Feature representation of audible sound signal in monitoring surface roughness of the grinding process

ABSTRACT

This study proposes the feature representation method of audible sound (AS) signal in the grinding process. The extracted sound feature is provided as the input for the machine learning model to predict the machining surface roughness. Firstly, a sensitive EEMD-IMPE feature set is extracted from the AS signal basing on the combination of the ensemble empirical mode decomposition (EEMD) and improved multiscale permutation entropy (IMPE) methods. Then, an optimized PSO-LS-SVR predictor model is- established basing on the particle swarm optimization algorithm (PSO) and least square support vector regression (LS-SVR) to predict the surface roughness. The experiments demonstrated the consistent AS feature, which is specific to the grinding surface quality in a cutting parameter set. The results of the PSO-LS-SVR model show that the extracted EEMD-IMPE feature is used to predict the grinding surface roughness with the high prediction accuracy and can be controlled within 8% of testing data.

KEYWORDS:

• Audible sound (AS)
• EEMD-IMPE feature representation
• surface roughness
• grinding
• optimized predictor model

1. Introduction

Machining sound usually reflects the working condition of the machine, cutting tool, and workpiece. A sound monitor system of the machining process is desired in intelligent manufacturing to increase machining efficiency (Frigieri et al., 2019; Mannan et al., 2000). Especially, the grinding surface roughness is critical when the machine parts are contacted with each other (Alexandre et al., 2017). During machining operations, the grinding wheel operates directly on the workpiece and thereby affects the texture of the workpiece surface. Under the grinding parameter, the machine and wheel conditions, the machining sound will be different, and many experienced operators can initially diagnose a machine just by listening to its machining sound. In this study, the machine learning technique is applied to learn the features in the sound of the machining process. The machining sound feature is extracted to training and testing the machine learning, which is then applied to forecast the surface quality of the machining process.

Surface quality of the workpiece is produced in the machining process, which requests to be monitored continuously in real-time to adjust the machining parameters, cutting tool, etc. In the machining grinding operation, researchers have investigated the correlation between surface roughness, texture and tool, and cutting condition (Carrino et al., 2020). They have studied and developed different methodologies for real-time monitoring in order to identify changes, failures, or tears or predict the machining quality or tool wear. The different source data of real-time are used such as cutting forces, vibration signals, acoustic emission (AE) and audible sound (AS), electric current, image, and many other sources to extract the informational feature thereby allowing online adjustments or offline forecasting for the machining process. In fact, two common acoustic-based data types including acoustic emission (AE) and audible sound (AS) are used to monitor the grinding conditions (Gok et al., 2012; Hosokawa et al., 2004). The AS signals have a strong correlation with surface roughness, which represents the full picture of the machine’s operating state (Downey et al., 2014; Frigieri et al., 2017). Motivated by these results, we investigate AS data from microphone sensor for the indirect monitoring of grinding surface quality in this study. The microphone sensor signal is used to predict the surface roughness that is generated by the metal-abrasive process. AS signal has observed that it correlates the sound energy with surface roughness in machining operations.

The combined techniques for processing the signal and extracting feature vectors are very important for machining sound prediction (H.-G. H.-G. Chen et al., 2019). Normally, the methods are used as the Fourier transform, wavelet transform, and spectral analysis (Nasir et al., 2019; Thomazella et al., 2019; Yang et al., 2014), (Lopes et al., 2021; Shrivastava & Singh, 2020), which were mostly based on the theory of Fourier transformation. These traditional methods are not applicable to processing signals of the grinding process, which are almost the non-stationary and nonlinear signals. They can only detect features if it is already in an almost fully developed stage and easy to extract clear information from original signals. To highly meet the demand of real-world production, it is necessary to detect the onset of chatter before chatter marks have been made on the workpiece. Given this requirement, EEMD method is selected in this study for analysing the nonlinearity of the signal in real sound (WU & HUANG, 2009). Because of their ease of use and excellent performance for complex signals, the method has been successfully applied in many scientific fields such as wind energy, economy, fault diagnosis, and monitoring of machining conditions (Buj-Corral et al., 2018; H.-G. H.-G. Chen et al., 2019; V. H. V. H. Nguyen et al., 2019; Raja et al., 2013; Wang et al., 2017). EEMD method is a noise‐assisted data analysis method by adding finite white noise to the investigated signal. EEMD can self‐adaptively decompose any signal into a set of intrinsic module functions (IMFs) that include different frequency characteristics. The IMFs generated by the EEMD method contain the machining information that is required to explore the feature of the original machining AS signal. The effectiveness of surface roughness prediction largely depends upon the quality of extracted features. To quantify these AS features, the entropy theory is introduced to states that result in different dynamic characteristics. Multiscale permutation entropy (MPE) method is a new method for analysing dynamic mutation and time series permutation, proposed on the basis of permutation entropy (PE) and has been applied in many fields (Aziz & Arif, 2005), (B. Chen et al., 2015; Nair et al., 2010; Pérez-Canales et al., 2012). Improved multiscale permutation entropy (IMPE) is then defined as the entropy of permutation at multiple scale factors, which can effectively obtain the machining information of AS signals at multiple scale factors and effectively characterize the random mutational behaviour of real-time series. The entropy value is calculated for each coarse-grained sequence, and then, the entropy value of the obtained coarse-grained time series is averaged as the final eigenvalue. This process greatly optimizes the inadequate coarse-grained process and better preserves the rich feature information contained in the AS signal at multiple scales. (Zhang et al., 2021), (Azami & Escudero, 2016). In this study, IMPE is used to calculate the entropy values of first several IMF for constructing the feature vector of AS signal, named EEMD-IMPE. The obtained feature vectors are then imported into the machine learning model to define the machining surface quality.

Machine learning approaches have shown potential for making better decisions to monitor and, finally, to automate the machining process (Carrino et al., 2020; Mirifar et al., 2020; Wuest et al., 2016). Different algorithms are used in the literature, such as Support Vector Machines (Cherukuri et al., 2019; Lu et al., 2019), (Qian et al., 2015), decision trees (Krishnakumar et al., 2015), and deep neural networks (Lee et al., 2020; V. Nguyen et al., 2020). In this study, a least squares version of support vector regression (LS-SVR) is employed. LS-SVR was performed to evaluate prediction in which LS-SVR presents a good estimation error when the training data set is reduced, and a greater capability of generalization in the prediction of the machining conditions, the non-sensitive loss function is replaced by a quadratic loss function, and the inequality constraints are replaced by equality constraints (Duan & Hao, 2014; Papandrea et al., 2020). Through constructing a loss function, the quadratic programming problem is translated into solving linear equation group problems. To obtain the highest level of forecasting accuracy, LS-SVR-based particle swarm algorithm (PSO; Chamkalani et al., 2014), named PSO-LS-SVR, is presented and applied to machining condition prediction. In which, PSO algorithm is a population-based optimization tool, which searches for optimum by updating generation (Eberhart & Kennedy, 1995). The PSO’s advantages are that PSO is easy to implement; and there are few parameters to adjust (Li & Tian, 2021; Xuemei et al., 2010). Therefore, PSO is used to find out the parameter pair of the LS-SVR model, i.e. PSO-LS-SVR model for predicting the feature. The advantages of EEMD-IMPE and PSO-LS-SVR are combined in this paper for detecting and identifying grinding sound.

The rest of the paper is organized as follows: Section 2 presents the proposed EEMD-IMPE method used to extract the machining features of AS signal. Section 3 represents the construction of the optimal PSO-LS-SVR predictor model. Section 4 presents the proposed method, achieved experimental results, and discussions. Finally, Section 5 presents the conclusions.

2. Proposed EEMD-IMPE of feature representation

This section represents the method for extracting the feature of AS signal. The EEMD is the basic method to decompose the signal into IMF set and calculate then the entropy energy values of first IMF. The obtained feature vector is represented the original machining signal.

2.1. EMD and EEMD method

EMD has been applied effectively for analysing the complex data of non-stationary, nonlinear (Lei et al., 2013). The EMD method is used to decompose a signal automatically into a set of band-limited functions, intrinsic mode functions (IMF). These functions are estimated by an iterative procedure called sifting. Each IMF should satisfy two basic conditions (Huang et al., 1998): (1) the number of extreme points and the number of zero crossings must either be equal or differ by one at most in the whole data, and (2) at every point, the mean value of the envelopes defined by local maxima and local minima is zero. The EMD can separate a segment of a real-time signal $p\left(t\right)$ into $n$ IMFs: $\left\{IM{F}_1,IM{F}_2,\dots ,IM{F}_n\right\}$, and a residue signal $r$. Hence, $p\left(t\right)$ can be reconstructed as a linear combination:

(1) $p\left(t\right)=\sum _{n=1}^{N}IM{F}_n+r$(1)

EMD is a sifting process and is a systematic way to extract IMFs. The procedure of EMD algorithm can be described as follows:

Given an input signal $p\left(t\right),r\left(t\right)=p\left(t\right),n=0$.

Step 1. Get the local maximum and local minimum of $p\left(t\right)$

Step 2. Get the upper envelope $e_{max}\left(t\right)$ by connecting all local maxima through cubic spline functions. Repeat the procedure for the local minima to produce the lower envelope $e_{min}\left(t\right)$.

Step 3. Calculate the mean value $m\left(t\right)$ at every point of the envelopes:

(2) $m\left(t\right)=\frac{1}{2}\left(e_{max}\left(t\right)+e_{min}\left(t\right)\right)$(2)

Step 4. Calculate $\hat{p}\left(t\right)=p\left(t\right)-m\left(t\right)$. If $\hat{p}\left(t\right)$ satisfies the IMF condition, then $n=n+1$, $IM{F}_n=\hat{p}\left(t\right)$ and go to Step 5; else $p\left(t\right)=\hat{p}\left(t\right)$, go to Step 1.

Step 5. Let $r\left(t\right)=r\left(t\right)-IM{F}_n$. If $r\left(t\right)$ is a monotonic function, end the sifting process, else $p\left(t\right)=r\left(t\right)$ and go back to Step 1.

Ensemble EMD (EEMD) method was developed by Wu and Huang (WU & HUANG, 2009) to eliminate the mode mixing problem in the decomposing complex signal. EEMD is based on the dyadic property of the EMD method and the addition of the white noise in the data analysis. EEMD can clearly separate the natural scale of signals and produce IMFs with full physical meaning. The provision of more credible IMFs than the previous EMD method is an advantage for analysing the complex data in its superiority and application (Jinshan & Qian, 2010; Lei et al., 2013). The principle advanced in EEMD can be crucially described as follows:

Step 1. Add the white noise $w_i\left(t\right),i=1,2,\dots ,N$ to the given signal, $n_i\left(t\right)=p\left(t\right)+w_i\left(t\right)$.

Step 2. Decompose the noisy signal $n_i\left(t\right)$ to get IMFs, $IM{F}_{i,j}\left(t\right),j=1,2,\dots ,K$ by using EMD algorithm.

Step 3. Increase $i$ value and repeat the step 1 and 2 with the number of trials $N$.

Step 4. Calculate the final IMFs after the number of trials, $N$, as $IM{F}_i=\left(1/N\right){\sum }_{i=1}^{N}IM{F}_{i,j}\left(t\right)$.

Figure 1 shows the effectiveness of both EMD and EEMD methods. Both EMD and EEMD method can decompose a complex AS signal into a series of intrinsic mode functions (IMFs). Each of the IMFs includes different frequency bands ranging from high-to-low stationary and implies a distinct time characteristic scale. Observed that EEMD method is better than the EMD method, EEMD can still decompose the data effectively and accurately when the EMD is invalid. The noise-assisted analysis EEMD method can both suppress the mode mixing effectively and improve the accuracy of decomposition (Fang et al., 2018).

Figure 1. A sample of AS signal is decomposed by EEMD and EMD: (a) original signal, (b) using EEMD and (c) using EMD.

2.2. Feature extraction based on EEMD-IMPE

To fully represent the fault information of the original signal, first five IMFs are used to extract the features. In this study, IMPE method is defined to measure the complexity of the first several IMF series, which is a nonlinear dynamic parameter. It can be used to reflect the complexity change of the AS signal, which will sense once the contact pressure of the workpiece and tool changes for the machining system.

Multiscale permutation entropy (MPE) is used to analyse more information on time series. MPE algorithm includes two main steps follow:

Step 1. Applying a ‘coarse-graining’ process to a real-valued time series $x_i$ of length N, $i=1,2,\dots ,N$. Each element of the coarse-grained time series $y_n^{\left(\tau \right)}$ is defined as:

(3) $y_n^{\left(\tau \right)}=\frac{1}{\tau }\sum _{i=\left(n-1\right)\tau +1}^{n\tau }{x}_i$(3)

where $n=1,2,\dots ,\left[N/\tau \right]$, $\tau$ is scale factor.

Step 2. Calculating the PE for each coarse-grained time series $H_p\left(m\right)$. The attained values can be plotted as a function of the scale factor $\tau$.

(4) $H_p\left(m\right)=-\sum _{k=1}^{m!}{P}_{k}ln{P}_k$(4)

where: $m$ represents the embedding dimension; $P_k$ is the probability distribution of each pattern $k,\left(k=1,2,\dots ,m!\right)$. In fact, two main drawbacks of the conventional MPE are not symmetric and the relative variability of the MPE results for long temporal scales. When the MPE is computed, in the coarse-graining process, the number of samples of the resulting coarse-grained sequence is $\left[N/\tau \right]$. When the scale factor $\tau$ is high, the number of samples in the coarse-grained sequence decreases. This may yield an unstable measure of entropy. To overcome the shortage of coarse-graining in MPE, this study proposes an improved MPE (IMPE; Azami & Escudero, 2016) that its algorithm can be described as follows:

Step 1. The coarse-grained sequence is obtained for the real-valued time series $x_i\left(i=1,2,...,N\right)$ of length N to obtain the coarse-graining sequence $y_k^{\left(\tau \right)}=\left\{y_{k,1}^{\left(\tau \right)},y_{k,2}^{\left(\tau \right)},\dots ,y_{k,\tau }^{\left(\tau \right)}\right\}$.

where $y_{k,j}^{\left(\tau \right)}=\frac{1}{\tau }{\sum }_{i=\left(j-1\right)\tau +k}^{j\tau +k-1}{x}_i$; $j=1,2,\dots ,\left[\left(N-\tau \right)/\tau \right]$ and $k=1,2,\dots ,\tau$

Step 2. For each scale factor $\tau$, the PE of each coarse-graining sequence $y_k^{\left(\tau \right)}$ is calculated, and then the IMPE value $P_{IMPE}$ is obtained by averaging $\tau$ entropy values.

(5) $P_{IMPE}\left(x,\tau ,m,i\right)=\frac{1}{\tau }\sum _{k=1}^{\tau }PE\left(y_k^{\left(\tau \right)},m,i\right)$(5)

Theoretically, IMPE takes into account information on all $\tau$ coarse-grained sequences with a scale factor of $\tau$, and can extract more information than MPE’s single coarse-grained sequence, thus avoiding the entropy fluctuation caused by a single coarse-grained sequence. In this study, we use the scale 3 to calculate the entropy value of the first five IMF of AS signal in the feature representation.

The EEMD-IMPE method is then used to extract the features from the original AS signal. These feature values are important and sensitive according to their locality preserving energy from high to low, which reflects the information of machining process. After that, the obtained EEMD-IMPE features of AS signal serves the predictor model with input. A function approximation based on LS-SVR is suitable for performing the regression problems of surface roughness mode. This model can select the optimal parameters by the evolutionary algorithm, PSO algorithm. The obtained classifier model is then used to automatically forecast surface roughness severity.

3. Optimized estimator PSO-LS-SVR model

This section represents the construction of optimal predictor model based on the basic LS-SVR method and the stochastic optimization technique. The PSO algorithm is used to explore the parameter pair of LS-SVR model.

3.1. Least square support vector regression

The Least Squares Support Vector Regression (LS-SVR) algorithm was proposed by Suykens (Suykens et al., 2002). The core of the algorithm changed a penalty term of the slack variable in the optimization goal to quadratic constraints by introducing the least squares linear system and then solved a quadratic programming problem by solving a system of linear equations to simplify the calculation process, greatly reducing the amount of calculation, and improve the computational efficiency.

By considering inputs $x_i$ and output $y_i$. According to the LS-SVR method, the nonlinear LS-SVR function can be expressed as:

(6) $f\left(x\right)=w^T\mathrm{\Phi }\left(x\right)+b$(6)

where $f\left(x\right)$ indicates the relationship between the input variables and predict and results, $w$ is weight vector, $\mathrm{\Phi }\left(\mathrm{x}\right)$ is mapping function to the high dimensional feature space, and $b$ is bias term. Using the function estimation error, the regression problem can be expressed regarding structural minimization principle as:

$minJ\left(w,e\right)=\frac{1}{2}||w||{ }^2+\frac{1}{2}\gamma \sum _{i=1}^n{e}_i^2$

(7) $\mathrm{S}\mathrm{u}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{t}\mathrm{o}{y}_i=w^T\mathrm{\Phi }\left(x_i\right)+b+e_i\left(i=1,2,\dots ,n\right)$(7)

where γ is the penalty parameter, and $e_i\in R$ are training error variables for $x_i$. The Lagrange multiplier optimal programming method is employed to solve Eq. (6)(6) $f\left(x\right)=w^T\mathrm{\Phi }\left(x\right)+b$(6) . The objective function can be determined by altering the constraint problem into an unconstrained problem. The Lagrange is then constructed as follows:

(8) $L\left(w,b,e,\alpha \right)=\frac{1}{2}||w||{ }^2+\frac{1}{2}\gamma \sum _{i=1}^l{e}_i^2-\sum _{i=1}^l{\alpha }_i\left(w^T\phi \left(x_i\right)+b+e_i-y_i\right)$(8)

where ${\alpha }_i$ are Lagrange multipliers. The optimal conditions can be obtained by taking the partial derivatives of Eq. (7)(7) $\mathrm{S}\mathrm{u}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{t}\mathrm{o}{y}_i=w^T\mathrm{\Phi }\left(x_i\right)+b+e_i\left(i=1,2,\dots ,n\right)$(7) with respect to $w,b,e$ and ${\alpha }_i$, respectively as follows:

(9) $\left\{\begin{array}{c}\begin{array}{c}\frac{\mathrm{\partial }L}{\mathrm{\partial }w}=0\Rightarrow w={\sum }_{i=1}^n{\alpha }_i\mathrm{\Phi }\left(x_i\right)\\ \frac{\mathrm{\partial }L}{\mathrm{\partial }b}=0\Rightarrow {\sum }_{i=1}^n{\alpha }_i=0\end{array}\\ \begin{array}{c}\frac{\mathrm{\partial }L}{\mathrm{\partial }{e}_i}=0\Rightarrow {\alpha }_i=\gamma e_i\\ \frac{\mathrm{\partial }L}{\mathrm{\partial }{\alpha }_i}=0\Rightarrow y_i=w^T\phi \left(x_i\right)+b+e_i\end{array}\end{array}\right.$(9)

Considering the kernel function $K\left(x,x_i\right)=\mathrm{\Phi }{\left(x_i\right)}^T\mathrm{\Phi }\left(x_i\right)$, he computed output result by the LS-SVR method $\left(\tilde{y}\right)$ is obtained as follow:

(10) $\tilde{y}=\sum _{i=1}^n{\alpha }_{i}K\left(x,x_i\right)+b$(10)

where, $K\left(x,x_i\right)$ is the kernel function. In this study, Gauss radial basic function (RBF) is chosen to map the samples into a high-dimensional feature space which can make LS-SVR get better performance and generalization, as shown in Eq. (11)(11) $K\left(x,y\right)=exp\left(-\frac{||x-y||{ }^2}{2{\sigma }^2}\right)$(11) .

(11) $K\left(x,y\right)=exp\left(-\frac{||x-y||{ }^2}{2{\sigma }^2}\right)$(11)

where: $\sigma$ is the parameter of the RBF. Finally, after the structure of LS-SVR is determined, the parameter pair $\left(\gamma ,\sigma \right)$ need to optimally select, which affects the learning performance of LS-SVR. In this study, the PSO algorithm is used to obtain the optimal values of this parameter pair.

3.2. PSO algorithm

The particle swarm optimization (PSO) technology was launched by (Eberhart & Kennedy, 1995), which conceptually simulates the social behaviour of groups, such as birds and fishes moving into achieving their goal in N-dimensional space (Chamkalani et al., 2013). Every character flies in the search space toward its optimum with a velocity, which is controlled by its information, and information is provided by other companions within its neighbourhood. At the time segment of $t$, the $ith$ individual is described as $X_i\left(t\right)=x_{i1}\left(t\right),x_{i1}\left(t\right),\dots ,x_{iN}\left(t\right)$. A set of locations of $m$ particles is recognized as $\mathrm{X}=\left\{x_1,x_2,\dots ,x_j,\dots ,x_l,\dots ,x_m\right\}$ in a multi-dimensional space. The finest last position, the point offering the best fitness extent, of the $ith$ individual is recorded and expressed as $P_i\left(t\right)=\left(p_{i1},p_{i2},\dots ,p_{iN}\right)$. The index of the best individual among entire the particles throughout the searching history, global model, and best particle among all the particles in its own experience are represented by the symbols $g$ and $l$, respectively. The velocity for particle $i$ at time element $t$ is shown as $V_i\left(t\right)=\left(v_{i1}\left(t\right),v_{i2}\left(t\right),\dots ,v_{iN}\left(t\right)\right)$. The moving activity of a particle is illustrated as:

(12) $v_i\left(t+1\right)=w{v}_i\left(t\right)+q_1{r}_1\left(p_{Best}-x_i\right)+q_2{r}_2\left(g_{Best}-x_i\right)$(12)

(13) $x_i\left(t+1\right)=x_i+v_i\left(t+1\right)$(13)

where: $q_1$ and $q_2$ are the positive constants, $r_1$ and $r_2$ are two random numbers, $r_1,r_2\in \left\{0,1\right\}$, and $w$ is the inertial weight.

The linear relationship of instantaneous inertial weight is presented as follows:

(14) $w_t=w_{max}-\frac{w_{max}-w_{min}}{t_{max}}t$(14)

The only alteration for the neighbourhood $\left(l_{Best}\right)$ system is to replace $p_g$ with $p_{in}$ for $p_g$ in the velocity equation. In the global model, this relationship is used to revise a particle’s new velocity based on its earlier velocity, the particle’s previous best location $\left(p_{Best}\right)$, and the global best location $\left(g_{Best}\right)$. The calculation methodology for the local model is almost the same. The best experience of neighbour particles is only used rather than the global best experience.

3.3. Optimized PSO-LS-SVR predictor model

The parameter pair of LS-SVR plays a key role in constructing the model, which can be obtained by using optimization algorithm. PSO algorithm is used to explore the search space of the given LS-SVR prediction problem to find the parameters required to minimize the particular objective of accuracy. The principled training phase of the optimal predictor PSO-LS-SVR model includes several main steps, which are implemented as follows:

Step 1. Determine the ranges of penalty coefficient $\gamma \in \left(0.1,1000\right)$ and kernel parameter $\sigma \in \left(0.01,100\right)$ of the least squares support vector regression model. The number of particles is N = 30.

Step 2. Take $\left(\gamma ,\sigma \right)$ as the parameter pair of PSO, initialize PSO algorithm parameters, initialize randomly the particle to form a group of the particles, and randomly generate the initial velocity of the particles. The fitness function is defined as follows:

(15) $F_{fitness}=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left({\tilde{y}}_i-y_y\right)}^2}$(15)

Step 3. Use the LS-SVR to train these particles after they are initialized, get individual fitness values according to Eq. (15(15) $F_{fitness}=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left({\tilde{y}}_i-y_y\right)}^2}$(15) ), and update the optimum values.

Step 4. Determine the termination condition, if the maximum number of iterations is reached, then stop; otherwise, produce a new group according to the velocity Eq. (12(12) $v_i\left(t+1\right)=w{v}_i\left(t\right)+q_1{r}_1\left(p_{Best}-x_i\right)+q_2{r}_2\left(g_{Best}-x_i\right)$(12) ), go to step (3), until the termination requirements. The smallest fitness value is optimal solution.

Step 5. Obtain the optimized PSO-LS-SVR model bay using the optimal $\left(\gamma ,\sigma \right)$ parameter pair in LS-SVR, then use test sample to get predictions.

4. EEMD-IMPE-PSO-LS-SVR method base grinding surface quality prediction

This section presents the experimental results and discussions of the proposed EEMD-IMPE-PSO-LS-SVR method. The surface roughness of the grinding process is predicted based on collected AS data.

4.1. Proposed EEMD-IMPE-PSO-LS-SVR method

The proposed technique based on EEMD-IMPE-PSO-LS-SVR is coherently represented in this section. This technique consists of two main stages: (1) EEMD-IMPE machining feature extraction and (2) the optimal PSO-LS-SVR predictor model construction. Firstly, EEMD-IMPE hybrid method is used to extract the machining features from the original audible sound signal. These features are great meaning and most responsive to increase the overall reliability and prediction accuracy of the predictor model. Secondly, an PSO-LS-SVR predictor model is optimally constructed and then used to forecast the grinding surface roughness. This method can be visualized by the flowchart in Figure 2, which can be described as follows:

Figure 2. Flowchart of predicting surface roughness via EEMD-IMPE-PSO-LS-SVR method.

Step 1. Acquire the AS signals of the machining process are taken by using the microphone sensor.

Step 2. Extract the machining feature using EEMD-IMPE method.

Step 3. Divide the extracted machining feature into the training data and testing data.

Step 4. Use the training data to train the optimal predictor model. The obtained predictor PSO-LS-SVR model is constructed follow the methodologies in Section 3.

Step 5. Estimate the testing data using the optimized predictor model. The prediction of surface quality based on EEMD-IMPE-PSO-LS-SVR demonstrated accuracy and reliability in experiments and comparison.

4.2. Experimental setup

The grinding tests were performed on ACRA model of automatic surface grinder machine. Figure 3 details the actual experimental setup, in which, experimental system uses the wheel type WA46J7V1A of white aluminium oxide as Figure 3b to grind tool steel materials ANSI T1 (W18Cr4V). The workpiece has a dimension of 250 mm in length and 40 mm in width. The grinding parameters were as follows: wheel speed: 2800 r*min-1, feed velocity: 20 m*min-1, depth of cut: 15 μm (Machinability-Data-Center, 1980). The AS signals during grinding process were collected at maximum 20 kHz by a microphone of B&K type 4189 mounted on the side face of the wheel guard; the location of the microphone in relation to the cutting interface is shown in Figure 3a. The 20 testing samples of the machining sound in the grinding operation are collected at the same grinding parameters. The collected machining sound is the target signals that the grinding wheel and workpiece actually contact. After that, the surface roughness has been measured using a Mitutoyo portable surface roughness model SJ-210. Figure 4 shows the diagram of surface roughness measurement.

Figure 3. Diagram of the experimental setup, a) experimental setup, b) grinding wheel.

Figure 4. Diagram of the measurement.

4.3. Prediction results and discussion

The AS of grinding operation hidden in the features of machining process needed to be extracted. The proposed EEMD-IMPE method is used to exploit the features. Firstly, machining sound data are decomposed into the IMFs, which contains the grinding feature information of the original signal. Secondly, IMPE method is applied to first five IMFs, which present the most important information on AS signal. The calculated entropy values are formed the feature vector of original data. The obtained EEMD-IMPE feature set is used to train and test the predictor model.

Thirdly, 16 extracted features (80% of the EEMD-IMPE feature) are used to search the optimal parameters of LS-SVR by the PSO algorithm; they are the training data for constructing the optimized predictor PSO-LS-SVR model. Finally, the optimized predictor PSO-LS-SVR model is used to forecast the testing data (20% of the remaining EEMD-IMPE feature). The predicted result value of training data is shown in Table 1, which is compared respectively with the measured value/ real value. Visually, Figure 5 shows the comparisons between the prediction values and experimental values of training data. This figure shows that the prediction values are very close to the real values of surface roughness. Actually, the accuracy reaches to 99.88% as high as by calculating the detail values, which means that the predicted values are close to the real values and the prediction precision is very high. The EEMD-IMPE-PSO-LS-SVR can reflect precisely the complex relationship between AS data of machining operations and surface roughness of training data.

Figure 5. Scatter diagram of the training data.

Table 1. Surface roughness prediction results of training data.

No	EEMD-IMPE Features					Ra (μm)		Error (%)
						Measured	Predicted PSO-LS-SVR
1	2.9839	2.8174	2.2316	1.7551	1.3995	0.372	0.3727	0.1993
2	3.0591	2.8485	2.2943	1.7834	1.4052	0.287	0.2874	0.1249
3	3.0012	2.8414	2.2018	1.7478	1.3793	0.410	0.4094	−0.0269
4	2.9946	2.7904	2.1472	1.7491	1.3544	0.366	0.3655	0.0063
5	3.0310	2.7802	2.2262	1.7526	1.3726	0.458	0.4581	0.0208
6	3.0897	2.4632	2.0904	1.6821	1.3813	0.382	0.3820	0.0004
7	2.9925	2.7277	2.2075	1.7413	1.3847	0.460	0.4585	−0.2186
8	2.9991	2.7615	2.2362	1.7553	1.3907	0.345	0.3466	0.6212
9	2.9146	2.7540	2.2724	1.7651	1.3802	0.371	0.3710	0.0061
10	3.0188	2.7850	2.3194	1.7698	1.3882	0.521	0.5209	−0.0198
11	3.0287	2.6711	2.1035	1.6947	1.3614	0.446	0.4456	0.0166
12	3.0567	2.8000	2.2650	1.7774	1.3905	0.414	0.4131	−0.0971
13	2.9940	2.8030	2.2471	1.7632	1.3983	0.376	0.3738	−0.4619
14	2.9067	2.8045	2.1827	1.7208	1.3684	0.401	0.4006	0.0234
15	2.9874	2.8105	2.2377	1.7175	1.4280	0.578	0.5779	−0.0099
16	2.9498	2.7758	2.2305	1.7232	1.3747	0.598	0.5974	−0.0234
Average error								0.1173

In order to verify the prediction and generalization ability of the established surface roughness prediction model, the other four sets of machining feature set, which are not used in the training data, are used as input values to predict the corresponding surface roughness. After normalizing, the test data are introduced into the established LS-SVR model and the prediction values are obtained. The prediction results are shown in Table 2. From this table, it can be seen that the prediction errors are almost within 8%, which means that most prediction values of the test data are close to the real values and the predicted surface roughness values can be trusted.

Table 2. Surface roughness prediction results of testing data.

No.	EEMD-IMPE Features					Ra (μm)		Error (%)
						Measured	Predicted PSO-LS-SVR
1	3.0087	2.8073	2.2764	1.7990	1.4678	0.460	0.4287	−6.8146
2	3.0195	2.7863	2.2599	1.7347	1.3931	0.383	0.3638	−5.0157
3	2.9685	2.7578	2.2326	1.7366	1.4066	0.470	0.4526	−3.6946
4	2.9801	2.7533	2.2003	1.7353	1.3777	0.478	0.5144	7.6197
Average error								5.7861

In order to prove the good performance of the PSO-LS-SVR predictor model in surface roughness prediction, the prediction accuracy of PSO-LS-SVR is compared with the accuracy of the other methods. We use the GA-LS-SVR model and classical predictor LS-SVR model to forecast the testing data with the same training data. The comparison results are shown in Figure 6 and Table 3. From Figure 6, it can be seen that the prediction values of PSO-LS-SVR are closer to the real values compared with those of other models. And from Table 3, it can be seen that the training average accuracy of PSO-LS-SVR predictor model can reach 99.88% and the testing average accuracy gets to 94.21%, which are higher than the other models.

Figure 6. Comparison between prediction values and experimental value of test data.

Table 3. Comparison of prediction accuracy between different predictor model.

Predictor	Training accuracy	Testing accuracy
PSO-LS-SVR	99.88	94.21
GA-LS-SVR	95.5	93.44
LS-SVR	98.65	92.48

To demonstrate the superiority of the proposed EEMD-IMPE method for extracting the machining features of grinding process, we made a comparison with the other methods. The methods based on multiscale permutation entropy (MPE) and singular value decomposition (SVD) are applied to EEMD method to extract the machining feature of original AS signal, named EEMD-MPE and EEMD-SVD, respectively. The extracted feature sets are used to training and testing the predictor models as above constructed. The comparison results are shown in Table 4. From Table 4, it can be seen that the prediction accuracy result based on extracted feature sets is lower than the obtained result of the proposed EEMD-IMPE feature set on the all-predictor models. The results of Tables 3 and 4 objectively reveal that the percentage prediction accuracy achieved by the proposed EEMD-IMPE-PSO-LS-SVR method is a significant result. To visualize the comparative results of the different forecast method, they are clearly depicted in the column chart in Figure 7 with both training data and testing data. This study verifies that the EEMD-IMPE-PSO-LS-SVR method proposed is suitable for surface roughness prediction. The AS feature of grinding process is used to establish the predictor model in the comparison reliability.

Figure 7. Comparison diagram of the prediction accuracy (a) training data, (b) testing data.

Table 4. Comparison of prediction accuracy between different extracted feature sets.

Predictor	EEMD-MPE		EEMD-SVD
	Training accuracy	Testing accuracy	Training accuracy	Testing accuracy
PSO-LS-SVR	87.59	93.06	84.82	89.58
GA-LS-SVR	88.17	92.46	84.87	90.08
LS-SVR	84.81	90.27	84.75	89.85

5. Results

This paper is based on a theoretical synthesis and experiments to propose a prediction technique for grinding surface roughness. A new prediction technique integrates the feature representation based on EEMD-IMPE and the ideal PSO-LS-SVR predictor model in experimental. In the predicting process, the EEMD method firstly decomposed the original AS signals into IMFs. The IMPE method of the optimal modal component is then used to calculate entropy value of the first five IMFs for constructing the feature vector. The results show that the EEMD-IMPE features have better stability and can more accurately characterize the complexity of the signal in the predictor model. Finally, these features are fed into the predictor model as the input for performing prediction. The optimized PSO-LS-SVR model is competent for surface roughness prediction. The experimental results showed the effective prediction performance. The predicting accuracy of the proposed EEMD-IMPE-PSO-LS-SVR technique is found to be 99.88% of training data, which is higher than that of other prediction techniques. The authors are confident that, this technique can be safely applied to other prediction fields in machining operations with nonlinear, non-stationary data.

Acknowledgments

The authors would like to express our gratitude to Faculty of Mechanical Engineering, Hanoi University of Industry.

Disclosure statement

No potential conflict of interest was reported by the author(s).