Analysis of cutting force signals by wavelet packet transform for surface roughness monitoring in CNC turning

Mechanical Systems and Signal Processing 98 (2018) 634–651

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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp

Analysis of cutting force signals by wavelet packet transform for surface roughness monitoring in CNC turning E. García Plaza ⇑, P.J. Núñez López Higher Technical School of Industrial Engineering, Energy Research and Industrial Applications Institute (INEI), Department Applied Mechanics & Engineering of Projects, University of Castilla-La Mancha, Avda. Camilo José Cela, s/n, 13071 Ciudad Real, Spain

a r t i c l e

i n f o

Article history: Received 14 December 2016 Received in revised form 11 April 2017 Accepted 7 May 2017

Keywords: Wavelet packet transform Surface finish Roughness Cutting forces CNC turning operations

a b s t r a c t On-line monitoring of surface finish in machining processes has proven to be a substantial advancement over traditional post-process quality control techniques by reducing inspection times and costs and by avoiding the manufacture of defective products. This study applied techniques for processing cutting force signals based on the wavelet packet transform (WPT) method for the monitoring of surface finish in computer numerical control (CNC) turning operations. The behaviour of 40 mother wavelets was analysed using three techniques: global packet analysis (G-WPT), and the application of two packet reduction criteria: maximum energy (E-WPT) and maximum entropy (SE-WPT). The optimum signal decomposition level (Lj) was determined to eliminate noise and to obtain information correlated to surface finish. The results obtained with the G-WPT method provided an indepth analysis of cutting force signals, and frequency ranges and signal characteristics were correlated to surface finish with excellent results in the accuracy and reliability of the predictive models. The radial and tangential cutting force components at low frequency provided most of the information for the monitoring of surface finish. The E-WPT and SEWPT packet reduction criteria substantially reduced signal processing time, but at the expense of discarding packets with relevant information, which impoverished the results. The G-WPT method was observed to be an ideal procedure for processing cutting force signals applied to the real-time monitoring of surface finish, and was estimated to be highly accurate and reliable at a low analytical-computational cost. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Machining processes are extensively used for the manufacture of mechanical components requiring dimensional accuracy and optimum surface finish. In order to achieve these standards, a well-balanced system of all the elements involved in the cutting process is essential to ensure stable and optimum machining. Under certain conditions, the dynamic character of the machining processes leads to the appearance of a physical phenomenon altering the stability of the process and marring the quality of the end product. In recent decades, the monitoring of cutting process to avert the manufacture of defective products has led to the design and development of an array of methods for monitoring the cutting process [1,2] by analysing aspects such as: chatter [3–5], dimensional deviation [6–8], surface finish [7–20], residual stress [21], chip form [22–24], tool condition [25–36], surface malfunction [37], and machine faults [38]. Monitoring techniques consists of three fundamental ⇑ Corresponding author. E-mail addresses: [email protected] (E. García Plaza), [email protected] (P.J. Núñez López). http://dx.doi.org/10.1016/j.ymssp.2017.05.006 0888-3270/Ó 2017 Elsevier Ltd. All rights reserved.

E. García Plaza, P.J. Núñez López / Mechanical Systems and Signal Processing 98 (2018) 634–651

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elements: (1) capturing signals using sensors strategically positioned in the machine-tool-workpiece system; (2) extracting signal information correlated to the aspect or parameter to be monitored by applying signal processing methods; (3) and the application of efficient predictive techniques for estimating the parameters under analysis. A key aspect to take into account in the monitoring of machining processes is the selection of the appropriate signal processing method to be applied according to the specific signal type acquired during the process. Numerous studies have been published to date using an array of signal processing methods, and the following are among the most extensively used: time direct analysis (TDA) [10,18], singular spectrum analysis (SSA) [9,34,35], principal component analysis (PCA) [37], fast Fourier transform (FFT) [10,31], power spectral density (PSD) [19], short-time Fourier transform (STFT) [37,38], and wavelet transform (WT) [14,27]. The wavelet transform (WT) method has been widely applied to the monitoring of machining processes. This method decomposes a signal into a shifted and scaled series of a prototype function called a mother wavelet characterized on a time-frequency scale [39]. The continuous form of the wavelet transform (continuous wavelet transform, CWT) requires the processing of substantial amounts of redundant information at a high computational cost, and its poor efficiency in on-line applications explains its limited use in the monitoring of machining processes [11]. In contrast, the discrete wavelet transform (DWT) has a much lower computational cost, making it apt for on-line applications. However, the DWT presents substantial limitations in providing an in-depth analysis of high frequency signal components. The DWT has been used to monitor mainly technological aspects related to tool conditions in machining processes [28,30,32,40]. To improve the analysis of high frequencies, the wavelet packet transform (WPT) was used to generate more frequency bands and enhancing the extraction of relevant information from the original signal. The WPT has been primarily employed for the monitoring of tool condition [5,26,29,31,41,42], whereas other technological aspects such as: chip formation [23,24,43], chatter [4,5], residual stress [21], and surface roughness [13,14] have received little attention in the literature. The application of the WPT method requires prior analysis of critical aspects to optimize the application to the type of signal such as: adequate mother wavelet, effective decomposition level (Lj), selection of parameters for statistical feature extraction, and an optimum packet selection method to estimate approximation and detail coefficients (packets) with effective frequency ranges. In the studies published to date on the application of the wavelet transform method to the monitoring of machining processes, no criteria for selecting the mother wavelet have been established, and according to Zhu et al. [27], standard practice involves random selection without any prior evaluation. Moreover, there are neither criteria on the treatment of decomposition levels (Lj) nor on frequency intervals into which the original signal should be decomposed. Thus, a number of studies have resorted to different methods according to the decomposition level (Lj) and packet selection, but none has established a clear criterion. Segreto et al. [13,14,21] and Naiki [41] analysed each packet independently without grouping. Whereas in other instances the volume of information and the computational cost are reduced, and criteria such as maximum energy or maximum entropy are applied. Wu and Du [5] selected maximum energy vibration signal packets for monitoring chatter in turning and tool wear in drilling. Kamarthi et al. [32] used the maximum energy criterion in acoustic emission signals to estimate flank wear in turning, and Sheffer and Heyns [29] applied the maximum entropy criterion in vibration and strain signals for wear monitoring. Zhu et al. [26], Xu et al. [42], and Danesh and Khalili [33] analysed packets in the last decomposition level and rejected all the other levels without any justification. Karam and Teti [23] selected packets with the highest ranked wavelet feature vectors. Packet reduction criteria minimize the volume of information, and substantially lower analytical-computational costs, but at the expense of losing relevant signal information, which undermines the estimates for monitoring process parameters. One of the key indicators for evaluating the quality of machining processes and the surface finish of manufactured products is surface roughness using the parameter arithmetical mean deviation of the assessed profile (Ra) [44]. Of all the parameters, (Ra) is the most widely used to characterise surface finish [45], and has been monitored in several studies [7–20]. The arithmetical mean deviation of the assessed profile (Ra) is used as an indicator of the behaviour of the cutting process as it relies on numerous aspects directly related to machining conditions, including both static aspects: tool geometry, cutting parameters, workpiece material and geometry, and the use of cutting fluids; and dynamic parameters: cutting-edge wear, appearance of chatter, dynamic machine-tool behaviour, dynamic tool-workpiece interaction, among others. In the monitoring of surface finish, many of the published studies have used the non-advanced signal processing methods in the time and frequency domain, such as TDA and FFT, respectively. In the time domain, Özel et al. [15] applied the TDA method to estimate the parameter Ra using cutting forces, consumed electrical power, cutting parameters, cutting time, and specific force. Azouzi and Guillot [8] employed TDA to monitor surface finish by sensor fusing (cutting forces, vibration, and acoustic emission), and incorporating cutting parameters. Risbood et al. [7], Upadhay et al. [18], Kirby and Chen [16], and Hessainia et al. [17] used TDA with vibration signals to monitor the parameter Ra by incorporating cutting parameters. In the time domain, the SSA advanced signal processing methods has been employed to monitor machining processes. García and Núñez [9] used SSA to monitor surface finish (Ra) in turning operations using only vibration signals. Salgado et al. [20] used vibration signals to estimate the parameter Ra in turning operations, using cutting parameters, and tool geometry. In the frequency domain, Abouleta and Mádl [19] estimated the parameter Ra using PSD method to process vibration signals by incorporating cutting parameters, tool geometry, and workpiece features. García et al. [10] estimated the parameter Ra using sensor fusion (acoustic emission, accelerometer, and dynamometer), and signals were analysed by TDA and FFT. In simultaneous time-frequency analysis, the application of advanced signal processing methods such as the WT to monitor surface finish in machining processes is very rare. Segreto et al. [13,14] monitored surface finish by fusing sensors (acoustic emission, strain gauge, and consumed current). Josso et al. [11,12] characterized surface roughness by applying

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post-process techniques based on microscopic imaging. Currently, there is no published research on the application of the WT, DWT, and WPT methods to on-line cutting force signals for the real-time monitoring of surface finish in machining processes. Most studies on the monitoring of surface finish have employed off-line data sources to complement the on-line signals obtained by sensors. These off-line parameters remain static during the monitoring process and make the monitoring systems rigid and imprecise. Thus, the monitoring system is incapable of detecting unexpected malfunctions occurring during the machining process. Moreover, the fusing of sensors raises the cost of the monitoring system due to the number of sensors in the signal processing system, which entails lengthy response times for on-line estimates, and hinders implementation in industrial equipment. Bearing in mind the aforementioned circumstances, the main objective of this study is to apply packet features extraction (WPT) to on-line cutting force signals for the real-time monitoring of surface roughness in automated manufacturing systems. Only one sensor for on-line cutting force signals was used for the real-time detection of unexpected malfunctions or failures in the cutting process, but no off-line variables were used that make the system rigid. This enables the on-line quality control of surface finish to make decisions on the acceptability of a workpiece. The original contributions of this work is to overcome the shortfalls detected in the WPT method by establishing clear criteria based on the analysis of fundamental aspects such as: adequate filtering of cutting force signals; analysis of forty wavelets using commercial software (Labview 2016) to optimize packet feature extraction; assessment of packets to determine the optimum decomposition level; the analysis of the influence of orthogonal cutting force components on surface roughness using statistical feature extraction; the determination of effective frequencies providing data correlated to surface roughness measures; the identification of statistical parameters to enable best packet feature extraction; and the analysis of packet selection methods by comparing the packet reduction methods of maximum entropy (SE-WPT) and maximum energy (E-WPT) with global packet analysis (G-WPT). In order to establish the idealness of packet feature extraction for the monitoring of surface finish using cutting force signals, the results are discussed in comparison to previously published studies. 2. Wavelet transform method The wavelet method is a signal processing technique to represent and analyse a time signal in the time-frequency domain. This method is based on the shifted and scaled signal decomposition of a prototype function called mother wavelet [27,39]. These functions are similar to the complex sinusoid used in the Fourier transform, except for two fundamental differences: (1) the complex sinusoid lasts infinitely, whereas the wavelets are functions of limited duration, which are located in time (translation) and frequency (dilatations); and (2) the sinusoid is smooth and predictable, whereas the wavelet tends to be irregular and asymmetric (Fig. 1). Let wðtÞ 2 L2 ðRÞ be a function called mother wavelet, then ws;u ðtÞ, with s; u 2 r, and s > 0 are a family of shifted and scaled functions of a mother wavelet. This provides a modulated window wðtÞ, which generates an entire family of elementary functions by dilatations or contractions, and translations in time defined by Eq. (1) [27,39]:

  1 tu wu;s ðtÞ ¼ pffiffi w s s

ð1Þ

where s is the scaling parameter, and u the position parameter. The wavelet transform (WT) in continues time of a function xðtÞ is called a continuous wavelet transform (CWT), which is calculated by the inner product of the analysed signal with a family of shifted and scaled wavelets, using the expression Eq. (2) [27,39]:

1 CWTxðs; uÞ ¼ hxðtÞ; wu;s ðtÞi ¼ pffiffi s

Z

1

xðtÞw

1

a

ð2Þ

b

c 2

0

-1

ψ(u,s)

2 ψ(u,s)

1 Amplitude

  tu dt s

0

2

4

6 t i me

8

10

0 -1

-2 0

1

0

1

u

2

2.9

0

Fig. 1. Differences between FFT and WT: (a) sinusoidal wavelet, (b) wavelet db2 and (c) wavelet db4.

5 u

6.8

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The CWT is a useful method for the analysis of non-stationary signals with different behaviours during the sampling time, enabling the temporal location of the components in the frequency domain. The main drawback is low analyticalcomputational efficiency limiting its use to off-line applications. For applications requiring real-time signal processing, wavelet analysis is performed using two methods termed discrete wavelet transform (DWT) [39], and wavelet packet transform (WPT) [46]. Both methods decompose the signal into a mutually orthogonal set of wavelets, derived from the application of a pyramidal algorithm of convolutions with quadrature mirror filters, based on the coefficients described in Eqs. (3) and (4)

Aj ðkÞ ¼

X

hðn  2kÞcj1 ðnÞ

ð3Þ

gðn  2kÞcj1 ðnÞ

ð4Þ

n

Dj ðkÞ ¼

X n

where Aj ðkÞ and Dj ðkÞ are scaling and wavelet coefficients, j is the number of transformation levels with j ¼ 1; 2; . . . ; k is the number of scaled and wavelet coefficients with k ¼ 1; 2; . . . ; N  2j , where N is the total number of samples of the original signal; h and g are low-pass and high-pass coefficients of the scaled function and wavelet function, respectively, based on a chosen mother wavelet; and n is the filter length. These coefficients successively decompose the original signal into approximation (low frequency) or detail (high frequency) signals using the scaled and wavelet coefficients, respectively. In the WPT method for 3-level decomposition (Fig. 2), at level L1 ðj ¼ 1Þ the original signal is decomposed in two frequency ranges: an approximation A (scaling coefficients) is calculated using a low-pass filter (H), and a detail D (wavelet coefficients) calculated with a high-pass filter (G). Low-pass filters remove high frequency fluctuations and preserve slow trends, and high-pass filters remove the slow trends and preserve high frequency. After filtering, the original signal is decimated by a factor of 2, so that the approximation and detail coefficients are equal in number to the sample data of the original signal. Moreover, this procedure eliminates redundant information and significantly enhances the performance of the algorithm. At decomposition level L2 ðj ¼ 2Þ, A and D are subdivided into approximation AA and AD, and detail DA and DD coefficients, respectively. At level L3 ðj ¼ 3Þ the procedure is repeated. The approximation and detail coefficients generate at each level independent frequency packets consisting of Nx2j coefficients. This procedure is repeated until the desired wavelet decomposition level is achieved. 3. Experimental setup The experimental test of this study consisted of 120 carbon steel AISI 1045 workpieces machined by exterior longitudinal turning on a numeric control lathe Goratu G CRONO 4S (50 kW, 3200 rpm), with a tool holder MWLNL 2020K08, and an uncoated cermet insert CNMG120404PF of titanium carbonitride Ti(C,N) [47]. The machined workpieces were 80 mm in diameter and 130 mm in length, of which 50 mm was used for clamping. In each machining trial, the workpiece was machined in a single pass with a new fresh edge to avoid interfering in the repeatability of workpieces. The experimental turning test was based on a factorial design combining the following cutting parameters: - Cutting speed (v) = 250, 275, 300, 325, 350 m/min. - Feed rate (f) = 0.08, 0.11, 0.14, 0.17, 0.20, 0.23 mm/min. - Cutting depth (d) = 0.5, 0.8, 1.1, 1.4 mm. For each machined workpiece, signals of the three orthogonal cutting force components (Fx, Fy, Fz) were registered using a system composed of a triaxial dynamometer Kistler 9121 and a charge amplifier Kistler 5019b (Fig. 3). The systems was connected by an interface BNC 2110 to a data acquisition card NI PCI-6133 with a sample frequency of fs = 5 ksamples/s. The computer monitoring system was developed using the Labview virtual platform. When workpieces undergo turning

Original Signal H

2

G

A H

H

2 AAA

2 AA G

2 DAA

2 D

H

G

2 DA

2 ADA

G

H

2 DDA

H

2 AAD

2 AD G

2 DAD

Fig. 2. The 3-level wavelet packet decomposition method.

H

G

2 DD

2 ADD

G

2 DDD

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Fig. 3. Experimental set-up.

processes with a free cantilever, the static and dynamic behaviour of the workpiece-tool system varies as the tool advances along the machined length. Thus, to ensure optimum signal characterisation, the machining length was divided into 3 equidistant sampling areas (SA1, SA2, SA3): one next to the clamping area, another in the middle of the sampling area, and a third at the free cantilever. Fig 3 shows the captured cutting force signals were subdivided into three parts coinciding with the three sampling areas (SA1, SA2, SA3). The test involved 120 workpieces  3 cutting forces components  3 sampling areas = a total of 1080 signals. The parameter selected to characterize surface finish was the arithmetical mean deviation of the assessed profile Ra [44], as measured with a stylus profilometer (2D contact method). Surface finish was evaluated using a 0.8 mm cut-off (kc) length, 5 sampling lengths, and an evaluation length of 4.0 mm [48]. For each sampling area a surface roughness value (RaSA1, RaSA2, RaSA3) was obtained from the arithmetic mean of three measures at different angles: 0°, 120°, and 240°, to obtain 120 workpieces  3 sample areas  3 angles = a total of 1080 roughness measurements. Table 1 shows the results of the arithmetical mean roughness Ra obtained in the workpiece sampling areas. The surface roughness for each sampling area (RaSA1, RaSA2, RaSA3) were associated with its corresponding cutting force signal registered in the turning test. A total of 360 experimental data were obtained (Table 1), 75% (270) of the data points were used for building the models, and the remaining 25% (90) were used for independent validation of the models. The validation data were selected from random uniform distribution signals.

4. Methodology This study analysed the behaviour of 40 mother wavelet functions (Table 2) for processing cutting force signals to monitor surface roughness (Ra). The wavelet packet transform (WPT) was applied to the signals obtained for each orthogonal cutting force component (Fx, Fy, Fz), with 5-level decomposition (L1, . . ., L5) of the original signal into approximation and detail packets (Fig. 4). Then, the information provided by each packet was evaluated for the prediction of surface finish using three methods: global analysis of all the packets (G-WPT) obtained at a decomposition level Lj, the analysis of maximum energy packets (E-WPT), and the analysis of maximum entropy packets (SE-WPT). Packets provided by the three methods were evaluated using the statistical features shown in Table 3 [49]. In order to process and evaluate the information obtained in each packet, predictive models were built, based on multivariable polynomial regression to assess the predictive power in estimating the arithmetical mean deviation of the assessed profile Ra. To obtain these models, forward stepwise regression was employed for a 95% confidence interval, and the p-value 0.05 to select the significant variables of the model. Combinations of variables and their interactions were analysed up to order 4, with the first order linear models offering the best results. Packet features extraction and the signal statistical features were analysed according to the goodness of fit and the predictive power of the models obtained. The goodness of fit to experimental data was analysed using the adjusted R-squared R2adj . The predictive power was estimated by the mean relative percentage error  er (Eq. (5)) obtained in the prediction of the experimental validation data, and the analysis of the correlations of the estimated data versus the experimental data. Model reliability was evaluated by the PRED(0.25) coefficient [50] that indicated the percentage of data predicted with a relative error of er 6 25% (Eq. (6)). All of the models under analysis

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E. García Plaza, P.J. Núñez López / Mechanical Systems and Signal Processing 98 (2018) 634–651 Table 1 Experimental test.

v (m/min)

d (mm)

f (mm/rev)

RaSA1 (mm)

RaSA2 (mm)

RaSA3 (mm)

f (mm/rev)

RaSA1 (mm)

RaSA2 (mm)

RaSA3 (mm)

f (mm/rev)

RaSA1 (mm)

RaSA2 (mm)

RaSA3 (mm)

250

0.5

0.08 0.17 0.08 0.17 0.08 0.17 0.08 0.17

0.62 2.18 0.69 2.06 0.58 1.82 0.79 1.67

0.64 2.28 0.74 2.06 0.62 1.83 0.83 1.70

0.67 2.31 0.79 2.08 0.66 1.84 0.82 1.71

0.11 0.20 0.11 0.20 0.11 0.20 0.11 0.20

1.04 2.73 1.05 2.47 1.06 2.23 1.08 2.14

1.06 2.75 1.03 2.47 1.08 2.24 1.09 2.16

1.07 2.76 1.06 2.47 1.09 2.25 1.11 2.15

0.14 0.23 0.14 0.23 0.14 0.23 0.14 0.23

1.59 3.14 1.51 2.77 1.43 2.77 1.35 2.58

1.61 3.14 1.50 2.78 1.44 2.75 1.37 2.56

1.61 3.15 1.52 2.79 1.42 2.79 1.39 2.59

0.08 0.17 0.08 0.17 0.08 0.17 0.08 0.17

0.74 2.45 0.61 1.79 0.69 2.14 0.54 1.53

0.80 2.46 0.62 1.81 0.73 2.17 0.57 1.54

0.83 2.48 0.66 1.80 0.73 2.21 0.58 1.54

0.11 0.20 0.11 0.20 0.11 0.20 0.11 0.20

1.40 2.69 0.97 2.26 1.12 2.48 0.89 1.83

1.42 2.71 0.94 2.27 1.13 2.50 0.90 1.84

1.44 2.70 0.96 2.28 1.16 2.52 0.91 1.84

0.14 0.23 0.14 0.23 0.14 0.23 0.14 0.23

1.90 2.81 1.30 2.59 1.64 2.78 1.19 2.15

1.91 2.81 1.30 2.62 1.65 2.80 1.22 2.18

1.92 2.81 1.31 2.60 1.66 2.85 1.20 2.22

0.08 0.17 0.08 0.17 0.08 0.17 0.08 0.17

0.62 2.72 0.51 1.79 1.03 2.02 0.52 1.51

0.67 2.73 0.54 1.80 1.06 2.04 0.50 1.51

0.69 2.72 0.59 1.79 0.97 2.05 0.56 1.54

0.11 0.20 0.11 0.20 0.11 0.20 0.11 0.20

1.39 3.02 0.84 2.20 1.22 2.34 0.74 1.94

1.43 3.05 0.85 2.19 1.29 2.38 0.75 1.96

1.45 3.05 0.86 2.20 1.27 2.38 0.78 1.98

0.14 0.23 0.14 0.23 0.14 0.23 0.14 0.23

2.17 3.34 1.25 2.58 1.62 2.73 1.07 2.45

2.20 3.32 1.25 2.58 1.61 2.71 1.08 2.46

2.21 3.37 1.25 2.60 1.62 2.71 1.06 2.50

0.08 0.17 0.08 0.17 0.08 0.17 0.08 0.17

0.48 1.24 0.67 1.86 0.73 1.77 0.63 1.43

0.65 1.30 0.62 1.85 0.76 1.77 0.73 1.42

0.51 1.23 0.66 1.87 0.83 1.78 0.77 1.50

0.11 0.20 0.11 0.20 0.11 0.20 0.11 0.20

0.73 1.93 0.94 2.32 1.03 2.20 0.94 1.73

0.78 1.95 0.96 2.31 1.03 2.24 0.96 1.80

0.78 1.94 0.97 2.32 1.06 2.23 0.98 1.78

0.14 0.23 0.14 0.23 0.14 0.23 0.14 0.23

0.77 2.69 1.31 2.76 1.28 2.76 1.19 2.17

0.82 2.71 1.35 2.75 1.35 2.79 1.19 2.23

0.90 2.69 1.32 2.77 1.36 2.80 1.22 2.27

0.08 0.17 0.08 0.17 0.08 0.17 0.08 0.17

0.40 2.17 0.59 1.79 0.76 1.75 0.74 1.79

0.61 2.18 0.72 1.84 0.78 1.78 0.62 1.82

0.58 2.20 0.62 1.84 0.75 1.78 0.73 1.80

0.11 0.20 0.11 0.20 0.11 0.20 0.11 0.20

0.91 2.38 0.96 2.31 1.01 2.14 0.97 2.29

0.93 2.39 0.96 2.32 1.01 2.21 0.99 2.36

0.99 2.41 1.01 2.34 1.01 2.18 0.98 2.36

0.14 0.23 0.14 0.23 0.14 0.23 0.14 0.23

1.55 2.71 1.29 2.68 1.24 2.62 1.33 2.87

1.54 2.71 1.35 2.70 1.31 2.61 1.32 2.86

1.55 2.72 1.31 2.70 1.34 2.63 1.29 2.90

0.8 1.1 1.4 275

0.5 0.8 1.1 1.4

300

0.5 0.8 1.1 1.4

325

0.5 0.8 1.1 1.4

350

0.5 0.8 1.1 1.4

Table 2 Mother wavelets used in this study. Type

Family

Order

Orthogonal

Daubechies Haar Coiflets Symmlets

db2, db3, db4, db5, db6, db7, db8, db9, db10, db11, db12 Haar coif1, coif2, coif3, coif4, coif5 sym2, sym3, sym4, sym5, sym6, sym7, sym8

Biorthogonal

Biorthogonal

bior1.3, bior1.5, bior2.2, bior2.4, bior2.6, bior2.8, bior3.1, bior3.3, bior3.5, bior3.7, bior3.9, bior4.4, bior5.5, bior6.8

met the minimum requirement of a mean relative error of prediction of er 6 25%, and reliability of PRED(0.25)  75% [50]. All models obtained were diagnosed by analysing atypical values, multicollinearity, independence and normality of the residuals, homoscedasticity, and contrasts and hypothesis tests. The statistical analysis and predictive models were performed with the Matlab 2016 software using the statistics and machine learning toolbox.

  i i  n  Ra exp  Rapred  1X   100;  er ð%Þ ¼  n i¼1  Raiexp 

ð5Þ

where n is the total number of surface roughness Ra values obtained in the selected workpiece for predictive model validation.

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ORIGINAL SIGNAL (Fx, Fy, Fz)

L1 L2 L3 L4

A

DA

AA

AAA

DAA

AAAA

DAAA

DDAA

ADAA

ADDA

L5 AAAAA

DAAAA

DDAAA

ADAAA

ADDAA

DDDAA

DADAA

AADAA

AADDA

0 78.125

78.125 156.25

156.25 234.375 234.375 312.5

312.5 390.625

390.625 468.75

468.75 546.875 546.875 625

625 703.125

L5 L4

0 - 156.25

L3

156.25 - 312.5

312.5 - 468.75

0 - 312.5

468.75 - 625

DDDA

DADDA

703.125 781.25

625 - 781.25

DDDDA

ADDDA

DADA

ADADA

937.5 781.25 859.375 859.375 937.5 1015.625 781.25 - 937.5

625 - 937.5

312.5 - 625

L2

ADA

DDA

937.5 - 1093.75 937.5 - 1250

625 - 1250

0 - 625

L1

0 - 1250 Frequency (Hz) Fig. 4. The WPT method applied to cutting force signals with 5-level decomposition (L1, . . ., L5).

Table 3 Statistical feature extraction of cutting force signals. Features

Nomenclature

Mean

X iF j

Standard deviation

riF j

Peak to peak amplitude

PPiF j

Skewness

SiF j

Kurtosis

K iF j

Shannon entropy

SEiF j

Where i is the wavelet packet and j is the Cartesian coordinates x, y, z.

eir ð%Þ ¼

Raiexp  Raipred Raiexp

!  100

ð6Þ

The WPT method applied to cutting force signals (Fx, Fy, Fz) for 5-level decomposition (L1, . . ., L5), and the packets obtained at each level and their corresponding frequency ranges are shown in Fig. 4. In first-level decomposition (L1), the approximation signal (A) corresponded to the original signal registered by the sensor, and the detail signal (D) was null as it was out of range of the sensor. This was due to the frequency range measured by the dynamometer used in the experiments was f D ¼ 1000 Hz, and the sample frequency recommended for optimum signal definition was f s ¼ 5f D ¼ 5000 samples/s, bearing in mind that only the band width corresponding to f s =2 could be represented. This explains why first-level approximation (A) provided signals in a frequency ranging from 0 to f s =4 Hz (0–1250 Hz), which is where the original signal registered by the dynamometry was found, whereas first-level detail (D) produced components in the frequency range of f s =4 to f s =2 Hz (1250–2500 Hz), a bandwidth out of the range of the sensor that could not be evaluated. Thus, only packets with frequencies within the range of the measuring dynamometry (0–1000 Hz) were evaluated (Fig. 4). Another crucial aspect to bear in mind is that the mathematical algorithm used to generate the wavelet packet transform provides components that are not ordered according to frequency. This phenomenon can be tested simply by calculating the WPT of a signal composed of several harmonics, so if the fast Fourier transform (FFT) is applied to each of the packets

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obtained, the spectral content stored in each of them can be analysed. Let x(t), with t 2 R, a continuous function defined by four harmonics Eq. (7):

 xðtÞ ¼ 3 sin

 1 xt þ sinð3xtÞ þ sinð7xtÞ þ 7 sinð9xtÞ 2

ð7Þ

In the frequency domain (FFT), Fig. 5 shows the approximation (A) and detail (D) coefficients of the signal x(t) in 2-level decomposition (L1, L2) for an angular frequency x ¼ 200p rad/s. In level L1, a frequency inverted growth was observed of the detail signal (D), increasing from right to left in the X-axis. In level L2, this phenomenon meant that high frequency content (750–1000 Hz) of the detail signal (D) was stored in the approximation signal (AD), and low frequency (500–750 Hz) in the detail signal (DD). Bearing this in mind, in Fig. 4 the packets were ordered in increasing order of frequency to improve the evaluation of the method.

5. Results and discussion 5.1. Analysis of mother wavelet behaviour in the monitoring of surface finish Forty mother wavelets available in Labview 2016 software were analysed to assess the filtering of cutting forces signals to obtain optimum packet feature extraction for monitoring the Ra parameter. Thus, 3760 predictive models generated with the combinations shown in Fig. 6 were analysed. As stated in the previous section, level L1 was not analysed because the approximation signal corresponded to the original signal registered by the sensor. As shown in Fig. 4, the 26 individual packets obtained between levels L2 and L5 corresponded to the first entry ‘‘26 individual packets” in Fig. 6. Moreover, all of the packets grouped according to levels were analysed, which corresponded to entry ‘‘packet grouping per level”. Thereafter, the orthogonal cutting force components are applied individually (Fx, Fy, Fz) and fused ðF x þ F y þ F z Þ to obtain 94 combinations of predictive models. If 40 mother wavelets are applied to each of these combinations, a total of 3760 predictive models are obtained and evaluated. Given the large volume of data processed, not all of the results of all of the configurations can be shown, and only the results of predictive models exhibiting a good fit to experimental data ðR2adj Þ and mean relative error ð er Þ for each decomposition level (Lj) and mother wavelet analysed are shown in Fig. 7. Though no significant differences were observed in the parameter R2adj (Fig. 7a), both the different mother wavelets and the decomposition levels analysed were in the range of

Original Signal

Amplitude

10 5 0 0

200

400

800 1000

600

Frequency (Hz)

A

D

Amplitude

Amplitude

10 5 0

10 5 0

500 250 Frequency (Hz)

AA

1000

DA

15

AD 15

Amplitude

Amplitude

Amplitude

15

0

0 0

250 Frequency (Hz)

750 500 Frequency (Hz)

DD

Amplitude

0

15

0 500

250 Frequency (Hz)

0 750 1000 Frequency (Hz)

Fig. 5. Approximation and detail coefficients of a signal x(t) in 2-level decomposition.

750

500 Frequency (Hz)

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26 Individual packets 3 Cutting force components (Fx, Fy, Fz) 3760 Regression models Packet grouping per level (4-Level decomposition) 40 Mother wavelets Fusion of cutting forces (Fx+Fy+Fz) Fig. 6. Predictive regression models analysed in this study.

Fig. 7. The R2adj and  er obtained in the prediction of Ra with cutting force signals for the different decomposition levels and mother wavelets analysed with the WPT method.

80% 6 R2adj 6 88%, with several mother wavelets, and levels L2 and L3 showing a poorer fit R2adj in comparison to levels L4 and L5. In Fig. 7b, the mean relative error ð er Þ showed levels L2 and L3 failed to extract full signal information, and generated predictive models with an  er > 14% in all of the mother wavelets. At higher decomposition levels, L4 and L5, better results were obtained and some functions of the daubechies and biorthogonal family showed predictive models with er < 14%. This highlights that L4 and L5 signal decomposition at shorter frequencies located frequency intervals effective for predicting

a 1.5

b 1.5

0.5

ψ

φ

1 0

0 -0.5

-1.5 0

2

4

6 u

8

10

0

2

4

6 u

8

10

Fig. 8. (a) Scale function and (b) wavelet function for the mother wavelet db06.

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surface finish (Ra). The best result was obtained for the mother wavelet daubechies 6 (db06) in decomposition level L4, with an er of 11.9%. Fig. 8 shows the scale function and wavelet function of the mother wavelet db06. 5.2. Individual analysis of packets and decomposition levels Having obtained the mother wavelet with the best behaviour (db06), the effect of decomposition level (Lj) on each of the cutting force signals (Fx, Fy, Fz) was analysed individually, and the information provided by each packet for the monitoring of

b

a 100 80

40

60

er (%)

R2adj (%)

50

Fx Fy Fz

40 20

30 20

0 AA

0 AA

DA Wavelet Decomposition

d Fx Fy Fz

40

60

30

40

20

20

DAA DDA Wavelet Decomposition

0 AAA

ADA

f

DAA DDA Wavelet Decomposition

ADA

50

Fx Fy Fz

80

40

60

er (%)

R2adj (%)

Fx Fy Fz

10

e 100

40

30 20

Fx Fy Fz

20

10

0 AAAA DAAA DDAA ADAA ADDA DDDA DADA Wavelet Decomposition

0 AAAA DAAA DDAA ADAA ADDA DDDA DADA Wavelet Decomposition

h

g 100

50

Fx Fy Fz

80

40 er (%)

60 40

30 20 10

0

0

Fx Fy Fz

AA AA DA A AA DD A AA AD A AA AD A DA DD A DA DA A DA AA A DA AA A DD DA A DD DD A DD AD A DD AD A AD A

20

AA AA DA A AA DD A AA AD A AA AD A DA DD A DA DA A DA AA A DA AA A DD DA A DD DD A DD AD A DD AD A AD A

R2adj (%)

50

er (%)

R2adj (%)

80

DA Wavelet Decomposition

c 100

0 AAA

Fx Fy Fz

10

Wavelet Decomposition

Wavelet Decomposition

Fig. 9. The R2adj and  er for the individual prediction of cutting force packets: (a) and (b) for L2; (c) and (d) for L3; (e) and (f) for L4; and (g) and (h) for L5.

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surface finish Ra was evaluated. Fig. 9a and b shows the results obtained for decomposition level L2, where the best results were obtained by the radial cutting force component Fx with a low frequency signal AA with a R2adj of 78:3% and an er of 17.0%. As for the component Fx, the high frequency packet DA worsened the results, indicating most of the signal information content of Fx correlated to the parameter Ra, was found at the interval (0–625 Hz). The other two components Fy and Fz obtained deficient results in all frequency ranges (AA and DA). In decomposition level L3 (Fig. 9c and d), the best predictions were obtained once again by the radial component Fx in the lowest frequency packet (AAA), with a R2adj of 78.9% and an er of 17.3%. The tendency was the greater the frequency, the worse the results. For the tangential component Fz a maximum fit and a minimum error was obtained for the DAA packet ðR2adj ¼ 60:7% and er ¼ 27:6%Þ; these results were better than in L2. The feed component Fy exhibited similar behaviour to level L2, once again with a better fit R2adj and error er with increasing signal frequency, but with no significant improvement in level L3. In decomposition level L4 (Fig. 9e and f) and L5 (Fig. 9g and h) the radial component Fx showed the same behaviour in fit and prediction as levels L2 and L3, with no significant improvement by increasing the decomposition level. In all of the levels analysed, component Fx provided the most information which was always found at a low frequency packet. For the tangential component Fz, better results were obtained in decomposition level L4 with a maximum R2adj and a minimum  er in the DAAA packet of 72.3% and 18.7%, respectively, which improved the results at lower levels (L3 and L2), with similar results to those obtained for the radial component Fx. At level L5 the results remained stable with no improvement in the results of the tangential component Fz. For the feed cutting force signal Fy, the increase in decomposition level failed to improve the results of the predictive models, and the best behaviour was observed in the high frequency packets, where the dynamic part of the signal was analysed [51], but with poor results in all of the decomposition levels and packets under analysis. The cutting force component Fy provided the least information for the monitoring of surface finish (Ra). 5.3. Global packet analysis (G-WPT) Having identified individually the packets and cutting force components (Fx, Fy, Fz) providing the most information for the monitoring of surface finish (Ra), signal fusion ðF x þ F y þ F z Þ was evaluated to examine if it improved the predictive models. Thus, global packet analysis (G-WPT) was applied using all of the packets obtained in each decomposition level (Lj). Moreover, the information content of each individual cutting force signal (Fx, Fy, Fz) was analysed in comparison to a threecomponent fusion model ðF x þ F y þ F z Þ using all of the packets at each level (Lj). Fig. 10 shows the fit R2adj and the prediction er of the experimental data were similar to those obtained in the individual analysis (Fig. 9) in all of the decomposition levels (Lj), without any improvement in the results. This implies the primary source of information of each cutting force component (Fx, Fy, Fz) was contained at a specific frequency interval, with the remaining intervals being practically negligible. Moreover, the increase in decomposition level (Lj) had a minor influence on the results of the radial force (Fx) and feed (Fy) components. In contrast, the tangential component (Fz) was significantly influenced by the decomposition level, which improved significantly with the increase in Lj up to level L4, with the results stabilising at L5 with no further improvement. This phenomenon highlights that the significant information contained in Fz was located at a specific frequency interval that was hidden when the signal was analysed at longer frequency ranges. The results of the fusion of the three cutting force signals ðF x þ F y þ F z Þ were quite similar to those obtained for the radial component Fx, with a slight improvement in levels L2, L3, and L4. This underscored that the radial component Fx was the primary information source for the monitoring of surface finish (Ra). In the G-WPT method, the best configuration obtained corresponded to the global analysis of packets with the fusion of the three orthogonal cutting force components ðF x þ F y þ F z Þ at level L4, with a fit to experimental data ðR2adj Þ of 87.9% and mean relative error ðer Þ of 11.9%.

a 100

b 50

Fx

Fy

Fz

Fx+Fy+Fz

40

60

er (%)

R2adj (%)

80

40 20

Fx

Fy

Fz

30 20 10

Fx+Fy+Fz

0

0 L2

L3

L4 Level

L5

L2

L3

L4

L5

Level

Fig. 10. The R2adj and  er obtained for the monitoring of the parameter Ra with the individual and fusion models of the cutting force components and decomposition levels Lj analysed using the G-WPT method.

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The significant statistical parameters with their respective type III sum of squares, p-values and the frequency intervals in the predictive model obtained with the G-WPT method are shown in Table 4. The results corroborated the individual behaviour of the cutting force components (Fx, Fy, Fz) analysed in Fig. 9 and 10, where the radial component Fx was the parameter with the most influence ðX AAAA Þ, considerably more than the other characterisation parameters, and thus the component proFx viding the most information for the prediction of surface finish (Ra). Likewise, in the tangential component Fz, parameters with high degrees of significance were observed, which underscored the relevance of this component as complementary to the radial component Fx for the monitoring of surface finish. The low frequency packets (AAAA, 0–156.25 Hz) provided the most significant characterisation parameters, indicating this frequency range was the most adequate for the characterisation of cutting force signals, as it was possible to visualize and measure the entire range of the amplitude of cutting force signals containing the largest percentage of the static part of the signal [51]. The arithmetic mean parameters X AAAA and X AAAA Fx Fz in the low frequency packets (AAAA, 0–156.25 Hz) measured the mean amplitude of the static component [51] of the cutting force signals in radial (Fx) and tangential (Fz) direction, respectively, corresponding to the load of the tool in either direction perpendicular to the axis of rotation, were responsible for flexing of the workpiece at the cantilever, leading to displacement and eccentric rotation of part of the workpiece mass, which in turn altered the dynamic behaviour of the workpiece-tool system, causing vibrations in workpiece-tool contact areas. The low-mean frequency (DAAA, 156.25–312.5 Hz) and high frequency (DADA, 937.5–1093.75 Hz) packets, with information on the dynamic part [51] of the force signal measuring dynamic signal behaviour provided a greater number of parameters but with little influence on the surface finish monitoring (Ra). The feed component Fy provided the least information to the model, with just one significant characterisation parameter, corresponding to the Kurtosis of the dynamic part of signal Fy at a very high frequency (DADA, 937.5–1093.75 Hz). 5.4. Analysis based on maximum energy packets (E-WPT) and maximum entropy packets (SE-WPT) The G-WPT method analysed all the packets obtained in signal decomposition. Highs decomposition levels may produce an excessive volume of information. Thus, the higher the decomposition level, the greater the volume of information processed and the subsequent delay in real-time estimates. Packet selection methods were applied according to the maximum energy (E-WPT) [5,32] or maximum entropy (SE-WPT) [29] criteria, in order to process fewer packets and facilitate signal processing, but at the expense of losing relevant information. The predictive models obtained by applying the maximum energy criterion (E-WPT) are shown in Fig. 11. The analysis of individual cutting force components (Fx, Fy, Fz) revealed feed Fy and tangential Fz components failed to obtain good results in all of the decomposition levels analysed. The radial component Fx also showed deficient results in L2 and L3, the increase in decomposition level significantly improved the results, obtaining a fit R2adj of 82.3% and an error  er of 18.1% for L4 and L5. The components most affected by packet reduction were tangential force (Fz) at levels L3, L4, and L5, and radial force (Fx) at L2 and L3, with a poorer R2adj reaching 40%, and a 20% increase in er in comparison to the G-WPT method. The fusion of all three cutting force signals ðF x þ F y þ F z Þ provided a good fit ð 82% 6 R2adj 6 85%Þ in all of the decomposition levels, but predictive power declined significantly, with the best model being decomposition level L4 ðR2adj ¼ 84:8% and er ¼ 17:6%Þ, with worse er results than those obtained with the G-WPT method (11.9%). For the maximum entropy criterion (SE-WPT), the feed Fy and tangential Fz components exhibited similar behaviour to the maximum energy criterion (E-WPT). Notwithstanding, the radial component Fx showed differences, since level L2 and L3 packets with the most information obtained with the G-WPT method were not eliminated, which improved the results obtained with E-WPT, and equalled those obtained for levels L4 and L5 for G-WPT. The predictive models built with the radial component Fx and the combination of cutting forces (Fx + Fy + Fz) exhibited the best results, the best fit was for the signal fusion model (Fx + Fy + Fz) with a R2adj of 82.01% ð er ¼ 19:85%Þ, and the best prediction range was for the radial component Table 4 Significant signal feature extraction for G-WPT. Cutting force component

Signal feature

Frequency (Hz)

Type III Sum of Sq

p-value

Fx

X AAAA Fx PP AAAA Fx X DAAA Fx DAAA Fx K DAAA ax SEDAAA Fx

0–156.25

10.99

6:51  1028

0–156.25

0.46

1:17  102

156.25–312.5

0.20

9:43  102

156.25–312.5

0.73

1:65  103

156.25–312.5

0.37

2:41  102

156.25–312.5

0.90

4:84  104

Fy

K DADA Fy

937.5–1093.75

0.74

1:45  103

Fz

X AAAA Fz

0–156.25

1.15

8:15  105

SEAAAA Fz

0–156.25

2.32

3:55  108

rDAAA Fz

156.25–312.5

0.38

2:28  102

SEDDAA Fz

3125.5–468.75

0.66

2:27  103

r

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b 50

ENERGY

80

40

60

30

er (%)

R2adj (%)

a 100

40 20

20 10

Fx

Fy

0 L2

Fx+Fy+Fz

Fz

L3

L4

ENERGY

Fx

0 L2

L5

Fy L3

Level

d 50

ENTROPY

80

40

60

30

40 20 Fy

L2

Fx+Fy+Fz

Fz

0 L3

L4

L5

L4

L5

ENTROPY

20 10

Fx

Fx+Fy+Fz

Level

er (%)

R2adj (%)

c 100

Fz

Fx

0 L2

Level

Fy

Fz

L3

Fx+Fy+Fz L4

L5

Level

Fig. 11. The R2adj and  er obtained in the prediction of the parameter Ra in the individual and fusion models of cutting force components for each decomposition level Lj analysed using the E-WPT and SE-WPT methods.

Fx with an  er of 17.0% ðR2adj ¼ 78:3%Þ, both predictive models obtained similar results. In terms of predictive power, the radial force model (Fx) for decomposition level L2 was selected as the best option for applying the SE-WPT criterion (R2adj ¼ 78:3% and  er ¼ 17:0%Þ. The significant statistical parameters with their respective type III sum of squares, p-values and the frequency intervals by applying E-WPT and SE-WPT criteria are shown in Table 5. In the E-WPT model all of the cutting force components (Fx, Fy, Fz) provided information relevant to the model, and their contributions were similar. Similarly to the G-WPT method, the low frequency packets (AAAA, 0–156.25 Hz) contained most of the relevant information for predicting surface finish (Ra). However, both the components evaluating the static part of the signal ðX AAAA ; X AAAA ; X AAAA Þ, and those evaluating the dynamic part Fx Fy Fz ðSEAAAA ; SEAAAA Þ made similar contributions to the predictive model. This was due to the elimination of significant packets in Fy Fz the G-WPT method that provided information to the model, which meant other characterisation parameters of the packets retained in the E-WPT model were now much more significant on account of certain correlations between them. In the SE-WPT method all of the characterisation factors providing information were from the radial component Fx, where low frequency packets (AAAA, 0–625 Hz) contained all of the information of the model. Similar to the G-WPT method, the

Table 5 Significant signal feature extraction for the E-WPT and SE-WPT methods. Method

Cutting force component

Signal feature

Frequency (Hz)

Type III Sum of Sq

p-value

E-WPT

Fx

X AAAA Fx

0–156.25

3.49

1:99  109

K DDDA ax

781.125–937.5

2.26

1:02  106

SEDADA Fx

937.5–1093.75

0.56

1:31  102

X AAAA Fy SEAAAA Fy X AAAA Fz SEAAAA Fz

0–156.25

5.08

9:92  1013

0–156.25

3.60

1:12  109

0–156.25

4.87

2:55  1012

0–156.25

5.07

1:04  1012

X AA Fx

Fy Fz

SE-WPT

Fx

0–625

9.19

rAA Fx

2:13  1015

0–625

3.10

1:69  106

SEAA Fx

0–625

2.82

4:74  106

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factor quantifying the static part of the force signal Fx ðX AA Fx Þ was the most significant characterisation parameter, whereas the AA factors characterising the dynamic part (rAA Fx , SEFx ) also provided information, but to a lesser extent.

5.5. Comparative analysis of G-WPT, E-WPT, and SE-WPT methods The results of the best predictive models obtained with each method are shown in Table 6. The three models showed high fit percentages of R2adj to experimental data, with the G-WPT and E-WPT methods obtaining the best results. Nevertheless, the predictive behaviour of the G-WPT model was considerably more superior to both the E-WPT and SE-WPT models, with a mean relative error of 11.9% and a standard deviation of 1.96%. As for reliability PRED(0.25), the G-WPT model obtained significantly better results predicting 88.6% of the data with an er 6 25%. Estimation time for the real-time monitoring of surface finish was low in all of the models analysed. The G-WPT model had the highest estimation time (24 ms), but these time periods were well below the minimums required for instant real-time estimates in continuous production processes. The analysis of the goodness of fit to the validation data of the G-WPT, E-WPT, and SE-WPT models (Fig. 12), showed that though the G-WPT method was the predictive model with the lowest mean relative error (Table 6), no significant differences were observed in the correlations between (R) the three methods. It is worth noting that the G-WPT model exhibited a uniform distribution in the whole range of Ra values under analysis, with a small area of overestimated roughness values Ra at the interval 2.7–3 lm, which was not particularly important given that these levels of roughness Ra were much higher than those required in most finishing operations. In contrast, the E-WPT model overestimated most of the data, with most variability located in Ra values ranging from 1.5 lm to 2 lm. Moreover, a slight predictive deficiency was observed in the lowest values of Ra, which were low, but significantly increased the mean relative error prediction. The SE-WPT model also overestimated the data in all of the ranges analysed, and data distribution was less uniform than in the two other methods. In the prediction error distribution of the validation data (Fig. 12d), the G-WPT model obtained the best results in the range of optimum predictions ðer 6 15%Þ; with 68.9%, versus 57.8% for the E-WPT model and 51.1% for the SE-WPT model. As for the range of acceptable predictions ðer 6 25%Þ; the new G-WPT model obtained the best results, with 86.6% of the data, in comparison to 72.2% and 70.0% of the E-WPT and SE-WPT models, respectively. The G-WPT was the only model to meet the minimum criterion of PRED(0.25)  75% [50]. This analysis underscored that the application of packet reduction criteria in the maximum energy (E-WPT) and maximum entropy (SE-WPT) methods reduced substantially the amount of signals processing information, leading to the loss of packets with relevant information, with negative repercussions on the accuracy and reliability of the estimates of the predictive models. The G-WPT method based on the global analysis of packets obtained excellent results in terms of accuracy and reliability at a low analytical-computational cost. 5.6. Discussion of results As stated in the introduction, the monitoring of surface finish in machining processes has been undertaken using a broad array of sensors and processing methods. Thus, in the studies published to date there are substantial differences in the experimental methodologies employed and in the construction and validation of predictive models. Moreover, most authors have integrated off-line parameters as an additional data sources to on-line signals captured by sensors. These factors should be borne in mind in any comparative analysis since they substantially condition the results obtained. Table 7 shows the main results of previously published studies on the on-line monitoring of surface finish in turning operations, as well as indicating the type of signal and off-line parameters, the signal processing method, the predictive results obtained, and the methodology for validating the results. As shown in Table 7, most of the studies used non-advanced signal processing methods in the time domain (TDA), whereas in the analysis of the frequency domain (FFT and PSD) have been used occasionally. In relation to advanced signal processing methods, only the time series analysis method SSA has been used, whereas methods of time-frequency analysis (WT, DWT and WPT) have not been used. Furthermore, as shown in Table 7, vibration and cutting force signals have been the most widely used information sources, whilst other types of signals such as acoustic emission and consumed power have not been frequently used. Table 7 shows most of the studies used cutting force signals, requiring complementary information on the cutting process with other sensors and off-line parameters. Azouzi and Guillot [8] estimated the parameter Ra by fusing cutting forces, vibration, acoustic emission signals, and cutting parameters. The signals were processed with the TDA method, and the results revealed the best combination was cutting conditions and cutting forces. The predictions obtained with relative errors

Table 6 Comparison of the results obtained for the G-WPT, E-WPT, and SE-WPT methods for the cutting forces signals. Method

R2adj (%)

 er (%)

rer (%)

PRED (0.25) (%)

Time (ms)

G-WPT E-WPT SE-WPT

87.9 84.8 78.3

11.9 17.6 17.0

1.96 3.36 2.59

88.6 72.2 70.0

24 17.15 3.43

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a

b 3.5

3.5

E-WPT

G-WPT 3

3

R=0.9386 Estimated Ra (μm)

Estimated Ra (μm)

R=0.9494 2.5 2 1.5 1

2 1.5 1 0.5

0.5

0

0 0

c

2.5

0.5

1 1.5 2 2.5 Experimental Ra (μm)

3

0

3.5

0.5

1

1.5

2.5

3

3.5

d

3.5 SE-WPT

80

3

G-WPT E-WPT SE-WPT

R=0.9338 2.5

Number test (%)

Estimated Ra (μm)

2

Experimental Ra (μm)

2 1.5 1

60

G-WPT: PRED(0.25) = 86.6% E-WPT: PRED(0.25) = 72.2% SE-WPT: PRED(0.25) = 70.0%

40

20

0.5 0

0 0

0.5

1 1.5 2 2.5 Experimental Ra (μm)

3

3.5

er≤15

15
e r>25

er (% )

Fig. 12. Estimated values versus real values of the parameter Ra for the following methods: (a) G-WPT; (b) S-WPT; and (c) SE-WPT, using cutting force signals. (d) Reliability of predictive models.

ranging from 2 to 25% were calculated with only 16 workpieces for the models and 5 for the validation, which was insufficient. A similar study was carried out by García et al. [10] without incorporating off-line parameters. In this study, signals were processed with the TDA and PSD methods, using artificial neural networks obtained an  er of 8.6% validated by only 12 workpieces selected under non-random conditions. Özel et al. [15] monitored surface finish using a combination of cutting forces, cutting parameters, cutting time, consumed electrical power, and specific force. The cutting force signals were processed by TDA method, and for an artificial neural network model a RMS error was obtained of 0.49% with insufficient data, hence this result is not comparable with the present study. Most of the studies using only vibration signals as an on-line information source have included off-line parameters in order to obtain satisfactory results. Kirby and Chen [16] used a single component of vibration signal and cutting conditions to monitor the parameter Ra. The vibration signal was processed by TDA and obtained models with a mean relative prediction errors of 5%. In this study, model validation was performed using only 7 workpieces selected under non-random cutting conditions, which was insufficient for satisfactory validation. A similar study by Hessainia [17] concluded that only cutting conditions were significant factors. The correlation between the estimated and the experimental data was very high ðR ¼ 99:9%Þ. However, it should be noted that this correlation was determined using the same data that was used to generate the predictive model, and with a small sample of 27 data. Moreover, Upadhay et al. [18] also monitored surface finish using vibration signals processed by the TDA method and cutting conditions, obtaining a prediction error of 3.5%. These low prediction errors may be explained by the small number of machined workpieces used i.e., 15 workpieces simultaneously used for the building and validation of the predictive models, which was insufficient. In the study of Risbood et al. [7], the parameter Ra was estimated using the radial vibration signal processed with TDA method and cutting conditions, with predictive models obtaining maximum relative errors of prediction of 20%, which were calculated using 20 validation workpieces obtained under random cutting conditions. Abouleta and Mádl [19] calculated the Ra parameter with vibration signals, cutting conditions, and tool and workpiece geometry features. A total of 480 workpieces were used to build the models without validating them, and a deficient fit of R2adj ¼ 35:9% was obtained. Salgado et al. [20] used vibration signals

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Sources

Cutting forces signal with other sources Azouzi and Guillot [8] Fx, Fy, Fz

Method

Results

Test num.

TDA

emin ¼ 2% r ¼ 25% emax r

MED: 16

ax, ay, az AE v, f, d

VED: 5

MED: 52

Fx, Fy, Fz

TDA

ax, ay, az AE

FFT

R2adj ¼ 96:8%  er ¼ 8:6%

Fx, Fy, Fz

TDA

RMSðerrorÞ ¼ 0:49%

MED: 18 VED: 9

az

TDA

 er ¼ 5%

MED: 83 VED: 7

Hessainia [17]

ax, az v, f, d

TDA

R ¼ 99:9%

MED: 27 VED = MED

Upadhyay et al. [18]

ax, ay, az

TDA

R2adj ¼ 93:2%  er ¼ 3:5%

García et al. [10]

Özel et al. [15]

v, f,

VED: 12

P, Ks, t Vibration signal with other sources Kirby and Chen [16]

v, f

v, f, d Risbood et al. [7] Abouleta and Mádl [19]

Salgado et al. [20]

MED: 15 VED = MED

ax

TDA

emax ¼ 20% r

MED: VED: 20

ax, ay v, f, d Material Tool geometry

PSD

R2adj ¼ 35:9%

MED: 480 VED: -

ax, ay, az

SSA

 er ¼ 5:74%

MED: 35 DEV: 20

ax, ay, az v, f, d

TDA

R2adj ¼ 70:5%

MED: 15 VED = MED

ax, ay, az

SSA

v, f, d

v, f, d

Tool geometry Only vibration signal Upadhyay et al. [18]

García et al. [9]

 er ¼ 8% R2adj ¼ 87:8%

MED: 270 VED: 90

 er ¼ 14:6% R ¼ 0:92 PREDð0:25Þ ¼ 91:1% Only cutting force signal Present study

Fx, Fy, Fz

WPT

R2adj ¼ 87:9%  er ¼ 11:9% R ¼ 0:94 PREDð0:25Þ ¼ 88:6%

MED: 270 VED: 90

Where: MED = Experimental data to build the predictive models; VED = Experimental data to validate the predictive models.

processed by SSA method, cutting conditions, tool angle and radius to estimate the parameter Ra, with an  er of 5.74%, and building models with 35 data and validating with 20. The study obtained very good results, but the use of many complementary off-line data sources led to system rigidity, and the validation data replicated the data for building the models. A few studies based solely on vibration signals have been undertaken. In the study of Upadhay et al. [18] surface finish was also monitored using only vibration signals processed by TDA method, obtaining models with a prediction error er of 8%. As previously stated, these low prediction errors may be explained by the small number of machined workpieces used. Similarly, García and Núñez [9] applied SSA to vibration signals to monitor surface finish, and obtained prediction results with an  er of 14.6% and 90% reliability, which were similar to the results obtained in the present study. It should be borne in mind that the SSA method requires a more complex matrix calculus at a higher computational cost, thus limiting its use in realtime monitoring. This review of the published studies on the monitoring of surface finish in turning processes has underscored that none of the studies used only one cutting force sensor. The studies based on cutting forces have used non-advanced methods (TDA or FFT) for signal processing, which limits considerably signal feature extraction. Hence, to obtain satisfactory results researchers have sought to complement information on cutting forces with other types of off-line signals and parameters. Moreover,

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the methods used for constructing and validating the predictive models are inadequate and not very robust with a small number of trials. This discussion of the results highlights that the signal processing method proposed in this study (WPT) enabled the monitoring of surface finish in turning processes with only one cutting force sensor, without the need for other off-line sensors and parameters as a complementary information source on the process. This time-frequency analysis improved the results of non-advanced methods in the time (TDA) and frequency domain (FFT). The methodology for constructing and validating the predictive models has served to develop a robust and reliable monitoring system with an er of 11.9%, a reliability of 88.6%, a correlation of 0.94, and a response time of 24 ms. 6. Conclusions In this study, packet features extraction (WPT) was applied to on-line cutting force signals for the real-time monitoring of surface roughness in automated machining systems. Only one on-line sensor without any need for off-line parameters was used to detect unexpected malfunctions in the cutting process, in order to make on-line decisions on the acceptability of workpiece surface quality. One of the main original contributions of the present study was to determine the optimum application of the WPT method to cutting force signals for the monitoring of surface roughness. Therefore, clear criteria have been established based on the analysis of fundamental aspects such as: the behaviour of forty mother wavelets, the optimum decomposition level; the best statistical features extraction, the effective signal frequency ranges, and the packet selection method. In the forty mother wavelets analysed, the mother wavelet daubechies 06 obtained the best results. But a broad set of mother wavelets exhibited good behaviour, and could be applied for the monitoring of surface finish (Ra). The analysis of 5-level decomposition revealed level L4 provided the best results for estimating the arithmetic mean deviation Ra. It should be noted that excessive decomposition of levels is not always the best option, and may even deteriorate the results obtained. Thus, data analysis at each level was essential to determine optimum packet decomposition. The fusion of the three orthogonal components of cutting forces (Fx + Fy + Fz) provided the best results for predicting the parameter Ra. Of the three components analysed, radial (Fx) and tangential (Fz) forces were the cutting force components providing most information for the monitoring of surface roughness (Ra). As for the analysis of frequency ranges, the most successful packets for the monitoring of surface roughness were found at low frequency (0–156.25 Hz) range. In relation to the statistical feature extraction, the arithmetic means evaluating the static part of the signal, and Shannon entropies and standard deviations evaluating the dynamic part of the signal were the best option to correlate signal features with roughness measures. The application of packet reduction criteria based on maximum energy (E-WPT) and maximum entropy (SE-WPT) significantly deteriorated the results for the surface finish monitoring (Ra) in comparison to the G-WPT method. This indicated that the elimination of packets had led to the loss of signal information and in turn deficient predictive models. The G-WPT method was found to be the best analytical method providing the best results for the monitoring of surface roughness (Ra). 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