Sensor data fusion and cutting tool status recognition by k-means clustering

1. Introduction

Recognizing the tool wear state for calculating tool life is a critical aspect of most metal cutting processes. Various techniques have been developed to assess the condition of cutting tools during the turning process. The most accurate, yet less efficient, methods involve direct examination of the tool using microscopes, laser devices, or machine vision systems [1-3]. Although these instruments are often more cost-effective than sensors used for indirect measurement, the effectiveness of direct methods is limited by the requirement to halt machining in order to assess tool condition. In contrast, indirect measurement methods incorporate sensors for continuous monitoring. Machine learning techniques can continuously evaluate sensor data relevant to tool wear conditions [4]. However, relying solely on sensory data for tool wear assessment can be unreliable due to the presence of noise and uncertainty [5, 6]. A viable solution to this challenge is sensor fusion, which combines inputs from multiple sensors to improve reliability. Decision-making based on multi-sensory observations has been shown to be distinctly superior to that based on single-sensor data. In multi-sensory observation, the data collected from various sensors must be processed to determine the condition of the cutting tool. Several data fusion strategies can be applied to integrate the extracted features, including the Indices Multiplication and Division Group (IMDG) [7], Comparison Group (CG) [8], Index Multiplication Group (IMG) [9], and Vector in Mapping Space Group (VMSG) [10]. The most common methods for final decision-making include artificial neural networks, fuzzy logic, hidden Markov models, support vector machines (SVM), and adaptive-network-based fuzzy inference systems [10, 11]. While these methods are widely used to predict or evaluate tool wear, they often lack the capability to classify data into clearly defined groups. This research investigates the application of multi-sensory data fusion using K-means clustering to monitor tool wear in the turning process. The key advantages of the proposed methodology are:

i) Real-time monitoring of tool wear states.

ii) Improved reliability through multi-sensor data integration.

iii) Faster convergence compared to many other machine learning techniques.

iv) Straightforward scalability with an increasing number and diversity of sensors

2. Literature review

This section reviews several pertinent published research contributions. These technologies either involve complex, systematic machine learning algorithms with promising results or utilize specific sensors for tool wear monitoring applications. Zheng et al. applied data fusion through a Long Short-Term Memory (LSTM) network to monitor tool wear status during the milling process under diverse cutting conditions [10]. Zhou et al. investigated tool wear conditions during milling operations using current sensors [12]. Laddada et al. employed wavelet transform and an enhanced Extreme Learning Machine (ELM) algorithm to monitor tool wear conditions [13]. Dai et al. developed and examined a machine vision system for monitoring the condition of micro milling tools [14]. Benkedjouh et al. utilized Continuous Wavelet Transform (CWT) and blind source separation techniques for tool wear monitoring [15]. Liu et al. assessed calibration-based tool condition monitoring for repetitive tasks [16]. Aghazadeh et al. employed spectral subtraction and convolutional neural networks (CNNs) for tool condition monitoring in the milling process [17]. Xie et al. proposed a feature selection method to enhance the efficacy of tool condition monitoring [18]. Ong et al. examined CNC tool condition using wavelet and neural network methodologies informed by machine vision [19]. Guo et al. investigated the use of support vector machines (SVM) and fluctuation analysis for tool condition monitoring in milling operations [20]. Rao et al. explored vibration-based tool condition monitoring in the milling of Ti-6Al-4V using an optimization model combining Grey Model (GM) and SVM [21]. Zhou et al. conducted tool wear condition monitoring using a two-layer angle kernel extreme learning machine and a sound sensor during the milling process [22]. Danesh et al. proposed an optimized artificial fuzzy inference sensor fusion system for tool wear monitoring [23]. Kuntoğlu et al. reviewed decision-making and indirect tool monitoring methodologies [11]. Zhu et al. conducted numerical simulations and applied a Generative Adversarial Network (GAN) to monitor tool wear states in intelligent milling processes [24]. Li et al. investigated the integration of mapping radar, AdaBoost-DT, and SBiLSTM techniques for tool wear monitoring [11]. He et al. introduced a deep learning approach utilizing stacked sparse autoencoders (SSAE) and multi-sensor feature fusion for milling tool wear prediction [25]. J. Fan et al. used the density peaks approach for grouping multisensory observation data for fusion [26]. Li and Wang introduced novel optimal C-means and K-means algorithms for clustering datasets using soft computing, demonstrating applications in biological data, language, texture, customer information, email messages, and image data [27, 28]. K-means clustering is widely used for recognizing tool wear states due to its simplicity and efficiency. However, the standard K-means algorithm is sensitive to centroid initialization, which can lead to inconsistent clustering results. To address this, enhancements such as Fixum K-means (F-Km) have been developed. These improve accuracy and robustness by refining the initial centroid selection process. F-Km has shown superior performance in clustering tool wear data, achieving higher precision and faster convergence compared to standard K-means and K-means++ algorithms [29]. Several variants of the K-means algorithm have been proposed to overcome its limitations, such as sensitivity to initial conditions and the requirement for a predefined number of clusters. For instance, the U-K-means algorithm automatically determines the optimal number of clusters without requiring prior parameter selection, enhancing its utility in unsupervised scenarios [30]. Additionally, multiple-kernel K-means clustering with late fusion has been introduced to reduce computational complexity while maintaining high clustering performance [31]. In the context of cutting tool state recognition, K-means clustering is used to classify tool conditions based on sensor data, such as cutting force measurements. This facilitates real-time monitoring and adaptive control of machining processes. For example, a real-time recognition system using K-means clustering has been developed to classify cutting tool states with high accuracy, enabling efficient machining of complex structural parts [32]. Moreover, integrating K-means with other clustering methods, such as Gaussian Mixture Models (GMM), has demonstrated improved stability and effectiveness in detecting machining chatter [33]. Despite its widespread use, K-means clustering faces challenges in handling high-dimensional data and detecting non-spherical cluster shapes. Future research is focused on developing more robust clustering algorithms that can automatically adapt to varying data characteristics and improve clustering accuracy in complex manufacturing environments [34, 35]. Furthermore, integrating advanced feature learning techniques, such as deep neural networks, with K-means clustering represents a promising direction for enhancing clustering performance in high-dimensional spaces [36].

3. Problem statement and the proposed solution

In machining shops, it is often more desirable to determine the condition of the cutting tool in terms of wear states – such as normal wear, medium wear, or critical wear – rather than measuring the exact value of tool wear. In this research, the K-means clustering method is employed for sensory data fusion and classification of tool wear states. One advantage of K-means clustering in cutting condition monitoring is its ability to create distinct boundaries between wear categories, in addition to providing an estimate of wear. Each cluster has a representative centroid that can be used to estimate the level of tool wear by comparing new data to these centroids, enabling predictions in subsequent tests. In this study, a K-means clustering model was developed to integrate features from surface imagery, motor current, mechanical strain, and vibrational signals. The proposed model includes four inputs and one output. The inputs are: (i) the entropy of the surface image filtered using the Stationary Wavelet Transform (SWT), (ii) the time-frequency marginal integral of the motor current, (iii) the Shannon entropy of strain signals, and (iv) the Shannon entropy of vibration signals. The output of the model is the estimated flank wear. The results show that the K-means clustering model effectively integrates signal features and accurately predicts tool flank wear. By clustering tool states based on integrated features, the model enhances the flexibility of tool replacement decisions in intelligent manufacturing systems. To validate the proposed tool monitoring system, an accelerometer was mounted on the shank of the cutting tool to measure vibrations caused by tool wear in the feed direction. A vision system was also employed to monitor tool condition by analyzing the surface texture of the workpiece, thereby corroborating the results across multiple tests. The findings demonstrate the robust performance of the proposed system and highlight its strong potential for practical application in tool wear detection. By utilizing four sensors – accelerometer, strain gauge, vision, and motor current – the system effectively addresses two primary challenges: signal noise and uncertainties inherent in both the system and experimental procedures.

4. Tool wear monitoring

The proposed tool wear monitoring system utilizes four sensors: an accelerometer, a strain gauge, a vision system, and a current sensor. This section details the methodology employed for signal analysis, feature extraction, data fusion, and clustering. Each stage plays a critical role in accurately identifying the condition of the cutting tool and ensuring the reliability of the monitoring system.

4.1. Motor spindle current sensing

Among the indirect methods for monitoring tool wear, motor current sensing offers the advantage of being non-intrusive to the cutting process while also being cost-effective. The relationship can be mathematically expressed as shown in Eq. (1) [37]:

1

$F_f=\varphi \left(\mathrm{\Delta }I,f{}_r{}^{\mathrm{}}\right).$

The $F_f$, $f_r$, $\mathrm{\Delta }I$, $I$, and $I_0$ refer to cutting force, rate of feed, current difference, motor current, and non-loading motor current, respectively. In this research, the method introduced in [1] is used to estimate tool wear based on motor current. In the machine tool’s engine, the alternating current (AC) of the spindle motor varies and can be used to estimate wear. Due to uncertainties in experimental conditions, waveform distortions are present. Experimental findings indicate that spindle current signals exhibit increased distortion as tool wear progresses [38]. The variation of harmonic and sinusoidal waves is considered, as discussed in [39]. According to the Fourier series theorem, any periodic waveform can be expressed as a combination of a fundamental waveform and a series of harmonic components. Harmonic frequencies are generally produced by nonlinear, load-attached devices [40]. In this study, the Short-Time Fourier Transform (STFT) of the motor current signal is first calculated, followed by the extraction of the time-frequency spectrogram. Then, to obtain the Frequency Marginal Integral (FMI), integration is performed along the time axis [41]. The mathematical definition of STFT is given in Eq. (2):

2

$STFT\left\{x\left(t\right)\right\}=\underset{-\infty }{\overset{+\infty }{\int }}x\left(t\right)w\left(t-\tau \right)e^{-jwt}dt.$

The $w\left(t\right)$, $x\left(t\right)$, and $\tau$ represent the window function, the signal, and the temporal index, respectively. The time-frequency spectrogram calculates the quadratic energy distribution of the signal, as defined in Eq. (3):

3

$S{}_p{}^{\mathrm{}}\left\{x\left(t\right)\right\}={\left|X\left(\tau ,w\right)\right|}^2.$

Here, to define the FMI, which corresponds to the smoothed power spectrum of the signal. The power spectrum illustrates how the signal’s power is distributed across different frequencies. Eq. (4) defines the frequency marginal integration:

4

$FMI={\int }_{-\infty }^{+\infty }{\left|X\left(\tau ,w\right)\right|}^{2}dw.$

In Eq. (5), the initial FMI value is subtracted from the FMI value obtained during machining:

5

$\mathrm{\Delta }{I}_{FMI}=I_{FMI}-I_{FM{I}_0}.$

Motor current can be used to approximate cutting forces, which in turn can be employed to estimate tool flank wear. It is important to note that the feed motor’s current differs between loaded and unloaded conditions. Motor current sensing is a valuable technique for indirect tool wear monitoring, as it does not interfere with the machining process and can be implemented at low cost. In engine lathes with feed mechanisms driven by the spindle motor, tool wear assessment relies solely on measuring the current signal of the alternating current (AC) spindle motor. Consider a power system comprising an AC power supply and an electrical load, as shown in Fig. 1(a). Under ideal conditions, the current signal obtained from the load would be a perfect sinusoidal waveform. However, in practical scenarios, such ideal conditions are rarely achieved, resulting in significant waveform distortions, as illustrated in Fig. 1(b). Experimental results from researchers show that spindle current signals become increasingly distorted as tool wear progresses. Fig. 1(b) presents a segment of the current signal from the spindle motor drive under two tool conditions: sharp and worn.

Fig. 1Power system: a) AC source and electrical load, b) electric current waveform using a sharp tool

a)

b)

The deviation from an ideal sinusoidal waveform is commonly quantified using the term harmonic distortion waveform. A periodic waveform can be represented as a combination of multiple waveforms: a fundamental frequency component and a series of harmonic components. Each harmonic component has a frequency that is an integer multiple of the fundamental frequency (Fig. 2). Harmonics may be generated either by the power supply or by the load. In most cases, the harmonics produced by the load originate from the nonlinear characteristics of the equipment.

Fig. 2Harmonics generation in a non-linear system

4.2. Surface imaging

Tool wear assessment using surface imagery is carried out in two phases. In the first phase, the Stationary Wavelet Transform (SWT) is applied to the surface image of the workpiece, decomposing it into four sub-images: low-low, low-high, high-low, and high-high components (see Fig. 3) [42-44].

Fig. 3Stationary wavelet transforms structure [43]

In the next stage, texture features derived from the Gray Level Co-occurrence Matrix (GLCM) are used to assess tool wear based on the selected sub-images. The results of the SWT decomposition are discussed later in this document. The spatial GLCM is a widely recognized and commonly used technique in texture analysis [45]. A GLCM represents image orientation by emphasizing spatial relationships between pixel intensities. Eq. (6) defines the Haralick entropy feature for texture analysis based on the GLCM. In this context, $p\left(i,j\right)$ is the matrix element that represents the probability of the $j$th gray level occurring to the right of the $i$th gray level in the image. Entropy, as described in Eq. (6), measures the degree of disorder or randomness within an image (for more details, refer to [24, 46-49]):

6

$Entropy=-{\sum }_i^{}{\sum }_j^{}p\left(i,j\right)\mathrm{l}\mathrm{o}\mathrm{g}\left(p\left(i,j\right)\right).$

5. K-mean clustering

In data-driven, K-means is an unsupervised method for clustering and classification data. To determine the similarity of the data, various measures and methods are used; one of which is the Euclidean distance, where current research has used it here, as well. The algorithm first determines the number of clusters to be considered. Then, the it selects the number of clusters we have specified by the existing data set and randomly selects a number as the center of each cluster. In the next step, other data are added to these clusters, and the average data of each cluster is considered as the center of that cluster. After selecting the new cluster centers, the data in the new clusters are regrouped. The K-means method assumes k-number clusters, and then follows the following process.

1. Initialize centroids. Choose $K$ initial centroids randomly from the dataset. These centroids can be chosen randomly and the K-means method for better initialization: ${\mu }_1,{\mu }_2,{\mu }_3,...,{\mu }_K$.

1.1 Choose the first centroid.

Randomly select the first centroid from the dataset.

1.2 Compute distances.

For every point of data $\left(x_i\right)$ was not selected as a central, calculate the nearest, $D\left(x_i\right)$, central point has been chosen before.

1.3 Probability distribution.

Select the next centroid from the data points with a probability proportional to $D\left(x_i\right)$. Specifically, a point $x_i$ will be chosen with a probability of Eq. (11):

where $X$ is the set of all data points.

1.4 Redo.

Reiterate steps 2 and 3 until $K$ centroids have been selected.

1.5 Proceed with K-means algorithm.

Once $K$ centroids have been initialized, proceed with the standard K-means algorithm (assignment and update steps 1.1 to 1.4).

2. Assignment step. For each data point $x_i$, find the closest centroid with Eq. (12):

where $x_i$ as data point is applied with assignment of cluster through $c_i$.

3. Update step. Eq. (13) updates the centroid of each cluster $k$:

where the $C_k$ is assigned as points with number $\left|C_k\right|$ in cluster $k$.

4. Repeat.

The assignment and update procedures until the centroids exhibit negligible changes: $\mathrm{\Delta }\mu <\epsilon$ for all $k$, where $\epsilon$ is a small threshold value indicating convergence. After the initial training process and convergence of the algorithm, the real-time date whose attribute falls within the range of each cluster range belongs to that specific cluster (for more information in MATLAB).

6. Experimental setup

AISI 4340 steel bars with a diameter of 20 mm and a length of 120 mm were used in the present research. The tool holder, shown in Fig. 4(d), was equipped with sensors and an insert of Sandvik type B210 (see Fig. 4(f)). The workpiece was mounted between the chuck and the tailstock. The conditions and equipment used in the lab are presented in Table 1.

Fig. 4Monitor procedures: a) sensor fusion, b) data logger, c) tool holder, workpiece, accelerometer, digital microscope, d) data acquisition, e) electrical equipment, 80I-600 AC, f) Sandvik type B210

a)

b)

c)

d)

e)

f)

As shown in Fig. 4(c), a digital microscope was mounted on the lathe carriage using a specially designed platform to capture surface images of the workpiece during each pass. A Fluke 80I-600 AC transmitter (Fig. 4(d)) was used to acquire the motor current signal. An accelerometer (Fig. 4(c)) was affixed to the shank of the cutting tool to measure longitudinal vibrations, while a strain gauge was attached to the workpiece to detect mechanical strain. The active dummy method was employed to compensate for the effect of machining temperature on the strain measurement. The Wheatstone bridge, depicted in Fig. 5(b), utilized two types of sensors: strain gauges and dummy gauges made from identical materials. The active strain gauge was attached to the cutting tool, while the dummy strain gauge was unbound to the temporal setting, resistance ratio, and voltage output. The close positioning of the active and dummy gauges helps minimize thermally generated strain under balanced bridge conditions.

Fig. 5Graphical process of data sampling: a) workpiece, b) Wheatstone bridge, c) strain gauge, d) data logger, e) monitoring

7. Results and discussion

7.2. Qualitative analysis via flank-wear photographs

To validate that each fusion-derived cluster corresponds to real flank-wear levels, we captured in situ images of the cutting insert flank after each pass. Fig. 6 shows three representative photographs with measured flank-wear values VB = 0.08 mm (low wear), VB = 0.18 mm (medium wear), and VB = 0.32 mm (high wear). Visual inspection confirms that:

– Low-wear cluster (0-0.1 mm) exhibits only minor discoloration and no pronounced crater or notch.

– Medium-wear cluster (0.1-0.2 mm) shows clear flank edge rounding and slight crater formation.

– High-wear cluster (> 0.2 mm) displays substantial crater depth and pronounced edge breakdown.

This qualitative correspondence demonstrates that the clustering boundaries align with human-interpretable wear features, bolstering confidence in the proposed recognition method. The reliability of tool wear monitoring has been questioned due to signal characteristics that are not directly dependent on tool wear, as well as the presence of variables and disturbances. One solution to this issue is sensor fusion, which integrates sensory inputs from diverse sources. This approach, combined with the emerging use of machine vision to assess the morphology of the wear zone, provides superior completeness, accuracy, reliability, and robustness compared to the individual use of each method. This research proposes a low-cost and reliable tool wear condition monitoring system that utilizes a combination of computer vision, motor current, strain, and vibration sensors. The system employs a Multiple Input Single Output (MISO) model with an Adaptive Neuro-Fuzzy Inference System (ANFIS) architecture. The study investigates a MISO system with four inputs and a single output. The inputs consist of the surface image entropy derived from wavelet transform, the frequency of the time-invariant motor current, Shannon entropy of mechanical strains, and vibration signals, with flank wear being the output. The findings indicate that the ANFIS model can accurately estimate tool flank wear. Fig. 6 illustrates the three-level Stationary Wavelet Transform (SWT) decomposition applied to the surface images, utilizing a low-pass filter on each row and column of the low-resolution primary image [44]. Similarly, the low-high sub-image was generated by applying low-pass filtering to each row and high-pass filtering to each column, with high-frequency details in the column direction influencing the low-high sub-image. The high-low sub-image was obtained by applying high-pass filtering to each row and low-pass filtering to each column, with high-frequency details in the row direction (feed marks) affecting the high-low sub-image. The high-high sub-image was generated using high-pass filtering applied to both rows and columns, with high-frequency details in the diagonal direction affecting the high-high sub-image.

Fig. 6Three-level SWT decomposition of surface image resulted from different tool wear levels

7.5. K-means modeling and simulation

For this performance evaluation, the K-means clustering method was employed to classify the experimental dataset of sensor fusion for tool wear monitoring during the milling process, using MATLAB coding in an M-file. The first step involved normalizing the dataset, followed by the application of the K-means algorithm to classify the data into three groups based on expert knowledge of the workpiece surface roughness. As shown in Fig. 8(a), normalizing a dataset in signal processing is essential for enhancing algorithm performance, ensuring numerical stability, and achieving consistent feature scaling. It facilitates meaningful comparisons across datasets, reduces unnecessary repetition and irrelevant information, and adheres to statistical assumptions. Moreover, normalization aids in visualization and improves the training of machine learning models by preventing the occurrence of local minima, ensuring convergence toward a global optimum. Normalization is the process of scaling data to a similar range, ensuring that all features contribute equally to the analysis, which leads to more accurate and reliable results. This performance evaluation focuses on real-life, off-line tool wear status monitoring, aiming to present an intelligent function for assessing tool wear in different statuses within the manufacturer’s recommended intervals for the milling process. This intelligence function utilizes fuzzy logic based on expert knowledge of the milling process (Fig. 8). Fig. 7 illustrates the K-means clustering process applied to the sensor data. Initially, the dataset is imported into the K-means algorithm (Fig. 8(b)), followed by classification into three tool-wear status indices based on expert knowledge (High, Medium, Low). Each index group is then linked to surface roughness levels. Finally, the results show each sensor's cluster based on tool wear, as illustrated in Fig. 9.

Fig. 7Simulation process of tool wear by k-means algorithm

Fig. 8Clustering of sensors output, a) normalization, b) original

a)

b)

Fig. 9Clusters of sensors fusion within centers

8. Conclusions

This study presents a multi-sensory data fusion approach for tool wear monitoring in turning processes, achieving a classification accuracy of 95 % across three wear states – low (0-0.1 mm), medium (0.1-0.2 mm), and high (> 0.2 mm) – using K-means clustering on data from four sensors: machine vision, electrical current, accelerometer, and strain gauge. Unlike traditional single-sensor methods, which often achieve accuracies below 80 % due to noise and uncertainty, this method leverages complementary sensory inputs to enhance reliability and robustness, as validated through experimental results on AISI 4340 steel workpieces. The method’s uniqueness lies in its unsupervised K-means clustering approach, which fuses heterogeneous data sources to create clear wear state boundaries, enabling precise tool replacement decisions without requiring extensive labeled data or computational resources – common drawbacks of neural networks and fuzzy logic systems. Its rapid convergence and scalability further distinguish it from existing techniques, making it ideal for real-time applications. However, limitations exist: the assumption of three wear clusters may oversimplify complex wear progressions, and the multi-sensor setup increases initial costs, potentially hindering adoption in smaller facilities. Future work could explore adaptive clustering for nuanced wear patterns and cost-effective sensor alternatives. For production implementation, the method integrates seamlessly with CNC machines via edge computing for real-time processing, calibrated to industry-standard permissible flank wear of 0.3 mm, beyond which tools require replacement. This ensures minimal downtime and improved efficiency. Overall, this research offers a practical, data-driven solution that advances tool condition monitoring, with clear potential for enhancing manufacturing precision and productivity. For future investigations, various aspects of this study can be explored further. In the preprocessing stage, the use of LS-Dyna and ANSYS for static, dynamic, and modal analyses is strongly recommended to evaluate natural frequencies, crashworthiness, damage evolution, crack propagation, and heat transfer under operational conditions based on condition and health monitoring [50-54]. From a manufacturing design perspective, several practical techniques are available to optimize and redesign the fabrication process [55-57]. Theoretically, hybrid topology optimization combined with metaheuristic algorithms such as MOPSO, PSO, and MOGA offers potential for developing innovative models [58, 59]. Experimentally, implementing diverse strategies for optimal placement of PZTs on the brake surface can generate new signal patterns for effective data processing related to crack detection and high-temperature monitoring [60-63]. Moreover, the study of meta-cell structures in the brake system – capable of altering band gaps in natural frequencies – presents a promising research direction [64]. Lastly, in terms of control systems, employing various controllers such as PWM, PID, H_∞, sliding mode, and fuzzy logic can enhance the precision of workpiece [65-69].