New Tool Wear Estimation Method of the Milling Process Based on Multisensor Blind Source Separation

Timely and eﬀective identiﬁcation and monitoring of tool wear is important for the milling process. However, traditional methods of tool wear estimation have run into diﬃculties due to under small samples with less prior knowledge. This article addresses this issue by employing a multisensor tool wear estimation method based on blind source separation technology. Stationary subspace analysis (SSA) technology is applied to transform multisensor signals to stationary and nonstationary sources without prior information of signals. Ten dimensionless time-frequency indices of the nonstationary signal are extracted to train least squares support vector regression (LS-SVR) to obtain a tool wear estimation model for small samples. The analysis and comparison of one benchmark tool wear dataset and tool wear experiments verify the feasibility and eﬀectiveness of the proposed method and outperform other two current methods.


Introduction
e computerized numerical control (CNC) milling machine provides an important source of power for hard machining. With the advantages of high automation and good precision, it is widely used in modern manufacturing. e cutter tool is the primary factor that affects the quality of the machine; its wear and damage can directly affect the surface quality of the workpiece as well as the machining efficiency. Tool wear accounts for 20-30% of the total downtime of a milling machine [1,2], and tools and tool changes account for 3-12% of the total machining cost [3]. erefore, online tool wear estimation has become an important research area in intelligent milling machining [4].
As shown in Figure 1, a typical online tool wear estimation method has three steps: (1) sensor signal acquisition, i.e., acquisition of physical field signals in the milling process by one or more sensors; (2) feature extraction, i.e., acquisition of received signals, such as by fast Fourier transform or wavelet analysis, to obtain information related to tool wear; and (3) monitoring, i.e., use of pattern recognition, neural networks, or regression analysis to classify or estimate tool failure.
In online tool wear estimation, many sensors have been used to obtain process signals [5], such as cutting force [6,7], acoustic emission (AE) [8,9], vibration [10,11], and current [12,13]. However, a single physical field signal has several shortcomings; for example, the cutting force is most sensitive to changes of tool wear, but commercial dynamometers are expensive and can increase manufacturing costs. An AE signal is measured at a high sampling rate, which leads to a large dataset and difficult processing and storage [14]. A vibration signal is difficult to filter, and it can be affected by the installation position. A current signal contains much noise, which makes it difficult to detect small fluctuations [15]. Due to the uncertainty and limitations of a single sensor, multisensor monitoring has become common due to its good performance and robustness [16]. Zhao et al. [17] applied a multisensor signal with a three-component dynamometer and three accelerometers to estimate tool wear using local feature-based gated recurrent unit networks. Zhou et al. [18] collected multisensor signals in a milling process and proposed a method to search for optimal feature parameter combinations in multisensor signals. Zhu et al. [19] proposed a smart tool condition monitoring system through several deep learning models with sensors, including cutting force, vibration, AE, CNC process data, and tool wear image. Multisensor methods can enhance the richness of information that contains potential tool wear levels and reduce the overall uncertainty of the measurement. In addition, several researchers determine the cutting tool life through mathematical methods. For example, Krolczyk et al. developed a mathematical model to predict the tool life by examining the influence of cutting parameters, namely, cutting speed, feed, and depth of cut onto tool life [20], researched the coated carbides tool life and the tool point surface topography [21], and analyzed the wear of milling cutters made of sintered carbide and of boron nitride [22], which provide a good theoretical basis for tool wear estimation. Moreover, hybrid intelligent methods have attracted considerable interest for tool fault diagnosis, e.g., wavelet transform (WT) and artificial neural network (ANN). e growth of deep learning (DL) in recent years has led to increasing interest in DL-based tool wear estimation methods [23,24]. However, these hybrid intelligent methods require the signal analyzed to satisfy certain conditions, such as huge number of training samples, independent and identical distribution, white Gaussian noise, or prior information of data. For example, WT-based feature extraction lies in selecting a wavelet basis function that matches the fault characteristic waveform. However, it is difficult to select the appropriate wavelet basis function for the recognition of an unknown milling cutter tool fault [3]. DL-based methods require large amounts of training sample data, which are costly and time-consuming for machining processes [25]. Accordingly, these above conditions are difficult to meet in practical situation [26,27], especially in time-varying and nonstationary nature of the NC machine complex cutting process. Moreover, there is little prior knowledge that can be available to detect and diagnose tool faults in NC machine currently [28]. e study of time-varying and nonstationary processes with less prior information is therefore well motivated. erefore, obtaining good accuracy of tool wear estimation under small sample is currently a hot topic. e main contributions of this article are as follows: (1) A tool wear estimation method for a milling process based on a multisensor blind source separation method is proposed, using small training sample sizes and not presetting model parameters (2) e proposed method based on SSA and LS-SVR significantly outperforms PCA according to milling tool wear experiments (3) Experiments with different cutting conditions verify that the proposed method is robust and promising for milling tool condition monitoring e remainder of this study is organized as follows. Section 2 describes the theoretical framework and proposed tool wear estimation method. Sections 3 and 4 verify the performance of the method with the benchmark PHM-2020 milling dataset and our tool wear experiments. Conclusions are given in Section 5.

Framework.
e proposed online milling tool wear estimation method includes the phases of model training and online tool wear estimation ( Figure 2). During model training, multidimensional signals are collected for different tool wear and divided into several stationary sources and one nonstationary source by SSA technology (Section 2.2). Statistical parameters in the time and frequency domains (Section 2.3) of the nonstationary source are calculated to train the LS-SVR model (Section 2.4). In online tool wear estimation, for a new tool to be tested in milling operation, multidimensional signals are collected by multiple sensors and then extracted the nonstationary source by SSA. Statistical parameters in the time and frequency domains of the nonstationary source are calculated and input to the LS-SVR to estimate the wear value.

Stationary Subspace
Analysis. SSA is a blind source separation algorithm proposed by von Bunau et al. [29]. In SSA, if two first-order parameters of a time series do not change with time, then it is stationary. SSA assumes that an observed multidimensional time series is a linear superposition of stationary sources that are constant over time and nonstationary sources that change with time [30]. An observed multidimensional time series X ∈ R D×N is defined as  where D and N are the dimension and number of data points, respectively; A ∈ R D×D is an unknown independent time matrix that is the linear superposition of the coefficient matrices of stationary and nonstationary sources; and S s t and S n t denote the d-dimensional stationary and (D − d)-dimensional nonstationary sources, respectively.
If d-dimensional stationary and (D − d)-dimensional nonstationary sources exist, then an inverse matrix A −1 can be constructed for the observation data X, such that To determine whether two first-order parameters of a time series change with time, the observed X is divided into continuous time segments, and each is compared with the whole time series through Kullback-Leibler (KL) divergence. e mean μ i and covariance matrix Σ i of each segment X i are calculated, and KL divergence is employed to compare the changes of their mean and covariance, X i (μ i , Σ i ) and X(μ 0 , Σ 0 ), respectively. e stationary index can be defined as To find the stationary mapping B, SSA minimizes the nonstationarity of the stationary direction to be estimated, and the optimal stationary mapping can be obtained by the solution of arg min To solve this problem, SSA uses an iterative operator to find B by updating an orthogonal matrix R. Starting from a random orthogonal matrix R 0 , and in each step k, the steepest descent direction U in a set of orthogonal transformations is found using the standard gradient descent strategy, and the following update is performed until the last step Q : R k+1 � UR k ; then, we obtain B s * � I d R Q W, where W is the whitening matrix.
It can be seen that SSA does not need a large amount of sample data for training nor does it require independent dimension components. As long as the number of segmentation time is not less (generally greater than the dimension of the observed time series), the blind source analysis can be realized.

Statistical Parameters in Time and Frequency Domains.
To overcome the drawback of features in a single domain, which lose some useful information related to the tool condition, we extract a few dimensionless statistical parameters in the time and frequency domains based on the literature [27,31,32] and our experimental studies [11,33]. Table 1 lists 10 statistical feature parameters related to tool wear from the time and frequency domains that were extracted as feature parameters.

Least Squares Support Vector Regression.
e aim of LS-SVR is to extract features from the original space and map the samples to a vector in a high-dimensional feature space, so as to solve the problem of linear indivisibility in the original space [34,35].
Given a training set D � {(X k , y k ) | k � 1, . . ., M}, X k ∈ R D×N , y k ∈ R, X k , and y k denote independent and response variables, respectively. e response function to be estimated is where e k is the error; α and b are the weight vector and bias, respectively, to be estimated; and φ(·) is a mapping function from low-dimensional space to high-dimensional feature space. e loss function J is the sum of squares due to error (SSE) and regularization of α. According to the Lagrange multiplier method, the following equation can be transformed [36] Let the partial derivatives of L to α, b, e, and c be equal to 0. Eliminating e and c, α and b to be estimated can be solved by the following matrix equation: LS-SVR employs a kernel function trick to overcome complex high-dimensional mapping operations of φ(·), such as a polynomial kernel, multilayer perceptual kernel, Bspline kernel, or RBF kernel.
us, the response variable corresponding to a new observed X' can be determined as follows: In this study, the RBF kernel function is used, as given in the following equation, and the hyperparameter h is optimized by leave-one-out cross-validation (LOOCV) due to a small training sample set [37].

Description of Dataset.
e PHM-2010 challenge milling dataset employed for validation testing of the proposed method was obtained from a milling machine under dry milling using a 2-flute ball nose cutter [38,39]. Figure 3 shows the device and sensors used in this experiment, and Table 2 lists the cutting parameters. ere were three types of signals: cutting force from a three-component dynamometer, vibration from three accelerometers, and AE from an AE sensor. erefore, each sample in the dataset included seven sensor channels' time series. e tool's flank wears were measured offline using a microscope after finishing each surface.

Analysis and Results.
According to the data file, three cutter records, C1, C4, and C6, could be used to verify the performance of tool wear estimation. C4 and C6 were used as the training set, and C1 as the testing set.
For each sample, a seven-dimensional signal was obtained from six stationary and one nonstationary source, and the 10 dimensionless statistical parameters listed in Table 1 were calculated as the input of the LS-SVR. ere are two reasons for selecting one nonstationary source: (1) it contains a variety of feature information than the stationary source to distinguish different tool wear; and (2) in the proposed method, it is easy to calculate the statistical parameters for the single nonstationary source.
To test the effectiveness of different methods, LS-SVR and principal component analysis (PCA) + LS-SVR were compared with the proposed SSA + LS-SVR. Ten      Mathematical Problems in Engineering e tool wear estimation results of tool C1 with three methods are shown in Figure 4, from which it can be seen that the estimation accuracy of the proposed method exceeds that of the other two methods. e error between the estimated and actual values of tool wear is presented in Table 3.
e RMSE of the proposed SSA + LS-SVR method was    Mathematical Problems in Engineering 8.4653, which was 83.7% and 62.4% less than that of the LS-SVR and PCA + LS-SVR, respectively. R was 0.9848 for the proposed method, which was 0.69 and 0.28 greater than that of the LS-SVR and PCA + LS-SVR, respectively. Figure 5 shows the experimental setup for milling tool wear estimation under various operating conditions. e workpiece was #45 steel with dimensions of 300 mm × 100 mm × 80 mm, machined by a vertical machining center using an uncoated three-tooth tungsten steel end milling cutter under dry millings. Each cutting was completed five times in finishing a surface, i.e., three times forward and two times back, as shown in Figure 6. A three-axis accelerometer was mounted under the workpiece with a magnetic base to measure its vibrations in the X, Y, and Z directions, and accelerometers were attached to the side of the spindle by strong glue to measure the vibrations of the spindle in the X and Y directions.

Experimental Setup.
ree current sensors were clamped on the machine motor wires to measure the three-phase current of the motor. A sound sensor was fixed near the workpiece to measure sound during the cutting process. erefore, the sensory data consisted of nine channels. ese signals were collected by a data acquisition instrument and stored on a personal computer (Figure 7(a)), with a continuous sampling frequency of 12 kHz during the tool wear test. e wear value of each individual flute was measured offline using a tool microscope after machining a surface (Figure 7(b)).
ere were 14 cutting tools used in our experiment with different cutting parameters, as given in Table 4. In each tool cutting experiment, there were five group signals after cutting a surface. e first four group signals were taken as training samples and the last as the test sample.

Analysis and Results.
A nine-dimensional sensing signal in each sample was transformed by SSA and converted to eight stationary sources and one nonstationary source.
e reason is the same as discussed in Section 3. Figures 8-10 show the transformation results through the SSA of tool 1 for three wear values (corresponding to the first, fifth, and tenth cutting). It can be seen that the time sequence diagram of the nonstationary source changes significantly after SSA transformation, while the changes of eight stationary sources after SSA transformation are not obvious. erefore, we only used the signal of the nonstationary source to estimate tool wear. Here, as in Section 3, the RBF kernel was selected as the kernel function of the LS-SVR, and the hyperparameter was optimized by LOOCV.  Table 5. e RMSE of the proposed SSA + LS-SVR method was 0.0529, which is 77.1% and 51.6% less than that of the LS-SVR and PCA + LS-SVR, respectively. R of the proposed method was 0.8923, which is 0.55 and 0.22 higher than that of the LS-SVR and PCA + LS-SVR, respectively.

Conclusion
In order to solve the problem of low performance of traditional methods for milling tool wear estimation under small sample with less prior knowledge, a multisensor tool wear estimation method based on SSA and LS-SVR was proposed. Taking the advantage of SSA without prior information of signals and parameter presetting, the multidimensional signals collected by sensors were decomposed into stationary and nonstationary sources through SSA, and 10 dimensionless time-frequency statistical parameters from the nonstationary source were extracted as the input parameters of the LS-SVR to obtain the tool wear estimation model under small sample. e proposed SSA + LS-SVR method was validated on the PHM-2010 challenge milling benchmark dataset and our tool wear experiments. e results indicated that the root mean square error and correlation coefficient of the proposed method were significantly better than LS-SVR and PCA + LS-SVR on two milling TCM experiments. Furthermore, the proposed method could be improved to enhance its performance under one-dimensional signal for tool wear estimation, in which the number of subsources needs to be optimized.

Data Availability
e datasets used and analyzed to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.