# Intelligent Turning Tool Monitoring with Neural Network Adaptive Learning

Authors: Maohua Du; Peixin Wang; Junhua Wang; Zheng Cheng; Shensong Wang
Journal: Complexity
 (2019)

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## Abstract

Tool state monitoring is a key technology in intelligent manufacturing. But it is still in a research stage and lacks general adaptability for different machining conditions. To overcome this limitation, this work systematically investigates an intelligent, real-time, and visible tool state monitoring through adopting integrated theories and technologies, i.e., (a) through distinctively designed experimental technique with comprehensive consideration of cutting parameters and tool wear values as variables, (b) through bisensor fusion for simultaneous measurements of low and high frequency signals, (c) through multitheory fusion of wavelet decomposition and the Relief-F algorithm for performing dual feature extraction and feature dimension reduction to achieve more accurate state identification using neural network, and (d) through an innovative programming technique of MATLAB-nested labVIEW. This tool monitoring system has neural network adaptive learning ability with the change of the experimental sample signals which are collected simultaneously by selected vibration and acoustic emission (AE) sensors inall factors turning experiments. Based on LabVIEW and MATLAB hybrid programming, the waveforms of signals are observed and the significant characteristics of signals are extracted through the time-frequency domain analysis and then the calculation of the energy proportion of each frequency band obtained using 4 levels of wavelet packet decompositions of the vibration signal as well as 8 levels of wavelet multiresolution decompositions of the AE signal; the ensuing Relief-F algorithm is used to further reextract the features that are most relevant to the tool state as input of neural network pattern recognition. Through the BP neural network adaptive learning, tool state recognition model is finally established. The results show that the correct recognition rate of BP network model after samples training is 92.59%, which can more accurately and intelligently monitor the tool wear state.


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## Body

## 1. Introduction

Tool condition monitoring is an indispensable technology in manufacturing automation and intelligence. The real-time monitoring of cutting tools can not only improve the quality of products and reduce production costs, but also reduce the downtime of machining centers and increase productivity.Over the years, researchers have done a lot of work on tool condition monitoring and put forward many monitoring methods, which can be classified into two major categories: direct and indirect methods.Direct methods [1, 2] are measurements of the cutting tool wear using optical, radioactive, electrical resistance sensors, etc. This kind of method directly measures the actual geometric parameters of the cutting tool [3], and the results are intuitive and reliable, and the measuring accuracy is high. However, the cutting zone is generally inaccessible during the cutting processes due to the continuous contact between the cutting tool and the workpiece, so it is impossible to realize online monitoring; and the sudden breakage of the cutting edge is unable to be monitored; and it is not feasible in the case of coolant. Hence it has limitations in practical applications.Indirect method is a new developed technology on the basis of modern sensors, signal analysis, and pattern recognition. It monitors tool wear through analyzing and processing measured physical signals in cutting processes. It is characterized by real-time performance, versatility, convenient installation, and low cost, so it is much easier to be employed in practice. In general, indirect tool condition monitoring system consists of sensors, the signal conditioner or amplifier, and the monitor. Sensors are very important elements which must monitor the target location (near the tip of the tool) as close as possible. Then the received signals by sensors are processed to get useful information. A monitor is a display unit for analyzing signals. The indirect state monitoring system usually consists of four parts: signal acquisition, signal processing, and feature extraction and pattern recognition. Figure1 shows the framework of tool monitoring system.Figure 1
The framework of the tool monitoring system.Indirect methods have been investigated by many researchers. The commonly monitored parameters with the change of tool include the cutting force, feed and spindle motor currents, vibration signal, acoustic emission (AE) signal, temperature, and surface roughness.Dimla and Lister [4] developed an online tool wear monitoring system. They used tool dynamometer to measure three vertical components of the cutting force and the tool wear state monitoring was studied through the analyses of time series and fast Fourier transform (FFT) of the signals. The results showed that the cutting force was mainly determined by the cutting conditions, especially the depth of cut and the feed rate; and the vertical component of cutting force and vibration characteristics (z direction) were most sensitive to tool wear. Ghasempoor et al. [5] experimentally verified the feasibility of the online tool state monitoring system by using different cutting force components. They correlated the cutting force components with the tool wear and observed that these parameters were very sensitive to the change of the cutting conditions. However, the prediction of the wear of the crescent tooth was not very accurate, and the possible reason was that the wear of the tool rake face had the counteraction on the component cutting forces. Sikdar and Chen [6] studied the relationship between the wear area of the tool flank and the cutting force in the cutting process. The experimental results showed that the cutting force gradually increased with the increase of the wear area of the tool flank. Nouri et al. [7] described a new method to monitor end milling tool wear in real-time by tracking force model coefficients during the cutting process. The behaviors of these coefficients were shown to be independent from the cutting conditions and correlated with the wear state of the cutting tool. Wang et al. [8] took milling force as the monitoring signal, and wavelet packet theory was used to analyze and extract the energy feature of the signal as a basis for diagnosis and then the Continuous Hidden Markov Model (CHMM) was used to diagnose tool wear state. The results indicated that CHMM tool condition monitoring required less training samples and produced results quickly. However, the diagnostic accuracy seemed obscure due to the lack of contrast between experimental and diagnostic results.Li et al. [9] presented that the feed cutting force estimation using the current from servo motor was applied to monitor the tool wear in turning. However, whether the feed force component could represent the influence of overall cutting physical parameters on tool wear still needs to be proved.Many researchers studied the tool state monitoring by analyzing the generated vibration in machining operations. Teti et al. [10] classified the vibration during metal cutting process as free vibration and forced vibration. The two groups are not mutually exclusive. Free vibration independent of metal cutting contains forced vibration caused by other machines or machine components, for example, vibration transmitted through foundations, unbalance of rotating parts, inertia forces of reciprocating parts, and kinematic inaccuracies of drives.Abouelatta and Madl [11] established the mapping relation between the surface roughness of the workpiece and the vibration by using the vibration signal. The surface roughness was measured using the Surtronic 3+ measuring instrument and the tool vibrations in radial and feed directions were measured by the FFT analyzer. It was found that the tool wear and the surface roughness could be predicted more accurately by the vibration model. Alonso and Salgado [12] developed a tool state monitoring system based on the tool vibration signal by using the singular spectrum analysis (SSA) and cluster analysis. SSA is a nonparametric technique of time series analysis. The sampled vibration signals can be decomposed into a group of time series, and the clustering analysis is used for grouping the time series of SSA decomposition to obtain several independent components in the frequency domain. The results showed that using SSA and clustering analysis to process signals could achieve more reliable results in the development of tool condition monitoring system.During the metal cutting process, the plastic deformation occurs when the tool cuts into the workpiece. Due to the plastic deformation, transient elastic stress waves are generated inside the material, which quickly releases strain energy from one or more local sources. The released energy is usually called acoustic emission (AE). Li [13] described that AE was one of the most effective methods to monitor tool wear. The main advantage of using AE to monitor tool state is that the frequency range of AE signal is much higher than that of the machine vibrations and environmental noises, and it does not interfere with the cutting process. Kakade et al. [14] predicted the tool wear and chip shape in the milling process through the analysis of AE signal. The tool flank wear and AE signal parameters were measured at the fixed distance interval of the tool pass and the chips were collected at the same time. The results indicated that the AE signal clearly demarcated the cutting action between sharp and worn-out tool and that signal features including ring down counts, rising time, and event duration were capable of reflecting the tool wears.It is normal and inevitable to generate heat in metal cutting process. The high temperature around the tip of the cutting tool will speed up the damage of the tool. To some extent, the tool temperature determines the tool wear rate. Korkut et al. [15] established the regression analysis (RA) and artificial neural network (ANN) model to predict the tool state by monitoring the chip interface temperature, and the results were verified by experiments. It was found that the proposed model had good accuracy and was suitable for predicting tool state.Surface roughness is widely used in quality evaluation of machined products, which indirectly indicates tool condition. Cutting conditions have considerable influences on tool wear and surface roughness. Ozel and Karpat [16] used neural network modeling to predict surface roughness and tool flank wear in finish hard turning. The regression model was developed to obtain the specific parameters in the cutting process. The results showed that decrease of the feed rate resulted in better surface roughness but slightly faster tool wear, and the increase of cutting speed resulted in a significant increase of tool wear but better surface roughness; the increase of workpiece hardness resulted in better surface roughness but higher tool wear.Artificial neural network (ANN) is a mathematical model for information processing by simulating the human brain. It consists of several processing units similar to neurons. It memorizes knowledge and stores it in the network by training and learning samples. Because of high fault tolerance and adaptability, noise suppression, and data driving, neural network classifier has been adopted by some researchers. Balazinski et al. [17] established three models: feedforward backpropagation neural network, fuzzy clustering analysis, and fuzzy reasoning based on neural network by collecting the cutting force signals during the cutting process. The results showed that the three models estimated tool wear with almost the same precision. But the fuzzy clustering analysis method was somewhat difficult to be applied in practice because it had to analyze the dependence of tool wear on the cutting force and the training time of the neural network method was long. Silva et al. [18] utilized two neural networks and an expert system using Taylor’s tool life equation to classify the tool wear state; the classification accuracy results, however, were puzzling because of the missing Figures 16–18 and the simple linear regression analysis. The research of monitoring tool wear using classifier fusion by Kannatey-Asibu et al. [19] illustrated that the classifier fusion performance reached 99.7% when a penalty vote was applied on the weighting factor. However, whether the demonstrated technique using AE monitoring is suitable for low frequency signal monitoring or not, further research is still needed.By and large, the tool state monitoring technology is not mature enough due to the complexity of the relationship between the measured physical quantities by sensors and the tool state, and thus the establishment of the accurate relationship between them is still a hard problem to be solved when we intend to develop a practical tool state monitoring system to meet various machining processes and environments. Specifically, there exist the following main problems. (1) First is the adaptability of monitoring models. Most of the existing monitoring models are suitable for narrow cutting conditions, and the reliability and effectiveness under variable cutting conditions cannot be guaranteed. The metal cutting process is very complex and has a lot of randomness, and different machine tools, cutting tools, workpiece materials and cutting parameters will make the monitored signal characteristics different. Thus it is of great significance to establish a tool state monitoring system that can adapt to the changeable cutting conditions. (2) Second is sample acquisition problem. Sample acquisition in cutting is difficult and costly in some cases. A large number of cutting experiments will cause high costs. Therefore, it is essential to establish a model with self-learning ability and little dependence on training samples. (3) Third is the difficulty of developing the monitoring system based on new sensor and signal analysis technology. Tool state monitoring involves a variety of sensors and signal analysis techniques, and the selection of the suitable sensors and signal analysis methods have not been systematically studied.Hence, the aim of this study is to investigate a method of achieving a visual, intelligent, and real-time tool state monitoring that is universal and can be used in practice. The implementation of tool wear monitoring is divided into two major parts: experimental details, and design and implementation of tool monitoring functions. The contents include (1) using bisensor fusion to measure the signals (low frequency vibration signal and higher frequency AE signal) in the turning process; (2) being based on hybrid programming technique of LabVIEW and MATLAB, analyzing and processing the signals, and extracting the most relevant features that reflect the tool wear state by the use of dual methods, i.e., the combination of the wavelet theory with the Relief-F algorithm; (3) using the extracted features as training samples of the neural network and then establishing the recognition model of tool state, such that intelligent recognition of the tool state is accomplished.The designed structure of lathe tool wear monitoring system is shown in Figure2.Figure 2
Structural frame of tool condition monitoring.


## 2. Experimental Details

Table1 lists the instrumentation and specifications of the experiments in this work.Table 1
Experimental instrumentation and specifications.
Name Specifications Lathe CA6140 Workpiece material Aeronautical aluminum alloy 7050, Φ98×500mm bar Cutting tool Carbide tool YT15 Vibration sensor Accelerometers; DH112 (Denmark, B & K), frequency range 0.5-7KHz Vibration signal amplifier 2635 (Denmark, B & K) Data acquisition card NI9215(US, NI company), 16 bit resolution, sampled at a rate of up to 7 kHz for 100 MS/s Sensor 2 AE sensor PAC WD US Pre-amplifier PAC2/4/6 (US) Data acquisition card PCI-9846H (Taiwan), 16 bit resolution, 40MS/s


### 2.1. Selection of Experimental Parameters

In the turning process, there are many factors affecting the signals of the sensors, such as cutting parameters, tool parameters, the machine tools, degrees of the tool wear, and the machining environment. And so many factors will inevitably bring difficulties to the experimental design, so we need to analyze the specific machining environment and remove some minor factors.On the premise of some fixed factors, such as the machine tools, the workpiece material, and the cutting tool, the machining parameters are changeable according to the machining requirements. The value of the tool wear is also a variable in the cutting process. Because the experimental objective is to obtain the mapping relations between the tool wear and the vibration plus AE signals characteristics, so the experimental factors include the cutting speed, the feed rate, the depth of cut, and tool wear.According to the specifications of the machine tools, the experimental parameters are designed, as presented in Table2, which also takes into account three VB values of the tool flank wear corresponding to the indices of tool wear criterions: sharp tool stage (initial wear), normal working stage (normal wear), and worn out stage (severe wear), as listed in Table 3. For each of the experimental cutting conditions, the observations of the vibration and AE signals are made and recorded corresponding to the three wear states of the tool flank.Table 2
Experimental parameters and levels.
Level Cutting speedvc Feed ratef Depth of cutap Tool wear value (m/min) (mm/rev) (mm) VB(mm) 1 64.6 0.11 0.8 0 2 80 0.13 1.0 0.2 3 98.5 0.15 1.2 0.4Table 3
The stages of tool wear.
Tool wear sharp tool stage normal working stage worn out stage (initial wear) (normal wear) (severe wear) VB(mm) 0 0.2 0.4


### 2.2. All Factors Experimental Technique

The orthogonal test is a frequently used method in experimental design. It can greatly reduce the number of trials, the test time, and costs. But the orthogonal test is inappropriate for the modeling and recognition of the neural network since the amount of data is relatively small. Therefore, in this work, the experiments ofall factors combinations are conducted for obtaining the data of tool state monitoring. According to the test factors and levels designed in Table 2, there are four factors and each factor has three levels. Therefore, thefour factors-three levels comprise 34=81 groups of experiments.


### 2.3. Bisensors Installation and Tool Wear Measurement

The most common waveform data in condition monitoring are vibration signals and acoustic emissions [20]. In this work, two sensors, i.e. vibration acceleration sensor and AE sensor, are simultaneously selected for measuring the cutting tool signals. The advantages of selecting them lie in that both vibration and AE signals can sensitively reflect the tool state in real time and that they are suitable for monitoring different machining processes. Figure 3 illustrates the experimental installation of sensors in the turning process. Both the vibration and AE sensors have magnetic bases, which can be installed onto the tool shank magnetically. Two sensors are installed close to the cutting tool. The vibration and the AE sensors are placed in the vertical direction (Z axis) and the horizontal direction (Y axis) of the shank and used to measure vibration and AE signals, respectively.Figure 3
Sensors installation.Three prepared cutting tools for each wear state in the experiments, as shown in Figure4, are used to cut the workpiece so that the signal data of each tool state can be correspondingly collected by sensors, respectively. Hence each tool wear state corresponds to its own signal data and three tool wear modes (initial, normal, and severe wear) will not mix together. A tool microscope (with five million pixels) that can magnify 100 times is used to measure the tool wear, as shown in Figure 5. It can be connected with the computer, and the tool wear can be observed and measured on the computer screen, and the measurement photos can also be taken.Figure 4
Cutting tools of three different wear stages: (a) sharp tool; (b) normal working tool; (c) worn-out tool.
(a) (b) (c)Figure 5
Universal tool microscope.


### 2.4. Signal Acquisition Procedure

The data acquisition is a process of collecting and storing the experimentally measured sensor signals in the turning process, such that it provides reliable sample data for later state recognition.The flow chart of the signal acquisition procedure is illustrated in Figure6. In the machining process, the vibration sensor and AE sensor collect the original tool state signals, which are weak and need to be amplified, buffered, and filtered via the amplifiers and data acquisition cards, and then the signals are entered into the computer for storage.Figure 6
The flow chart of the signal acquisition.


## 2.1. Selection of Experimental Parameters

In the turning process, there are many factors affecting the signals of the sensors, such as cutting parameters, tool parameters, the machine tools, degrees of the tool wear, and the machining environment. And so many factors will inevitably bring difficulties to the experimental design, so we need to analyze the specific machining environment and remove some minor factors.On the premise of some fixed factors, such as the machine tools, the workpiece material, and the cutting tool, the machining parameters are changeable according to the machining requirements. The value of the tool wear is also a variable in the cutting process. Because the experimental objective is to obtain the mapping relations between the tool wear and the vibration plus AE signals characteristics, so the experimental factors include the cutting speed, the feed rate, the depth of cut, and tool wear.According to the specifications of the machine tools, the experimental parameters are designed, as presented in Table2, which also takes into account three VB values of the tool flank wear corresponding to the indices of tool wear criterions: sharp tool stage (initial wear), normal working stage (normal wear), and worn out stage (severe wear), as listed in Table 3. For each of the experimental cutting conditions, the observations of the vibration and AE signals are made and recorded corresponding to the three wear states of the tool flank.Table 2
Experimental parameters and levels.
Level Cutting speedvc Feed ratef Depth of cutap Tool wear value (m/min) (mm/rev) (mm) VB(mm) 1 64.6 0.11 0.8 0 2 80 0.13 1.0 0.2 3 98.5 0.15 1.2 0.4Table 3
The stages of tool wear.
Tool wear sharp tool stage normal working stage worn out stage (initial wear) (normal wear) (severe wear) VB(mm) 0 0.2 0.4


## 2.2. All Factors Experimental Technique

The orthogonal test is a frequently used method in experimental design. It can greatly reduce the number of trials, the test time, and costs. But the orthogonal test is inappropriate for the modeling and recognition of the neural network since the amount of data is relatively small. Therefore, in this work, the experiments ofall factors combinations are conducted for obtaining the data of tool state monitoring. According to the test factors and levels designed in Table 2, there are four factors and each factor has three levels. Therefore, thefour factors-three levels comprise 34=81 groups of experiments.


## 2.3. Bisensors Installation and Tool Wear Measurement

The most common waveform data in condition monitoring are vibration signals and acoustic emissions [20]. In this work, two sensors, i.e. vibration acceleration sensor and AE sensor, are simultaneously selected for measuring the cutting tool signals. The advantages of selecting them lie in that both vibration and AE signals can sensitively reflect the tool state in real time and that they are suitable for monitoring different machining processes. Figure 3 illustrates the experimental installation of sensors in the turning process. Both the vibration and AE sensors have magnetic bases, which can be installed onto the tool shank magnetically. Two sensors are installed close to the cutting tool. The vibration and the AE sensors are placed in the vertical direction (Z axis) and the horizontal direction (Y axis) of the shank and used to measure vibration and AE signals, respectively.Figure 3
Sensors installation.Three prepared cutting tools for each wear state in the experiments, as shown in Figure4, are used to cut the workpiece so that the signal data of each tool state can be correspondingly collected by sensors, respectively. Hence each tool wear state corresponds to its own signal data and three tool wear modes (initial, normal, and severe wear) will not mix together. A tool microscope (with five million pixels) that can magnify 100 times is used to measure the tool wear, as shown in Figure 5. It can be connected with the computer, and the tool wear can be observed and measured on the computer screen, and the measurement photos can also be taken.Figure 4
Cutting tools of three different wear stages: (a) sharp tool; (b) normal working tool; (c) worn-out tool.
(a) (b) (c)Figure 5
Universal tool microscope.


## 2.4. Signal Acquisition Procedure

The data acquisition is a process of collecting and storing the experimentally measured sensor signals in the turning process, such that it provides reliable sample data for later state recognition.The flow chart of the signal acquisition procedure is illustrated in Figure6. In the machining process, the vibration sensor and AE sensor collect the original tool state signals, which are weak and need to be amplified, buffered, and filtered via the amplifiers and data acquisition cards, and then the signals are entered into the computer for storage.Figure 6
The flow chart of the signal acquisition.


## 3. Tool Monitoring Functions and Implementation Methods

This tool monitoring design includes three functions: signal acquisition or reading, signal processing and feature extraction, and state recognition.


### 3.1. Signal Acquisition Function

The signal acquisition module in this work has the functions of signal display and storage, which is developed using the LabVIEW software. LabVIEW is a graphical programming language. The LabVIEW program is called virtual instrument (VI), which provides lots of graphical controls and functions used in the data analysis and processing in engineering fields. We devise desirable functions and drag graphical controls into the program diagram and then connect the wires according to the needs of programming, and finally the instrument functions and the parameters settings can be realized. LabVIEW also provides the interface with MATLAB, i.e., MATLAB Script. Using MATLAB programming for numerical calculation and analysis can greatly shorten the time of the system development and finish a completely automated test system. LabVIEW software has two human-machine interaction interfaces: the front panel and the rear panel. The front panel provides many graphical controls that are similar to the appearance of actual instruments. Graphical controls on the front panel are manipulated by using icons and wires on the rear panel.


### 3.2. Signal Analysis and Method Fusion of Dual Feature Extraction

In the metal cutting process, the original signals collected by the sensors contain a lot of noises and useless information. They cannot be used directly to identify the tool state and only the extracted characteristics are useful for the state recognition. The collected vibration and AE signals are dynamic signals. The signal components are very complex and the background noise comes from many sources, such as cutting environment, machining conditions, and material properties. There exist both stationary and nonstationary signals. The time domain analysis of signal can only represent time history of the signal amplitude characteristic, but cannot clearly reveal the frequency compositions of the signal. And the frequency domain analysis can represent the frequency structure of the signal and the amplitude of the frequency components, but cannot provide time information and judge the change of local signal with the time. The time-frequency analysis method can reflect the signal characteristics both in time domain and in frequency domain; that is, it can satisfy the requirements of nonstationary signal analysis and processing. Thus the time-frequency domain analysis is used based on the initial time domain analysis and frequency domain analysis.In this work, firstly, the time domain analysis mainly focuses on the time domain waveform display for observing the waveform change rules, and, secondly, some statistical eigenvalues (mean valuex-, variance σ2, and root mean square valueXrms) are calculated according to the sampling number of each signal through LabVIEW programming. The expressions of three statistical characteristics are presented in the following, respectively.(1)x-=1N∑i=1Nxi(2)σ2=1N∑i=1Nxi-x¯2(3)Xrms=1N∑i=1Nxi2wherexi is the collected signal data by the sensor; mean value x- indicates the constant component of a signal; variance σ2 describes the deviation from the mean value of a random signal; root mean square value Xrms describes the intensity of a random signal, i=1, 2,...N; and N is sample number.Figures7 and 8, respectively, show the typical time domain waveforms of the experimentally collected vibration and AE signals in different cutting tool wear stages (cutting speed 64.6m/min; feed rate 0.11mm/r; depth of cut 1.2mm). The abscissa is sampling time and the ordinate is the amplitude of the signal.Figure 7
Time domain waveforms of vibration signal: (a) machine idling; (b) initial tool wear; (c) normal tool wear; (d) severe tool wear.
(a) (b) (c) (d)Figure 8
Time domain waveforms of AE signal: (a) machine idling; (b) initial tool wear; (c) normal tool wear; (d) severe tool wear.
(a) (b) (c) (d)It can be seen from Figure9 that the frequency components of the vibration signal are not very rich, mainly ranging from 2 to 4 kHz. The signal energy in this frequency band varies noticeably in different wear stages and in other frequency bands it has no observable change. As can be seen from Figure 10, the AE signal contains rich frequency components, which mainly exist between the frequency band 0-50kHz and 100-150 kHz. The signal energies in these two frequency bands change obviously in different tool wear stages, and the energies keep almost unchanged in other frequency bands.Figure 9
Frequency domain waveforms of the vibration signal (amplified 100 times): (a) initial tool wear; (b) normal tool wear; (c) severe tool wear (cutting speed 64.6m/min; feed speed 0.11mm/r; depth of cut 1.2mm).
(a) (b) (c)Figure 10
Frequency domain waveforms of AE signal: (a) initial tool wear; (b) normal tool wear; (c) severe tool wear (cutting speed 64.6m/min; feed speed 0.11mm/r; depth of cut 1.2mm).
(a) (b) (c)We can see that, according to the time domain analysis and frequency domain analysis on Figures7–10, it is difficult to describe the characteristics of the tool state and to do the quantitative analysis. Thus further analysis is necessary.Due to the nature of manufacturing processes, the signals are usually nonstationary and the signal processing approaches that deal with nonstationary signals are more appropriate for process monitoring [3]. We have known that time-frequency analysis is usually used to analyze nonstationary signals which often have both high and low frequency components. And wavelet transform is one of the commonly used time-frequency analysis methods, because it has the zoom function and can adaptively adjust the time-frequency resolution of the signal according to the difference of decomposition scale. Wavelet analysis has good localization property in both time domain and frequency domain and permits adaptive time-frequency representation. Dividing the frequency band into multiple levels can improve frequency resolution of both high and low frequencies. Zhu et al. [3] reviewed that, due to the advantages of wavelet decomposition, wavelet methods have been studied in many aspects, such as signal denoising, feature extraction, and compression, or used as classifier in tool condition monitoring. Gong et al. [21] showed that the wavelet analysis was more sensitive and reliable than the Fourier analysis for recognizing the turning tool wear states. Yoon and Chin [22] verified the reliability of the wavelet transform compared with the spectra method of Fast Fourier transform (FFT).Continuous wavelet transforms (CWT) are recognized as effective tools for both stationary and nonstationary signal processing. However, it involves much redundant information and takes long computational time. Mallat [23] developed discrete wavelet transform (DWT) which is an algorithm based on the conjugate quadratic filter (CQF) and preferable in the time-frequency analysis because of no redundancy and fast computation. Wavelet and scaling functions of different scales are generated from a scaling function ϕ(t) with two-scale difference equations [24]:(4)ϕt=2∑khkϕ2t-k(5)ψt=2∑kgkϕ2t-k,(6)gk=-1kh1-kwhereh(k) and g(k) are filter coefficients of low-pass and high-pass filters; ϕ(t) and ψ(t) are scaling and wavelet functions at scale spacej=1, respectively.Assuming cj,k, dj,k are scaling coefficient and wavelet coefficient, respectively, they are derived from the projection of the signal onto the spaces of scaling function ϕj,k (t) and wavelet function ψj,k (t),and m is the filter length, then(7)cj,k=∑mhm-2kcj+1,m(8)dj,k=∑mgm-2kcj+1,mFigure11 shows a schematic diagram [25] of feature extractions for the signal representation with 3 levels of wavelet packet decompositions. The decomposition process is as follows: assuming that the frequency range of the signal S is [0,f], after the first level decomposition, S is decomposed into two parts, i.e., high frequency part D1 and low frequency part A1. Among them, the frequency range of high frequency signals is [f/2, f], and the low frequency range is [0,f/2]. Then, in the second level decomposition, A1 obtained from the first level is decomposed to get the low frequency part AA2 and the high frequency part DA2, and D1 is decomposed to obtain low frequency part AD2 and the high frequency part DD2. Their corresponding frequency ranges are [0,ƒ/4], [ƒ/4,ƒ/2], [ƒ/2, 3ƒ/4], and [3ƒ/4,ƒ], respectively. And likewise, the original signal is decomposed level by level. The decomposition relation of the signal S in Figure 11 can be expressed as the following:(9)S=AAA3+DAA3+ADA3+DDA3+AAD3+DAD3+ADD3+DDD3Figure 11
Wavelet packet decomposition structure.S is initial signal; A1, A2, and A3 are the first, second, and third level of low frequency after decomposition, respectively; D1, D2, and D3 are the first, second, and third level of high frequency after decomposition, respectively.Figure12 shows 3 levels of tree structure of wavelet multiresolution decomposition. It can be clearly seen from Figure 12 that multiresolution analysis is actually equivalent to a bandpass filter, and only the low frequency component is decomposed at each level without considering the high frequency. This decomposition process is that the frequency range of the signal S is [0,ƒ], and S is divided into two parts after the first level decomposition, i.e., the high frequency part of D1 and the low frequency part A1. The frequency range of high frequency component is [ƒ/2,ƒ], and the low frequency part is [0,ƒ/2]. When the second level is decomposed, the high frequency part D1 obtained from the first level decomposition is no longer decomposed; only the low frequency part A1 is decomposed, and it is also decomposed into two parts: high frequency part D2 and low frequency part A2. The frequency range of the high frequency part D2 is [ƒ/4,ƒ/2], and the low frequency part A2 has a frequency range of [0,ƒ/4]. The third level of decomposition is the same as the second level and only the low frequency part A2 is decomposed into two parts, i.e., the high-frequency part D3 and the low frequency part A3. And likewise, the signal is decomposed level by level. After the signal S is decomposed by the three levels of multiresolution, the signals A3, D3, D2, and D1 are obtained, and the corresponding frequency ranges are [0,ƒ/8], [ƒ/8,ƒ/4], [ƒ/4,ƒ/2], and [ƒ/2,ƒ]. Therefore, we have the following formula:(10)S=A3+D3+D2+D1Figure 12
Tree structure for three level of wavelet multiresolution analysis.When the signal is decomposed by wavelet packet, if the number of decomposed levels is too many, the calculation time of the computer will increase; if the number is too little, the resolution will reduce and many useful information may not be resolved. The number of decomposition levels depends on the signal itself and the requirements of the characteristic parameters. In this work, considering that the frequency of the vibration signal is relatively low and the frequency of AE signal is high, in order to achieve good frequency resolution effects, the vibration signal is decomposed by four levels of wavelet packet analysis, and the AE signal is decomposed by eight levels of multiresolution analysis. After this, the energy proportion of each frequency band is extracted. This process is realized by mixed programming of LabVIEW and MATLAB. Figure13(a) shows the block diagram of the 4 levels of wavelet packet decompositions for vibration signal. Figure 13(b) is the front panel of the time-frequency analysis, which can observe the waveform of the frequency bands and the energy proportion of each frequency band after the signal is decomposed by wavelet analysis.Figure 13
(a) (upper) Block diagram of the 4 levels of wavelet packet decompositions for vibration signal; (b) (lower) front panel of the time-frequency analysis.
(a) (b)


#### 3.2.1. Wavelet Packet Analysis of Vibration Signal and Characteristic Extraction

The experimental sampling frequency of the vibration signal is 25.6 KHz. According to the Nyquist sampling theorem (the sampling frequency is two times more than the actual maximum frequency), the available frequency is 12.8 KHz. Therefore, the collected vibration signal is decomposed into four levels by the wavelet packet analysis, and the frequency resolution is 0.8 KHz. Finally, the vibration signal is decomposed into 16 frequency bands (A1-A16), and the frequency distribution of each frequency band is presented in Table4.Table 4
Frequency bands of 4 levels of wavelet packet decompositions for the vibration signal.
Sequence No. A1 A2 A3 A4 A5 A6 A7 A8 Frequency band (KHz) 0-0.8 0.8-1.6 1.6-2.4 2.4-3.2 3.2-4 4-4.8 4.8-5.6 5.6-6.4  Sequence No. A9 A10 A11 A12 A13 A14 A15 A16  Frequency band (KHz) 6.4-7.2 7.2-8 8-8.8 8.8-9.6 9.6-10.4 10.4-11 11.2-12 12-12.8Figure14 shows the amplitudes and waveforms of the vibration signal with the change of the tool wear state, so the internal relationship of the amplitude with the tool state can be studied by further analysis of the change of each frequency band.Figure 14
Waveforms of the vibration signal after Wavelet packet decompositions.
(a)
Initial tool wear (b)
Normal tool wear  (c)
Severe tool wearIn order to find out the change rules of each frequency band, we quantify the amplitude of Figure14 by summing up the squared wavelet coefficients of the decomposed 16 frequency bands and then by normalizing to obtain energy proportion of each frequency band. Table 5 lists the energy proportion of the signal for three different tool states under a given cutting condition (cutting speed 64.6m/min; feed rate 0.11mm/r; cutting depth 1.2mm).Table 5
Energy proportion (×102) of the vibration signal in each frequency band after wavelet packet decompositions.
No. A1 A2 A3 A4 A5 A6 A7 A8 Initial wear 9.955 2.999 17.77 5.762 3.607 3.146 17.85 6.105 Normal wear 12.42 2.252 16.44 2.877 3.708 2.87 15.68 5.308 Severe wear 4.575 0.965 19.20 1.283 3.218 2.298 11.19 3.675  No. A9 A10 A11 A12 A13 A14 A15 A16  Initial wear 2.115 2.325 6.591 3.453 4.055 3.371 6.933 3.953 Normal wear 2.27 2.556 8.706 4.231 3.92 3.493 8.855 4.408 Severe wear 1.976 2.854 15.43 6.708 3.346 3.649 13.72 5.903The histogram for Table5 is drawn to give a more direct view of the energy proportion change in each frequency band and the comparison of the energy proportion of three tool wear states in each frequency band, as shown in Figure 15. It can be seen from Figure 15 that the energy of the vibration signal is mainly distributed in several frequency bands (A1, A3, A7, A11, and A15). The energy proportion of frequency bands A2, A4, A7, and A8 decreases with the increase of tool wear, and the energy proportion of frequency bands A11, A12, and A15 increases with the tool wear. The change in other frequency bands is irregular or no obvious change.Figure 15
Energy proportion of the vibration signal in each frequency band after wavelet packet decompositions.Figure 16
Waveforms of AE signal by wavelet multiresolution decompositions (cutting speed 64.6m/min; feed speed 0.11mm/r; depth of cut 1.2mm).
(a)
Initial tool wear (b)
Normal tool wear (c)
Severe tool wearFigure 17
Energy proportion of AE signal after wavelet decompositions in each frequency band.Figure 18
The average weight of the classification ability of each feature.


#### 3.2.2. Wavelet Multiresolution Analysis of AE Signals and Characteristic Extraction

The experimental sampling frequency of AE signal is 1MHz. According to Nyquist sampling theorem, we know that the available frequency of AE signal is 500 KHz. After 8 levels of wavelet multiresolution analysis, the frequency resolution of AE signal is 1.95 KHz. Finally, AE signal is decomposed into 9 bands (A1, D1-D8), and the distribution of each frequency band is listed in Table6.Table 6
Frequency bands of AE signal after eight levels of multiresolution decompositions.
No. A8 D8 D7 D6 D5 D4 D3 D2 D1 Frequency band (KHz) 0-1.95 1.95-3.9 3.9-7.8 7.8-15.6 15.6-31.25 31.25-62.5 62.5-125 125-250 250-500The multiresolution waveform diagram of the AE signal is shown in Figure16. It can be seen that the amplitudes in some frequency bands vary with the change of the tool state. So we can study the internal relationship of the amplitude with the tool state by further analysis of the change of each frequency band.The amplitude of each frequency band is quantized by the sum of the squared wavelet coefficients of the AE signal in nine bands obtained after the decompositions and by normalization to obtain the energy proportion of each frequency band. Table7 lists the energy proportion of AE signal for three different tool states under a given cutting condition (cutting speed 64.6m/min; feed rate 0.11mm/r; depth of cut 1.2mm).Table 7
Energy proportion (×102) of AE signal after wavelet decompositions in each frequency band.
A8 D8 D7 D6 D5 D4 D3 D2 D1 Initial wear 0.019 0.77 0.268 3.092 8.868 11.683 47.688 26.72 0.892 Normal wear 0.041 0.993 0.373 6.331 16.38 16.969 38.883 19.24 0.79 Severe wear 0.178 4.411 1.116 21.599 23.418 16.601 17.31 9.754 5.613The histogram for Table7 is shown in Figure 17. It can be seen from Figure 17 that the energy of the AE signal is mainly distributed in several frequency bands of D2, D3, D4, D5, and D6. The energy proportions in D2 and D3 bands decrease with the increase of tool wear, and the energy proportions in the D5 and D6 frequency bands increase with the tool wear.By now, after the signal analyses of 81 groups of experimental sample data in three tool states (initial wear, normal wear, and severe wear), the mean value, variance, and root mean square value for each group of the vibration signal data and the energy proportions of 16 frequency bands after 4 levels of wavelet packet decompositions are extracted. Meanwhile, the mean value, variance and root mean square value for each group of the AE signal data and the energy proportions of 9 frequency bands by the 8 levels of wavelet multiresolution decompositions are also extracted. Therefore, these characteristics for each group of vibration and AE signal data can compose a 31-dimensional fusion characteristic vector, as listed in Table8.Table 8
A total of thirty-one extracted characteristics.
Extracted characteristics of the vibration signal  No. 1 2 3 4 5 6 7 8 9 10 11 12  Feature Mean value Variance Root mean square A1 A2 A3 A4 A5 A6 A7 A8 A9  No. 13 14 15 16 17 18 19  Feature A10 A11 A12 A13 A14 A15 A16  Extracted characteristics of AE signal  No. 20 21 22 23 24 25 26 27 28 29 30 31  Feature Mean value Variance Root mean square A8 D8 D7 D6 D5 D4 D3 D2 D1In Table8, some characteristics are useless, which not only increase the computation, but also affect the classification effect. Therefore, further feature selection is necessary.


#### 3.2.3. Feature Re-Extraction with Relief-F Algorithm

Feature reextraction is to select a few features that are the most relevant with the tool state to compose the feature vectors by calculating each feature in a group of multidimensional features so that feature extraction and dimension reduction are achieved. In this work, a well-known filtering feature selection method called Relief-F algorithm is adopted. The principle of Relief-F algorithm is that the weight of each feature is calculated and then these weights are contrasted, the greater the weight value is, the stronger the classification ability will be.When dealing with multiclassification problems, Relief-F algorithm takes a sample R randomly from the training sample set each time and searches the nearest neighbor samples (near-hit)Hj(j=1,2,…k) from the sample set of the same class as R and then finds out the nearest neighbor samples (near-miss)Mj(C) from the sample set of different class from R and then updates the weightW(A) of each feature A, as shown in (11)WA=WA-∑j=1kdiffA,R,Hjmk+∑C∈ClassRpC/1-pClassR∑j=1kdiffA,R,MjCmkwhere diff (A,R1,R2) is the difference of sampleR1 andR2 on feature A,p (C) is the proportion of this class;p (Class (R)) is the proportion of the class of a randomly selected sample; Mj(C) is thejth nearest neighbor sample in class C∉class(R);m is the sampling number; andk is the number of nearest samples.(12)diffA,R1,R2=R1A-R2Amax⁡A-min⁡A,ifAiscontinuous0,ifAisdiscreteandR1A=R2A1,ifAisdiscreteandR1A≠R2AThe weight of each feature is calculated with MATLAB based on Relief-F algorithm. In Table8, the characteristics are numbered for the convenience of feature selection. We specify that the intentionally selected number of features is 8, and then the corresponding sequence number of the feature level after 8 will be removed. So the most optimal feature vectors for the classification of cutting tool states can be selected.Figure18 is the histogram for the averaged 30 calculation results of each feature weight. The distribution of the classification ability of each feature can be seen from the diagram, and the weight of each feature is arranged in order of value and Table 9 is obtained, which clearly reflects the correlation between each feature and the tool wear. The bigger the weight value is, the greater the correlation between them is.Table 9
Feature ranking of the classification ability.
Sequence 1 2 3 4 5 6 7 8 9 10 11  Feature No. 7 28 30 3 18 9 26 14 19 2 10 Weight 0.33 0.26 0.24 0.22 0.21 0.19 0.18 0.17 0.16 0.16 0.15  Sequence 12 13 14 15 16 17 18 19 20 21 22  Feature No. 29 25 5 4 12 1 31 15 17 6 13 Weight 0.13 0.11 0.10 0.10 0.10 0.09 0.09 0.08 0.06 0.06 0.05  Sequence 23 24 25 26 27 28 29 30 31  Feature No. 27 11 23 24 16 8 22 21 20 Weight 0.05 0.02 0.02 0.01 0.01 0.00 0.01 0.01 -0.1From Figure18 and Table 9, we can see that the numbers of the feature vectors are 7, 28, 30, 3, 18, 9, 26, and 14 after the Relief-F algorithm calculations. Therefore, checking Table 8, we know that the eight features including frequency bands A4, A6, A11, A15 and the root mean square of the vibration signal, and frequency bands D2, D4, and D6 of AE signal can be selected as the input of the subsequent state recognition.


### 3.3. State Recognition Using BP Neural Network

State recognition plays an important role in tool state monitoring. It is to classify the cutting tool state in the cutting process by inputting the extracted tool state features into the recognition model, enabling the mapping from the feature space to the state space. At present, the most commonly used state recognition methods in tool state monitoring are artificial neural network, fuzzy reasoning, etc.In this work, the state recognition model is established by using BP neural network based on the analysis results of the signal processing and extraction with the hybrid programming of LabVIEW and MATLAB in Section3.2.The structure of BP artificial neural network is divided into input layer, hidden layer, and output layer, as shown in Figure19. In the structure, the network is trained by the training sample set of the input. During the training process, the error is constantly propagated and corrected, and the network parameters, such as the weight and the threshold value (see Figure 20), are also adjusted to enable the network to approach the desired mapping relationship between the input and output.Figure 19
BP neural network structure.Figure 20
Artificial neuron model.


#### 3.3.1. The Establishment of Adaptive BP Neural Network Model

The establishment of adaptive BP neural network model mainly includes the determination of the number of nodes in the input, hidden and output layer, selection of the transfer function, the training algorithm, and the setting of the target error.(  1) The Number of Input Layer Nodes. The number of input layer nodes of the BP neural network is equal to the dimension of the input vector. Because 8 features are retained after the feature selection, so the number of the input layer nodes is 8.(  2) The Number of Output Layer Nodes. Since there are three kinds of tool wear: initial wear, normal wear, and severe wear, which are represented by binary numbers [100], [010], and [001], respectively, so the number of the output layer nodes is 3.(  3) The Number of Hidden Layer Nodes. The number of hidden layer nodes determines the performance of the network model. If the number is too small, then the division of the model space is rough, and the network fault tolerance performance and recognition ability are low; if the number is too large, then the model space division is too fine, and the network convergence speed is slow or not convergent, and the training time is long. Based on the empirical formula (13), preliminary calculations are carried out, and the number of hidden layer nodes is changed and tested repeatedly. Finally, the number of hidden layer nodes is determined to be 11.(13)p=n+m+awherep is the number of hidden layer nodes; n is the number of input nodes; m is the number of output nodes; and a∈(1, 10).Thus an adaptive BP neural network model of 8-11-3 structure is obtained, and Figure20 shows the artificial neuron model. The S type tangent function (Tansig) is selected for the transfer function of the hidden layer neurons, and the S type logarithmic function (logsig) is selected for the output layer neuron transfer function. Levenberg-Marquart's improved algorithm is used as the learning algorithm. The maximum number of training steps is 1000, the target error is 1e-6, and the performance parameter is 0.001.


#### 3.3.2. Determination of Samples

After the signal analysis and features selection in Section3.2,8 dimensional-81 groups offeature-sample set are formed. This work selects 54 groups of samples as a training set and 27 groups of samples as a test set.The range of numerical values of different types of features in the samples is inconsistent, so we need to normalize the sample set with MATLAB and to limit the numerical values of different types of features in the range of (-1, 1) according to(14)y=ymax-ymin×x-xminxmax-xmin+yminwhereymax=1,ymin= -1;xandyare feature values to be normalized and the corresponding value after normalization, respectively;xmax andxmin are the maximum and minimum values of the features to be normalized, respectively.


#### 3.3.3. Training Results of Adaptive BP Neural Networks

Fifty-four groups of sample data in training set are input into adaptive BP neural network model for training and learning. Figure21 shows the training state diagram of the BP neural network. It can be seen from Figure 21 that the model reaches the convergence precision at step 49.Figure 21
Training state diagram of BP neural network.


## 3.1. Signal Acquisition Function

The signal acquisition module in this work has the functions of signal display and storage, which is developed using the LabVIEW software. LabVIEW is a graphical programming language. The LabVIEW program is called virtual instrument (VI), which provides lots of graphical controls and functions used in the data analysis and processing in engineering fields. We devise desirable functions and drag graphical controls into the program diagram and then connect the wires according to the needs of programming, and finally the instrument functions and the parameters settings can be realized. LabVIEW also provides the interface with MATLAB, i.e., MATLAB Script. Using MATLAB programming for numerical calculation and analysis can greatly shorten the time of the system development and finish a completely automated test system. LabVIEW software has two human-machine interaction interfaces: the front panel and the rear panel. The front panel provides many graphical controls that are similar to the appearance of actual instruments. Graphical controls on the front panel are manipulated by using icons and wires on the rear panel.


## 3.2. Signal Analysis and Method Fusion of Dual Feature Extraction

In the metal cutting process, the original signals collected by the sensors contain a lot of noises and useless information. They cannot be used directly to identify the tool state and only the extracted characteristics are useful for the state recognition. The collected vibration and AE signals are dynamic signals. The signal components are very complex and the background noise comes from many sources, such as cutting environment, machining conditions, and material properties. There exist both stationary and nonstationary signals. The time domain analysis of signal can only represent time history of the signal amplitude characteristic, but cannot clearly reveal the frequency compositions of the signal. And the frequency domain analysis can represent the frequency structure of the signal and the amplitude of the frequency components, but cannot provide time information and judge the change of local signal with the time. The time-frequency analysis method can reflect the signal characteristics both in time domain and in frequency domain; that is, it can satisfy the requirements of nonstationary signal analysis and processing. Thus the time-frequency domain analysis is used based on the initial time domain analysis and frequency domain analysis.In this work, firstly, the time domain analysis mainly focuses on the time domain waveform display for observing the waveform change rules, and, secondly, some statistical eigenvalues (mean valuex-, variance σ2, and root mean square valueXrms) are calculated according to the sampling number of each signal through LabVIEW programming. The expressions of three statistical characteristics are presented in the following, respectively.(1)x-=1N∑i=1Nxi(2)σ2=1N∑i=1Nxi-x¯2(3)Xrms=1N∑i=1Nxi2wherexi is the collected signal data by the sensor; mean value x- indicates the constant component of a signal; variance σ2 describes the deviation from the mean value of a random signal; root mean square value Xrms describes the intensity of a random signal, i=1, 2,...N; and N is sample number.Figures7 and 8, respectively, show the typical time domain waveforms of the experimentally collected vibration and AE signals in different cutting tool wear stages (cutting speed 64.6m/min; feed rate 0.11mm/r; depth of cut 1.2mm). The abscissa is sampling time and the ordinate is the amplitude of the signal.Figure 7
Time domain waveforms of vibration signal: (a) machine idling; (b) initial tool wear; (c) normal tool wear; (d) severe tool wear.
(a) (b) (c) (d)Figure 8
Time domain waveforms of AE signal: (a) machine idling; (b) initial tool wear; (c) normal tool wear; (d) severe tool wear.
(a) (b) (c) (d)It can be seen from Figure9 that the frequency components of the vibration signal are not very rich, mainly ranging from 2 to 4 kHz. The signal energy in this frequency band varies noticeably in different wear stages and in other frequency bands it has no observable change. As can be seen from Figure 10, the AE signal contains rich frequency components, which mainly exist between the frequency band 0-50kHz and 100-150 kHz. The signal energies in these two frequency bands change obviously in different tool wear stages, and the energies keep almost unchanged in other frequency bands.Figure 9
Frequency domain waveforms of the vibration signal (amplified 100 times): (a) initial tool wear; (b) normal tool wear; (c) severe tool wear (cutting speed 64.6m/min; feed speed 0.11mm/r; depth of cut 1.2mm).
(a) (b) (c)Figure 10
Frequency domain waveforms of AE signal: (a) initial tool wear; (b) normal tool wear; (c) severe tool wear (cutting speed 64.6m/min; feed speed 0.11mm/r; depth of cut 1.2mm).
(a) (b) (c)We can see that, according to the time domain analysis and frequency domain analysis on Figures7–10, it is difficult to describe the characteristics of the tool state and to do the quantitative analysis. Thus further analysis is necessary.Due to the nature of manufacturing processes, the signals are usually nonstationary and the signal processing approaches that deal with nonstationary signals are more appropriate for process monitoring [3]. We have known that time-frequency analysis is usually used to analyze nonstationary signals which often have both high and low frequency components. And wavelet transform is one of the commonly used time-frequency analysis methods, because it has the zoom function and can adaptively adjust the time-frequency resolution of the signal according to the difference of decomposition scale. Wavelet analysis has good localization property in both time domain and frequency domain and permits adaptive time-frequency representation. Dividing the frequency band into multiple levels can improve frequency resolution of both high and low frequencies. Zhu et al. [3] reviewed that, due to the advantages of wavelet decomposition, wavelet methods have been studied in many aspects, such as signal denoising, feature extraction, and compression, or used as classifier in tool condition monitoring. Gong et al. [21] showed that the wavelet analysis was more sensitive and reliable than the Fourier analysis for recognizing the turning tool wear states. Yoon and Chin [22] verified the reliability of the wavelet transform compared with the spectra method of Fast Fourier transform (FFT).Continuous wavelet transforms (CWT) are recognized as effective tools for both stationary and nonstationary signal processing. However, it involves much redundant information and takes long computational time. Mallat [23] developed discrete wavelet transform (DWT) which is an algorithm based on the conjugate quadratic filter (CQF) and preferable in the time-frequency analysis because of no redundancy and fast computation. Wavelet and scaling functions of different scales are generated from a scaling function ϕ(t) with two-scale difference equations [24]:(4)ϕt=2∑khkϕ2t-k(5)ψt=2∑kgkϕ2t-k,(6)gk=-1kh1-kwhereh(k) and g(k) are filter coefficients of low-pass and high-pass filters; ϕ(t) and ψ(t) are scaling and wavelet functions at scale spacej=1, respectively.Assuming cj,k, dj,k are scaling coefficient and wavelet coefficient, respectively, they are derived from the projection of the signal onto the spaces of scaling function ϕj,k (t) and wavelet function ψj,k (t),and m is the filter length, then(7)cj,k=∑mhm-2kcj+1,m(8)dj,k=∑mgm-2kcj+1,mFigure11 shows a schematic diagram [25] of feature extractions for the signal representation with 3 levels of wavelet packet decompositions. The decomposition process is as follows: assuming that the frequency range of the signal S is [0,f], after the first level decomposition, S is decomposed into two parts, i.e., high frequency part D1 and low frequency part A1. Among them, the frequency range of high frequency signals is [f/2, f], and the low frequency range is [0,f/2]. Then, in the second level decomposition, A1 obtained from the first level is decomposed to get the low frequency part AA2 and the high frequency part DA2, and D1 is decomposed to obtain low frequency part AD2 and the high frequency part DD2. Their corresponding frequency ranges are [0,ƒ/4], [ƒ/4,ƒ/2], [ƒ/2, 3ƒ/4], and [3ƒ/4,ƒ], respectively. And likewise, the original signal is decomposed level by level. The decomposition relation of the signal S in Figure 11 can be expressed as the following:(9)S=AAA3+DAA3+ADA3+DDA3+AAD3+DAD3+ADD3+DDD3Figure 11
Wavelet packet decomposition structure.S is initial signal; A1, A2, and A3 are the first, second, and third level of low frequency after decomposition, respectively; D1, D2, and D3 are the first, second, and third level of high frequency after decomposition, respectively.Figure12 shows 3 levels of tree structure of wavelet multiresolution decomposition. It can be clearly seen from Figure 12 that multiresolution analysis is actually equivalent to a bandpass filter, and only the low frequency component is decomposed at each level without considering the high frequency. This decomposition process is that the frequency range of the signal S is [0,ƒ], and S is divided into two parts after the first level decomposition, i.e., the high frequency part of D1 and the low frequency part A1. The frequency range of high frequency component is [ƒ/2,ƒ], and the low frequency part is [0,ƒ/2]. When the second level is decomposed, the high frequency part D1 obtained from the first level decomposition is no longer decomposed; only the low frequency part A1 is decomposed, and it is also decomposed into two parts: high frequency part D2 and low frequency part A2. The frequency range of the high frequency part D2 is [ƒ/4,ƒ/2], and the low frequency part A2 has a frequency range of [0,ƒ/4]. The third level of decomposition is the same as the second level and only the low frequency part A2 is decomposed into two parts, i.e., the high-frequency part D3 and the low frequency part A3. And likewise, the signal is decomposed level by level. After the signal S is decomposed by the three levels of multiresolution, the signals A3, D3, D2, and D1 are obtained, and the corresponding frequency ranges are [0,ƒ/8], [ƒ/8,ƒ/4], [ƒ/4,ƒ/2], and [ƒ/2,ƒ]. Therefore, we have the following formula:(10)S=A3+D3+D2+D1Figure 12
Tree structure for three level of wavelet multiresolution analysis.When the signal is decomposed by wavelet packet, if the number of decomposed levels is too many, the calculation time of the computer will increase; if the number is too little, the resolution will reduce and many useful information may not be resolved. The number of decomposition levels depends on the signal itself and the requirements of the characteristic parameters. In this work, considering that the frequency of the vibration signal is relatively low and the frequency of AE signal is high, in order to achieve good frequency resolution effects, the vibration signal is decomposed by four levels of wavelet packet analysis, and the AE signal is decomposed by eight levels of multiresolution analysis. After this, the energy proportion of each frequency band is extracted. This process is realized by mixed programming of LabVIEW and MATLAB. Figure13(a) shows the block diagram of the 4 levels of wavelet packet decompositions for vibration signal. Figure 13(b) is the front panel of the time-frequency analysis, which can observe the waveform of the frequency bands and the energy proportion of each frequency band after the signal is decomposed by wavelet analysis.Figure 13
(a) (upper) Block diagram of the 4 levels of wavelet packet decompositions for vibration signal; (b) (lower) front panel of the time-frequency analysis.
(a) (b)


### 3.2.1. Wavelet Packet Analysis of Vibration Signal and Characteristic Extraction

The experimental sampling frequency of the vibration signal is 25.6 KHz. According to the Nyquist sampling theorem (the sampling frequency is two times more than the actual maximum frequency), the available frequency is 12.8 KHz. Therefore, the collected vibration signal is decomposed into four levels by the wavelet packet analysis, and the frequency resolution is 0.8 KHz. Finally, the vibration signal is decomposed into 16 frequency bands (A1-A16), and the frequency distribution of each frequency band is presented in Table4.Table 4
Frequency bands of 4 levels of wavelet packet decompositions for the vibration signal.
Sequence No. A1 A2 A3 A4 A5 A6 A7 A8 Frequency band (KHz) 0-0.8 0.8-1.6 1.6-2.4 2.4-3.2 3.2-4 4-4.8 4.8-5.6 5.6-6.4  Sequence No. A9 A10 A11 A12 A13 A14 A15 A16  Frequency band (KHz) 6.4-7.2 7.2-8 8-8.8 8.8-9.6 9.6-10.4 10.4-11 11.2-12 12-12.8Figure14 shows the amplitudes and waveforms of the vibration signal with the change of the tool wear state, so the internal relationship of the amplitude with the tool state can be studied by further analysis of the change of each frequency band.Figure 14
Waveforms of the vibration signal after Wavelet packet decompositions.
(a)
Initial tool wear (b)
Normal tool wear  (c)
Severe tool wearIn order to find out the change rules of each frequency band, we quantify the amplitude of Figure14 by summing up the squared wavelet coefficients of the decomposed 16 frequency bands and then by normalizing to obtain energy proportion of each frequency band. Table 5 lists the energy proportion of the signal for three different tool states under a given cutting condition (cutting speed 64.6m/min; feed rate 0.11mm/r; cutting depth 1.2mm).Table 5
Energy proportion (×102) of the vibration signal in each frequency band after wavelet packet decompositions.
No. A1 A2 A3 A4 A5 A6 A7 A8 Initial wear 9.955 2.999 17.77 5.762 3.607 3.146 17.85 6.105 Normal wear 12.42 2.252 16.44 2.877 3.708 2.87 15.68 5.308 Severe wear 4.575 0.965 19.20 1.283 3.218 2.298 11.19 3.675  No. A9 A10 A11 A12 A13 A14 A15 A16  Initial wear 2.115 2.325 6.591 3.453 4.055 3.371 6.933 3.953 Normal wear 2.27 2.556 8.706 4.231 3.92 3.493 8.855 4.408 Severe wear 1.976 2.854 15.43 6.708 3.346 3.649 13.72 5.903The histogram for Table5 is drawn to give a more direct view of the energy proportion change in each frequency band and the comparison of the energy proportion of three tool wear states in each frequency band, as shown in Figure 15. It can be seen from Figure 15 that the energy of the vibration signal is mainly distributed in several frequency bands (A1, A3, A7, A11, and A15). The energy proportion of frequency bands A2, A4, A7, and A8 decreases with the increase of tool wear, and the energy proportion of frequency bands A11, A12, and A15 increases with the tool wear. The change in other frequency bands is irregular or no obvious change.Figure 15
Energy proportion of the vibration signal in each frequency band after wavelet packet decompositions.Figure 16
Waveforms of AE signal by wavelet multiresolution decompositions (cutting speed 64.6m/min; feed speed 0.11mm/r; depth of cut 1.2mm).
(a)
Initial tool wear (b)
Normal tool wear (c)
Severe tool wearFigure 17
Energy proportion of AE signal after wavelet decompositions in each frequency band.Figure 18
The average weight of the classification ability of each feature.


### 3.2.2. Wavelet Multiresolution Analysis of AE Signals and Characteristic Extraction

The experimental sampling frequency of AE signal is 1MHz. According to Nyquist sampling theorem, we know that the available frequency of AE signal is 500 KHz. After 8 levels of wavelet multiresolution analysis, the frequency resolution of AE signal is 1.95 KHz. Finally, AE signal is decomposed into 9 bands (A1, D1-D8), and the distribution of each frequency band is listed in Table6.Table 6
Frequency bands of AE signal after eight levels of multiresolution decompositions.
No. A8 D8 D7 D6 D5 D4 D3 D2 D1 Frequency band (KHz) 0-1.95 1.95-3.9 3.9-7.8 7.8-15.6 15.6-31.25 31.25-62.5 62.5-125 125-250 250-500The multiresolution waveform diagram of the AE signal is shown in Figure16. It can be seen that the amplitudes in some frequency bands vary with the change of the tool state. So we can study the internal relationship of the amplitude with the tool state by further analysis of the change of each frequency band.The amplitude of each frequency band is quantized by the sum of the squared wavelet coefficients of the AE signal in nine bands obtained after the decompositions and by normalization to obtain the energy proportion of each frequency band. Table7 lists the energy proportion of AE signal for three different tool states under a given cutting condition (cutting speed 64.6m/min; feed rate 0.11mm/r; depth of cut 1.2mm).Table 7
Energy proportion (×102) of AE signal after wavelet decompositions in each frequency band.
A8 D8 D7 D6 D5 D4 D3 D2 D1 Initial wear 0.019 0.77 0.268 3.092 8.868 11.683 47.688 26.72 0.892 Normal wear 0.041 0.993 0.373 6.331 16.38 16.969 38.883 19.24 0.79 Severe wear 0.178 4.411 1.116 21.599 23.418 16.601 17.31 9.754 5.613The histogram for Table7 is shown in Figure 17. It can be seen from Figure 17 that the energy of the AE signal is mainly distributed in several frequency bands of D2, D3, D4, D5, and D6. The energy proportions in D2 and D3 bands decrease with the increase of tool wear, and the energy proportions in the D5 and D6 frequency bands increase with the tool wear.By now, after the signal analyses of 81 groups of experimental sample data in three tool states (initial wear, normal wear, and severe wear), the mean value, variance, and root mean square value for each group of the vibration signal data and the energy proportions of 16 frequency bands after 4 levels of wavelet packet decompositions are extracted. Meanwhile, the mean value, variance and root mean square value for each group of the AE signal data and the energy proportions of 9 frequency bands by the 8 levels of wavelet multiresolution decompositions are also extracted. Therefore, these characteristics for each group of vibration and AE signal data can compose a 31-dimensional fusion characteristic vector, as listed in Table8.Table 8
A total of thirty-one extracted characteristics.
Extracted characteristics of the vibration signal  No. 1 2 3 4 5 6 7 8 9 10 11 12  Feature Mean value Variance Root mean square A1 A2 A3 A4 A5 A6 A7 A8 A9  No. 13 14 15 16 17 18 19  Feature A10 A11 A12 A13 A14 A15 A16  Extracted characteristics of AE signal  No. 20 21 22 23 24 25 26 27 28 29 30 31  Feature Mean value Variance Root mean square A8 D8 D7 D6 D5 D4 D3 D2 D1In Table8, some characteristics are useless, which not only increase the computation, but also affect the classification effect. Therefore, further feature selection is necessary.


### 3.2.3. Feature Re-Extraction with Relief-F Algorithm

Feature reextraction is to select a few features that are the most relevant with the tool state to compose the feature vectors by calculating each feature in a group of multidimensional features so that feature extraction and dimension reduction are achieved. In this work, a well-known filtering feature selection method called Relief-F algorithm is adopted. The principle of Relief-F algorithm is that the weight of each feature is calculated and then these weights are contrasted, the greater the weight value is, the stronger the classification ability will be.When dealing with multiclassification problems, Relief-F algorithm takes a sample R randomly from the training sample set each time and searches the nearest neighbor samples (near-hit)Hj(j=1,2,…k) from the sample set of the same class as R and then finds out the nearest neighbor samples (near-miss)Mj(C) from the sample set of different class from R and then updates the weightW(A) of each feature A, as shown in (11)WA=WA-∑j=1kdiffA,R,Hjmk+∑C∈ClassRpC/1-pClassR∑j=1kdiffA,R,MjCmkwhere diff (A,R1,R2) is the difference of sampleR1 andR2 on feature A,p (C) is the proportion of this class;p (Class (R)) is the proportion of the class of a randomly selected sample; Mj(C) is thejth nearest neighbor sample in class C∉class(R);m is the sampling number; andk is the number of nearest samples.(12)diffA,R1,R2=R1A-R2Amax⁡A-min⁡A,ifAiscontinuous0,ifAisdiscreteandR1A=R2A1,ifAisdiscreteandR1A≠R2AThe weight of each feature is calculated with MATLAB based on Relief-F algorithm. In Table8, the characteristics are numbered for the convenience of feature selection. We specify that the intentionally selected number of features is 8, and then the corresponding sequence number of the feature level after 8 will be removed. So the most optimal feature vectors for the classification of cutting tool states can be selected.Figure18 is the histogram for the averaged 30 calculation results of each feature weight. The distribution of the classification ability of each feature can be seen from the diagram, and the weight of each feature is arranged in order of value and Table 9 is obtained, which clearly reflects the correlation between each feature and the tool wear. The bigger the weight value is, the greater the correlation between them is.Table 9
Feature ranking of the classification ability.
Sequence 1 2 3 4 5 6 7 8 9 10 11  Feature No. 7 28 30 3 18 9 26 14 19 2 10 Weight 0.33 0.26 0.24 0.22 0.21 0.19 0.18 0.17 0.16 0.16 0.15  Sequence 12 13 14 15 16 17 18 19 20 21 22  Feature No. 29 25 5 4 12 1 31 15 17 6 13 Weight 0.13 0.11 0.10 0.10 0.10 0.09 0.09 0.08 0.06 0.06 0.05  Sequence 23 24 25 26 27 28 29 30 31  Feature No. 27 11 23 24 16 8 22 21 20 Weight 0.05 0.02 0.02 0.01 0.01 0.00 0.01 0.01 -0.1From Figure18 and Table 9, we can see that the numbers of the feature vectors are 7, 28, 30, 3, 18, 9, 26, and 14 after the Relief-F algorithm calculations. Therefore, checking Table 8, we know that the eight features including frequency bands A4, A6, A11, A15 and the root mean square of the vibration signal, and frequency bands D2, D4, and D6 of AE signal can be selected as the input of the subsequent state recognition.


## 3.2.1. Wavelet Packet Analysis of Vibration Signal and Characteristic Extraction

The experimental sampling frequency of the vibration signal is 25.6 KHz. According to the Nyquist sampling theorem (the sampling frequency is two times more than the actual maximum frequency), the available frequency is 12.8 KHz. Therefore, the collected vibration signal is decomposed into four levels by the wavelet packet analysis, and the frequency resolution is 0.8 KHz. Finally, the vibration signal is decomposed into 16 frequency bands (A1-A16), and the frequency distribution of each frequency band is presented in Table4.Table 4
Frequency bands of 4 levels of wavelet packet decompositions for the vibration signal.
Sequence No. A1 A2 A3 A4 A5 A6 A7 A8 Frequency band (KHz) 0-0.8 0.8-1.6 1.6-2.4 2.4-3.2 3.2-4 4-4.8 4.8-5.6 5.6-6.4  Sequence No. A9 A10 A11 A12 A13 A14 A15 A16  Frequency band (KHz) 6.4-7.2 7.2-8 8-8.8 8.8-9.6 9.6-10.4 10.4-11 11.2-12 12-12.8Figure14 shows the amplitudes and waveforms of the vibration signal with the change of the tool wear state, so the internal relationship of the amplitude with the tool state can be studied by further analysis of the change of each frequency band.Figure 14
Waveforms of the vibration signal after Wavelet packet decompositions.
(a)
Initial tool wear (b)
Normal tool wear  (c)
Severe tool wearIn order to find out the change rules of each frequency band, we quantify the amplitude of Figure14 by summing up the squared wavelet coefficients of the decomposed 16 frequency bands and then by normalizing to obtain energy proportion of each frequency band. Table 5 lists the energy proportion of the signal for three different tool states under a given cutting condition (cutting speed 64.6m/min; feed rate 0.11mm/r; cutting depth 1.2mm).Table 5
Energy proportion (×102) of the vibration signal in each frequency band after wavelet packet decompositions.
No. A1 A2 A3 A4 A5 A6 A7 A8 Initial wear 9.955 2.999 17.77 5.762 3.607 3.146 17.85 6.105 Normal wear 12.42 2.252 16.44 2.877 3.708 2.87 15.68 5.308 Severe wear 4.575 0.965 19.20 1.283 3.218 2.298 11.19 3.675  No. A9 A10 A11 A12 A13 A14 A15 A16  Initial wear 2.115 2.325 6.591 3.453 4.055 3.371 6.933 3.953 Normal wear 2.27 2.556 8.706 4.231 3.92 3.493 8.855 4.408 Severe wear 1.976 2.854 15.43 6.708 3.346 3.649 13.72 5.903The histogram for Table5 is drawn to give a more direct view of the energy proportion change in each frequency band and the comparison of the energy proportion of three tool wear states in each frequency band, as shown in Figure 15. It can be seen from Figure 15 that the energy of the vibration signal is mainly distributed in several frequency bands (A1, A3, A7, A11, and A15). The energy proportion of frequency bands A2, A4, A7, and A8 decreases with the increase of tool wear, and the energy proportion of frequency bands A11, A12, and A15 increases with the tool wear. The change in other frequency bands is irregular or no obvious change.Figure 15
Energy proportion of the vibration signal in each frequency band after wavelet packet decompositions.Figure 16
Waveforms of AE signal by wavelet multiresolution decompositions (cutting speed 64.6m/min; feed speed 0.11mm/r; depth of cut 1.2mm).
(a)
Initial tool wear (b)
Normal tool wear (c)
Severe tool wearFigure 17
Energy proportion of AE signal after wavelet decompositions in each frequency band.Figure 18
The average weight of the classification ability of each feature.


## 3.2.2. Wavelet Multiresolution Analysis of AE Signals and Characteristic Extraction

The experimental sampling frequency of AE signal is 1MHz. According to Nyquist sampling theorem, we know that the available frequency of AE signal is 500 KHz. After 8 levels of wavelet multiresolution analysis, the frequency resolution of AE signal is 1.95 KHz. Finally, AE signal is decomposed into 9 bands (A1, D1-D8), and the distribution of each frequency band is listed in Table6.Table 6
Frequency bands of AE signal after eight levels of multiresolution decompositions.
No. A8 D8 D7 D6 D5 D4 D3 D2 D1 Frequency band (KHz) 0-1.95 1.95-3.9 3.9-7.8 7.8-15.6 15.6-31.25 31.25-62.5 62.5-125 125-250 250-500The multiresolution waveform diagram of the AE signal is shown in Figure16. It can be seen that the amplitudes in some frequency bands vary with the change of the tool state. So we can study the internal relationship of the amplitude with the tool state by further analysis of the change of each frequency band.The amplitude of each frequency band is quantized by the sum of the squared wavelet coefficients of the AE signal in nine bands obtained after the decompositions and by normalization to obtain the energy proportion of each frequency band. Table7 lists the energy proportion of AE signal for three different tool states under a given cutting condition (cutting speed 64.6m/min; feed rate 0.11mm/r; depth of cut 1.2mm).Table 7
Energy proportion (×102) of AE signal after wavelet decompositions in each frequency band.
A8 D8 D7 D6 D5 D4 D3 D2 D1 Initial wear 0.019 0.77 0.268 3.092 8.868 11.683 47.688 26.72 0.892 Normal wear 0.041 0.993 0.373 6.331 16.38 16.969 38.883 19.24 0.79 Severe wear 0.178 4.411 1.116 21.599 23.418 16.601 17.31 9.754 5.613The histogram for Table7 is shown in Figure 17. It can be seen from Figure 17 that the energy of the AE signal is mainly distributed in several frequency bands of D2, D3, D4, D5, and D6. The energy proportions in D2 and D3 bands decrease with the increase of tool wear, and the energy proportions in the D5 and D6 frequency bands increase with the tool wear.By now, after the signal analyses of 81 groups of experimental sample data in three tool states (initial wear, normal wear, and severe wear), the mean value, variance, and root mean square value for each group of the vibration signal data and the energy proportions of 16 frequency bands after 4 levels of wavelet packet decompositions are extracted. Meanwhile, the mean value, variance and root mean square value for each group of the AE signal data and the energy proportions of 9 frequency bands by the 8 levels of wavelet multiresolution decompositions are also extracted. Therefore, these characteristics for each group of vibration and AE signal data can compose a 31-dimensional fusion characteristic vector, as listed in Table8.Table 8
A total of thirty-one extracted characteristics.
Extracted characteristics of the vibration signal  No. 1 2 3 4 5 6 7 8 9 10 11 12  Feature Mean value Variance Root mean square A1 A2 A3 A4 A5 A6 A7 A8 A9  No. 13 14 15 16 17 18 19  Feature A10 A11 A12 A13 A14 A15 A16  Extracted characteristics of AE signal  No. 20 21 22 23 24 25 26 27 28 29 30 31  Feature Mean value Variance Root mean square A8 D8 D7 D6 D5 D4 D3 D2 D1In Table8, some characteristics are useless, which not only increase the computation, but also affect the classification effect. Therefore, further feature selection is necessary.


## 3.2.3. Feature Re-Extraction with Relief-F Algorithm

Feature reextraction is to select a few features that are the most relevant with the tool state to compose the feature vectors by calculating each feature in a group of multidimensional features so that feature extraction and dimension reduction are achieved. In this work, a well-known filtering feature selection method called Relief-F algorithm is adopted. The principle of Relief-F algorithm is that the weight of each feature is calculated and then these weights are contrasted, the greater the weight value is, the stronger the classification ability will be.When dealing with multiclassification problems, Relief-F algorithm takes a sample R randomly from the training sample set each time and searches the nearest neighbor samples (near-hit)Hj(j=1,2,…k) from the sample set of the same class as R and then finds out the nearest neighbor samples (near-miss)Mj(C) from the sample set of different class from R and then updates the weightW(A) of each feature A, as shown in (11)WA=WA-∑j=1kdiffA,R,Hjmk+∑C∈ClassRpC/1-pClassR∑j=1kdiffA,R,MjCmkwhere diff (A,R1,R2) is the difference of sampleR1 andR2 on feature A,p (C) is the proportion of this class;p (Class (R)) is the proportion of the class of a randomly selected sample; Mj(C) is thejth nearest neighbor sample in class C∉class(R);m is the sampling number; andk is the number of nearest samples.(12)diffA,R1,R2=R1A-R2Amax⁡A-min⁡A,ifAiscontinuous0,ifAisdiscreteandR1A=R2A1,ifAisdiscreteandR1A≠R2AThe weight of each feature is calculated with MATLAB based on Relief-F algorithm. In Table8, the characteristics are numbered for the convenience of feature selection. We specify that the intentionally selected number of features is 8, and then the corresponding sequence number of the feature level after 8 will be removed. So the most optimal feature vectors for the classification of cutting tool states can be selected.Figure18 is the histogram for the averaged 30 calculation results of each feature weight. The distribution of the classification ability of each feature can be seen from the diagram, and the weight of each feature is arranged in order of value and Table 9 is obtained, which clearly reflects the correlation between each feature and the tool wear. The bigger the weight value is, the greater the correlation between them is.Table 9
Feature ranking of the classification ability.
Sequence 1 2 3 4 5 6 7 8 9 10 11  Feature No. 7 28 30 3 18 9 26 14 19 2 10 Weight 0.33 0.26 0.24 0.22 0.21 0.19 0.18 0.17 0.16 0.16 0.15  Sequence 12 13 14 15 16 17 18 19 20 21 22  Feature No. 29 25 5 4 12 1 31 15 17 6 13 Weight 0.13 0.11 0.10 0.10 0.10 0.09 0.09 0.08 0.06 0.06 0.05  Sequence 23 24 25 26 27 28 29 30 31  Feature No. 27 11 23 24 16 8 22 21 20 Weight 0.05 0.02 0.02 0.01 0.01 0.00 0.01 0.01 -0.1From Figure18 and Table 9, we can see that the numbers of the feature vectors are 7, 28, 30, 3, 18, 9, 26, and 14 after the Relief-F algorithm calculations. Therefore, checking Table 8, we know that the eight features including frequency bands A4, A6, A11, A15 and the root mean square of the vibration signal, and frequency bands D2, D4, and D6 of AE signal can be selected as the input of the subsequent state recognition.


## 3.3. State Recognition Using BP Neural Network

State recognition plays an important role in tool state monitoring. It is to classify the cutting tool state in the cutting process by inputting the extracted tool state features into the recognition model, enabling the mapping from the feature space to the state space. At present, the most commonly used state recognition methods in tool state monitoring are artificial neural network, fuzzy reasoning, etc.In this work, the state recognition model is established by using BP neural network based on the analysis results of the signal processing and extraction with the hybrid programming of LabVIEW and MATLAB in Section3.2.The structure of BP artificial neural network is divided into input layer, hidden layer, and output layer, as shown in Figure19. In the structure, the network is trained by the training sample set of the input. During the training process, the error is constantly propagated and corrected, and the network parameters, such as the weight and the threshold value (see Figure 20), are also adjusted to enable the network to approach the desired mapping relationship between the input and output.Figure 19
BP neural network structure.Figure 20
Artificial neuron model.


### 3.3.1. The Establishment of Adaptive BP Neural Network Model

The establishment of adaptive BP neural network model mainly includes the determination of the number of nodes in the input, hidden and output layer, selection of the transfer function, the training algorithm, and the setting of the target error.(  1) The Number of Input Layer Nodes. The number of input layer nodes of the BP neural network is equal to the dimension of the input vector. Because 8 features are retained after the feature selection, so the number of the input layer nodes is 8.(  2) The Number of Output Layer Nodes. Since there are three kinds of tool wear: initial wear, normal wear, and severe wear, which are represented by binary numbers [100], [010], and [001], respectively, so the number of the output layer nodes is 3.(  3) The Number of Hidden Layer Nodes. The number of hidden layer nodes determines the performance of the network model. If the number is too small, then the division of the model space is rough, and the network fault tolerance performance and recognition ability are low; if the number is too large, then the model space division is too fine, and the network convergence speed is slow or not convergent, and the training time is long. Based on the empirical formula (13), preliminary calculations are carried out, and the number of hidden layer nodes is changed and tested repeatedly. Finally, the number of hidden layer nodes is determined to be 11.(13)p=n+m+awherep is the number of hidden layer nodes; n is the number of input nodes; m is the number of output nodes; and a∈(1, 10).Thus an adaptive BP neural network model of 8-11-3 structure is obtained, and Figure20 shows the artificial neuron model. The S type tangent function (Tansig) is selected for the transfer function of the hidden layer neurons, and the S type logarithmic function (logsig) is selected for the output layer neuron transfer function. Levenberg-Marquart's improved algorithm is used as the learning algorithm. The maximum number of training steps is 1000, the target error is 1e-6, and the performance parameter is 0.001.


### 3.3.2. Determination of Samples

After the signal analysis and features selection in Section3.2,8 dimensional-81 groups offeature-sample set are formed. This work selects 54 groups of samples as a training set and 27 groups of samples as a test set.The range of numerical values of different types of features in the samples is inconsistent, so we need to normalize the sample set with MATLAB and to limit the numerical values of different types of features in the range of (-1, 1) according to(14)y=ymax-ymin×x-xminxmax-xmin+yminwhereymax=1,ymin= -1;xandyare feature values to be normalized and the corresponding value after normalization, respectively;xmax andxmin are the maximum and minimum values of the features to be normalized, respectively.


### 3.3.3. Training Results of Adaptive BP Neural Networks

Fifty-four groups of sample data in training set are input into adaptive BP neural network model for training and learning. Figure21 shows the training state diagram of the BP neural network. It can be seen from Figure 21 that the model reaches the convergence precision at step 49.Figure 21
Training state diagram of BP neural network.


## 3.3.1. The Establishment of Adaptive BP Neural Network Model

The establishment of adaptive BP neural network model mainly includes the determination of the number of nodes in the input, hidden and output layer, selection of the transfer function, the training algorithm, and the setting of the target error.(  1) The Number of Input Layer Nodes. The number of input layer nodes of the BP neural network is equal to the dimension of the input vector. Because 8 features are retained after the feature selection, so the number of the input layer nodes is 8.(  2) The Number of Output Layer Nodes. Since there are three kinds of tool wear: initial wear, normal wear, and severe wear, which are represented by binary numbers [100], [010], and [001], respectively, so the number of the output layer nodes is 3.(  3) The Number of Hidden Layer Nodes. The number of hidden layer nodes determines the performance of the network model. If the number is too small, then the division of the model space is rough, and the network fault tolerance performance and recognition ability are low; if the number is too large, then the model space division is too fine, and the network convergence speed is slow or not convergent, and the training time is long. Based on the empirical formula (13), preliminary calculations are carried out, and the number of hidden layer nodes is changed and tested repeatedly. Finally, the number of hidden layer nodes is determined to be 11.(13)p=n+m+awherep is the number of hidden layer nodes; n is the number of input nodes; m is the number of output nodes; and a∈(1, 10).Thus an adaptive BP neural network model of 8-11-3 structure is obtained, and Figure20 shows the artificial neuron model. The S type tangent function (Tansig) is selected for the transfer function of the hidden layer neurons, and the S type logarithmic function (logsig) is selected for the output layer neuron transfer function. Levenberg-Marquart's improved algorithm is used as the learning algorithm. The maximum number of training steps is 1000, the target error is 1e-6, and the performance parameter is 0.001.


## 3.3.2. Determination of Samples

After the signal analysis and features selection in Section3.2,8 dimensional-81 groups offeature-sample set are formed. This work selects 54 groups of samples as a training set and 27 groups of samples as a test set.The range of numerical values of different types of features in the samples is inconsistent, so we need to normalize the sample set with MATLAB and to limit the numerical values of different types of features in the range of (-1, 1) according to(14)y=ymax-ymin×x-xminxmax-xmin+yminwhereymax=1,ymin= -1;xandyare feature values to be normalized and the corresponding value after normalization, respectively;xmax andxmin are the maximum and minimum values of the features to be normalized, respectively.


## 3.3.3. Training Results of Adaptive BP Neural Networks

Fifty-four groups of sample data in training set are input into adaptive BP neural network model for training and learning. Figure21 shows the training state diagram of the BP neural network. It can be seen from Figure 21 that the model reaches the convergence precision at step 49.Figure 21
Training state diagram of BP neural network.


## 4. Results Analysis

Twenty-seven groups of test sample data are input into the trained adaptive network model for testing, and the obtained test results are presented in Table10. From Table 10, we can see that the recognition results of the network model contain two incorrect outputs; hence the correct recognition rate is u=25/27=92.59%. This indicates that the state recognition model established by adaptive BP algorithm can better accomplish the tool state recognition. If the first number of the actual output value of adaptive BP neural network is maximum, then the output shows [100], indicating that the tool is in the initial wear state; if the second number is maximum, the output is [010] and the tool is in the normal wear state; and if the third number is maximum, the output is [001] and the tool is in severe wear state.Table 10
Recognition results of cutting tool state.
No. Tool wear state Output Recognition results Actual results Result judgment 1 Initial wear 0.9999 0.5000 0.5000 1 0 0 1 0 0 Correct 2 Normal wear 0.5000 0.9999 0.5000 0 1 0 0 1 0 Correct 3 Severe wear 0.5000 0.5000 0.9998 0 0 1 0 0 1 Correct 4 Initial wear 0.9999 0.5000 0.5000 1 0 0 1 0 0 Correct 5 Normal wear 0.5000 0.9999 0.5000 0 1 0 0 1 0 Correct 6 Severe wear 0.5000 0.5000 0.9999 0 0 1 0 0 1 Correct 7 Initial wear 0.9999 0.5000 0.5000 1 0 0 1 0 0 Correct 8 Normal wear 0.5000 0.9991 0.5000 0 1 0 0 1 0 Correct 9 Severe wear 0.5000 0.5000 0.9999 0 0 1 0 0 1 Correct 10 Initial wear 0.9998 0.5000 0.5000 1 0 0 1 0 0 Correct 11 Normal wear 0.5000 0.9999 0.5000 0 1 0 0 1 0 Correct 12 Severe wear 0.5000 0.5000 0.9994 0 0 1 0 0 1 Correct 13 Initial wear 0.8765 0.5000 0.5000 1 0 0 1 0 0 Correct 14 Normal wear 0.5000 0.9999 0.5000 0 1 0 0 1 0 Correct 15 Severe wear 0.5000 0.5000 0.9999 0 0 1 0 0 1 Correct 16 Initial wear 0.5003 0.7265 0.5000 0 1 0 1 0 0 Incorrect 17 Normal wear 0.5000 0.9615 0.5000 0 1 0 0 1 0 Correct 18 Severe wear 0.5000 0.5000 0.9998 0 0 1 0 0 1 Correct 19 Initial wear 0.9999 0.5000 0.5000 1 0 0 1 0 0 Correct 20 Normal wear 0.5000 0.9999 0.5000 0 1 0 0 1 0 Correct 21 Severe wear 0.5000 0.5000 0.9999 0 0 1 0 0 1 Correct 22 Initial wear 0.5003 0.6465 0.5000 0 1 0 1 0 0 Incorrect 23 Normal wear 0.5000 0.9999 0.5000 0 1 0 0 1 0 Correct 24 Severe wear 0.5000 0.5000 0.9999 0 0 1 0 0 1 Correct 25 Initial wear 0.9999 0.5000 0.5000 1 0 0 1 0 0 Correct 26 Normal wear 0.5000 0.9615 0.5000 0 1 0 0 1 0 Correct 27 Severe wear 0.5000 0.5000 0.9998 0 0 1 0 0 1 Correct


## 5. Discussion

This work systematically investigates the approaches of realizing a visual, intelligent, and real-time tool state monitoring based on hybrid programming of LabVIEW and MATLAB. Both the multitheories used in the study and the experimental method can adapt to various machining processes and environments. The reasons are discussed as follows.(  1) Advantages of Experimental Scheme. The experimental objective is to obtain the mapping relations between the tool wear and the measured physical signals that are able to reflect the tool state in cutting processes. Therefore, the determination of experimental factors is one of the key issues. For this, the experimental scheme is designed according to the specifications of the machine tools used in this work. Except some fixed factors affecting the signals such as the machining environment and cutting tool parameters, other variable factors such as cutting parameters including the cutting speed, the feed rate, the depth of cut, and tool wear are determined, among which three VB values of the tool flank wear corresponding to the indices of general tool wear criterions, sharp tool stage (initial wear), normal working stage (normal wear), and worn out stage (severe wear), are taken into account, as presented in Tables 2 and 3. Based on this scheme,all-factors experiments are conducted, which is a very important aspect for obtaining the sufficient data of the later task on modeling and recognition of the neural network. Hence, there are four factors and each factor has three levels thereby 34=81 groups of experiments.Secondly, tool state monitoring involves a variety of sensors and signal analysis techniques, and the selection of the suitable sensors is the second key issue. Due to the nature of manufacturing processes, the signals are usually nonstationary, which often contain both high and low frequency components. Therefore, bisensors, i.e., vibration acceleration sensor and AE sensor, are simultaneously selected for measuring the low frequency vibration signal and higher frequency AE signal in this work. Therefore, the advantages of bisensors lie in that they can sensitively and entirely reflect the tool state in real time and are suitable for monitoring different machining processes.(  2) Significance of Dual Feature Extraction of Signals. This work extracts the signal features that are most relevant with the tool state by the use of the method fusion of wavelet theory and Relief-F algorithm. The reason is that dual feature extraction of signals can achieve the dual effects of finding out the most relevant features and feature dimension reduction. Wavelet analysis has good localization property in both time domain and frequency domain and permits adaptive time-frequency representation. Dividing the frequency band into multiple levels can improve frequency resolution of both high and low frequencies. Through the signal analyses of 81 groups of experimental sample data in three tool states (initial wear, normal wear, and severe wear), 4 levels of wavelet packet decompositions of the vibration signal and the 8 levels of wavelet multiresolution decompositions of the AE signals can satisfy the requirement of the frequency resolution and 31 characteristics for each group of signal data are extracted, as listed in Table 8. However, some characteristics are useless in Table 8, which not only increase the computation, but also affect the state recognition effect. Therefore, feature reextraction using Relief-F algorithm is carried out to select a few features that are the most correlated with the tool state. Figure 18 shows the histogram for the averaged 30 calculation results of each feature weight. From Figure 18 and Table 9, we can see that the sequence numbers of the feature vectors are 7, 28, 30, 3, 18, 9, 26, and 14 after the Relief-F algorithm calculations. Therefore, by the inspection of Table 8, they are 8 corresponding features including frequency bands A4, A6, A11, A15, the root mean square of the vibration signal, and frequency bands D2, D4, and D6 of AE signal. That is, the number of features is reduced from 31 to 8.(  3) Success Rate of State Recognition Using BP Neural Network. In this investigation, it is found that the number of hidden layer nodes is one of BP network training conditions determining the success of network recognition. The number of hidden nodes is changed and tested repeatedly after the initial calculation using the empirical formula (13). The network is trained by the training sample set of the input. During the training process, the network parameters, such as the weight and the threshold value, also need to be adjusted to enable the network to approach the desired mapping relationship between the input and output. This work selects 54 groups of samples as a training set and 27 groups of samples as a test set. It can be seen from Figure 21 that the adaptive BP neural network model for training and learning reaches the convergence precision at step 49. Test results show that the correct recognition rate can reach 92.59%.


## 6. Conclusions

A tool wear monitoring through hybrid programming technique of LabVIEW and MATLAB is accomplished, which can more accurately complete the intelligent and real-time recognition of the tool state with the correct recognition rate of 92.59%.Vibration and AE signals are ideal signals for tool monitoring. Bisensor fusion can collect both the relatively low frequency of the vibration signal and the high frequency of AE signal and thus can sensitively and entirely reflect the tool state in real time.The method fusion of wavelet decompositions and relief-F algorithm can achieve dual extraction of signal features and feature dimension reduction, such that computation is fast and real-time performance is good. The results show that the number of features that are relevant with the tool wear state is reduced from 31 of each group of signal data to 8, which are of the frequency bands most relevant to tool wear states including A4 (2.4-3.2 KHz), A6 (4-4.8 KHz), A11 (8-8.8 KHz), A15 (11.2-12 KHz) of vibration signal and D2 (125-250 KHz), D4 (31.25-62.5 KHz), and D6 (7.8-15.6 KHz) of AE signal. Obviously vibration signal and AE signal can complement each other in tool wear monitoring.The tool wear monitoring method shows the generality. This is because the experimental scheme, hybrid programming technique, the dual feature extraction, and BP network recognition model in this work have generality, which can be applied to any other different machining operations such as milling, drilling, boring, forming, and shaping, combined with different cutting tools including single point tool (shaping) and multipoint tool (milling, drilling) in machining any kinds of workpiece materials. This can be accomplished only through changing the installation locations of the vibration and AE sensors. If necessary, the sampling parameters can easily be set in the system and can reextract the different features by implementing the Relief-F algorithm and can also reset the parameters of the BP neural network.



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*Source: 8431784-2019-06-10.xml*