part geometry flexibility, and the elimination of cut-ting fluid use (König et al. 1984; Tönshoff et al. 2000). Amongthe available tool materials, cubic boron nitride (CBN), sec-ond to diamond in hardness and inert to steel materials, hasbeen recommended as the best hard turning tool materialand widely used for hard turning operations. However, oneof the major hurdles affecting the wide implementation ofhard turning in industry is the severe wear of CBN tools. Thecost of hard turning tools and the tool change down-timedue to rapid tool wear can impact the economic viability ofprecision hard turning. For a given tool and workpiece com-bination, the ability to estimate the tool wear as a functionof cutting conditions, which include cutting speed, feed rate,and depth of cut, is critical to the overall optimization of ahard turning process.

It is ideal that the CBN tool wear in hard turning canbe modeled using a model-driven approach. However, CBNtool wear mechanisms in hard turning are still not yet wellunderstood (Huang et al. 2007), and as a result, the model-driven approach is short of robustness and accuracy. As analternative, the data-driven approach is usually favored to

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capture the tool wear progression. For example, artificial neu-ral network (ANN) is generally implemented to model non-linear dynamic systems including the tool wear progression(Chryssoluouris and Guillot 1990; Das et al. 1996; Dimlaand Lister 2000; Haber and Alique 2003). However, ANN-based estimator modeling performance is usually not satis-factory if the network architecture is not properly selected,and how to design an efficient and effective ANN for toolwear modeling is still a research topic. Even for the mostwidely implemented multilayer perceptron neural network(MLP), there are still no general rules to specify the numberof hidden layers, the number of neurons for each layer, andthe network connection to achieve an optimized modelingeffect. If ANN is selected as a tool wear modeling approach,such challenges must be carefully addressed.

The objective of this study is to design a novel but easy tobe implemented ANN-based generalized optimal estimatorfor CBN tool wear modeling in hard turning. The estimator isdesigned based on a fully forward connected neural network(FFCNN) and trained using the extended Kalman filter (EKF)algorithm. Network connectivity optimization is achievedusing a destructive approach. The paper first introduces thetheoretical background of the proposed estimator design, andthen evaluates the estimator’s modeling performance basedon two hard turning studies. The learning convergence speed,generalization capability, sensitivity, and training cost-benefitanalysis of this designed optimized fully forward connectedneural network (optimized FFCNN) estimator are further dis-cussed. Finally, some conclusions are made regarding theproposed estimator. Although the proposed estimator is forCBN tool wear modeling, it is expected that this approachshould be also applicable for other tool wear modelingapplications.

Background

CBN tool wear in CBN hard turning

The cutting edge of a tool insert in machining is subject to acombination of high stresses, high temperatures, and perhapschemical reactions which cause the tool wear due to one orseveral mechanisms. These mechanisms depend on the tooland workpiece material combination, cutting geometry, envi-ronment, and mechanical and thermal loadings encountered.Different classifications of tool wear processes have beenaddressed in the literature. Basically, five wear mechanismsor any combinations of them are involved in the tool wearprogression. They are abrasion, adhesion, fatigue, dissolu-tion/diffusion, and tribochemical process. It is well acceptedthat the tool wear mechanisms in machining involve morethan one wear mechanism and it is difficult to predict the rela-tive importance of any one of them (Huang et al. 2007). Crater

VB

rake face

flank face

flank wear

100 µm

Fig. 1 Typical tool wear picture in CBN hard turning

and flank wear are most reported wear patterns in machin-ing including hard turning. Crater wear is mainly causedby physical, chemical, and/or thermomechanical interactionsbetween the rake face of the insert and the hot metal chip, andflank wear occurs primarily when the flank face rubs againstthe workpiece surface.

CBN tool flank wear length or wearland (VB), as shownin Fig. 1 which is drawn based on a typical CBN tool wearobservation (Dawson 2002), is generally regarded as the toollife criterion or an important index to evaluate the tool per-formance in hard turning (Takatsu et al. 1983; Abrao et al.1995; Dewes and Aspinwall 1996), and the CBN tool flankwear is of interest in this study. The tool wear rate is assumeduniform across the width of cut as shown in Fig. 1. The mainwear mechanisms in CBN turning hardened steels are gen-erally considered to be a combination of abrasion, adhesion,and diffusion, and the contribution of each wear mechanismis related to cutting conditions, tool geometry, and materialproperties of the tool and the workpiece as follows (Huangand Liang 2004a):

dVB

dt= (cot γ + tan α)R

[VB (R − VB tan γ )

]

×{

0.0295K

(Pn−1

a

Pnt

)VcVBσ

+ 1.4761 × 10−14e9.0313×10−4T Vcσ

+ 5.7204 × 106√

VcVBe− 20460T +273

}(1)

where VB is the length of flank wear, γ is the clearance angle,α is the rake/chamfer angle, R is the tool nose radius, Pa andPt are the hardness of abrasive particle and tool respectively,K and n is a known function of Pt/Pa, Vc is the cutting speed,σ is the average normal stress, and T is the temperature onthe tool–workpiece interface.

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Tool wear modeling in machining

Tool wear modeling has been studied by numerous research-ers and can be classified into four main categories: analyti-cal model-based approach which models the tool wear as afunction of cutting conditions, machining environment, toolgeometry and property, and/or workpiece property (Usui etal. 1978; Kramer 1986; Huang 2002); computational method-based approach which applies the finite element method(FEM) to model the wear development process (Yen et al.2004; Xie et al. 2005); artificial intelligence (AI)-based app-roach which includes ANN (Wang and Dornfeld 1992), fuzzylogic (Kuo and Cohen 1998), and support vector machine(Sun et al. 2004); and parametric model-based approach incl-uding the Taylor tool life model (Poulachon et al. 2001) andthe regression model (Ozel and Karpat 2005). With respectto CBN tool wear modeling in hard turning, the main endeav-ors include the analytical model-based approach (Huang andLiang 2004a,b; Huang and Dawson 2005), the AI-basedapproach (Ozel and Nadgir 2002; Ozel and Karpat 2005),and the Taylor tool life equation-based approach (Poulachonet al. 2001; Dawson 2002).

Although the analytical models help to provide betterinsight to underlying physical wear mechanisms in hard turn-ing, they are usually less satisfactory in modeling wear pro-gression due to model simplifications and assumptions(Scheffer et al. 2003; Huang et al. 2007). The FEM approachalso provides insight into the tool wear process; however,it is too computational time demanding and not suitable foroptimization using current computing technologies. The timeseries (Boyd et al. 1996) and regression models (Ozel andKarpat 2005) are typically less accurate when compared withthe AI-based approaches. If both accuracy and speed are ofinterest instead of underlying wear physics, the AI-basedmodeling approaches are generally favored for real appli-cations. Among the AI-based approaches, ANN is a viable,reliable, and attractive approach for tool wear modeling(Chryssoluouris and Guillot 1990; Das et al. 1996; Dimlaand Lister 2000; Haber and Alique 2003) due to the fol-lowing reasons: (1) ANN is capable of modeling non-linearprocess which makes it suitable for modeling the tool wearprocess; (2) The data-driven feature of ANN makes it pow-erful in parallel computing and be capable of handling largeamount of data; and (3) ANN has a good fault tolerance andadaptability and is good for modeling tool wear in machiningwhich is always subject to noisy environments. Both sens-orless and sensor-based approaches have been studied as theANN inputs in tool wear modeling/monitoring (Sick 2002).

ANN-based tool wear modeling

Different ANN architectures have been researched or appliedto solve the tool wear modeling challenge (Dimla et al. 1997;

Sick 2002) such as MLP (Liu and Altintas 1999), radial basisfunction ANN (Elanayar and Shin 1999; Kuo and Cohen1999), self-organizing map (SOM) (Kamarthi et al. 1991;Scheffer et al. 2003), neuro-fuzzy ANN (Chungchoo andSaini 2002), time delay ANN (Sick 1998), and ART2 ANN(Obikawa and Shinozuka 2004), to name a few. Some stud-ies (Lin and Ting 1995; Sick 1998) have even tested a fewdifferent network architectures to find the best network archi-tecture. However, there is still a need to have a system-atic way to determine the optimal network architecture fortool wear modeling applications. Modeling performance ofANN-based estimators is usually undermined if the networkarchitecture is not properly selected. For most ANN archi-tectures, some critical questions should be addressed first inorder to better implement an ANN-based estimator: (1) howmany hidden layers should be selected; (2) how many neu-rons should be assigned to each hidden layer; and (3) how todetermine the connectivity relationship between each neuronpair. If ANN is selected as a tool wear modeling approach,some of the aforementioned concerns should be carefullyaddressed.

As a simple and easy implementation, the back propaga-tion (BP) algorithm has been typically chosen as the learningalgorithm for most ANN-based tool wear modeling applica-tions, but its learning converge speed, efficiency, and accu-racy are not satisfactory for tool wear modeling/monitoring(Sarkar 1995). Other advanced ANN architectures and/ortraining/optimization algorithms have been pioneered withencouraging results, but they are difficult to be widely imple-mented due to their complexity.

Among the studied ANN architectures, MLP-based ANNhas been widely implemented due to its simplicity and suf-ficient effectiveness in modeling the tool wear progression(Chryssoluouris and Guillot 1990; Rangwala and Donfeld1990; Monostori 1993; Lin and Ting 1995; Das et al. 1996;Kuo and Cohen 1998; Sick 1998; Dimla and Lister 2000;Ozel and Nadgir 2002; Haber and Alique 2003; Sivarao 2005;Panda et al. 2006), and the BP algorithm has been commonlyused to train such MLP-based ANNs. Based on the univer-sally accepted MLP structure, this study aims to develop anovel but easy to be implemented a fully forward connectedneural network-based generalized optimal estimator for CBNtool wear modeling in hard turning (i.e., optimized FFCNN),and this estimator is trained using the EKF algorithm andoptimized using a destructive approach. There are three mainadvantages of the proposed NN approach over other existingANN-based approaches:

(1) The structure of the proposed ANN is much more gener-alized. For the proposed fully forward connected neuralnetwork, only the number of hidden neurons is to be pre-determined instead of the number of hidden layers andthe neuron number for each hidden layer, which makes

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it a much more generalized modeling approach. Thehidden neurons are to be organized into several layersequivalently using the proposed training and optimiza-tion algorithm.

(2) The network structure is optimized given the numbers ofinput, hidden, and output neurons, respectively. Throughconnectivity optimization, some unnecessary networkconnections are removed to form an optimized and con-cise network structure, leading to increased networkrobustness (KrishnaKumar and Nishta 1999).

(3) The network training convergence performance isimproved using the EKF algorithm. The training conver-gence speed and training accuracy using the EKF algo-rithm are much better than those of the BP algorithm(Li 2001).

Theoretical background of proposed modelingapproach

As detailed in the following, the proposed CBN tool wearestimator is designed based on a generalized fully forwardconnected neural network, which is trained by the Kalmanfilter algorithm and optimized using a destructive approach.

Fully forward connected neural network (FFCNN)

ANN is an emulation of the structures of the human brain,where the nodes correspond to neurons and the weights cor-respond to synaptic connections. Its universal input-outputmapping approximation property is also mathematicallyguaranteed (Haykin 1999). This paper proposes an optimizedFFCNN as an ANN-based estimator to model the CBN toolwear progression. As shown in Fig. 2, the FFCNN architec-ture proposed by Werbos (1990) is adopted as the backbonefor this study since it is more general than the MLP approachproposed by Rumelhart and McClelland (1986). For FFCNN,the network is composed of three sections, namely input neu-ron section, hidden neuron section, and output neuron sectionrespectively, and every neuron takes connections from everyneuron to the left of it. FFCNN is also viewed as a general-ized version of MLP (KrishnaKumar 1993). However, oncethe number of hidden neurons is given, there is no need tospecify the number of hidden layers for FFCNN in contrast tothat of MLP. The FFCNN hidden neurons are fully forwardconnected as many MLPs.

The FFCNN learning process includes two passes—theforward pass aiming to calculate the network outputs andthe backward pass aiming to update the weights of networkconnections. In the forward pass, the activation (output) ofa particular neuron depends on the activations (outputs) ofneurons to the left of it (Werbos 1990; KrishnaKumar 1993).

j

Input neurons Hidden neurons

1, …, 1, …,

Output neurons

Feedforward loops (solid lines)1, …,

i

Wij

in hn on

Fig. 2 Architecture of a fully forward connected neural network

Forward pass computation

For each forward pass, the net input to the neuron i iscomputed as follows:

neti =i−1∑

j=1

Wi j X j 1 ≤ i ≤ ni + nh + no (2)

and the output of the neuron i is computed using an activationfunction as follows:

Xi = Fi (neti ) 1 ≤ i ≤ ni + nh + no (3)

where ni , nh , and no represent the number of the input neu-rons, hidden neurons, and output neurons respectively, netirepresents the net input to the neuron i, Wi j represents theweight connecting the neuron j to the neuron i, Xi representsthe output of the neuron i , and Fi ( ) represents the activationfunction used for the neuron i .

For neurons in the hidden section, a unipolar sigmoidactivation function is used:

Fi (neti ) = 1

1 + e−netini < i ≤ ni + nh (4)

For neurons not in the hidden section, a linear activationfunction is used:

Fi (neti ) = neti

1 ≤ i ≤ ni or ni + nh < i ≤ ni + nh + no (5)

Then the neural network outputs are calculated as follows:

Yi = Fi+ni +nh (neti+ni +nh ) = Xi+ni +nh 1 ≤ i ≤ no (6)

where Yi represents the output of the output neuron i .

Backward pass computation

The EKF algorithm was first introduced to train neural net-works by Singhal and Wu (1989). With the EKF approach, thenetwork weights are viewed as the states of the non-linear sto-chastic process that the ANN describes. Compared to the BPalgorithm in training the network weights, the EKF learningalgorithm has the following advantages and drawbacks. Themain advantages are: (1) The EKF algorithm helps to reachthe training steady state much faster than the BP algorithm

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for non-stationary processes (Zhang 2005); (2) The EKFalgorithm excels the BP algorithm when the training data islimited (Puskorius and Feldkamp 1994); and (3) The adjust-ment of coefficients using the EKF algorithm are based onphysical characteristics of the described process such as thevariance of process noise Q and the variance of measurementnoise R (Alessandri 2002), while for the BP algorithm theoptimization of the learning coefficients such as the adjust-ment of the learning rate and momentum is carried out bya trial-and-error method. On the other hand, the computa-tional expense of the EKF learning algorithm is higher thanthat of BP (Alessandri 2002), and EKF also requires highercomputational precision (Bierman 1977; Lary and Mussa2004). Fortunately, these computation-related drawbacks ofthe EKF algorithm have been offset thanks to significantcomputing technology advances. Hence the EKF learningalgorithm (Puskorius and Feldkamp 1994; Haykin 1999) isfavored here, and the EKF-based network updating approachis introduced as follows. For the backward pass, the connec-tion weights are updated by minimizing the error E betweenthe neural network output Yi and the desired output Di asfollows:

E = 1

2

no∑

i=1

(Yi − Di )2 (7)

The ordered derivatives of the output vector Y with respectto weights are computed as follows:

∂+Y

∂Wi j= ∂+Y

∂ Xi

∂ Xi

∂netiX j=

⎛

⎝ni +nh+no∑

j=i+1

∂+Y

∂ X j

∂ X j

∂ Xi

⎞

⎠ ∂ Xi

∂netiX j

=⎛

⎝ni +nh+no∑

j=i+1

∂+Y

∂ X j

∂ X j

∂(net j )W ji

⎞

⎠ ∂ Xi

∂netiX j (8)

The network trainable weights Wi j are arranged into an Mdimensional vector W , and the elements of ordered deriva-tives ∂+Y

∂Wi jare arranged into an M × no matrix H (Haykin

1999) at the mth step, where M is the number of trainableweights. The trainable weights are further updated using theEKF algorithm. The Kalman filter gain matrix K at the mthstep is computed as follows:

Km = Pm−1 Hm[Rm + H Tm Pm−1 Hm]−1 (9)

The network weight vector Wm , which is the vector W at themth step, is updated as follows:

Wm = Wm−1 + Km(dm − ym) (10)

Once Wm is updated, it is restored to form the weight matrix[Wi j ](ni +nh+no)×(ni +nh+no). The error covariance matrix Pm

is further computed as:

Pm = Pm−1 − Km H Tm Pm−1 + Qm (11)

where the subscript m represents the mth step, Km is theKalman gain matrix, dm is the target vector, ym is the outputvector of the network, Wm is the weight vector, Wm and Wm−1

are the estimate of the weight vectors Wm and Wm−1 respec-tively, Hm is the derivatives matrix of the network outputswith respect to the trainable weights, Rm is the covariancematrix of measurement noise, Qm is the covariance matrixof process noise, and Pm is normally initialized as a diagonalmatrix with large diagonal elements such as 100 at m = 0(Puskorius and Feldkamp 1994).

Network optimization

ANN-based tool wear modeling approach has some commonissues such as under-training problem, convergence prob-lem, overfitting problem, and topology optimization problem(Danaher et al. 2004). While the first two can be mitigatedby carefully selecting stopping criteria, the latter two are ofinterest here through an optimization approach, which opti-mizes the network topology as well as reduces the risk ofoverfitting.

In this study, a topology destructive optimization approachis utilized to optimize the FFCNN estimator. First, the num-ber of hidden neurons is chosen based on a-trial-and-errorapproach (Schalkoff 1997), and then the network topologyis optimized by disconnecting some weights among the net-work neurons using a method proposed by KrishnaKumar(1993). Such a pruned and optimized network has beenproven to be simpler, more accurate, and more robust(KrishnaKumar and Nishta 1999). An example of the optimi-zation result is illustrated in Fig. 3, where FFCNN originallyhas a structure of 1-3-1, and two connections (C31 and C42)are disconnected after optimization. The detailed optimiza-tion algorithm can be found in (KrishnaKumar 1993).

Forward pass for optimization

To optimize the network connectivity, a function g(Ci j ) isintroduced as Eq. 12 to represent the connections for each

Before optimization

31 2 54Input

After optimization

Connections will be removed

31 2 54Input Output

Output

Fig. 3 An example of connectivity optimization effect

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neuron pair. If g(Ci j ) = 1.0, this implies there is a connec-tion between the i th and j th neurons; and if g(Ci j ) = 0, itimplies there is no connection.

g(Ci j ) = 1

1 + e−Ci j(12)

where Ci j is the connection coefficient from the neuron j tothe neuron i .

With g(Ci j ), the forward pass computation procedure cor-responding to Eq. 2 is rewritten as follows:

neti =i−1∑

j=1

Wi j g(Ci j )X j 1 ≤ i ≤ ni + nh + no (13)

Other network forward pass calculations are the same as insection “Forward pass computation”.

Backward pass for optimization

With g(Ci j ) embedded inside the network as in Eq. 8, theordered derivatives of the output vector Y with respect to theweights are computed as follows:

∂+Y

∂Wi j= ∂+Y

∂ Xi

∂ Xi

∂(neti )g(Ci j )X j (14)

The ordered derivatives of the output vector with respect tothe connection coefficients are computed as follows:

∂+Y

∂Ci j= ∂+Y

∂ Xi

∂ Xi

∂(neti )Wi j X j

∂(g(Ci j ))

∂Ci j(15)

Then both the weights and connection coefficients areupdated using the EKF algorithm (Eqs. 9–11 with differentH matrices) as discussed in section “Backward pass compu-tation”. At the beginning of optimization, each Ci j is set as 0.When the training stopping criteria have been met, the con-nections with Ci j < 0 are disconnected by setting g(Ci j ) = 0and the others stay connected by setting g(Ci j ) = 1.

Training procedure

The training process of optimized FFCNN includes the twosteps: the network connection is first optimized and then theweights of the optimized network are further refined usingthe same training data.

Input normalization

In order to avoid the saturation problem in training, all inputsare first normalized before they are fed into the network. Thenormalization is performed using a linear function as follows:

XN = (X − Xmin)XN max − XN min

Xmax − Xmin+ XN min (16)

where XN is the normalized inputs, X is the original valueof inputs, XN max and XN min are the maximum and mini-mum values of the normalized inputs, and Xmax and Xmin

are the maximum and minimum values of the inputs beforenormalization.

Network training and testing

Network training stop criteria are vital to the performanceof trained FFCNN estimators. If the stopping criteria are toostrict, they will cause an over-training problem so that thenetwork is trained to map not only the concerned patternsbut also the noise features of training data, and as a result,the generated model can not fit testing data well. On the con-trary, if the stopping criteria are too loose, they will causethe training process to end prematurely which often resultsin the under-training problem.

The stopping criteria of the studied FFCNN and optimizedFFCNN are determined by trial-and-error as follows: (1) Thenumber of training cycle should be less than 4,500 and thetraining process stops after 4,500 cycles if no other stoppingcriteria are met before; or (2) if the error is less than 0.03and the difference between the current error and the error of50 epochs before is less than 0.0004, then the training processstops.

During the training process, the trainable parameters aredetermined to minimize the error E . Once the training stop-ping criteria are met, the training process is terminated andboth the structure and weights of ANNs are fixed. During thetesting process, the testing data are fed into the trained ANNby following the aforementioned forward pass computationin section “Forward pass computation”.

Experimental validation

Validation with Ozel and Nadgir’s experimental results

Hard turning experiment setup and tool wearestimator design

In the work by Ozel and Nadgir (2002), hardened H-13 steeltube workpiece (55 HRC) was turned using two types ofCBN tools: chamfered tool with a chamfer length 0.1 mmand chamfer angle 25◦ and honed tool with a 0.02 mm edgeradius. The tool holder had a negative five-degree rakeangle. Different settings of cutting velocities (200, 250, and300 m/min) and feed rate (0.05 and 0.1 mm/rev) were usedin the experiments.

Besides their experimental measurements, Ozel andNadgir have also tried to model tool wear using a three-layerneural network (MLP) (Ozel and Nadgir 2002). The topol-ogy of neural network was determined as 5-30-8 based on

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a trial-and-error method, and the network was trained usingthe BP algorithm. The neural network inputs included cut-ting velocity, feed rate, cutting force ratio, and depth of cut,which was constant (2.5 mm). The network output was thecoded tool flank wear depth. Twenty five data sets of thechamfered tool and 18 data sets of the honed tool were usedas the training data, respectively. The output layer consistedof 8 neurons which represented the 8 binary values of flankwear.

For comparison, the FFCNN and optimized FFCNN esti-mators are applied to model this tool wear progression (Ozeland Nadgir 2002). The topologies of these two estimatorarchitectures are both 5-7-1. Five inputs are the cutting speed,feed rate, depth of cut (DOC), machining time and a constantbias of 1. No force ratio information is required as the inputin contrast to that of Ozel and Nadgir (2002). The output isthe tool flank wear estimation. The number of hidden neu-rons is chosen based on a trial-and-error method. Based onthe recommendation that ANN with 2ni + 1 hidden neuronsis enough for a satisfactory modeling accuracy (Schalkoff1997), 12 hidden neurons are first chosen, then the numberof hidden neurons is gradually reduced until a better per-formance is achieved. This process results in a structure of7 hidden neurons and the overall network architectures areshown in Fig. 4. The training data used are the same as thoseof Ozel and Nadgir (2002).

The EKF algorithm is applied to train both the FFCNNand optimized FFCNN estimators. The diagonal elements ofthe process noise covariance matrix Q is initialized as 0.01and this value descends linearly within 10,000 training cyclesuntil Q reaches a minimum limit of 0.000001. The diagonalelements of the measurement noise covariance matrix R isinitialized as 100 and it also descends linearly until R reachesa minimum boundary of two. Both R and Q help the trainingprocess to converge to a global minimum.

Performance comparison

The modeling performance of FFCNN and optimizedFFCNN is compared with the MLP approach of Ozel andNadgir (2002). The comparisons are based on the data from

Feed Rate

Depth of Cut

Cutting SpeedFFCNN

or

Optimized FFCNN

Machining Time

Bias

Flank Wear

Fig. 4 Input and output feature for proposed FFCNN and optimizedFFCNN

both the chamfered and honed tools. In modeling thechamfered tool wear progression, the connections arereduced from 68 for FFCNN to 37 for optimized FFCNN.In modeling the honed tool wear progression, the networkconnections are reduced from 68 for FFCNN to 35 for opti-mized FFCNN.

Two typical training results are shown in Fig. 5. The train-ing error is 0.92% for FFCNN versus 0.45% for optimizedFFCNN in chamfered tool cutting and 0.60% for FFCNN ver-sus 0.37% for optimized FFCNN in honed tool cutting. Fig-ure 6 shows the predicted flank wear progressions from MLP(Ozel and Nadgir 2002), FFCNN, and optimized FFCNNfor the two representative testing cases. For both the test-ing cases, the performance of optimized FFCNN is slightlybetter than that of FFCNN. From Fig. 6a, it can be seen thatthe accuracy of optimized FFCNN is slightly better and moreconsistent than that of MLP; however, the modeling accuracyof optimized FFCNN is much better than that of MLP for theother testing case as shown in Fig. 6b. The detail testing errorcomparisons are shown in Table 1. The error here is defined as√∑

(Xi − Xi )2∑

X2i

× 100%

where Xi and Xi are the actual measurements and the ANNestimator outputs, respectively.

Validation in CBN hard turning of hardened steel

Experimental setup

To better appreciate the validity in applying the proposedoptimized FFCNN estimator for CBN tool wear modeling,hardened AISI 52,100 bearing steel with a hardness 62 HRCwas machined on a horizontal Hardinge lathe using a lowCBN content tool insert (Kennametal KD050) with a −20◦and 0.1 mm wide edge chamfer and a 0.8 mm nose radius. TheDCLNR-164D (ISO DCLNR-164D) tool holder was used.No cutting fluid was applied. Flank wear length was mea-sured using an optical microscope (Zygo NewView 200).The experiment was stopped when sudden force jump wasobserved signaling a chipping or broken tool condition.

Cutting tests were performed based on a standard centralcomposite design test matrix with an alpha value of 1.414.The center point (0,0) was determined based on the toolmanufacturer’s recommendation (Huang and Liang 2004a).A typical depth of cut was suggested as 0.203 mm, whichwas used in the test matrix. The test conditions are shown inTable 2. Conditions 4, 7, and 11 were identical in this exper-imental design. To further investigate the effect of depth ofcut on tool wear, experiments with various depths of cut werealso studied according to Table 2. Uncertainty characteriza-tion is not offered here due to the size of the experimental

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Fig. 5 Training performancecomparison for (a) chamferedtool at cuttingspeed=200 m/min andfeed=0.1 mm/rev and (b) honedtool at cuttingspeed=200 m/min andfeed=0.05 mm/rev

10 20 30 40 50 600.03

0.04

0.05

0.06

0.07

0.08

0.09

Time (min))

mm(

raew

knalF

Desired outputsFFCNN outputsOptimized FFCNN outputs

20 30 40 50 600.05

0.06

0.07

0.08

0.09

0.1

0.11

Time (min)

)m

m(rae

wkn al

F

Desired outputs

FFCNN outputsOptimized FFCNN outputs

(a) (b)

Fig. 6 Testing performancecomparison for (a) chamferedCBN tool and (b) honed CBNtool at cuttingspeed=250 m/min andfeed=0.05 mm/rev

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Table 1 Testing errorcomparison based on Ozel andNadgir’s data (Ozel and Nadgir2002)

MLP FFCNN Optimized(%) (%) FFCNN (%)

Test 1 (Fig. 6a) 10.17 7.60 7.39Test 2 (Fig. 6b) 59.14 5.08 4.83Average error 34.66 6.34 6.11Error variance 1199.03 3.18 3.28

data set. Under the high cutting speed of Condition six, thebreak-in period accounted for a large portion of tool flankwear and microchipping was a dominant factor of tool life,the tool wear progression under Condition six is not of inter-est here.

Tool wear estimator design and performancecomparison

In this study, MLP, FFCNN and optimized FFCNN are struc-tured to model the CBN tool wear progression based onthe experimental measurements, and their modeling perfor-mance is compared with the measurements as well as theanalytical predictions (Huang and Liang 2004a). The net-work structure (5-7-1) selected in section “Validation withOzel and Nadgir’s experimental results” is also used here.The inputs for the ANN estimators are the cutting speed,feed rate, depth of cut, machining time, a constant bias of 1,and the output is the tool flank wear length. The data of con-ditions 1, 5, 9, 10, and a are used for training and the rest are

used for testing. For MLP, the learning rate and momentumare set to be 0.1 and 0.8 respectively, and the limit for train-ing epochs is set to be 20,000. Other network configurationsare the same as those in section “Validation with Ozel andNadgir’s experimental results”.

Two typical training results are shown in Fig. 7. All train-ing results of the three investigated ANNs are very similarand all of them model the tool wear progression very well asin section “Validation with Ozel and Nadgir’s experimentalresults”. However, the differences in modeling generaliza-tion capability can be seen from the five testing cases asshown in Fig. 8 and Table 3. Optimized FFCNN, which has35 connections for this case, excels all other three approachesunder Conditions 3, 4, and b, but be second to MLP underCondition 2 and the analytical approach under Condition8. Overall, it can be seen that the optimized FFCNN-basedapproach has the least modeling error and error variance asshown in Table 3. For all the testing cases, optimized FFCNNexcels FFCNN, which confirms the effectiveness of the con-nectivity optimization algorithm. It should be noticed that

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Table 2 Experimental cuttingconditions (Conditions 4, 7, and11 were identical in thisexperimental design)

Condition Speed Feed Depth of cutindex (m/s) (mm/rev) (mm)

1 3.05 0.152 0.2032 1.52 0.152 0.2033 3.05 0.076 0.2034 2.29 0.114 0.2035 1.52 0.076 0.2036 3.36 0.114 0.2037 2.29 0.114 0.2038 2.29 0.061 0.2039 2.29 0.168 0.20310 1.21 0.114 0.20311 2.29 0.114 0.203a 1.52 0.076 0.102b 1.52 0.076 0.152

Fig. 7 Training performancecomparison under (a) Condition5 and (b) Condition 10

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Condition 5 Condition 10(a) (b)

the proposed optimized FFCNN estimator delivers the worsttesting performance under Condition three and it is attributedto rapid and stochastic tool wear under the aggressive cuttingconditions.

Discussion

Experimental data from section “Validation in CBN hardturning of hardened steel” are further used to appreciatethe proposed optimized FFCNN estimator performance interms of learning convergence speed, generalization capabil-ity, model sensitivity, network training cost-benefit analysis,and effect of cutting conditions on tool wear.

Learning convergence speed

Figure 9a provides the learning convergence speed compar-ison between the BP learning and the EKF learning algo-rithms for FFCNN. It is obvious that FFCNN trained bythe EKF algorithm converges much faster than BP. Thisobservation also agrees with the previous findings (Zhang2005). Figure 9b compares the learning convergence speedbetween FFCNN and optimized FFCNN, and both the ANNsare trained by EKF. The comparison shows that the learningconvergence speed of optimized FFCNN is even faster than

that of FFCNN. Note that for this comparison, some connec-tions of optimized FFCNN have been removed already andthe convergence study is based on the network refining phaseas discussed in section “Training procedure”.

Generalization capability

Once the proposed optimized FFCNN estimator is trainedusing the training data, its generalization capability in mod-eling tool wear is further studied using the testing data. Basedon the comparisons of the different ANN-based approachesas seen in Table 3, it is concluded that the optimized FFCNN-based tool wear estimator is the most accurate and effectiveestimator among the three ANN-based modeling approaches.Furthermore, the variance of errors of optimized FFCNN isthe smallest (10.04) when compared with those of the otherapproaches (184.01, 175.56, and 65.54) for all the testingcases. The above observation concludes that the general-ization ability of optimized FFCNN is the best among thethree investigated ANNs for CBN tool wear modeling in hardturning.

Modeling sensitivity to network structure variation

The structure 5-7-1 has been selected based on a trial-and-error approach and satisfactory modeling accuracy has been

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Fig. 8 Testing performancecomparison under Conditions 2,3, 4, 8, and b

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Condition 2 Condition 3

Condition 4 Condition 8

Condition b

Table 3 Testing errorcomparison in CBN hardturning

Analytical model (%) MLP (%) FFCNN (%) Optimized FFCNN (%)

Condition 2 25.63 8.37 10.65 10.29Condition 3 14.49 39.45 26.32 12.77Condition 4, 7, or 11 11.96 17.94 22.03 11.51Condition 8 6.27 15.57 15.27 13.71Condition b 40.52 5.96 6.50 5.60Average error 19.77 17.46 16.15 10.78Error variance 184.01 175.56 65.54 10.04

achieved. However, it is of much interest to investigate thedeterioration of neural network estimating capability amongMLP, FFCNN, and optimized FFCNN when the networkstructure is modified. If the network outputs are less sensitiveto its structure change, it means that such a network is robustsince its performance may vary less after any unnecessarystructure alteration. In order to study the structure sensitivity

characteristic of the investigated ANNs, two more experi-ments are done by altering the number of hidden neuronsof ANNs from seven to five and nine, respectively. Table 4lists the statistical performance of the investigated ANNsdue to this structure variation. As expected, the modelingperformance degrades after altering the ANN structure, andFFCNN is the most sensitive to the network structure change

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Fig. 9 Learning convergencecomparison between (a) MLPand FFCNN, and (b) optimizedFFCNN and FFCNN

Table 4 ANNs’ performancedegradation due to hiddenneuron number alteration

MLP (%) FFCNN (%) Optimized FFCNN (%)

With 5 hidden neurons Avg. error 19.35 28.01 12.81Avg. deviation 80.09 284.57 18.88

With 9 hidden neurons Avg. error 22.63 27.12 12.41Avg. deviation 239.45 516.84 25.52

7 to 5 hidden neurons Avg. error change 1.89 11.86 2.03Avg. deviation change 95.47 219.03 8.84

7 to 9 hidden neurons Avg. error change 5.17 10.97 1.63Avg. deviation change 63.89 451.30 15.48

as shown in Table 4. Among the cases investigated, the aver-age estimating errors of FFCNN are the largest, and opti-mized FFCNN excels in modeling performance and has muchsmaller deviation values.

To further compare the relative performance degradationof the three ANNs, the changes in the average and variance ofestimating errors due to the hidden neuron number alterationare also listed in Table 4. When the hidden neuron numberdecreases from seven to five, the incremental average error ofMLP is slightly smaller than that of optimized FFCNN; how-ever, optimized FFCNN excels both MLP and FFCNN for allthe other changes. The results prove that optimized FFCNNis the least sensitive to the structure alteration among thethree ANNs investigated.

Cost-benefit analysis of ANN training

The proposed optimized FFCNN estimator excels in mod-eling performance but requires more computational time intraining due to the EKF training algorithm and additionalstructure optimization process. A cost-benefit analysis is con-ducted to better appreciate the proposed estimator. MLP andoptimized FFCNN are trained to model the CBN hard turn-ing tool wear progression in section “Validation in CBNhard turning of hardened steel”. If the networks are trainedby 1,200 iterations, training MLP costs 3.2 s, resulting in a17.53% training error, and training optimized FFCNN costs483.2 s, resulting in a 1.94% training error. It shows that theproposed estimator requires much more time for each train-ing epoch; however, the proposed estimator has an increasedtraining convergence speed as discussed in section “Learn-

ing convergence speed” and higher modeling accuracy andefficiency as discussed in section “Generalization capabil-ity”. Considering the significant advances in computationalpower, the weakness in computational cost will be less pro-nounced, and the proposed estimator is preferred for mosttool wear modeling cases.

Effect of cutting conditions on tool wearusing optimized FFCNN

CBN tool performance in terms of tool life is further eval-uated as a function of the cutting conditions (cutting speed,feed rate and depth of cut) based on the developed optimizedFFCNN estimator. For comparison, the cutting conditionsand tool life criteria are selected based on a previous study(Huang and Liang 2004c). The estimator prediction resultsare also compared with those of experimental measurementsand theoretical predictions (Huang and Liang 2004a) asshown in Figs. 10–12.

The effect of cutting speed on the tool wear is first inves-tigated. For this case, both the feed rate and the depth of cutare fixed at some representative values, 0.114 mm/rev and0.203 mm, respectively, and the tool life is investigated byvarying the cutting speed from 1.20 to 3.02 m/s. The toollife criterion here is selected as 150 µm as in (Huang andLiang 2004c). As shown in Fig. 10, the tool life curves fromthe analytical model and optimized FFCNN match each otherclosely, and both are close to the experimental measurements.

The effect of feed rate is also investigated. For this case,cutting speed and depth of cut are set as 2.29 m/s and0.203 mm respectively. The tool life is investigated by varying

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1.5 2 2.5 35

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Fig. 10 Effect of cutting speed on tool life (feed=0.114 mm/rev anddepth cut=0.203 mm)

0.06 0.08 0.1 0.12 0.14 0.16 0.184

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Analytical predictionsExperimental data

Fig. 11 Effect of feed rate on tool life (cutting speed=2.29 mm/revand depth cut=0.203 mm)

the feed rate from 0.076 to 0.168 mm/rev. The tool life crite-rion here is specified as 110 µm (Huang and Liang 2004c).As seen from Fig. 11, the optimized FFCNN estimator pro-vides a better estimation of the tool wear progression thanthat of the analytical model in Huang and Liang (2004a).

The effect of depth of cut is investigated as well. For thiscase, the cutting speed and the feed rate are set as 1.52 m/sand 0.076 mm/rev respectively, and the tool life is investi-gated by varying the depth of cut from 0.102 to 0.203 mm.The tool life criterion here is specified as 125 µm (Huang andLiang 2004c). As seen from Fig. 12, the optimized FFCNNestimator provides a better estimation of the tool wear pro-gression than that of the analytical model in Huang and Liang(2004a).

It can be seen that the tool life predictions using the opti-mized FFCNN estimator are closer to the experimental mea-

0.1 0.12 0.14 0.16 0.18 0.2 0.2220

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Fig. 12 Effect of depth of cut on tool life (cutting seed=1.52 m/revand feed=0.076 mm/rev)

surements than those using the analytical model (Huang andLiang 2004a). As seen from these figures, the cutting speedis the most significant factor in determining the tool life, andthe depth of cut is the least significant factor.

Conclusions

An FFCNN-based generalized optimal estimator is proposedto model CBN tool wear in hard turning, and this estimatorhas the following advantages:

(1) It is easily implemented as a generalized perceptron-based neural network, and it is not necessary to specifythe number of hidden layers and the neuron number foreach hidden layer once the total hidden neuron numberis given.

(2) The neuron connections are optimized automatically toachieve increased network robustness.

(3) The network training convergence performance isimproved using the EKF algorithm.

That is, such an estimator for tool wear modeling can be auto-matically designed to achieve a better and robust estimatingperformance once the numbers of inputs, outputs, and hiddenneurons are specified.

The modeling performance of the proposed neuralnetwork-based estimator has been evaluated using the exper-imental measurements as well as compared with the othercommon ANN-based approaches, and the comparisons showthat the optimized FFCNN estimator excels in modeling CBNtool wear in hard turning. Furthermore, the optimizedFFCNN estimator has the fastest learning convergence speed,best generalization capability, and least sensitive to the net-

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work structure alteration. It is believed that this modelingapproach is also applicable to other machining tool wearmodeling studies.

In conclusion, the optimized FFCNN tool wear estima-tor has been proven to be faster, more accurate, and morerobust when compared with the other approaches investi-gated, and it will help to better optimize the cutting condi-tions for hard turning as well as other machining processes.Although the tool geometry effect is not explored in thisstudy, it can also be studied using the proposed estimator.Furthermore, future work may integrate a recurrent approachto better capture the non-stationary property of tool wearprogression in machining.

Acknowledgments The financial support from the South CarolinaSpace Grant Consortium and NASA Ames Research Center is highlyappreciated.

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