Machine learning based tool condition classification using acoustic emission and vibration data in high speed milling process using wavelet features

Abstract

It is important to develop an intelligent tool condition monitoring system to increase productivity and promoting automation in metal cutting process. Many attempts have been made in the past to develop such systems using signals from various sensors such as dynamometer, current, accelerometer, acoustic emission, current and voltage, etc. But the successes of different sensor based systems are limited due to the complexity of tool wear process. The research is still ongoing for improved tool condition monitoring system with applications of advance signal processing techniques and artificial intelligent models. In this study, tool conditions are monitored using the vibration and acoustic emission signatures during high speed machining of titanium alloy (Ti-6Al-4V). Using discrete wavelet transforms wavelets coefficients of vibration and acoustic emission signals are extracted using haar, daubechies, biorthogonal and reverse biorthogonal wavelets. Machine learning algorithms such as decision tree, naive bayes, support vector machine and artificial neural networks are used to predict the tool condition. Results indicate the effectiveness of acoustic emission and vibration data using wavelets for classifying the tool conditions with the aid of machine learning algorithms. A correlation is established between the tool conditions and sensor data. Support vector machine trained by vibration data appears to be predicting the tool conditions with good accuracy compared to decision trees, naive bayes and artificial neural network. Results obtained in this study will be useful to develop an intelligent on-line tool condition monitoring system.

Keywords

High speed milling vibration acoustic emission wavelet machine learning classification

1. Introduction

Modern manufacturing machine tools have to be dependable, sustainable and have to operate without any errors. Off late, concept of condition monitoring has gained remarkable importance in the manufacturing industries. Major problems of manufacturing industries in the metal cutting are tool wear and tool breakage. These two problems lead to frequent stoppage of machines and leading to the decrease in utilization of the machines. In industries approximately 20% of down time is reported due to the tool failure [1]. The costs of cutting tools are approximately amounts to 3 to 12% of the total manufacturing cost. Monitoring and control of production process is inevitable for the sustainability of metal cutting industries.

Titanium alloys are known as hard-to-machine material. The challenges in machining titanium alloys are due to the variation of chip thickness, high thermal stress, low-thermal conductivity of the material, high pressure loads and residual stresses induced during the machining process. These factors are accountable for higher tool wear and inferior surface integrity of the machined surface. High Speed Machining (HSM) of aluminum alloys has been applied in industries successfully for more than a decade. Off late, researchers and practicing engineers are working towards finding optimum process parameters for HSM of titanium alloys. Titanium alloys are generally difficult to machine at cutting speeds of over 30 m/min with HSS tools, and over 60 m/min with plain cemented tungsten carbide tools. In an automated environment, monitoring tool conditions in HSM is important. Development of tool condition monitoring system is one of the thrust areas of research in the field if HSM of Titanium alloy. Most of the studies in the machining of titanium are focused on turning operations. In this study, high precision, high speed machining centre is used for conducting the experiments.

For monitoring and control of production processes, sensors are being used to observe the variation of the processes. The sensor information is used for making decisions for an effective control of the process. In tool condition monitoring, one of the important aspect is to monitor the tool wear. A suitable sensor has to be chosen for effective monitoring of the tool. The tool wear sensors requirements include [2]; a) good correlation between the sensor signal and tool condition b) response should be faster c) simple in design and rugged in construction d) accurate and reliable, preferably non-contact and e) no interference with the machining process.

There are two methods by which tool wear can be measured using the sensors, one is direct method and the other is indirect method. Most commonly used direct sensing methods are proximity methods, radioactive sensors and vision sensors. These techniques hold higher degree of accuracy but used only in the laboratory level not in the actual conditions. Indirect method of sensing is to capture the tool condition in real time using an appropriate sensor. The features are extracted from the signals acquired from the sensors and are estimated to predict the condition of the tool. Indirect methods are less accurate than the direct methods, but less complex and more suitable for monitoring processes such as turning, milling, drilling and grinding etc. Sensors which are commonly used in tool condition monitoring [3] are microphones, optical sensors, acceleration sensor, vibration sensor, acoustic emission sensor, and motor current sensor and force sensor for the diverse manufacturing processes. Among these, sensing of motor current, cutting forces, vibration and acoustic emission are found to be very effective in monitoring the tool conditions.

2. Sensors for tool condition monitoring

Electric motors and spindles provide mechanical force to the cutting tool for removing the material from the work piece. Motor current or the motor power will be able to detect the variation in the cutting process due to the tool wear or tool breakage. Kim and Ahn [4] studied the state of the chip disposal during drilling process by acquiring the motor current. Brophy et al. [5] captured the spindle power signal and classified drilling operations as normal and abnormal. Li et al. [6] studied the tool condition during milling process using motor current signals. Major advantage of using current or power signature is that the measuring device does not affect the cutting process.

Many researchers have extensively used force sensors for monitoring the cutting process because of its high sensitivity and faster response to the change in the state of the tool due to the progress of the wear or tool breakage. Strain based sensors or piezo-electric based sensors types are used for force measurement. These sensors will convert the applied force into deformation of an elastic element. Jun et al. [7] evaluated a force based sensor for diagnosing faults in machining operation. A spindle force measuring system was proposed by Park and Altintas [8] for tool condition monitoring for milling. A tool wear monitoring system for CNC end milling using cutting force signals were presented by Lee et al. [9]. Byrne and O’Donnell [10] proposed a force sensor model for monitoring drilling process. Surface quality in an ultra-precision machining is monitored using various sensors such as accelerometers, dynamometer and AE sensor [11].

2.1 Vibration and acoustic emission based sensors for tool condition monitoring

The variation in the cutting forces during the machining process leads to vibrations. Self-exited vibrations can be monitored during the cutting process using piezo-electric type of sensors. As indicated by Tati et al. [3], the self-exited vibrations primarily occur due to the “waviness generation caused by the interaction between material surface and tool at particular spindle rotational frequencies, and by mode coupling where relative vibration between tool and work piece occurs concurrently between two directions in the plane of cut”. Self-exited vibrations also called as ‘chatter’ are harmful to the tool life and surface finish of the work piece. These self-exited vibrations are monitored using piezo-electric sensors. Piezo-electric sensors are effective in capturing the various conditions of the tools such as good condition, worn-out condition, and tool breakage etc. Dimla [12], correlated vibration signature features to the tool wear in a turning process and concluded that “vibration signatures satisfy the conditions of robustness, reliability and applicability requiring fewer peripheral instruments than acoustic emission”. A surface prediction system was proposed in [13] for turning process using vibration signatures. Zhong et al. [14], conducted studies on dry milling based on vibration signatures. Chatter and tool wear were monitored in high speed milling by Lamraoui et al. [15]. Tool wear condition prediction using vibration signatures in HSM of titanium alloys were studied by Krishnakumar et al. [16]. Zhang et al. [17] studied the tool wear and remaining useful life of the tool in dry milling process using tri-axial accelerometer.

During metal cutting, plastic deformation of the work will take place due to the application of cutting force. Deformation of the work material mainly results in a) tool wear b) tool breakage c) chip-formation d) chip-breakage e) chip-removal f) collision among tool and work piece. Materials which have elastic property will get strained due to the application of forces. The materials subjected to strain will spring-back when forces are removed. Higher cutting force resulting in higher elasticity leads to higher elastic energy in the material. Fracture of the materials occurs immediately when elastic limit is crossed in the case of brittle materials. In ductile materials, fracture will occur after plastic deformation. Internal stress due to the cutting force and plastic deformation is dispersed in the material and spread through the material and create tiny surface displacement. The rapid release of elastic energy in the materials undergoing deformation or fracture or both is called as ‘Acoustic Emission (AE)’.

The major advantage of using AE sensor is that the frequency range of AE signals are much higher than that of machine vibrations and environmental noise. AE signals do not interfere with the cutting operation. Dornfeld [18] listed the originating sources of AE during machining process. The locations include the places where the plastic deformation takes place during the cutting process in the work-piece and during chip deformation, friction contact between the flank face of the tool and work-piece causing flank wear and friction contact between rake face of the tool and chip resulting in crater wear, collision point between the chip and tool, chip breakage and tool fracture.

The AE signatures derived from metal cutting processes are continuous and transient [19]. These continuous and transient signatures exhibit the machining characteristic such as tool wear or the surface roughness produced on the part [20]. AE will happen over a broad frequency array but usually from 100 kHz to 1 MHz [21]. The emission signal is usually detected by a piezo-electric sensor mounted in the work or the tool. The acoustic emission signal is carefully analyzed to filter the cutting signal from the other signals produced from the machine. For a tool condition monitoring system, in addition to the sensors, signal amplifiers, signal filters and signal processing software and hardware are necessary.

Figure 1.

Working of machine learning algorithm.

Ravindra et al. [22] proposed AE based tool condition monitoring system in metal cutting. Hutton and Hu [23], studied acoustic emission sensing of tool wear in end milling. Applications of acoustic emission sensor for monitoring machining process were discussed in his research article by Inasaki [24]. Karpuschewski et al. [25], proposed a grinding tool monitoring system using power and acoustic emission sensing. Hase et al. [26], established a relationship between AE and cutting conditions in turning process. Marinescu and Axinte [27], studied the effectiveness of AE signals to detect malfunction of tool in milling process. Han and Wu [28], studied the performance of acoustic emission in precision and high efficiency grinding process. In their study, advantage of AE over vibration based approaches in terms of high signal to noise ration and sensitivity at ultra-precision scale were discussed. Arun et al. [29] studied the surface roughness using the AE signature in a cylindrical grinding process. A detailed review on tool condition monitoring focusing on sensors and signal processing techniques and application areas were presented by various researchers [1, 3, 20, 21, 30].

3. Vibration and AE signal processing

The signal acquired from the sensor is of analogue in nature. The analogue signals are first pre-processed. In the pre-processing stage, the analogue signals are filtered, amplified, converted into digital form and segmented for further processing. Choice of data processing method is an important activity in tool condition monitoring since the cutting process is assumed to be non-linear and non-stationary. Some of the important signals processing methods are a) Time-domain analysis b) Frequency-domain analysis and c) Time-Frequency domain analysis. The main objective of signal processing is to extract relevant information called “features” about the condition of the process from the raw signal acquired from the sensor. The vibration or acoustic emission signals collected during the metal cutting process may be analyzed in time domain or in frequency domain.

In general, important features extracted from the time-domain signals are arithmetic mean, average value, magnitude, root mean square (RMS), variance or standard deviation, skewness, kurtosis, signal power, peak to peak, crest factor, ratios of signals and signal increments. Some of the important features applicable to AE are hit, event, ringing, amplitude, RMS, ASL, energy, absolute energy, signal strength, time of duration, raising time, average frequency, initial frequency, inverse frequency, center frequency and peak frequency [31].

For deriving the frequency information of the signal, signal in the time-domain is transferred into frequency-domain using Fast Fourier Transform (FFT). Time-domain signal demonstrates how a signal changes over time. Frequency-domain signature provides knowledge about the frequency contents (components) of the signal. This frequency information is missing in time domain. In the Fourier Transform (FT) of a signal, the frequency-amplitude representation of the signal is obtained. The frequency-amplitude representations of the signal provide no information regarding what time those spectral components appear. When the time localization of the spectral components is needed, a transform giving the time-frequency representation of the signal is required. One such transformation is called wavelet transform. Wavelet transform is a dominant mathematical tool for classification of non-stationary signals. It has the potential to decompose the source signals of varying time and frequency resolutions, which are the characteristics of the defect mechanisms associated with the cutting process. The wavelet transform converts the wave into wavelet to extract the hidden features representing the condition of cutting tool.

Number of features existing in the time-domain or frequency-domain spectrum is huge. Performing signature analysis using all the features is time consuming and also results in redundancy of information. Relevant features which contain information about the cutting process have to be chosen; thereby time-complexity of the processing algorithm may be reduced. Decision trees are widely used for selecting dominant features from the time-domain or frequency-domain spectrum for condition monitoring problems. The selected features having rich information will be useful in identifying the condition of the cutting process.

4. Tool condition classification using machine learning algorithms

Mitchell [32] defined machine learning as “a computer program is said to learn from experience with respect to some task and some performance measure, if its performance on task, as measured by performance measure, improves with experience”. A typical working of machine learning algorithm is shown in the Fig. 1. For example, tool condition during metal cutting is considered as a task, this task is run through a machine learning algorithm with labeled data (training data) and, if it has successfully “learned”, then the programme will predict the tool conditions for the fresh data acquired from the metal cutting process. The different tool conditions may be good tool, worn-out tool, and tool breakage etc.

There are two broad classifications in machine learning activity a) supervised learning and b) unsupervised learning. In supervised learning, the algorithm trained with past experience is used for prediction. Whereas in unsupervised learning, the algorithm will find patterns and relationships for the input data provided to the algorithm without any training. In tool condition classification, supervised learning algorithms are widely used for predicting the condition of the tool. For data classification problems such as tool condition classification, researches have applied machine learning algorithms such as neural network, decision tree, naive bayes and support vector machines.

Tool wear monitoring using ANN was studied by Sick [33] and carried out a detailed review of the application of ANN for tool wear monitoring. Tool wear prediction model using least squares SVM was proposed by Shi and Gindy [34]. Machine learning algorithms were applied to classify the tool conditions for turning process using vibration signals [35, 36, 37]. In their study, bayes classifier, SVM, and decision tress were used for classification of tool conditions using vibration signals. Wang et al., [38] studied the machine tool condition using SVM. Wang et al. [39] proposed the tool condition classification using machine learning models with vibration signals for machining of titanium alloy. Machine learning algorithms, decision tree and ANN were used for tool condition monitoring in high speed machining of titanium alloys [16]. Zhang et al. [17] proposed a neuro-fuzzy model to predict the tool wear using vibration signatures.

Literature on sensors, signal processing and decisi-on-making strategies for process condition monitoring was reviewed in [3]. Machine learning algorithms applied to tool condition monitoring for metal cutting processes such as turning, milling, drilling and grinding are reviewed in [29]. In their studies, it was concluded that “in spite of tremendous recent advances, the area of TCM still faces several challenges that need to be overcome”.

Figure 2.

High speed machining centre mounted with accelerometer and AE sensor.

The noise from the metal cutting process will disturb the desired signals, which are used for the tool condition monitoring. Studies made in [40] show that using AE sensors, it is possible to minimize the noise contamination into the desired signal. AE frequencies are usually in the rage 100 kHz to 1 MHz. Acoustic emission distributes at frequencies above that of spindle rotation or natural frequencies. AE is more beneficial comparing with force or vibration based condition monitoring due to their better signal to noise ratio and sensitivity especially in precision machining.

Identifying appropriate data processing method is important for a non-linear and non-stationery signals acquired from metal cutting process. Fourier transform is applied by many researches for signal processing. FFT algorithm is the standard technique for monitoring signals in the frequency domain. FFT averages the frequency component over the time length of the signal with set decree of the whole frequency range. To tackle this issue, signals are analyzed in time-frequency domain. Time-frequency depiction of the signal discloses the signal performance in real time and its equivalent frequency property. Off late, wavelet transforms has been applied for tool condition monitoring problems. Discrete wavelet transforms are found to be faster in terms of computational complexity comparing with continuous wavelet transforms.

In this study, tool conditions in a high-speed machining center are monitored using vibration and AE sensor. Machining of titanium alloy has been carried out using multipoint end mill cutter. During machining, vibration and AE signals are captured. Signal processing has been carried out using discrete wavelet transforms. Signal decomposition has been carried out and wavelet coefficients are extracted. Machine learning algorithms are trained with wavelet coefficients and tool conditions are predicted.

5. Experimental setup

An experimental set-up is established for machining titanium alloy in a precision highspeed machining centre with approprate sensors for capturing vibration and AE signatures during machining. The experimental set-up consisting of “Sodic make HSL4-30L – ultra precision machining centre” with the maximum spindle speed of 40,000 rpm. The machine has a precision of providing an input increment of 0.0001 mm and rapid feed rate of 36 m/min. Experiments were conducted to arrive at optimum machining parameters with an objective of maximizing the tool life with good surface finish. Depth of cut as 0.3 mm, feed rate of 300 mm/min and cutting speed of 225 m/min are chosen as operating parameters for conducting experiments. Flank wear, $V_{b}$ of 0.024 is considered as a reference value to decide the change of tool (tool worn-out condition). The work piece material chosen in this study is an alloy of titanium (Ti-6Al-4V). A block of size, 100 $\times$ 100 $\times$ 50 mm is utilized for experimental purpose. A 4 flute coated carbide end mill cutter of 4 mm diameter with a flute length of 10 mm and shank diameter of 6 mm is considered for machining. Tool conditions based on flank wear such as a) good b) tool at middle of its life and c) worn-out condition are taken into consideration for feature selection and classification. A non-contact tool wear measurement system using a high resolution CCD camera is utilized for measuring the tool wear during the machining process. Cutting tool is allowed to machine the Ti alloy with the new tool until it reaches the maximum tool wear of 0.024 (Vb, Flank wear). During the entire machining cycle, vibration and AE signals are captured. The experimental set-up used in this study is shown in the Fig. 2.

During the entire machining cycle, vibration signals were captured using the piezo-electric accelerometers fixed in the machine spindle of the HSM. The vibration signals are fed into the FFT analyser. From the FFT analyser the signals are sent to the computer and are stored in the digital form for extracting wavelet features. Wavelet coefficients are extracted from mother wavelets of haar, daubechies, biorthogonal and reverse biorthogonal. The wavelet coefficients are fed into machine learning algorithms for tool condition classification. The algorithms used in this study for classification are decision tree, SVM, naive bayes and ANN.

For capturing the acoustic emission signals, AE sensor is fixed on the surface of the work piece. AE sensor of type “Micro 30D” is used in this study. It is a differential sensor designed for applications where high background noise is a major concern. It has very good sensitivity and frequency response over the range of 100–350 kHz. The two signal leads from the sensing element is fed into a differential pre-amplifier which eliminates common-mode noise resulting in a lower noise output. AE sensor translates the mechanical energy carried by the elastic wave into electrical energy. Piezo-electric type transducer is used for sensing the elastic wave. Couplent is used for mounting the transducer over the surface of the work piece. AE sensor along with the data acquisition card and software were supplied by Physical Acoustics Corporation (PAC), USA. The important features of the AE signal processing board used in this study includes; very low noise, internal 18 bit A/D conversion (high resolution), real time feature extraction, waveform processing and AE data streaming. The software used for AE signal processing is “AEwin” by “MISTRAS Corporation, USA”.

5.1 Methodology and objective

Methodology adopted in this study is schematically represented in the Fig. 3. Data acquired with AE sensor is subjected to discrete wavelet transform. Wavelet coefficients are extracted using the wavelets of haar, daubechies, bi-orthogonal and reverse biorthogonal. Features extracted from the wavelet coefficients are given as an input to machine learning algorithms for training. The trained machine learning algorithm is tested for predicting the tool conditions. Decision tree algorithm, naive bayes, ANN and SVM are used in this study for tool condition classification.

Figure 3.

Methodology.

The important objective of this study is to establish a correlation between the wavelet features extracted from vibration and AE with the tool condition using machine learning algorithms. To accomplish the objective of this study, following activities have been carried out:

An experimental set-up has been established consisting of high-speed machining centre with vibration and AE sensor along with related hardware and software.

Signatures of vibration and AE are studied in frequency-time domain using the wavelets by extracting wavelet coefficients

Classification of tool conditions using machine learning algorithms; decision tree, naive bayes, ANN and SVM.

6. Discrete wavelet transform

6.1 Introduction

Time series analysis has gained considerable interest in deteocting various characteristics of the system behavior. The important approaches include filtering, Fourier Transform-FT and Wavelet Transform-WT. These transformations will help to identify the concealed information that is not readily accessible in the raw data. FT is a popular approach used to acquire the frequency content of the signal. The main disadvantage of FT is that it will reveal only the frequency component of the signal. Time – Frequency details of the signal cannot be seen at a time in the FT. Signals such as vibration and AE signals used for tool condition monitoring are not stationery. For developing TCM systems, it is important to know at what time the frequency components will occur. To arrive time-frequency information of the signals, Short Time Fourier Transforms (STFT) and Wavelet Transforms (WT) are generally used. STFT results in poor resolution due to narrow window, where in each widow signal is assumed as stationery. WT investigates the signals at different frequencies at different resolutions which make it as an important technique for analyzing non-stationery signals such as vibration and AE used in tool condition monitoring.

6.2 Signal decomposition

The wavelet analysis decomposes the signal into scaled and translated version of a base wavelet, $\psi(t)$ [41]. The wavelet transform can be represented in CWT and DWT. The continuous wavelet transform of a signal, $x(t)$ can be expressed as,

$wt\left({s,\tau}\right)=\frac{1}{\sqrt{s}}\int\limits_{-\infty}^{\infty}{x% \left(t\right)}\,\psi^{\ast}\left({\frac{t-\tau}{s}}\right)\;dt$ (1)

Figure 4.

DWT Signal decomposition process.

Where $s>0$ represents the scaling parameter. ‘ $\tau$ ’, represents the shifting parameter and ‘ $\psi^{*}(.)$ ’ is the complex conjugate of $\psi(t)$ . The scaling parameter determines the time and frequency resolutions of the scaled base wavelet, $\psi(\frac{t-\tau}{s})$ . The shifting parameter translates the scaled wavelet along the time axis. In CWT, it is hard to calculate the wavelet coefficients as a continuous function of scale parameter and translation parameter. It results in more computation time, increase in memory size and redundant information. To surmount the drawback of the CWT, the scale and translation parameters are discretised as DWT. The discretisation is expressed as; $=s^{j}_{0}$ ; $\tau=k\tau_{0}s^{j}_{0}$ , where $s_{0}<1$ , $\tau_{0}\neq 0$ , $j\in Z$ , $k\in Z$ . The symbol ‘ $Z$ ’ denotes an integer. In the various form of wavelet discretisation, the discretisation with $s_{0}=2$ and $\tau_{0}=1$ has been widely used [42]. The discrete wavelet transform of the signal $x(t)$ can be expressed as,

$\displaystyle wt\left({j,k}\right)=\left({x\left(t\right),\psi_{j,k}\left(t% \right)}\right)=\frac{1}{\sqrt{2^{j}}}\int\limits_{-\infty}^{\infty}{x\left(t% \right)}\,\psi^{\ast}\left({\frac{t-k2^{j}}{2^{j}}}\right)\;dt$ (2)

The DWT decompose the signal $x(t)$ into a series of wavelet coefficients. The wavelet coefficients $wt(j,k)$ represent the amplitudes of the contributing wavelets. The hierarchically structured decomposition produced in wavelet analysis is called multi-level wavelet decomposition.

DWT of the signal is determined by passing it through series of high pass and low pass filters for the signal decomposition. The DWT signal decomposition process is shown in Fig. 4. In the decomposition process, the input signal $X[n]$ is first passed through the high pass filter and low pass filter. In the Fig. 4, $G[n]$ and $H[n]$ represent the low-pass and high-pass filter respectively. The outputs of both high pass and low pass filters are decimated by a factor of 2. The high pass filtered data set is the detail coefficients at level 1 and the low pass filtered data set is the approximation coefficients at level 1. This decomposition is repeated at level 2, 3, 4, etc., to further improve the frequency resolution of the signal. In this study the wavelet decomposition level of 8 is used to extract the wavelet features.

Variety of base wavelets and their families were proposed by the researchers in diverse areas of signature processing over the years. The wavelets vary in terms of a) symmetry, b) regularities, c) vanishing moments and d) length. In each wavelet family, there are many child wavelets. The child wavelets are differentiated based on their coefficients. The commonly used wavelets for performing DWT are haar wavelet, daubechies wavelet, coiflet wavelet, symlet wavelet, Meyer wavelet, biorthogonal and reverse-biorthogonal wavelet. Detailed description of wavelets and its application is presented in [43]. The wavelets are selected based on the criteria; a) the wavelet that extracts large amount of energy from the signal, b) The wavelet that minimizes the Shannon entropy of the wavelet coefficients, and c) the wavelet that has produced the maximum energy to Shannon entropy ratio should be chosen as the most appropriate wavelet.

Figure 5.

Wavelet decomposition process for the acoustic emission signal using db11 wavelet.

The wavelet energy, entropy and energy to entropy ratio is used as a feature for machine learning based fault diagnosis [44]. The total energy of wavelet may be defined as the sum of square of detailed wavelet coefficients. The wavelet energy coefficients $c(t)$ for the signal ‘ $s(t)$ ’ can be defined as; $E(s(t))=\sum_{j=1}^{N}{a_{j}}c_{j}^{2}$ , with suitable scaling coefficient ‘ $a_{j}$ ’ for the coefficient ‘ $c_{j}$ ’ found from the corresponding signal ‘ $s(t)$ ’. Wavelet entropy is an important measure to determine the information available in the vibration and AE signals associated with the metal cutting process. Shannon entropy is one of the significant measures for investigating and comparing the probability distributions of the process. The shannon entropy is defines as $E(s)=\sum_{i}s_{i}^{2}\log(s_{i}^{2})$ , where, ‘ $s_{i}$ ’ represents the coefficient of the signal ‘s’ in orthonormal basis. A combination of energy and shannon entropy content of the signal’s coefficient is expressed as energy to entropy ratio is also an important measure used as a feature for defect classification. In this study, daubechies wavelet, haar wavelet, biorthogonal and reverse biorthogonal wavelets are used for tool condition classification. Among these wavelets, haar is a single wavelet with no child wavelet and the remaining wavelets contain child wavelets.

6.3 Extraction of wavelet coefficients

Wavelet coefficients were extracted using mother wavelets of haar, daubechies, biorthogonal and reverse biorthogonal wavelets. These wavelets are used in tool condition classification. In bi-orthogonal wavelet family, child wavelets, bior3.9, bior4.4 and bior5.5 are considered. In the daubechies family, child wavelets, db11, db12, db13 and db14 wavelets are considered. Child wavelets of rbio4.4, rbio5.5 and rbio6.8 are considered from the family of reversed bi-orthogonal wavelet family. The vibration and acoustic emission signals are decomposed by discrete wavelet transform.

Daubechies [45] proposed the daubechies wavelets, which are not symmetric and compactly orthogonal. These wavelets are “a family of orthogonal wavelets defining a DWT transform and distinguished by a maximal number of vanishing moments for some given support”. The most frequently used wavelets in this family are db2, db3, …, db20. For an instance, db4 represents polynomial with two coefficients and four vanishing moments. In this study, coefficients of db11, db12, db13 and db14 are considered for tool condition classification.

The Haar wavelet is helpful when the signals are with sudden transition. Haar is the simplest possible wavelet, which are not continuous and differentiable. The wavelet is square-shaped and is symmetrical and compactly orthogonal with number of vanishing moments as 1. Reverse-biorthogonal wavelets are symmetric, and having arbitrary no. of vanishing moments and they are not orthogonal. Three reverse bi-orthogonal child wavelets such rbio4.4, rbio5.5 and rbio6.8 are considered in this study. Discrete wavelet transforms of vibration and AE signals using these wavelets results in the wavelet coefficients at various levels of decomposition.

Eight levels of decomposition of the vibration and AE signature were carried out in this study. As an example, decomposition of db11 wavelet for AE signature is shown in the Fig. 5. In the figure, ‘s’ represents the acoustic emission signal, ‘ $d_{1}$ ’ to ‘ $d_{8}$ ’ represents the detailed wavelet coefficients and ‘ $a_{8}$ ’ represents the approximated wavelet coefficients at wavelet decomposition level ‘8’. The eight detailed coefficients are designated as ‘a’ to ‘h’ and approximated coefficient designated as ‘i’. These nine wavelet features ‘a’ to ‘i’ were used in machine learning process. These coefficients refer to different conditions of the tool. Similar to this for all the eleven wavelets considered in this study, the signals of vibration and AE are subjected to wavelet decomposition and respective coefficients were obtained. Wavelet features are extracted from the coefficients and are fed into machine learning algorithms for tool condition classification.

7. Tool condition classification using machine learning algorithms

In this study, machine learning algorithms namely decision trees, naive bayes, SVM and ANN are used for classifying the tool conditions by training the algorithm using the wavelet coefficients acquired from the vibration and AE signature.

Table 1
Confusion matrix for a 3-class problem

		Predicted class
		Class A	Class B	Class C
		(Good tool)	(Tool at middle of its life)	(Worn-out tool)
Actual class	Class A (Good tool)	$F_{aa}$	$F_{ab}$	F ${}_{ac}$
	Class B (Tool at middle of its life)	$F_{ba}$	$F_{bb}$	$F_{bc}$
	Class C (Worn-out tool)	$F_{ca}$	$F_{cb}$	$F_{cc}$

Figure 6.

Decision tree of bior3.9 wavelet.

7.1 Performance evaluation of machine learning algorithms

Performance evaluation of a machine learning algorithm is based on the counts of test records correctly and incorrectly predicted by the model. These counts are tabulated and called as confusion matrix. Table 1 depicts the confusion matrix for a three class classification problem. Each entry ‘ $F_{ij}$ ’ in this table denotes the number of records from ‘class i’ predicted to be of the ‘class j’. For instance, ‘ $F_{ba}$ ’ is the number of records from ‘class B’ is incorrectly predicted as ‘class A’. The total number of correct predictions made by the classifier is ‘ $F_{aa}+F_{bb}+F_{cc}$ ’. The total number of incorrect predictions made by the classifier is ‘ $F_{ab}+F_{ba}+F_{ac}+F_{cb}+F_{bc}+F_{ca}$ ’.

Confusion matrix provides the information needed to decide how well a classification model is performing. Summarizing this information with a single number would be more suitable to evaluate the performance of different algorithms. This can be done using the performance metric such as accuracy, error rate and kappa metrics [46]. In this study, machine learning algorithms are compared based on accuracy of classification, error rate and kappa metrics.

The kappa statistic can be found by using the observed accuracy and expected accuracy. Observed accuracy is the no. of instances that were classified correctly throughout the entire confusion matrix and expected accuracy is directly related to the no. of instances of each class, along with the no. of instances that the machine learning classifier agreed with the ground truth label. For evaluating the performance of the classifier, Landis and Koch [46], consider kappa value, 0–0.20 as poor agreement, 0.21–0.40 as fair agreement, 0.41–0.60 as moderate agreement, 0.61–0.80 as substantial good agreement, and 0.81–1 as almost perfect and very good classifier for the problem considered. Kappa statistics “indicates the extent to which the observed probability of agreement is in excess of the probability of agreement hypothetically expected under the baseline constraint”. Kappa statistics are also equivalent to the correlation-coefficient obtained from analysis of variance and can be used to measure the performance of the classifier.

$\displaystyle\text{Accuracy}=\frac{\text{Number of correct predictions}}{\text% {Total number of predictions}}=$ (3)

$\displaystyle\text{Error rate}=\frac{\text{Number of in-Correct predictions}}{% \text{Total number of predictions}}=$ (4)

$\displaystyle\text{kappa}\!=\!\frac{\text{(Observed accuracy \!--\! Expected % accuracy)}}{(1-\text{Expected accuracy)}}$

7.2 Tool condition classification using decision tree algorithm

Decision tree c4.5 algorithm introduced by Quinlan [47] is one of the widely used algorithms to generate decision tree. Decision trees are non-parametric and supervised learning algorithm represents the information in the signal in the form of a tree. The classification is carried out through the decision tree with its leaves representing the different conditions of the tool using the concept of information entropy. The sequential branching process ending up with the leaves is based on conditional probabilities associated with individual coefficients of the wavelets. Decision trees are simple and easy to implement. The training data is a set of already classified samples. Each sample consists of ‘p’ dimensional vector representing attributes or features of the sample and as well as class in which it falls. At each node of the tree, c4.5 algorithms choose the attribute of the data that most effectively split the set of samples into subsets enriched in one class or the other. The splitting criterion used in c4.5 algorithm is the normalized information gain, i.e., the difference in entropy. The feature with the utmost information gain is chosen to make the judgment. The algorithm then persists on the smaller sub lists. This algorithm has fewer base cases. When all the samples in the list belong to the same class, the algorithm creates a leaf node of the decision tree saying to choose that class. If none of the feature provides any information gain, the algorithm generates a decision node higher up the tree by means of the expected value of the class. Same procedure is repeated in the case of algorithm find any previously unseen data. Kotsiantis et al. [48], reviewed the classification techniques using machine learning approaches.

Table 2
Confusion matrix for bior3.3 wavelet for AE data

	Predicted class (No. of samples)
		Class A	Class B	Class C	Classification	Accuracy,
					overall, nos.	%
Actual class	Class A	80	12	8	100	80
	Class B	20	79	1	100	79
	Class C	5	2	93	100	93
	Classification-overall	105	93	102	300	–
	Accuracy, %	76.19	84.94	91.18
Overall accuracy, %		84.0

Note: Class A: Tool at good condition; Class B: Tool at its middle of its life; Class C: Tool at worn-out condition.

Table 3

Performance of decision tree algorithm using wavelet coefficients for vibration and AE data

Mother wavelet	Child wavelet	Vibration data		AE data
		Classification	Kappa	Classification	Kappa
		efficiency, %	statistics	efficiency, %	statistics
Daubechies wavelet	db11	75.56	0.633	86.00	0.790
	db12	71.11	0.567	85.67	0.785
	db13	81.48	0.722	85.00	0.775
	db14	75.56	0.633	84.33	0.765
Haar wavelet	–	94.07	0.911	72.67	0.590
Bi-orthogonal wavelet	bior 3.9	88.89	0.833	84.00	0.760
	bior 4.4	77.79	0.667	88.33	0.825
	bior 5.5	72.59	0.589	84.33	0.765
Reversed bi-orthogonal wavelet	rbio 4.4	82.96	0.744	86.67	0.800
	rbio 5.5	86.67	0.800	84.33	0.765
	rbio 6.8	75.56	0.633	85.67	0.785

The extracted wavelet features from the vibration and AE signal are used to classify the tool condition using decision tree classifier. Decision trees were built using the c4.5 algorithm. Decision tree built by the c4.5 algorithm for a child wavelet (bior3.9) of bi-orthogonal wavelet is shown in the Fig. 6. The root nodes ‘b’, ‘r’, ‘e’, ‘c’ and ‘g’ represent the signal decomposition levels. In the similar manner decision trees were built for all the 11 wavelets considered in this study using vibration and AE data.

Performance evaluation of algorithms are based on the number of test cases appropriately and wrongly classified by the model. These classification details are tabulated in the form of confusion matrix. Confusion matrix for the tool condition classification problem (3 conditions) for bior3.3 wavelet for AE data is shown in Table 2.

In the confusion matrix, ‘Class A’, ‘Class B’, and ‘Class C’ indicate the tool at good condition, at middle of its life and worn out stage respectively. Out of 300 data points presented to the decision tree 120 were correctly classified and 15 were misclassified. The classification efficiency (accuracy) is 88.89%. The error rate is 11.11%. The kappa metric is found to be 0.819. Similar manner, performance statistics are calculated for all wavelets using the decision tree algorithm with the help of confusion matrix.

Table 4

Classification efficiencies of naive bayes for wavelets using vibration and AE data

Mother wavelet	Child wavelet	Vibration data		AE data
		Classification	Kappa	Classification	Kappa
		efficiency, %	statistics	efficiency, %	statistics
Daubechies wavelet	db11	71.85	0.578	77.00	0.655
	db12	68.15	0.522	76.67	0.650
	db13	65.93	0.489	75.00	0.625
	db14	65.19	0.478	74.67	0.620
Haar wavelet	–	91.85	0.878	74.67	0.620
Bi-orthogonal wavelet	bior 3.9	83.70	0.756	76.00	0.640
	bior 4.4	80.00	0.700	79.33	0.690
	bior 5.5	72.59	0.589	78.00	0.670
Reversed bi-orthogonal wavelet	rbio 4.4	82.22	0.733	79.67	0.695
	rbio 5.5	82.22	0.733	79.33	0.690
	rbio 6.8	72.59	0.589	76.00	0.640

Table 5

Classification efficiencies of ANN for wavelets using vibration and AE data

Mother wavelet	Child wavelet	Vibration data		AE data
		Classification	Kappa	Classification	Kappa
		efficiency, %	statistics	efficiency, %	statistics
Daubechies wavelet	db11	94.07	0.911	90.67	0.860
	db12	97.04	0.955	89.33	0.840
	db13	95.55	0.933	88.67	0.830
	db14	96.30	0.944	89.00	0.833
Haar wavelet	–	85.93	0.789	79.33	0.690
Bi-orthogonal wavelet	bior 3.9	94.81	0.922	84.67	0.770
	bior 4.4	92.59	0.889	87.00	0.805
	bior 5.5	93.33	0.900	90.33	0.855
Reversed bi-orthogonal wavelet	rbio 4.4	88.89	0.833	89.33	0.840
	rbio 5.5	94.07	0.911	88.33	0.825
	rbio 6.8	97.78	0.966	86.33	0.795

The classification efficiency and kappa statistics for decision tree algorithm using vibration and AE signatures for the wavelets are presented in the Table 3. Results show that, haar wavelet is producing a classification efficiency of 94.07% with a kappa value of 0.911 for the vibration data. The performance of algorithms for AE data is consistent for all the wavelets. Using reversed bi-orthogonal wavelet, decision tree is producing a classification efficiency of 87.67% with kappa value of 0.80.

7.3 Classification of tool conditions using naive bayes algorithm

Naive bayes algorithm is working on the basis of bayes theorem and presumes that the presence of a feature in a class is not related to the existence of any other feature [49]. Using bayes theorem, posterior probabilities $P(c|x)$ are computed from $P(c)$ , $P(x)$ and $P(x|c)$ . The posterior probability, $P(c|x)=\frac{P(x|c)P(c)}{P(x)}$ , where, $P(c)$ is the prior probability of the class, $P(x|c)$ is the likelihood which is the probability of predictor in the given class and $P(x)$ is the prior probability of the predictor.

The posterior probability is expanded as,

$\displaystyle P(c|x)=P(x_{1}|c)\times P(x_{2}|c)\times\ldots\times\ P(x_{n}|c)% \times P(c),$ (6)

Where, $x_{1}$ , $x_{2}$ , …, $x_{n}$ are the attributes for the given target ‘c’. The naive bayes is proved to be fast in predicting the class of test data and also performs well for a multi-class classification problem.

The extracted wavelet coefficients from bi-orthog-onal (bior3.9, bior4.4, and bior5.5), daubechies (db11, db12, db13 and db14), haar and reverse bi-orthogonal (rbio4.4, rbio5.5 and rbio6.8) wavelets are used to classify the tool condition using naive bayes classifier. A total of 300 test cases are presented to the algorithm for classification. Classification efficiencies of naive bayes for wavelets using vibration and AE data are presented in the Table 4. The results indicate similar performance of naive bayes for vibration and AE data. Haar wavelet is appears to be performing well with a classification efficiency of 91.85% with a kappa value of 0.878 for vibration data.

7.4 Classification of tool conditions using ANN

Table 6
Performance of SVM algorithm using wavelet coefficients for vibration and AE data

Mother wavelet	Child wavelet	Vibration data		AE data
		Classification	Kappa	Classification	Kappa
		efficiency, %	statistics	efficiency, %	statistics
Daubechies wavelet	db11	93.33	0.900	89.67	0.845
	db12	98.52	0.978	88.00	0.820
	db13	93.33	0.900	89.00	0.835
	db14	99.26	0.989	89.67	0.845
Haar wavelet	–	94.07	0.911	84.33	0.765
Bi-orthogonal wavelet	bior 3.9	95.56	0.933	83.67	0.755
	bior 4.4	91.85	0.878	90.00	0.850
	bior 5.5	95.56	0.933	90.00	0.850
Reversed bi-orthogonal wavelet	rbio 4.4	94.07	0.911	89.33	0.840
	rbio 5.5	96.56	0.933	89.67	0.845
	rbio 6.8	98.52	0.978	90.00	0.850

Computation in ANN is carried out in a distributed manner using the inter-connected processing elements called neurons which operate in parallel. No. of neurons and no. of layers of the neurons may vary depends on the type of problem. Neural network get the knowledge by training by mapping the known input vector and output. More details about the ANN and its working are found in [50]. For problems like, tool condition prediction, supervised learning NN is used. In supervised learning, back propagation NN and feed forward NN are used in this study. A feed forward back propagation neural network is trained with back-propagation training algorithm. In back propagation algorithm, error signal is obtained by subtracting the trained output with the desired value. The error signal is sent back to adjust the weights in the input and hidden layers to reduce the error. Once the network is trained, is used for predicting.

Features extracted from the wavelet coefficients considered in this study are given as an input to ANN. Feed forward back propagation type network is selected with 10 hidden neurons. The network is simulated for different wavelet coefficients. The artificial neural network model is simulated using all the eleven wavelets considered in this study. Tenfold cross validation is performed. To study the performance of ANN, 300 data points are presented to ANN. The output of ANN is recorded in the form confusion matrix. Classification efficiency of ANN with respect to the wavelets are tabulated and shown in the Table 5. Classification performance of ANN is good in comparison with decision trees and naive bayes algorithms. ANN performance is found to be good using daubechies, bi-orthogonal and reverse bi-orthogal wavelets for vibration data in comparison with AE data.

7.5 Tool condition classification using SVM

SVM is based on statistical learning theory and is originally proposed by Cortes and Vapnik [51]. SVM belongs to a class of supervised learning algorithm which constructs an optimal hyper plane for linearly separable patterns to classify the data into different categories. It extends to patterns that are not linearly separable by transformations of original data to map into new space with the help of kernel functions. SVM uses kernel functions like linear, polynomial, sigmoid, radial basis function, etc, to convert the data from linearly non separable domain to a linearly separable domain. Two variants of SVM such as c-SVC and $\gamma$ -SVC were studied with different kernel functions for the AE and vibration data. The formulation of C-SVC and $\gamma$ -SVC are detailed in Chang and Lin [52].

Two variants of SVM models such as c-SVC, and $\gamma$ -SVC were tried with different kernel functions with an objective of maximizing the classification efficiency. In $\gamma$ -SVM a parameter ‘ $\gamma$ ’ is introduced with an objective of optimizing the number of support vectors to reduce the training errors. Tenfold cross validation is performed in this study. It is found the c-SVC type of SVM with radial basic kernel function is producing better performance over $\gamma$ -SVC type of SVM. SVM model of c-SVC type is chosen for further studies by using vibration and AE data.

The extracted wavelet features from bi-orthogonal (bior3.9, bior4.4, and bior5.5), daubechies (db11, db12, db13 and db14), haar and reverse bi-orthogonal (rbio4.4, rbio5.5 and rbio6.8) wavelets are used to classify the tool condition using c-SVM classifier. The classification efficiency of SVM is computed by using the confusion matrix. The performance of SVM is shown in Table 6. By comparing the vibration and AE approaches using SVM, vibration based approach is found to be superior in terms of tool condition classification. Almost all the wavelets are producing consistent and good quality results using vibration data.

8. Summary of results

Performance of machine learning algorithms using vibration and AE data were studied based on classification efficiency and kappa statistics. For every wavelet, the performance of the algorithm using vibration data and AE data is studied and presented in the Figs 7 and 8 respectively using kappa statistics. Kappa statistics are comparable to the correlation-coefficient obtained from analysis of variance and can be used to measure the performance of the machine learning algorithms. Landis and Koch [46] classified the algorithms based on kappa value; 0–0.20 as poor agreement, 0.21–0.40 as fair agreement, 0.41–0.60 as moderate agreement, 0.61–0.80 as substantial good agreement, and 0.81–1 as almost perfect very good classifier.

Figure 7.

Performance of machine learning algorithms using vibration data.

Figure 8.

Performance of machine learning algorithms using AE data.

Decision tree algorithm using haar wavelet for the vibration data is appears to be a perfect classifier with a kappa value of 0.911 with a classification efficiency of 94.07%. Again the haar wavelet for vibration data is able to classify the tool conditions with a classification efficiency of 91.85% with a kappa value of 0.878. Except harr wavelet, ANN has good agreement for vibration and AE data. Overall, ANN is classifying the tool conditions with better classification efficiency than the AE data.

SVM is predicting with greater accuracy using vibration data irrespective of type of wavelet considered in this study. SVM is able to predict the tool conditions with an accuracy of more than 90% using vibration data for all the wavelets conceded in this study. This shows the robustness of SVM in tool condition classification. The performance of SVM for AE is not as good as using vibration data. But AE is also predicting the tool conditions with good accuracy for daubechies and orthogonal wavelets using SVM.

In summary, it is observed that SVM algorithm is comparatively performing better for the wavelet features of vibration data than the wavelet features of AE data compared with c4.5 decision tree, naive bayes and ANN. This may be because AE produces bust signals during rupture of tool tip and the signals produced during continuous wear are not very transient. Wavelets have the ability to capture the transients in the signal. Wavelets extracted from vibration signals are able to help the SVM algorithm to attain good tool condition classification efficiency. Using daubechies-db14 wavelet, SVM is predicting the tool condition with a classification efficiency of 99.26% with a kappa value of 0.989. The performance of ANN is good for vibration data. Decision tree and naive bayes are producing good classification accuracy using haar wavelet.

The computational time required by the algorithms for processing the time domain vibration and AE data were studied. All the classifies were allowed to run in the Intel i3 processor with 4 GB of internal memory. For extracting wavelets features from the raw time series data takes 12 seconds using the Matlab application package for the vibration data. Extracting wavelet features takes 15 seconds from the AE signature. After extracting the features, classifiers are used for training and prediction of the machine tool conditions. For vibration features, SVM takes a minimum of 10 sec and a maximum of 12 seconds for various types of wavelets considered in this study. Using the AE features SVM takes minimum of 20 seconds and maximum of 25 seconds for classification. ANN classifier with vibration data takes an average of 31 seconds for training and classification. Using AE data, an average of 35 seconds required for training and classification. Naïve bayes classifier seems to be relatively faster compared to SVM and ANN. It takes 10 seconds for vibration data and 20 seconds for AE data for wavelet features considered in this study.

9. Conclusion

In this study, time domain vibration and acoustic emission signatures during high speed machining of titanium alloy are captured by conducting experiments under optimum machining conditions. Different stages of tool conditions such as good, tool at middle of its life and worn-out tool were considered based on flank wear criteria. Wavelet features were extracted from wavelet families of haar, daubechies, bi-orthogonal and reverse biorthogonal wavelets by performing discrete wavelet transforms. Wavelet features are provided as an input to machine learning algorithms for tool condition classification. The performances of the decision tree, naive bayes, SVM and ANN are evaluated based on the classification efficiency and kappa statistics using confusion matrix. The performance of SVM is consistent and producing good quality results for all the wavelets used in this study using vibration data. SVM is predicting the tool condition with a classification efficiency of 99.26% with a kappa value of 0.989 for daubechies-db14 wavelet. ANN appears to be the second best performing algorithm considered in this study. Decision tree and naive bayes are producing good classification accuracy using haar wavelet. From the results, it appears that SVM algorithm using wavelet coefficients extracted from the vibration data are classifying the tool conditions better than the AE data during high speed machining of titanium alloys. These finding will be useful for developing an intelligent on-line tool condition monitoring system in the automated machining environment.

Footnotes

Acknowledgments

This research is supported by Directorate of Extramural Research and Intellectual Property Rights (ER & IPR), Defense Research and Development Organization (DRDO), ERIP/ER/0803740/M/01/1194, 13.1. 2010.

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Machine learning based tool condition classification using acoustic emission and vibration data in high speed milling process using wavelet features

Abstract

Keywords

1. Introduction

2. Sensors for tool condition monitoring

2.1 Vibration and acoustic emission based sensors for tool condition monitoring

4. Tool condition classification using machine learning algorithms

5.1 Methodology and objective

6.1 Introduction

6.2 Signal decomposition

7. Tool condition classification using machine learning algorithms

Table 1 Confusion matrix for a 3-class problem

Table 2 Confusion matrix for bior3.3 wavelet for AE data

Table 6 Performance of SVM algorithm using wavelet coefficients for vibration and AE data

8. Summary of results

Footnotes

Acknowledgments

References

Table 1
Confusion matrix for a 3-class problem

Table 2
Confusion matrix for bior3.3 wavelet for AE data

Table 6
Performance of SVM algorithm using wavelet coefficients for vibration and AE data