Establishment and Solution Test of Wear Prediction Model Based on Particle Swarm Optimization Least Squares Support Vector Machine

Abstract

Traditional tool wear identification methods are usually based on the framework of “feature extraction + machine learning”, but these methods often have problems of low efficiency and low recognition accuracy. To address these problems, this paper proposes a tool wear state identification model based on particle swarm optimization (PSO) and least squares support vector machine (LS-SVM), namely the PSO-LS-SVM model. By integrating data collected by multiple sensors, key feature information reflecting the tool wear state is extracted; dimensionality reduction techniques such as principal component analysis (PCA) are used to optimize feature vectors to improve the distinguishability of features. The model parameters are optimized by the two-dimensional coordinates (c and g) of the particle swarm algorithm to adapt to the given training sample set. During the training process, the fitness of each particle is calculated and compared with its historical optimal fitness to update the optimal fitness of the particle. This process is iterated until the global optimal solution is found, thereby achieving accurate identification of the tool wear state. Experimental results show that the PSO-LS-SVM model shows high accuracy and good performance in tool wear state identification, which verifies the effectiveness of the algorithm in improving tool efficiency and extending tool life. The study is the first to combine PSO and LS-SVM for tool wear prediction in multi-sensor data fusion. This advanced recognition technology can significantly reduce the waste of resources caused by premature tool replacement, while improving the stability of the machining process and the consistency of the product.

1. Introduction

In CNC batch processing, tool wear is inevitable. In particular, when the tool wears too much, it affects the quality of the workpiece and can even cause a machine tool safety accident. Therefore, the tool must be replaced or sharpened in time before it wears out. However, if the tool is replaced when the remaining lifespan of the tool is very long, it reduces the economic efficiency of the tool and increases the production cost of the enterprise. In batch processing, it also disrupts the production rhythm and reduces production efficiency [1]. Therefore, how to accurately identify the wear of a tool is the basis for formulating a tool replacement strategy. As industrial production develops towards intelligence and automation, the physical signals related to tool wear during the cutting process can be used to realize the real-time detection of tool wear [2]. Tool wear status monitoring can be divided into direct monitoring and indirect monitoring through different monitoring technologies. The direct monitoring method can provide accurate tool wear data, but it usually needs to be measured when the machine tool is stopped. For example, researchers such as Peng Ruitao directly captured the wear image of the back of the tool through an optical sensor system, used these images as feature signals, and combined them with intelligent algorithms to identify the tool wear status, achieving a high recognition accuracy [3]. Subramanian, K., et al. attempted to monitor tool wear by measuring radioactivity in chips, but this method is not suitable for actual production due to the threat of radioactive contamination to human health [4]. Although the direct monitoring method has advantages in accuracy, its disadvantages are also obvious. For example, it can only be detected when the machine is stopped, which seriously affects production efficiency. Therefore, domestic and foreign researchers have focused more on indirect monitoring methods [5]. Indirect monitoring methods use the influence of tool wear changes on physical signals in the cutting process to infer the tool wear status by monitoring the changes in these physical signals. The following are some commonly used monitoring signals:

(1)

Cutting force signal

Toshiyuki et al. collected three-axis force signals through experiments, extracted multidimensional features using a variety of data preprocessing techniques, and used neural network algorithms to comprehensively analyze these features, successfully realizing tool wear monitoring [6]. Patra, K., et al. studied the changes in cutting force with the increase in the number of holes processed under different feed rates and drilling speeds for force signals in micro-scale machining processes and established a prediction model using artificial neural networks. The experimental results show that the model based on cutting force data has a high consistency with the prediction of the actual number of holes drilled [7].

Dimla et al. also collected three-axis force signals in the experiment; conducted a static analysis of the forces in the X, Y, and Z directions; and compared them with vibration signals and power signals. The study found that the cutting force signal is much more sensitive to tool wear than the vibration and power signals. In particular, among the three-axis force signals, the feed force direction signal is the most sensitive to tool wear [8].

(2)

Vibration signal

As tool wear increases, the cutting force in the cutting process also increases, resulting in increased vibration of the cutting system, and in severe cases, even making the cutting process unable to continue. Since vibration signals are sensitive to tool wear and easy to measure, it is very common to use vibration signals to identify tool wear status in industrial applications.

Ratava, J., et al. collected vibration signals in intermittent cutting experiments; constructed a tool wear classification model based on cutting depth, feed speed, and acceleration signals; associated the vibration signals with tool deflection and cutting force signals; and used this model to identify tool wear status [9]. Dai Wen et al. collected three-axis vibration signals during milling processing. During data processing, they used a stacked sparse autoencoder network to optimize and reduce the time domain and frequency domain features and used an adaptive step-size cuckoo algorithm to optimize the LS-SVM model parameters. They established a tool wear status prediction model based on vibration signals and achieved a high prediction accuracy [10].

(3)

Current and power signals

Tool wear increases the friction between the workpiece and the tool, which will not only increase the motor current but also increases the load power, which will eventually manifest as an increase in the total spindle power. Using current and power signals to monitor tool wear is a convenient method. Through the OPC UA server and Ethernet connection, the power data of the machine tool during the cutting process can be obtained in real time, while avoiding the influence of factors such as cutting, machine tool vibration, and tool temperature change. However, in finishing and semi-finishing cutting, the changes in machine tool power and current caused by tool wear are not obvious, and there is a certain hysteresis. Therefore, this method is more suitable for processing occasions with large cutting consumption [11].

Li Congbo and colleagues analyzed the relationship between cutting power and tool wear and verified the influence of processing parameters on cutting power through experiments. On this basis, a regression model between cutting power, processing parameters and tool wear was established, and an online tool wear monitoring system with the real-time alarm threshold updates was developed using this model [12]. Romero-Troncoso and colleagues constructed a theoretical model between power, current, and tool wear and conducted cutting processing experiments. The experimental results show that during the wear process of the tool from the new state to the passivated state, the machine tool power increases by about 20%, indicating that the tool state can be monitored by observing the change in machine tool power [13]. Yang Tao and colleagues established a mathematical model for extracting cutting power from machine tool power and, combined with workpiece quality information, proposed a tool change strategy suitable for mass production. On this basis, tool change decision software was also developed [14].

Lin Yang analyzed the milling force signal generated during high-speed milling by applying wavelet transform, successfully extracted the energy distribution characteristics of different frequency bands, and constructed a preliminary feature model based on this [15]. Subsequently, he used an unsupervised learning network to teach these feature models, and finally used deep learning technology to predict the wear state of the tool. On the other hand, He Donglei and others collected acoustic emission signals in milling processing experiments and proposed an improved EEMD method to process these signals and extract the first six IMF components from them [16]. They further extracted the corresponding Shannon entropy features based on different stages of tool wear and established a feature model. Finally, they used support vector machine technology to identify different stages of tool wear.

Cao Dali and others proposed a tool wear state recognition model based on convolutional neural networks to solve the problem of feature extraction in tool wear state recognition [17]. The model used a deep learning network to perform adaptive feature extraction, effectively avoiding the data loss problem that may occur in the traditional manual feature extraction process and was able to mine subtle features that are not easy to detect in the signal. The research results show that the model has improved both recognition accuracy and generalization ability.

Xie Yangyang et al. used the frequency domain signal of the acoustic emission signal as an input to construct a double hidden layer stacked denoising autoencoder network and used a supervised training method to globally fine-tune the network, achieving the high-precision recognition of tool wear status [18].

However, the existing tool wear monitoring methods still have some shortcomings. Although the direct monitoring method is accurate, it requires shutdown measurement, which significantly affects production efficiency. Although the indirect monitoring method can be used in real time during the processing process, the single sensor signal can only reflect local information and is easily interfered with by the outside world, resulting in low monitoring accuracy.

In view of the shortcomings of the existing methods, this paper proposes a tool wear state recognition model based on particle swarm optimization (PSO) and least squares support vector machine (LS-SVM), namely the PSO-LS-SVM model. The model extracts key feature information reflecting the tool wear state by integrating data collected by multiple sensors such as vibration signals and force data and optimizes the feature vector using dimensionality reduction techniques, such as principal component analysis (PCA), to reduce the complexity of the feature space. At the same time, the LS-SVM model parameters are optimized by particle swarm algorithm to further improve the recognition accuracy and adaptability of the model.

2. Analysis of Tool Wear Status

2.1. Selection of Monitoring Signals

In milling, as the tool wear condition continues to deteriorate, machine tool vibration, spindle power, milling force, acoustic emission, etc., which are closely related to tool wear conditions, will change regularly. Thus, the obtained signal contains rich information about the tool wear condition. By modeling these signals and the tool wear state, the current tool wear condition can be identified.

Milling is an intermittent cutting process, and its machining process presents nonlinear and non-stationary characteristics, resulting in a large amount of ambiguity in the machining process. A single sensor signal can only reflect local information at a certain level of machining. Due to the influence of external factors, the monitoring signal is random. The reliability and accuracy of identifying the tool using a single sensor signal are very poor. Therefore, in the identification of tool wear status, it is often achieved through multiple sensor signals [19]. The tool wear monitoring method based on multi-sensor information is adopted. Through the reasonable selection of multi-dimensional sensor signals, it can not only effectively improve the reliability and accuracy of tool wear status identification but also enhance the robustness of the body.

In the selection of appropriate monitoring signals, the following conditions need to be met:

(1)

The sensor signal is more sensitive to changes in tool wear conditions and is not affected by the external environment. The characteristics contained in the signal can be used to construct a characterization model of the tool wear state.

(2)

The device is easy to install, and the sensor has no effect on the processing technology;

(3)

The system consists of multiple sensors, which work stably and reliably without mutual interference;

(4)

The sensor signal has good real-time performance and can provide real-time feedback on the current wear condition of the tool [20].

Based on the above requirements, it is not appropriate to use acoustic emission sensors as monitoring signals in view of the harsh environment in which the research in this paper was carried out, and the AE signal decays very quickly, which is not conducive to data collection. To this end, in this paper, a preliminary selection of tool wear conditions during milling was made and three types of information were integrated: vibration, force, and power. Compared with using a single sensor as a monitoring signal acquisition system, it has the following advantages:

(1)

During milling, tool wear will cause changes in milling force. Therefore, using force signals as monitoring signals can accurately reflect tool wear in real time. It also has high anti-interference and high sensitivity. It is currently the most widely used and mature monitoring signal. In addition, due to the change in milling force during machining, the power consumption of the machine tool also changes accordingly. The power signal is hardly affected by external factors such as cutting fluid, and the signal can be easily obtained. Therefore, it can also be used to detect tool wear [21]. During milling, the rotation of the tool is a periodic motion. As the tool wear changes, a periodic vibration signal will be generated, which will also cause instability in the cutting system. Therefore, the vibration signal also contains rich tool wear information, which can be used to identify tool wear.

(2)

Force–vibration–power signals are signals in three dimensions. There is a certain complementary relationship between them, which can reflect the wear status of the tool from multiple aspects. In addition, since the installation of the acceleration sensor and the force sensor is relatively simple, the two will not interfere with each other, and the output is simultaneously transmitted through the OPC UA server, so the signal acquisition process will not affect the milling process [22].

2.2. Force Signal Acquisition

The acquisition of force signals is divided into two parts: hardware and software. For this experiment, the Kistler Type 9272 dynamometer, developed by Kistler of Switzerland (manufacturer: Kistler, city: Winterthur, country: Switzerland ), was selected. It can synchronously collect milling force signals in three milling directions. It has a high protection level and can adapt to various harsh processing conditions. In addition, it has strong rigidity and will not be affected by machine tool vibration, so it is very suitable for this experiment. During processing, the dynamometer is first installed on the workbench of the machine tool, and then the workpiece and the dynamometer are connected with screws. During milling, the dynamometer outputs a charge signal, which is amplified by the Kistler 5070 A charge amplifier and then transmitted to the computer. The DynoWare software (DynoWare software Type 2825A) produced by Kistler of Switzerland is used in conjunction with force sensors, data acquisition cards, charge amplifiers, and other equipment to realize the real-time acquisition of force signals [23]. In order to prevent the loss of missed tools, the sampling frequency of the force signal is set at 10,000 Hz. The dynamometer model used in this experiment was the Kistler Type 9272 dynamometer, as shown in Figure 1.

2.3. Vibration Signal Acquisition

The vibration signal acquisition system consisted of an accelerometer, a dynamic signal analyzer, and a microcomputer. In this experiment, the 1A302E three-axis piezoelectric accelerometer (Jiangsu Donghua Testing Technology Co., Ltd., Taizhou, China) was selected. It includes three sensor chips perpendicular to each other, a four-pin connection, and multiple independent cables to output X, Y, and Z axis acceleration signals, respectively. A strong magnet is installed at the rear end of the accelerometer. When the signal is collected, the accelerometer is attracted to the vicinity of the machine spindle. It is matched with the DH5927N dynamic signal detection and analysis system, which can realize the real-time acquisition, storage, and display of acceleration signals in three directions through Ethernet communication [24]. In addition, the sampling frequency of the vibration signal was set to 10,000 Hz to ensure the synchronization of the vibration signal and the force signal. The accelerometer used in this experiment was the 1A302E three-axis piezoelectric accelerometer produced by Donghua Testing, as shown in Figure 2, and is equipped with the DH5927N dynamic signal test and analysis system, as shown in Figure 3.

2.4. Tool Wear and Surface Roughness Collection

This paper uses a GAOSUO handheld digital microscope to test tool wear images. Existing cutting experiments all remove the tool before testing, but this method causes the workpiece and tool to cool down, which affects the wear process of the tool. In order to minimize tool wear during the test, this study fixed the microscope on the workbench and focused it in advance. After each pass, the tool was moved under the microscope with the spindle to photograph the tool wear and measure its wear amount [25]. This method minimizes the test time, realizes the cutting process in actual production, eliminates the assembly error caused by frequent tool disassembly and assembly, and reduces the reduction in tool life caused by temperature fluctuations. A lightweight, contact-equipped roughness tester was selected. The tester only needs to be placed with the probe flat on the test piece to detect the test object and transmit it to the computer through the USB interface. The GAOSUO handheld digital microscope was used to measure tool wear images, as shown in Figure 4.

2.5. Original Signal Analysis

Milling force signals in three directions under different wear conditions during milling. The results show that compared with the X-direction force and the Z-direction force, the Y-direction force is the largest. The Z-direction force decreases with the change in tool wear state, and there is a large fluctuation in the rapid wear stage, indicating that the stability of the cutting system will decrease under high wear conditions [26]. However, in each wear stage, due to the zero drift of the dynamometer signal acquisition, the X-direction force fluctuates around the zero point. Therefore, the X-direction force signal must be preprocessed before subsequent data processing in order to eliminate the influence of the zero-drift field on the signal and improve the signal-to-noise ratio of the entire signal.

Like the force signal, the vibration signal that occurs during the milling process as the tool wears is also shown in Figure 5. The research results show that as the tool wear condition changes, the amplitude of the vibration signal increases, and as the tool wear degree increases, the fluctuation amplitude also increases. This shows that the vibration signal has a significant influence on the stability of the machining process [27]. In this way, the vibration signal can be used to identify the wear condition of the tool. However, since the obtained vibration signal contains multiple factors, such as the vibration of the machine itself and the vibration of the outside world, in order to obtain information that can effectively reflect its wear state, it is necessary to conduct in-depth research on it.

Through the analysis of the original vibration and force signals, it was found that these two original signals can more intuitively reflect the wear condition of the tool. However, these two signals contain too many disturbance factors and cannot be directly used to correlate with the wear condition of the tool. It is also necessary to use a variety of data processing methods to extract characteristic information that can reflect the wear condition of the tool.

3. Wear Stage Identification Model and Parameter Optimization

3.1. Least Squares Support Vector Machine Classification Theory

Support vector machines are effectively combined with kernel function technology. At the same time, this paper takes minimizing structural risk as the criterion and has made breakthroughs in solving problems such as over-learning, dimensionality disaster, and linear inseparability. It has been widely used in fault diagnosis and has strong promotion value [28]. Like neural networks, it uses a large number of samples to train the model and then judges the type and degree of the fault based on the existing model. LS-SVM transforms the inequality problem of general SVM into a one-dimensional linear system, which not only retains the advantages of SVM in classification but also reduces the computational complexity of the training process and improves its execution efficiency [29]. LS-SVM is derived according to the following steps:

Assume that the training set samples are expressed as Formula (1):

$$S=\left\{\right(\begin{array}{c}{x}_i,y_i\end{array}\left)\right|\begin{array}{cc}{x}_i\in R^n,y_i\in \left\{-1,+1\right\},i=1,& \cdots \cdots ,n\end{array}\left\}\right\}\#$$

(1)

where n is the number of samples x_i and y_i is the input and output of n-dimensional sampling.

The objective function of LS-SVM is [30] as follows:

$$minj\left(w,e\right)={\displaystyle \frac{1}{2}}{W}^{T}W+{\displaystyle \frac{1}{2}}\gamma \sum _{i=1}^n {e_i}^2$$

(2)

$$y_i\left[W^T\phi \left(x_i\right)+b\right]=1-e_i,i=1,\cdots \cdots ,n$$

(3)

where w is the weight vector, b is the offset, and γ is an adjustable parameter; e_i is an uncertain variable and φ(x) is a core function.

In solving the above equations, we introduced the Lagrange multiplier to transform the above optimization problem into the following:

$$L\left(w,b,e,\alpha \right)=j\left(w,e\right)-\sum _{i=1}^n {\alpha }_i\left[y_i\left(W^T\phi \left(x_i\right)+b\right)-1+e_i\right]$$

(4)

The solution to the above formula can be calculated using the following matrix equation:

$$\left[\begin{array}{cccc}1& 0& 0& -{\mathrm{Z}}^T\\ 0& 0& 0& -{\mathrm{Y}}^T\\ 0& 0& \gamma 1& -1\\ Z& Y& 1& 0\end{array}\right]\left[\begin{array}{c}w\\ b\\ e\\ \alpha \end{array}\right]=\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$$

(5)

By solving the above equation, we obtained the two parameters, α and b, and thus obtained the LS-SVM model.

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

(6)

In the formula, K is the kernel function. In practical applications, there is still no clear conclusion on how to choose a suitable kernel function. A new kernel function based on a radial basis is proposed, requiring the determination of two parameters: penalty factor c and core parameter g.

$$K\left(x,y\right)=e^{-\frac{{∥x-y∥}^2}{2{\sigma }^2}}$$

(7)

3.2. LS-SVM Parameter Optimization Based on Particle Swarm Algorithm

Compared with neural networks, the LS-SVM classification algorithm has a higher accuracy and can achieve good recognition results even with a small number of samples. It is widely used in fault diagnosis [31]. However, the recognition accuracy of LS-SVM depends heavily on the penalty factor c and kernel parameter g of the kernel function. Therefore, the one difficulty of the least squares support vector machine is that its recognition accuracy cannot be determined in advance. This method also has problems such as long solution time, complex structure, and weak global optimization ability. At the current stage, scholars have been able to efficiently optimize parameters through intelligent algorithms. Common parameter optimization methods are shown in

Table 1. Optimization algorithm names and characteristics.

Algorithm	Features
Ant Colony Algorithm	It has good optimization performance and robustness but is prone to local optimality and converges slowly.
Genetic Algorithms	It has good global optimization capabilities but is time-consuming and unstable.
Simulated Annealing Algorithm	It has good local optimization ability but is easily affected by model parameters and easily falls into local optimality.
Particle Swarm Optimization	It has good parallelism, robustness, fast optimization, and simple structure.

.

Considering that the penalty coefficient c and the core parameter g must be optimized efficiently at the same time, the efficiency of the algorithm must be guaranteed while reducing the complexity of the model, the particle swarm optimization algorithm [32] was selected based on LS-SVM. The detailed process of the PSO algorithm is shown in Figure 6:

The detailed process of the PSO algorithm is as follows:

(1)

Determination of the objective function

The ultimate goal of optimizing the target parameters c and g is to improve the accuracy of LS-SVM model identification. Therefore, the final identification accuracy of the LS-SVM model is used as the objective function, which is also the fitness function of the particle swarm algorithm.

$$f={\displaystyle \frac{y_t}{y_t+y_f}}$$

(8)

where y_t and y_f represent the correct number and the wrong number of recognition states, respectively.

(2)

Divide the standardized feature vector into several training samples and several test samples.

(3)

Set various parameters in the algorithm.

Table 2. Particle swarm algorithm parameter settings.

Iterations	Population Size	Learning Factors c1, c2	Penalty Factor c Range	Kernel Parameter g Range
50	20	c1 = 1.5 c2 = 1.7	0.1~1000	0.1~1000

lists the relevant parameters of the particle swarm algorithm.

(4)

With c and g as the two-dimensional coordinates of the particle swarm algorithm, the tool wear recognition model is trained using the training samples given in (2), and the current fitness of the particles is calculated. By comparing it with its optimal solution, the particle optimal solution is updated. Finally, by comparing it with the global optimal solution, the global optimal solution of the swarm is updated.

(5)

When PSO finds the optimal solution, the particle swarm updates its own velocity vi and position xi information, as described below.

$${\nu }_{id}\left(t+1\right)={\nu }_{id}+c_1{r}_1\left(p_{id}-x_{id}\left(t\right)\right)+c_2{r}_2\left(p_{gd}-x_{id}\left(t\right)\right)$$

(9)

$$x_{id}\left(t+1\right)=x_{id}\left(t\right)+{\nu }_{id}\left(t+1\right)$$

(10)

where c₁ and c₂ are learning coefficients, t is the number of repetitions, w is the weighting coefficient, and r₁ and r₂ are random numbers from 0 to 1.

(6)

Check whether the current termination condition is met. If yes, terminate the operation and output the currently optimized parameters c and g and the fitness (i.e., classification accuracy) at this time. If the termination condition is not met, return to (4) and continue the optimization. The set termination condition is the maximum number of repetitions.

(7)

As shown in Figure 7, the particle fitness curve shows that after more than 25 generations of iterations, the optimal fitness of the particle is close to stability, and its accuracy is 97.21%. Therefore, setting the number of iterations to 50 generations not only results in sufficient optimization and the most optimal parameters but also ensures that the calculation is not too large [33]. After 50 iterations of optimization, the optimal parameters c = 53.8742 (g = 11.2323) were obtained. Finally, the PSO-LS-SVM identification model was constructed and the training set was input for verification.

4. Experimental Analysis

4.1. Feature Extraction and Optimization

4.1.1. Time Domain Characteristics

The time domain analysis of signals refers to the analysis of the signals in the time domain and ultimately expressing the changing state of the signals as a parameter. It is the most basic and easy-to-understand form of expression. Moreover, no matter whether the frequency band of the signal is high or low, it can be extracted using the time domain analysis method [34]. The elements in the time domain can be divided into two types according to their dimensionlessness. On this basis, the characteristic signals in the time domain are selected.

In order to observe the general changes in the signal time domain characteristics, the time domain characteristics of each pass were calculated according to the formula in

Table 3. Time domain characteristics.

Time Domain Characteristics	Expression	Illustrate
Maximum	$X_{max}=max\left\{\begin{array}{c}{x}_1,x_2,...x_i....,x_n\end{array}\right\}$	Reflects the instantaneous maximum peak value of the signal
Minimum	$X_{min}=min\left\{\begin{array}{c}{x}_1,x_2,...x_i...,x_n\end{array}\right\}$	Reflects the instantaneous minimum peak value of the signal
Peak	$X_{peak}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N} x_{peak\left(i\right)}$	The maximum value of a signal in one cycle
Peak-to-peak value	$X_{peak}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N} x_{peak\left(i\right)}$	The absolute value of the difference between the peak and the trough
Mean	$\overline{X}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n} x_i,x_i\in \left\{\begin{array}{c}{x}_1,x_2,...,x_n\end{array}\right\}$	Indicates the average level of the signal, the static component of the signal
variance	${\sigma }^2={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N} {\left(X_i-\overline{X}\right)}^2$	Expresses the degree of fluctuation of the signal around the mean and the dynamic component of the signal
RMS amplitude	$X_{rms}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N} x_i^2}$	Represents the average energy of the signal
Average amplitude	$X_{\sigma \nu }={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N} |x_i|$	Reflects the change in the average energy of the signal

, and the relationship between certain time domain characteristics and the number of passes (i.e., cutting time) was obtained as shown in Figure 8.

By analyzing the results of feature extraction, the results show that the dimensionless method can better characterize the wear status of the tool; in particular, the Y-axis, which is the feed direction, is closely related to the tool wear, and the X-axis, which is the vertical direction, is closely related to the tool wear. The feed signal is related to the loss of the tool. However, the Z direction signal in the time domain cannot reflect it directly. Only when the tool is worn will the stability of the system decrease. Compared with the dimensionless characteristic signal, the sizing characteristics do not change significantly with the increase in tool wear.

4.1.2. Frequency Domain Characteristics

The vibration and force signals in milling processing are affected by factors such as spindle rotation, cutting, and tool wear. Therefore, during the machining process, the signal changes in a cycle. The tool wear information that can be obtained by the traditional time domain analysis method is very limited, and the time domain analysis method can only reflect the vibration and force amplitude changes that occur with the tool wear state. The actual signal often contains information in multiple frequency bands. Therefore, the frequency domain analysis method must be used to conduct a more in-depth study. In the frequency domain, feature extraction is to first perform FFT transformation on the signal and then calculate its characteristic quantity in the frequency domain based on the expression of the eigenvalue. The usual frequency domain characteristics are as follows:

Center of gravity frequency:

$$FC=\sum _{i=1}^N f_i{p}_i/\sum _{i=1}^N p_i$$

(11)

This can reflect the changes in the center of the tool vibration signal spectrum under various working conditions.

Frequency variance:

$$VF={\displaystyle \frac{\sum _{i=1}^N \left(f_i-f\right)}{\sum _{i=1}^N p_i}}$$

(12)

This can explain the discreteness of the signal.

Mean square frequency:

$$MSF={\displaystyle \frac{\sum _{i=1}^N f_i^2{p}_i}{\sum _{i=1}^N p_i}}$$

(13)

During the cutting process, according to the average frequency during the cutting process, this can be used to characterize the vibration frequency of the tool during the cutting process. Taking the vibration signal in the feed direction as an example, it can be seen from Figure 9 and Figure 10 that when the number of tool movements increases, its center frequency also decreases; during the initial wear process, the average frequency and frequency of the system do not change, although there are significant changes in the middle and late stages of wear. This is mainly because the stability of the system will decrease during the wear process, and the frequency response characteristics are more sensitive to the stability of the system; thus, in the late stages of wear, the frequency characteristics of the system show large fluctuations. Existing research shows that during the cutting process, as the cutting speed increases, the changing pattern will gradually intensify. However, based on this changing trend alone, it is impossible to construct an accurate tool wear characteristic model.

4.1.3. Time–Frequency Domain Feature Extraction Based on EEMD

In view of the complex characteristics of the tool wear process, during analysis, changes in the time domain and frequency domain must both be taken into account. The existing wavelet analysis and empirical mode decomposition (EMD) are compared with wavelet decomposition (WT). The EMD algorithm does not need to set the basis function in advance and only decomposes according to the time scale characteristics of the signal itself. Therefore, it shows unique advantages when processing non-steady-state data such as vibration and force perception. However, when using the empirical mode decomposition method to decompose the signal, modal aliasing will occur. To address this problem, researchers have proposed a mode confusion problem based on ensemble empirical mode decomposition (EEMD). The basic idea of this method is to introduce Gaussian white noise into the original signal so that the signal maintains good continuity at multiple scales and effectively suppresses the mode mixing phenomenon. To address this problem, this paper uses EEMD to decompose the vibration and force signals and extract features in the time domain and frequency domain. The specific EEMD algorithm steps are shown in Figure 11.

Here, the detailed steps of EMD are as follows:

(1)

First find all local extreme values of the original signal X(t);

(2)

Use the cubic spline curve to fit the local maximum and minimum points to obtain the upper and lower envelopes and use u(t) to represent the upper and lower envelopes. Then, based on the upper and lower envelopes, obtain the average curve m(t):

$$m\left(t\right)={\displaystyle \frac{u\left(t\right)+d\left(t\right)}{2}}$$

(14)

(3)

Let h₁ represent the difference between the mean values of the initial data X(t) and m(t), then

$$h_1=X\left(t\right)-m\left(t\right)$$

(15)

At this time, h₁ is regarded as a new initial signal, and the above three steps are repeatedly performed until h₁ is satisfied.

Across the entire time range, the number of function zeros and local poles is the same or differs by one at most; in the signal segment, the average of the upper and lower envelope surfaces is 0. At this point, h₁ is the first-order IMF at the screening location, as denoted by C₁. In general, C₁ contains the highest frequency component of the original signal.

(4)

Remove a maximum frequency component from the original signal to obtain a difference signal, r₁:

$$r_1=X_{\left(t\right)}-C_1$$

(16)

Taking r₁ as the new initial signal, repeat the above three steps until the residual signal obtained is a monotonic function without a maximum value and the IMF component can no longer be screened.

$$r_n=r_{n-1}-C_n$$

(17)

(5)

Finally, mathematically speaking, the original signal X(t) can be expressed as the sum of n IMFs and 1 residual.

$$X_{\left(t\right)}=\sum _{j=1}^n C_j\left(\begin{array}{c}t\end{array}\right)+r_n\left(\begin{array}{c}t\end{array}\right)$$

(18)

Of these, r_n(t) is used as a parameter to express the average trend of the signal, and C_j(t) represents the IMF components, ranging from high frequency to low frequency.

4.1.4. Feature Optimization Based on PCA

On the basis of the above research, the characteristics of load, vibration, and other signals were analyzed, respectively, and finally, 90 time domain features were obtained, which are labeled sT. There are 18 feature vectors in the frequency domain, and these are represented by hT. In total, 108 time–frequency feature vectors are proposed, which are labeled Tsh. These three feature vectors are connected in sequence to form a new joint multi-feature vector denoted as Tcs, so that the multi-feature vector is 216. If Tcs is used as a characterization vector of tool wear state, it not only requires a large amount of data but also contains a large number of redundant feature vectors, which will inevitably reduce the recognition efficiency and recognition accuracy. In view of the redundant and irrelevant characteristics existing in the joint multi-feature vector, the PCA method is used to optimize it.

The core idea of this method is to construct a series of new variables based on the original attributes by linearly combining the original attributes, making their number much smaller than the original data, and to keep the effective information in the original data as much as possible, remove redundant information, and achieve dimensionality reduction in the projection space. By constructing the orthogonal relationship between the new variables, the correlation between the original variables can be effectively removed and the dimension of the data can be greatly reduced. The new features of dimensionality reduction obtained through principal component analysis are shown below.

The new feature cannot fully represent the original feature. It is a linear combination of several interrelated old features. The two elements are perpendicular to each other, not interrelated. The new feature size is much smaller than the original feature size. The feature dimension reduction optimization method using principal component analysis is as follows:

(1)

Standardize the feature vector. Here, max–min normalization is used. The calculation formula is as follows. The standardized data are used to generate the sample matrix X.

$$x^{\ast }={\displaystyle \frac{x-x_{min}}{x_{max}-x_{min}}}$$

(19)

(2)

Calculate the mean of the sample matrix X:

$$u={\displaystyle \frac{1}{N}}\sum _{i=1}^n x_i$$

(20)

(3)

Calculate the covariance matrix for the sample matrix X:

$$R_x=\sum _{i=1}^n (x_i-u)(x_i-u{)}^T$$

(21)

(4)

A new mathematical representation model is established.

PCA is used to reduce the dimension of the original feature vector and obtain its principal component coefficient matrix C:

$$C=\left[\begin{array}{cccc}k{p}_{\mathrm{1,1}}& k{p}_{\mathrm{2,1}}& \cdots & k{p}_{\mathrm{216,1}}\\ k{p}_{\mathrm{1,2}}& k{p}_{\mathrm{2,2}}& \cdots & k{p}_{\mathrm{216,2}}\\ \dots & \dots & \dots & \dots \\ k{p}_{\mathrm{1,200}}& k{p}_{\mathrm{2,200}}& \dots & k{p}_{\mathrm{216,200}}\end{array}\right]$$

(22)

The contribution of the system is sorted according to the new vector reconstructed after dimensionality reduction. The number of principal components is determined by principal component variance–cumulative contribution (CPV), and its value can be determined by the formula below. The number of principal components is selected according to the criterion that CPV is no less than 95% to ensure the completeness of the information.

$$CPV={\displaystyle \frac{\sum _{i=1}^k \left|s_i\right|}{\sum _{i=1}^m \left|s_i\right|}}\times 100\%$$

(23)

The first 10 principal elements were selected as new eigenvectors and were described to obtain new eigenvectors.

$$C_{kp}=\left[\begin{array}{cccc}k{p}_{\mathrm{1,1}}& k{p}_{\mathrm{2,1}}& \cdots & k{p}_{\mathrm{10,1}}\\ k{p}_{\mathrm{1,2}}& k{p}_{\mathrm{2,2}}& \cdots & k{p}_{\mathrm{10,2}}\\ \dots & \dots & \dots & \dots \\ k{p}_{\mathrm{1,200}}& k{p}_{\mathrm{2,200}}& \dots & k{p}_{\mathrm{10,200}}\end{array}\right]$$

(24)

4.2. Analysis of Test Results

Before inputting the data into the model, they must be split into a training set and a test set. Taking the milling cutter as an example, according to the vibration data from its entire lifecycle, 70% of the samples are used as training samples and 30% of the samples are used as test samples at a ratio of 7:3. The specific division method is as follows: expand the data through the sliding window one by one, rearrange the data after the sliding window, and then partition them; then choose the random sampling partition method.

(1)

Impact of input on recognition effect

To solve the above problems, this paper adopts the PSO-LSSVM method, takes the characteristic information of single and multiple signals as input, and uses the PSO-LSSVM method to experimentally study the multiple signal recognition method. The initial wear states (1, 2, 3, 4) are marked as states 1, 2, 3, 4. The recognition results are shown in Figure 12.

The recognition accuracy of each stage for different input signals is shown in

Table 4. Model recognition rate at each stage under different input signals.

Input Signal	Wear Status
	Initial Stage of Wear	Stable Wear Period	Rapid Wear Period	Tool Expiration Date	Total Recognition Rate
Force signal	88.6%	84.5%	81.4%	84.7%	84.7%
Vibration signal	74.2%	73.2%	88.2%	84.7%	79.8%
Vibration and force signals	91.4%	92.4%	89.4%	89.9%	90.4%

.

The results show that when a single signal is used as input, its recognition rate is lower than that of multiple signal inputs. From the recognition situation of each stage, in the first two states, the recognition rate of the force signal is relatively high, and the recognition rate in the last two states is mainly determined by the force signal. This is because in the early stage of wear and steady state, the tool is relatively sharp, making the whole process more stable. Only the vibration signal is used for identification, and its feature resolution ability is not strong. The force signal can intuitively reflect the friction coefficient during the tool wear process. In the first two stages, it shows better recognition results than the vibration signal. However, when the wear is advanced, the contact area between the tool tip and the workpiece becomes larger, thereby reducing the stability of the system. At this time, the sensitivity of the vibration signal to force is greater than that of the force signal, and the complexity of the vibration signal is also high. This characteristic is reflected in the entropy value in the time–frequency domain. Using vibration and force signals as monitoring signals can overcome the incomplete information that can be reflected by a single signal, thereby improving the accuracy of model identification. However, when two different signals are input, it will lead to an increase in feature dimensions and a decrease in performance, so it needs to be optimized.

(2)

Impact of input characteristics on recognition results

The PSO-LSSVM method is used to learn and identify the time domain, frequency domain, time domain, frequency domain, and multiple features at once. The final identification results are shown in Figure 13, and the identification rate of each specific stage is shown in

Table 5. Recognition rate of each stage of the model under different input features.

Input Features	Wear Status
	Initial Stage of Wear	Stable Wear Period	Rapid Wear Period	Tool Expiration Date	Total Recognition Rate
Time domain characteristics	84.6%	89.7%	89.7%	81.7%	88.5%
Frequency domain characteristics	69.8%	91.7%	71.6%	84.6%	79.8%
Time–frequency domain features	89.9%	79.8%	87.4%	84.6%	85.4%
Multiple feature input	91.7%	91.7%	89.9%	89.9%	91.4%

.

The results show that using multiple features as the input of the model can improve the overall recognition rate and the recognition rate at each stage. Existing research mainly focuses on the modeling of a single type of feature, which contains less tool wear information and cannot fully reflect the change law of various physical parameters under the tool wear state. Although the training and recognition efficiency will decrease when multiple features are introduced into the modeling, it contains a large amount of tool wear information and can effectively improve the recognition accuracy of the model.

(3)

The impact of optimal feature selection on recognition results

Although the simultaneous input of multiple sources and multiple features can effectively improve the model recognition accuracy, the simultaneous input of multiple sources and multiple features will inevitably lead to an increase in feature vectors and redundant and irrelevant information, which is not conducive to the identification of tool wear status. To this end, this paper further optimizes the features, takes the feature vectors before and after optimization as input, and uses PSO-LS-SVM as input to realize the identification of tool wear status. Its recognition results are shown in Figure 14, and the recognition rate of each specific stage is shown in

Table 6. Recognition rate of each stage of the model before and after feature optimization.

Model Input	Wear Status
	Initial Stage of Wear	Stable Wear Period	Rapid Wear Period	Tool Expiration Date	Total Recognition Rate
Before feature optimization	91.6%	91.6%	89.8%	89.8%	91.6%
After feature optimization	100%	100%	100%	91.8%	98.6%

.

The results show that before feature optimization, the overall recognition rate can reach 91.6%, and after feature optimization, the overall recognition rate can reach 98.1%. The overall recognition rate and the recognition rates at each stage have improved to varying degrees. In addition, through feature optimization, a large number of redundant and irrelevant features are removed, and the original 216 dimensions are reduced to 10 dimensions, thereby greatly improving the training and recognition efficiency of the model.

(4)

Impact of parameter optimization on identification effect

The optimal feature vector is used as the input of the LS-SVM and PSO-LS-SVM support vector machines, which are then studied and identified. The final recognition effect is shown in Figure 15.

The experimental results show that the recognition rate of LS-SVM optimized by this method is significantly higher than that of unoptimized LS-SVM. Compared with the unoptimized LS-SVM, the overall recognition rate of PSO-LS-SVM reaches 98.6%, while that of the unoptimized LS-SVM is only 92.4%. The results show that after the optimization of the particle swarm algorithm, the recognition accuracy of the entire model and the recognition accuracy of tool wear at each stage are improved. The LS-SVM optimization method based on PSO can better solve the problems existing in LS-SVM in practical applications. As shown in

Table 7. Recognition rate of different wear stages before and after parameter optimization.

Identification Method	Wear Status
	Initial Stage of Wear	Stable Wear Period	Rapid Wear Period	Tool Expiration Date	Total Recognition Rate
Before optimization	91.6%	97.6%	100%	84.6%	92.4%
After optimization	100%	100%	100%	92.7%	98.6%

.

5. Conclusions

In this study, a wear prediction model based on particle swarm optimization (PSO) and least squares support vector machine (LS-SVM), namely the PSO-LS-SVM model, was successfully developed and verified. The model fuses data from multiple sensors, including vibration signals and force data, and extracts key feature information reflecting the tool wear state. By using principal component analysis (PCA) for dimensionality reduction and feature optimization, the model significantly improves the distinguishability of features and reduces the complexity of the feature space.

The PSO-LS-SVM model optimizes the model parameters to adapt to the given training sample set through the two-dimensional coordinates (c and g) of the particle swarm algorithm, and its effectiveness is demonstrated. The optimal fitness of the particles is continuously updated by iteratively calculating the fitness and comparing it with the historical optimal fitness, so as to determine the global optimal solution and accurately identify the tool wear state. Experimental results demonstrate that the PSO-LS-SVM model shows high accuracy and good performance for tool wear state identification.

In summary, the PSO-LS-SVM model provides a promising method for tool wear prediction, which has significantly improved efficiency and accuracy over traditional methods. This study contributes to the field of CNC machining and provides a reliable and effective tool wear prediction model that can be integrated into smart manufacturing systems to optimize production processes and maintain high quality standards.