Wear Prediction of Tool Based on Modal Decomposition and MCNN-BiLSTM

Abstract

Metal cutting is a complex process with strong randomness and nonlinear characteristics in its dynamic behavior, while tool wear or fractures will have an immediate impact on the product surface quality and machining precision. A combined prediction method comprising modal decomposition, multi-channel input, a multi-scale Convolutional neural network (CNN), and a bidirectional long-short term memory network (BiLSTM) is presented to monitor tool condition and to predict tool-wear value in real time. This method considers both digital signal features and prediction network model problems. First, we perform correlation analysis on the gathered sensor signals using Pearson and Spearman techniques to efficiently reduce the amount of input signals. Second, we use Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to enhance the local characteristics of the signal, then boost the neural network’s identification accuracy. In addition, the deconstructed signal is converted into a multi-channel input matrix, from which multi-scale spatial characteristics and two-way temporal features are recovered using multi-scale CNN and BiLSTM, respectively. Finally, this strategy is adopted in simulation verification using real PHM data. The wear prediction experimental results show that, in the developed model, C1, C4, and C6 have good prediction performance, with RMSE of 8.2968, 12.8521, 7.6667, and MAE of 6.7914, 9.9263, and 5.9884, respectively, significantly lower than SVR, B-BiLSTM, and 2DCNN models.

1. Introduction

Tool wear and fracture can directly impair surface quality and machining precision throughout the manufacturing process. In severe circumstances, they can potentially lead to machine tool accidents. Traditional machining procedures rely on manual experience to identify when to change tools, such as running duration, cutting sound, and tool surface color, whereas subjective judgment approaches have drawbacks [1]. According to the results in [2], tool breakage accounts for 7% of machine downtime. Tool monitoring systems are expected to be a necessary and vital component of manufacturing systems with the increasing use of flexible manufacturing systems, intelligent manufacturing systems and computer-integrated manufacturing systems [3].

1.1. Literature Review

Three types of widely used prediction models are empirical, mechanism analysis-based, and data-driven [4]. Most academics currently use data-driven life monitoring techniques, since empirical models and mechanism analysis are not universally applicable, and building complicated models is challenging. Machine learning models and degradation-based models are the two primary categories of data-driven models. Cutting tool degradation models have been broken down by researchers into approaches based on gamma processes [5], Markov processes, and Wiener processes [6]. The accuracy of tool life prediction will be impacted by the choice of degradation models, since different types of cutting tools have distinct degradation models. By continually developing the corresponding relationship between the real-time equipment monitoring data (or extracted characteristics) and the present wear value, tool wear prediction is accomplished using machine learning prediction methods. Machine learning-based approaches can solve the issue of incorrect or ambiguous tool degradation model selection; meanwhile, the input of the model is not constrained to a particular type of monitoring data.

The cutting force, vibration, and acoustic emission signals are the most commonly used in tool monitoring studies [7,8,9,10]. The cutting force signal rises when the tool is passivated [11,12]. Acoustic emission signals are created during the machining process as a result of the cutting tool’s quick interaction with the treated material. Acoustic emission sensors have also been widely employed due to their high sensitivity, excellent anti-interference capabilities, and ease of installation [13,14]. Because friction between the cutting tool and the workpiece can modify the dynamic component of the cutting force, vibration during the cutting process includes vital information regarding the cutting tool’s wear condition [15].

The traditional machine learning approaches for predicting tool wear status primarily use multi-layer perceptron (MLP) [16,17], radial basis function (RBF) [18,19], extreme learning machines (ELMS) [20,21], and support vector machines (SVM) [22,23]. However, as sensor technology is rapidly developed in the big data, cloud computing age, industrial systems can now receive an increasing amount of monitoring data. It is challenging to automatically grasp and evaluate large amounts of monitoring data using traditional neural network techniques. With its potent feature extraction capabilities, deep learning, a new technique derived from neural networks, offers a new prediction strategy for training huge amounts of data. Convolutional neural networks (CNN) [24,25] and recurrent neural networks (RNN) [26,27] are the two primary types of prediction algorithms in use today. Additionally, deep learning prediction has been effectively used in several technical disciplines, including the prediction of natural gas and oil extraction [28,29], industrial system faults [30,31], and others.

A brief synopsis of the literature under study is given in

Table 1. Literature review summary.

Ref.	Method	Advantage	Deficiency
Li [33]	SVR	Analyzing the characteristics of specific tools resulted in high prediction accuracy	The time required for analysis is long, and the model lacks universality
Ren [34]	GRU	Multi sensor feature fusion	The network is simple, but its performance is poor when dealing with big data
Li [35]	SVR	EMD decomposition of signals to amplify signal features	The network is simple, but its performance is poor when dealing with big data
Wang [36]	Physical model	Integrating data-driven models to improve universality	The network is simple, but its performance is poor when dealing with big data
Huang [8]	DCNN	Multi sensor feature fusion	Manually extracting features while ignoring hidden features of the data itself
Xu [37]	CNN	Built a more powerful neural network	The original signal has noise, which affects the prediction speed and accuracy
Liang [38]	SVM	Integration with data-driven models, mining more features	The model has no universality
He [39]	BPNN	Designed a new SSAE model to learn more valuable and deeper features from the original signal	Only one monitoring signal was used, without considering predictive stability
Duan [40]	SVR	Integrating MS-SPCANet for autonomous feature extraction	Principal component analysis, difficult to mine hidden features in data
Li [41]	Physical model	Integrating the parameters of empirical equations to improve the interpretability of modeling	The time required for analysis is long, and the resulting model is not universally applicable

. Specific material physical models, neural networks, support vector machines, deep learning models, and other machine learning techniques have demonstrated great performance in the research of tool wear prediction while processing sizable volumes of nonlinear data. To disclose the intrinsic properties of the sensor signal in the cutting process and increase prediction accuracy, researchers employ methods including attention mechanisms, principal component analysis, and multi-channel fusion. Monitoring the wear status of cutting tools by collecting sensor signals, metal cutting is still a challenging process with highly unpredictable and nonlinear dynamic behavior. It is required to separate out characteristics from a vast number of non-stationary data gathered by sensors to anticipate tool wear effectively and dependably. In addition to information on tool wear, sensor signals also contain a variety of interference signals, such as noise. In order to anticipate the wear state, it is therefore important to analyze the original signal suitably and extract signal elements linked to the tool state along with a better neural network prediction model [32].

1.2. Research Gaps and Contributions

Following the introduction above, the main contributions of this study are summarized as follows:

(1) To reduce the signal amount of the input deep learning model, amplify local signal features, and increase the identification accuracy of the prediction model for tool wear status, correlation analysis and signal modal decomposition algorithms are introduced in the signal processing of the collected tool wear sensor.

(2) To increase the predictability of tool wear status, the tool wear prediction model employs a combination prediction technique, paired with residual structure, employing MCNN to extract multi-scale spatial features and BiLSTM to extract bidirectional temporal features.

The remainder of this paper is organized as follows. The monitoring framework and data processing algorithm design for tool wear status in this study are covered in the second part; Section 3 demonstrates the design of the Deep Learning Network; Section 4, Experimental validation and analysis using real data, compares and analyzes the experimental results of the proposed technique with Support Vector Regression (SVR), Gated Recurrent Unit Neural Network (GRU), Bayesian optimization LSTM and BiLSTM, One-Dimensional Convolutional Neural Network (1DCNN) and LSTM combination prediction algorithm and two-dimensional Convolutional Neural Network (2DCNN).

2. Problem Description

The quality of feature extraction limits the accuracy of the “feature extraction + machine learning model” in its conventional sense. There may be some information loss when converting signals to frequency or time-frequency domains for analysis. In addition to being adept at watching and finding, researchers also need to have a certain set of abilities and expertise in order to extract characteristics that are highly associated with tool wear state [42]. Additionally, the retrieved characteristics have poor universality and interpretability, and it is possible that more delicate traits were left out. For the self-coding network, if the number of network layers is too great, the model may not succeed owing to the lack of global optimization of the entire model. The model built by a convolutional neural network relies on the extraction of high-dimensional features by a convolution operation, but a small number of convolution operations cannot accurately predict the tool wear. The method proposed in this article aims to accurately predict the wear value changes of cutting tools during machining by collecting multidimensional sensor signals, as shown in Figure 1. The accuracy of prediction methods is crucial for the operation and efficiency of enterprise production and machine tool processing.

3. Predicting Tool Wear Based on MCNN BiLSTM

3.1. Tool Wear Prediction Framework

Force, vibration, and acoustic emission sensors are employed during the cutting process to gather indications pertaining to tool wear. The sensor installation is displayed. A three-dimensional force measurement device is installed between the workstation and the object to be machined in order to gauge the cutting forces in the X, Y, and Z axes; a piezoelectric accelerometer is installed on the workpiece to track the X, Y, and Z vibration signals as the tool is being processed; and for the purpose of measuring the high-frequency stress waves produced during the cutting process, an acoustic emission sensor is mounted on the workpiece. Consequently, the data’s final dimension is seven. A structural charge amplifier boosts the sensor signal, which is then recorded by a data gathering system. A microscope is used to assess the tool’s back face offline wear state after the tool’s end face has been milled. A deep learning network is used to process and import the signal for training, creating an entire tool mode monitoring and prediction system. Data processing is used to enhance signal features [43], deep learning networks are used to process and import signals for training, and the entire tool pattern monitoring and prediction system is created, as shown in Figure 2.

3.2. Data Processing

3.2.1. Multivariate Correlation Analysis

A prominent technique for data correlation analysis is Pearson and Spearman correlation analysis [44]. It may be applied to determine the linear correlation, or relationship between two variables. The related formulae are shown by Equations (1) and (2),

$$P_{xy}=\frac{\sum _{i=1}^n\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right) }{\sqrt{ \sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2\sum _{i=1}^n{\left(y_i-\bar{y}\right)}^2}}$$

(1)

$$\begin{array}{c}{S}_{xy}=1-\frac{6\sum _{i=1}^n{\left(R\left(x_i\right)-R\left(y_i\right)\right)}^2 }{n\left(n^2-1\right)}\end{array}$$

(2)

where $P_{xy},S_{xy}$ are Pearson correlation coefficients and Spearman correlation coefficients, respectively; $x_i$ and $y_i$ are the signals for each cutting, respectively; $\bar{x}$ and $\bar{y}$ are the mean values of two n-dimensional signals, respectively; and $R\left(x_i\right)$ and $R\left(y_i\right)$ are the sorting in their respective signals.

3.2.2. Empirical Mode Decomposition

Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is an improved empirical mode decomposition (EMD) method that can better handle nonlinear and non-stationary signals [45]. CEEMDAN obtains multiple sets of Intrinsic Mode Function (IMF) components by randomly perturbing and decomposing the signal multiple times and averages them to obtain the final IMF component. Let $E_i(.)$ represent the ith subsequence obtained by EMD decomposition. $C_i\left(t\right)$ represents the ith subsequence obtained by CEEMDAN decomposition, $v^j$ represents the Gaussian white noise signal satisfying the standard normal distribution, j = 1, 2, N represents the number of additions of white noise, d represents the standard white noise table, and $y\left(t\right)$ represents the signal to be decomposed. The specific steps of the CEEMDAN method are illustrated as follows [46].

(1)

Perform multiple random perturbations on the original sensor signal $y\left(t\right)$ to obtain multiple sets of disturbance signals: $y\left(t\right)+{(-1)}^q\epsilon v^j\left(t\right)$, $q=\mathrm{1,2}$; EMD decomposes the new signal to obtain the first subsequence:

$$E\left(y\right(t)+{(-1)}^q\epsilon v^j(t\left)\right)=C_1\left(t\right)+r^j$$

(3)

(2)

By averaging the created N subsequences, the first subsequence of the CEEMDAN decomposition is obtained, and the residual of the first subsequence is also calculated to be removed.

$$\left\{\begin{array}{c}{C}_1\left(t\right)=\frac{1}{N}{\sum }_{j=1}^N{C}_1^j\left(t\right)\\ r_1\left(t\right)=y\left(t\right)-C_1\left(t\right)\end{array}\right.$$

(4)

(3)

Add a pair of positive and negative white Gaussian noise to $r_1\left(t\right)$ to obtain a new signal. Use the new signal as the carrier for EMD decomposition to obtain the first subsequence $D_1$, from which we can obtain the second subsequence of CEEMDAN decomposition and the residual after eliminating the second subsequence.

$$\left\{\begin{array}{c}{C}_2\left(t\right)=\frac{1}{N}{\sum }_{j=1}^N{D}_1^j\left(t\right)\\ r_2\left(t\right)=y\left(t\right)-C_2\left(t\right)\end{array}\right.$$

(5)

(4)

Repeat the above steps until the residual signal obtained is a monotonic function and cannot be further decomposed. The original signal is reproduced as follows:

$$y\left(t\right)={\sum }_{k=1}^k{C}_k\left(t\right)+r_k\left(t\right)$$

(6)

The CEEMDAN method can better handle nonlinear and non-stationary signals; by multiple random perturbations and decomposition, the pseudo-components and modal aliasing phenomena of EMD methods can be reduced; the CEEMDAN method does not require a predetermined number of components in the signal and can adaptively decompose the signal. Therefore, the CEEMDAN method has been widely applied in the field of signal processing [47].

3.3. Deep Combination Prediction Model

The MCNN-BiLSTM composite model includes a multi-scale convolution layer, batch normalization layer, activation function layer, max pooling layer, BiLSTM layer, full connection layer and dropout layer. The residual block in the input block consists of two branches: the main path and the branch path. The main path contains convolutional layers, BN layers, and ReLu activation layers, while the branch path only contains max pooling layers. According to the input tensor of the residual block, the two tensors are added through the main and branch paths to form the output of the residual block. Multiple residual blocks are stacked repeatedly using a multi-layer perceptron method. The output block uses the sample specification layer, ReLu activation layer, and fully connected layer to process the output tensor of multiple residual blocks. After passing through the tiling layer, the BiLSTM module generates the output of the entire model, where the model’s diagram is shown in Figure 3. The input of the model is filtered multi-channel signal data, with the corresponding label being the minimum wear label. Extracting features from different signals using multi-scale convolution with kernel sizes of 3 × 3, 4 × 4 and 5 × 5. The number of convolutional layers is set to 64, and the number of layers for BiLSTM is set to 128.

The multi-scale convolutional layers can be expressed as:

$$f_{\mathrm{j}}^i={\sigma }_{\mathrm{r}}\left(\sum W_{\mathrm{j}}^i\mathrm{*}{X}_{\mathrm{j}}^i+B_{\mathrm{j}}^i\right)$$

(7)

where $X_{\mathrm{j}}^i$ is the input of the model; $W_{\mathrm{j}}^i$ is the convolution kernel for each layer of convolution; $B_{\mathrm{j}}^i$ is the number of offsets for each layer of convolution; and $f_{\mathrm{j}}^i$ feature vectors extracted for each convolutional block.

An often-used activation function is ReLu. An activation function in neural networks is used to alter neurons’ output, making them nonlinear. The output of the ReLU activation function is zero when the input is negative, while the function is equal to the input when the input is positive. ReLu’s key benefits are its simplicity, quickness, and effective performance in real-world applications. It can efficiently lessen the gradient vanishing issue, speed up neural network training, and improve the accuracy of neural network output. The ReLu activation function is expressed as follows:

$${\sigma }_{\mathrm{r}}\left(x\right)=\left\{\begin{array}{l}0,x<0\\ x,x\ge 0\end{array}\right.$$

(8)

The flatten layer’s primary function is to reduce multidimensional data structures to one-dimensional ones. This may provide the next fully linked layer or output layer a flattened data structure. The flatten layer is described by the expression:

$$f^i=flatten\left(f_{\mathrm{j}}^i\oplus M_{\mathrm{j}}^i\right)$$

(9)

where $f_{\mathrm{j}}^i$ represents the feature vectors extracted from each convolutional block, and $M_{\mathrm{j}}^i$ represents the feature vectors after passing through the maximum pooling layer.

The expression for BiLSTM monitoring module to achieve prediction is shown in Equations (10)–(13):

$$h^i={\sigma }_{\mathrm{t}}\left(W_1{f}^i+W_3{h}^{i-l}\right)$$

(10)

$$r^i={\sigma }_{\mathrm{t}}\left(W_2{f}^i+W_5{r}^{i+1}\right)$$

(11)

$$Y^i={\sigma }_{\mathrm{t}}\left(W_4{h}^i+W_6{r}^i\right)$$

(12)

$${\sigma }_{\mathrm{t}}\left(x\right)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$$

(13)

where $W_1$ and $W_3$ have a weight matrix for feature vectors; $W_2$ and $W_5$ have a weight matrix that maps the forward and reverse layer calculation times to the current calculation times; and $W_4$ and $W_6$ have a weight matrix that maps the forward and reverse layer outputs to the output layers.

4. Validation and Analysis

4.1. Raw Data

4.1.1. Dataset Selection

The performance of the model was assessed in this study using the public dataset from the 2010 Monitoring Data Challenge [37]. Using the workpiece as a test object, six tungsten carbide ball end cutting tools (C1–C6) were employed for milling trials. Forward milling and dry cutting were used. The workpiece was made of stainless steel HRC52. Accurate cutting standard: feed speed of 1555 mm/min; cutting depths of 0.125 mm in the Y direction and 0.2 mm in the Z direction; spindle speed of 10,400 rpm. The KISTLER three-dimensional force measurement device, KISTLER piezoelectric accelerometer, and KISTLER acoustic emission sensor are the sensor models for gathering signals. The data acquisition card utilizes NIDAQPC1200, and the charge amplifier is a KISTLER charge amplifier.

Force, vibration, and acoustic emission sensors are utilized to gather electrical signals on tool wear while cutting, and Figure 4 shows the sensor installation position. A KISTLER three-dimensional force measurement device was installed between the workstation and the object to be machined in order to gauge the cutting forces in the X, Y, and Z axes; a KISTLER piezoelectric accelerometer was installed on the workpiece to track the X, Y, and Z vibration signals as the tool is being processed; and to track high-frequency stress waves produced during cutting, a KISTLER acoustic emission sensor was mounted on the workpiece. A KISTLER charge amplifier is used to increase the sensor’s output signal, and the NIDAQPC1200 is used to collect it at a sampling frequency of 50 kHz. The LEICAMZ12 microscope was used to assess the tool rear face’s wear state offline after completing 108 mm of end-face milling in the X direction. The data of 315 cuts of a tool were recorded.

Given that the dataset only contains wear-value labels for C1, C4, and C6, a cross-validation approach was utilized to verify the generalizability of the suggested strategy and assess the effectiveness of the suggested model while making full use of the dataset. C1 is the prediction set, for instance, if C4 and C6 are the training sets.

4.1.2. Data Filtering

To limit the amount of data input into the model in this study while minimizing the accuracy of network prediction, the relationship between the gathered seven-dimensional sensor signals and tool wear was checked mathematically and statistically. Thus, using Equations (1) and (2), the Pearson and Spearman correlation coefficients between sensor signals and tool wear values were determined. The results are presented in

Table 2. Correlation coefficient between multi-dimensional sensing signal and wear value.

Signal	Select or Not	Pearson	Spearman
Fx	yes	0.9716	0.9937
Fy	yes	0.9293	0.9541
Fz	yes	0.9750	0.9182
Vx	no	0.0697	0.0583
Vy	no	0.0604	0.0845
Vz	no	0.0603	0.1054
AE	yes	0.5707	0.4892

.

According to Table 2, the correlation between force signals and wear values has the greatest Pearson and Spearman correlation coefficients, but the connection between triaxial vibration signals and wear values is nearly zero. As a result, the next study will focus on the signals Fx, Fy, Vy, and AE.

4.1.3. Mode Decomposition

This study employs the CEEMDAN to decompose the signal into multiple sub-signals, each with a distinct frequency range, to avoid the deep learning model not completely mining the features in the signal. This makes it possible for the neural network to learn and interpret information throughout various frequency bands more effectively. In the circumstances, CEEMDAN can enhance the capacity of signals to extract local features, hence enhancing the recognition precision of neural networks. The performance of the neural network may be enhanced by feeding it the signal that CEEMDAN has decomposed in order to better extract its characteristics.

Therefore, this study first performs max–min normalization on sensor signals Fx, Fy, Fz, AE with greater correlation between wear values. At the same time, CEEMDAN is used to decompose the normalized signal. Taking the Fy signal as an example, 16 groups of decomposed subsequences are obtained, as shown in Figure 5. The decomposed subsequences of Fx, Fy, Fz and AE signals were combined with the corresponding original signals into a 100 × 17 × 4 multi-channel input matrix, as shown in Figure 6, for the feature extraction and mining timing rules of the model in this paper.

4.2. Evaluating Indicator

This research employs root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination ($R^2$), which are frequently used in workpiece life prediction, as quantitative indicators to evaluate the influence of the prediction model. A considerable mistake in the prediction findings is shown by bigger values for $P_{\mathrm{m}\mathrm{a}\mathrm{e}}$ and $P_{\mathrm{r}\mathrm{m}\mathrm{s}\mathrm{e}}$; a greater degree of accuracy is indicated by lower values for $P_{\mathrm{m}\mathrm{a}\mathrm{e}}$ and $P_{\mathrm{r}\mathrm{m}\mathrm{s}\mathrm{e}}$.

$$P_{mae}=\frac{1}{n} {\sum }_{k=1}^n\left|y_k^{pre}-y_k\right|$$

(14)

$$P_{rmse}=\sqrt{\frac{1}{n}{\sum }_{k=1}^n{\left(y_k^{pre}-y_k\right)}^2 }$$

(15)

$$R^2=\frac{\sum {(y_k^{pre}-y_k)}^2}{\sum {(y_k-{\overline{y}}^{pre})}^2}$$

(16)

where $y_k$ is actual data, $y_k^{pre}$ is predicted data, $\overline{y}$ is average predicted data, and n is the number of test samples.

4.3. Experimental Environment

An experimental analysis was conducted on the MATLAB 2021b software platform, with hardware configuration of Intel I CoITM 7700HQ CPU and 16GB RAM, NDIVIA GTX1050, GPU; the operating system is Windows 10.

The proposed MCNN-BiLSTM prediction model includes two parts:

MCNN feature extraction and BiLSTM timing prediction. For the feature extraction part of MCNN, please note that all 2D Convs are used here, and 3D Convs are used for feature extraction, with Conv sizes of {3 × 3, 4 × 4, 5 × 5} with the 64 hidden layers. After two residual extractions, the size of Conv in the residual module is 3 × 3. The activation function of the network is ReLu; for the prediction part of BiLSTM, BiLSTM consists of a one-layer network with 128 hidden layers. The training parameters of other prediction models are shown in

Table 3. Model parameter setting.

Variable	Description	Value
Epoch	Training rounds	500
Batch size	Batch size	24
Learning rate	Learning rate	0.001
Step size	Interval of learning rate decline	1000
Gamma	Adjustment multiple of learning rate	1
Dropout rate	Dropout rate	0.3

.

4.4. Result Analysis

4.4.1. Module Verification

The prediction results of the proposed model under three different test tools are shown in Figure 7. In machine tool processing, milling is a slow process, and the time required for CEEMDAN’s data decomposition as well as the prediction of the model is negligible, so there is not much discussion here. It is clear that the model provides accurate tool prediction results. To better show the effectiveness of the model, the training and validation loss of the model are shown in Figure 8.

Figure 9 shows the prediction results of the original signal directly input into the proposed model, and it can be seen that the prediction effect is not as good as Figure 7.

A more thorough data comparison, examining the quantitative value of the influence of signal decomposition on model performance, may be seen in

Table 4. Impact of multi-scale signal decomposition on model performance.

Method	C1			C4			C6
	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2
Developed model	11.2946	9.5785	0.95364	18.3126	14.0382	0.77384	8.6167	6.7801	0.92771
Developed model *	8.2968	6.7914	0.96468	12.8521	9.9263	0.88154	7.6667	5.9884	0.95794

Note: * represents the use of CEEMDAN algorithm.

. It can be clearly seen that the RMSE and MAE of the signals predicted by tool C1 decreased by 26.54% and 29.10%, respectively, after CEEMDAN decomposition. The RMSE and MAE of C4 decreased by 29.82% and 29.29%, respectively. The RMSE and MAE of C6 decreased by 11.03% and 11.68%, respectively. In addition, the $R^2$ also increased, which means that using CEEMDAN results in a higher fit for both the predicted and true values.

Residual structures were introduced to the model to improve the network’s representation capabilities. As seen in Figure 10, the deep learning model with residual structures outperforms the one without the res-module. The residual network can solve the vanishing gradient problem. The gradient signal will be backpropagated numerous times in the deep neural network as the network layers expand, resulting in the gradient gradually becoming less. The residual structure allows the input signal to be directly added to the output signal, allowing the gradient of the network to be better propagated and avoiding the vanishing gradient problem. Second, the residual structure enables the network to learn the residual component, allowing it to adapt to complicated data distributions and nonlinear transformations more effectively [48]. Furthermore, employing residual structures can boost the network’s learning efficiency.

4.4.2. Comparison with Other Models

Numerous tool wear prediction techniques were chosen for quantitative comparison in order to confirm the benefits of this suggested methodology. The selected algorithms include: Support Vector Regression (SVR), Gated Recurrent Unit Neural Network (GRU), Bayesian optimization LSTM and BiLSTM, One-Dimensional Convolutional Neural Network (1DCNN), LSTM combination prediction algorithm, and Two-Dimensional Convolutional Neural Network (2DCNN).

For SVR, since SVR cannot handle sequence data, feature extraction must be carried out first. It is necessary to extract 11 characteristics from seven channel data in the time domain, including mean, standard deviation, skewness, kurtosis, pulse factor, peak factor, shape factor, marginal factor, peak-to-peak value, root mean square, and energy. The frequency domain is used to extract four characteristics, including the sk mean, sk standard deviation, and sk kurtosis, giving the seven-dimensional signal a total of 105-dimensional time-frequency features. A 105 × 1 matrix was used to represent each trimmed feature and was entered into the ensuing regression model. The optimal regularization parameters of the SVR model are selected from {0.001, 0.01, 0.1, 1,10}, and the kernel uses the Gaussian basis function (RBF) by default.

For GRU, a layer of GRU, with 64 hidden layers, regularization parameters of 1 × 10⁻², and an initial learning rate of 1 × 10⁻² is considered.

For both LSTM and BiLSTM, model parameter optimization is achieved through Bayesian parameter estimation. LSTM considers one layer, while BiLSTM considers two layers. The maximum number of Bayesian parameter estimates is 30, the regularization range is {1 × 10⁻¹⁰, 1 × 10⁻²}, and the initial learning rate range is {1 × 10⁻³, 1}.

For both 1DCNN-BiLSTM and 2DCNN, the seven channels of original data are the original input for the 1DCNN-BiLSTM prediction model, and the seven channels of signals from the CEEMDAN are the input for the 2DCNN prediction model after they have been decomposed.

Table 5. Model Comparison.

Method	RMSE	MAE
SVR	31.5	24.9
GRU	36.3615	31.422
B-LSTM	33.859	28.9897
B-BiLSTM	26.4284	21.1652
1DCNN-BiLSTM	12.396	10.9944
2DCNN	15.3604	11.4455
Developed model	7.6667	5.9884

displays the comparative outcomes of trials (using tool C6 as an example).

Compared to a Recurrent Neural Network (RNN), the GRU model can process sequence data better than the SVR model. SVR, on the other hand, is a variation of the Support Vector Machine (SVM) that is frequently employed for regression issues but has poor processing capability for sequential data. SVR, however, outperforms GRU when the dataset is limited, since GRU needs a bigger dataset to train on and making parameter adjustments before overfitting is a possibility. On tiny datasets, SVR performance is a little bit more consistent. In contrast to the GRU model, B-LSTM, and B-BiLSTM, Bayesian optimization establishes a Gaussian process model in the explored parameter space to estimate the unknown region of the function to be optimized, avoiding the need to search the entire parameter space, conserving computing resources, and speeding up the evaluation of the optimal solution. Compared to unidirectional LSTM, BiLSTM utilizes information from both the front and back directions, enabling a more comprehensive understanding of time series data and achieving better results.

According to Table 5, when compared to SVR, GRU, B-LSTM, and B-BiLSTM models, the suggested model in this study dramatically lowers RMSE and MAE. The comparison results demonstrate that the multi-scale data fusion model derived by this model is more sensitive to changes in tool wear status than the spatial or temporal correlation features extracted by conventional deep learning network models. The traditional machine learning approach also requires manual feature extraction and selection, which depend on the expertise and wealth of experience of professionals. In addition, feature adaptation and wear value prediction are carried out separately, and simultaneous optimization of both parts cannot be achieved. Therefore, the model prediction accuracy can easily achieve the upper limit.

4.4.3. Exploring the Expandability of Models

In the aforementioned study, cross experiments were conducted on the data sets C1, C4, and C6 to confirm the model’s efficacy and show its superiority to other models. All of the data from C1 through C6 will be used in the study to examine its generalizability. The output is the tool’s remaining use times, and the input is the matrix following CEEMDAN decomposition and rebuilding. Figure 11 continues the cross-validation using C1,C4,C6, and in Figure 12, if C1 is the validation set, then C2–C6 is the training set.

The prediction results are shown in Figure 11 and Figure 12. The MAE of C1 is 8.1137 and 5.4846, and the RMSE is 11.0498 and 7.3676, respectively. The MAE and RMSE of C4 were 8.1863 and 6.2208, 10.2017 and 8.7289, respectively. The MAE of C6 is 18.7712 and 12.0137, and the RMSE is 22.0223 and 15.9872, respectively. It can be seen that when the dataset is enlarged, the MAE predicted by the model shrinks by 30% and the RMSE by 25% on average. In practical application, with the more data obtained in the actual processing, the more abundant the data of the training model, the life degradation prediction model proposed in this paper will have better accuracy.

5. Conclusions

This study provides a combined prediction method based on modal decomposition, multi-channel input, MCNN and BiLSTM. Using the milling dataset of PHM2010 for experiments and validation, we draw the following conclusions:

(1)

The sensor signals during tool processing may better handle nonlinear and non-stationary signals after filtering and CEEMDAN, boosting local characteristics.

(2)

The developed model will predict tool wear values more accurately because it can more efficiently mine spatiotemporal properties in cutting signals.

(3)

This method’s prediction accuracy outperforms the SVR model, GRU model, B-LSTM model, B-BiLSTM model, 1DCNN-BiLSTM model, and 2DCNN model.

The research on tool wear prediction provided in this article is based on the machining circumstances of utilizing the same type of tool in the same working environment due to the dearth of rich data. Different tools and machining environments still provide difficult issues in actual machining production. This work presented an approach that will be utilized for later research to explore the usage of various cutting tools under various operating circumstances in order to further validate the precision of the forecast and the generalizability of this strategy.