Knot-TPP: A Unified Deep Learning Model for Process Incidence and Tool Wear Monitoring in Stacked Drilling

Abstract

In drilling Carbon-Fibre-Reinforced Polymers (CFRP)/Al stacks, adaptive drilling facilitates the optimisation of cutting parameters for each constituent stack layer and tool wear, thus enhancing cutting efficiency and borehole quality. This study proposed a knot–Temporal Pyramid Pooling (TPP) model aimed at monitoring both process incidences and tool wear in the drilling of hybrid stacks, which subsequently informs the machine tool to adjust cutting parameters or, if necessary, replaces the tool. TPP is introduced to remove the restriction of input dimensions, allowing for the acceptance of inputs with arbitrary shapes. On the other hand, a knot structure has been proposed to incorporate the classification of process incidences into the tool wear analysis, thereby enhancing prediction accuracy. The proposed model achieves a process incidence identification accuracy of 99.19% and a Mean Absolute Error (MAE) of 10 μm in tool wear prediction, demonstrating robust performance across a wide range of sampling conditions. This achievement facilitates decision-making and optimisation relating to cutting parameters and tool replacement in the context of adaptive drilling of aerospace materials.

1. Introduction

Both civil and military aviation manufactures have been progressively integrating multi-material stacked structures, including CFRP and aluminium, as structural supports within their designs due to their advantageous properties like high specific stiffness, formability, and good corrosion fatigue resistance [1,2]. The assembly of components comprised hybrid stacks, usually jointed using bolts, screws, and rivets, requires strict tolerances, making drilling one of the most frequently executed operations [3]. For example, within Airbus, more than 100 million holes are drilled annually in their machining departments, accounting for approximately one third of all machining activities [4]. Due to the fact that boreholes failing to meet their specified tolerances account for more than 60% of all rejected parts [5], the quality of the holes is a significant determinant of the productivity of the fabrication and assembly line [6]. Consequently, it is evident that to improve product quality and minimise waste resulting from workpiece damage and tool failure, drilling operations with adequate reliability are indispensable.

When drilling hybrid stacks, multiple material layers are clamped and drilled together to avoid misalignment of the holes in each layer and, thus, reduce the cost of later assembly [7]. Traditionally, process parameters in hybrid stack drilling are chosen as a compromise of one or both layers throughout the entire drilling cycle, i.e., one set of cutting parameter for all stack layers, resulting in all or at least part of the stack not being drilled with the ideal cutting parameters [5]. In many cases this results in the generation of higher than usual cutting force, accelerated tool wear and intensified thermal impact, all of which leading to a reduced borehole finish, which leads to a large number of scrapping products and becoming the main reason for high machining costs of CFRP [8]. To resolve this, aircraft manufacturers are keen on using what is referred to as adaptive drilling, where the cutting parameters are adjusted based on which stack layer the drilling tool is engaged in. As this allows each stack layer to be machined with optimised cutting parameters, stack drilling typically results in substantial improvements in both hole quality and process efficiency [4]. However, it requires knowledge of which layer the drilling tool is engaged in at any time throughout the drilling cycle, to allow the machine carrying out the drilling to operate at the correct set of cutting parameters.

In the case of drilling, a process incidence describes a distinct stage of the drilling cycle. For a single layer material, this would be when tool starts to engage with the material, when it is fully engaged with the material and, finally, when it exits the material. Taking commonly used CFRP/Al stacks as an example, five process incidences can be identified, namely tool engagement (i.e., the tool entering the top layer), cutting CFRP (i.e., the tool being fully engaged in the top layer), material transition (i.e., the tool moving from the top layer into the bottom layer), cutting Al (i.e., the tool being fully engaged in the bottom layer) and tool disengagement (i.e., the tool exiting the bottom layer), see Figure 1. In an adaptive drilling system, the layer within which the drilling tool is engaged is identified and the cutting parameters adjusted to match the optimal cutting parameters for this specific material. This is to reduce failures and prevent damage to the material, as well as reduce tool wear. For example, whilst drilling CFRP, the feed rate is kept low to avoid delamination, especially at the bottom of the CFRP layer. Later, when drilling through the aluminium layer, the feed rate should be increased to reduce the thermal impact and increase productivity [9]. During disengagement when the exit burr is being formed, which has a huge impact on the overall assembly quality [10], the feed rate should be adjusted again in order to inhibit burr formation. Ideally, when choosing the ideal parameters, tool wear should also be taken into consideration. For example, in the case that tool wear is significant, a reduction in feed rate will accelerate abrasion wear, which in turn results in material degradation and surface damage [11]. Therefore, in order to provide a reliable basis for adaptive drilling and to ensure a safe and valid optimisation of the machining process, both the drilling stage and tool wear need to be accurately identified.

Another factor that strongly impacts the borehole quality ans surface integrity is the tool wear, as excessive tool wear leads to severe heat generation and thermal damage of the part and the assembly [12]. Particularly in the context of drilling CFRP, which is widely acknowledged as a material that is challenging to cut, the severity of tool wear is greater than that experienced with conventional materials, thereby presenting significant challenges to maintaining product quality [8]. Thus, the incorporation of tool wear monitoring systems can enable the pre-emptive replacement of cutting tools prior to their failure, thereby alleviating the detrimental effects of tool wear on the drilling process and safeguarding both product quality and assembly integrity. Furthermore, during the adjustment of cutting parameters in an adaptive drilling context, predicting tool wear can offer a dependable foundation for comprehensive optimisation. The estimation of tool wear is, however, exceedingly complex due to its time-varying and non-linear characteristics, coupled with numerous potential interferences [13]. Furthermore, the presence of occlusion and cutting fluid renders it impractical to directly assess tool wear conditions during the machining process. Moreover, the absence of an accurate physics-based model further complicates tool wear estimation, which creates the gap between knowledge and experience [12,14]. Hence, the implementation of precise tool wear monitoring is imperative for the enhancement of the drilling processes involving CFRP/Al stacks.

Despite advancements in the precise identification of process incidence, tool wear continues to pose significant challenges in the drilling of hybrid stacks [4,15,16]. Neugebauer et al. [15] adopted a slope-based decision method to identify the engagement and disengagement of drilling tools using Acoustic Emission (AE), but their approach is unable to identify the incident ‘material transition’ once the signal becomes chaotic due to excessive tool wear. Fortunately, as the introduction of deep learning technology, the identification on process incidence monitoring can achieve a very high accuracy with Minimum Sufficient Unit (MSU) condition explored as investigated in Zhang et al. [16]. On the contrary, while tool wear monitoring is extensively investigated for a single material type, predicting tool wear presents considerable challenges due to the complex progression of wear during the drilling of CFRP and aluminium [12,17]. This intricacy results in a constrained scope of research in the context of drilling hybrid stacks [18]. Most studies in tool wear monitoring focus drilling CFRP rather than the hybrid stacks. In the study of Teti et al. [19], signal characteristics from thrust force and torque in both time and frequency domain is extracted to predict tool wear using Spearman correlation coefficients in drilling CFRP. Extending this method, Caggiano et al. [20] incorporated autoencoders and memory-based networks to monitor tool wear in the drilling of the CFRP/CFRP stacks. However, due to the disparity in materials between CFRP/Al, the notable difference in tool wear patterns observed in the drilling of CFRP and aluminium further complicates the evolution of tool wear and renders existing research challenging to apply [18]. Therefore, to mitigate these challenges, it is prudent to integrate the findings from process incidence monitoring into tool wear prediction models. This approach allows the model to focus exclusively on a singular type of wear pattern within a single cutting material, as opposed to dealing with the complexities inherent in hybrid stacks, which calls for the proposal of unified monitoring approaches. Furthermore, this integration can save time and resources in training and incorporating separate models, enhancing computational efficiency and practicality in industry. Nonetheless, there exists a paucity of relevant studies addressing unified monitoring for multiple objectives within tool condition monitoring. It is thus imperative to bridge the gap between the existing body of knowledge and practical industrial applications.

In the comprehensive prediction of process incidence and tool wear, it is essential to acknowledge the varying levels of task urgency. Given that stack drilling typically takes a shorter duration, it is crucial to maintain the responsiveness of process incidence; otherwise, any delay in identification may lead to a discrepancy between cutting parameters and process incidence, thereby undermining adaptive drilling efficacy [4]. This typically necessitates that the sampling duration for process incidence be minimised as much as possible, indeed approaching MSU [5]. Conversely, the progression of tool wear occurs gradually, permitting a more extended duration for observation and analysis. As investigated in Zhang et al. [5], the extending of sampling duration usually brings benefits to identification accuracy according to Continuous Classification Equivalent Accuracy (CCEA) theorem. In conventional models, because of the constraints in input dimension, distinct combinations of sample duration and frequency necessitate the training of separate models, a process that can be resource-intensive and time-consuming [21]. In the context of image processing, He et al. [22] propose Spatial Pyramid Pooling (SPP) to remove the constraint in input shape to natively accommodate and recognise an image of arbitrary size. Wang et al. [23] applied this to one-dimensional TPP to tackle video-based action. As this variant does not take an actual signal as the input but focuses on temporal dependencies in motion, it needed to be modified so that it can be applied to the problem addressed in this paper.

To address the previously mentioned limitations, a knot–TPP model capable of predicting both process incidence and tool wear based on signals of arbitrary shapes is proposed. To mitigate the dependency on the dimensionality of the input signal, TPP is introduced, facilitating task urgency adaptation to achieve a balance between immediacy and certainty. The knot structure is proposed to embed precise process incidence predictions into the context vector of the monitoring of tool wear, thereby simplifying the complexity of the issue and improving the quality of predictions. The integration of these methodologies enables model to simultaneously predict two objectives with unified set of parameters and the contextual reinforcement from predictions using signal of arbitrary shape, which bridges the gap of multiple-objective tool condition monitoring and removes the constraints of input shape of deep learning model. This eventually can offer more reliable predictions essential for the deployment of adaptive drilling within the aerospace sector.

2. Methodology

2.1. Temporal Pyramid Pooling

As mentioned before, the adaptation in TPP architecture is necessary for processing signal of arbitrary shape in drilling of hybrid stacks. Therefore, the technique in TPP is employed prior to the fully connected layer in the Convolutional Neural Network (CNN), thereby eradicating the limitations of fixed input size and facilitating the processing of signal inputs with arbitrary sampling durations and frequencies, as demonstrated in Figure 2.

TPP generates a constant-shaped output by applying a sequence of progressively larger max pooling operations over the temporal feature map [24]. The input shape of TPP is specified as $(N,L,C)$, where N denotes the number of batches, L the length, and C the channel of the input, respectively. In this layer, the feature map is initially divided into distinct temporal segments based on the number of pooling regions. As depicted in Figure 2, three pooling quantities, 1, 2, and 4, are utilised, resulting in regions comprising one vector with dimensions $(N,L,C)$, two vectors with dimensions $(N,L/2,C)$, and four vectors with dimensions $(N,L/4,C)$. Subsequently, max pooling operations are executed on these vectors, and the resultant maximum values are aggregated into a one-dimensional vector with dimensions $(N,(1+2+4)\times C)$, thereby producing an output of consistent shape irrespective of input length.

The introduction of TPP can bring benefits to the prediction of process incidence and tool wear. For instance, a reduced signal duration may be employed to promptly ascertain process occurrence, whereas an extended duration with enhanced precision, is preferable for monitoring the progressive nature of tool wear. Without the costs in re-training, re-verifying and deployment, TPP architecture can bring benefits to strike a balance between accuracy and immediacy by flexibly accepting signals of different duration.

2.2. Knot Structure to Integrate Tool Wear Prediction with Process Incidence

In our investigation, two primary objectives have been delineated and exhibit varying levels of difficulty. Although the precision in the classification of process incidence is reported to be relatively high, as indicated by Zhang et al. [16], the issue of tool wear continues to present significant challenges. Therefore, the integration of process incidence with tool wear prediction can bring benefits to the overall classification. For instance, owing to the disparities in material properties, the drilling of CFRP and aluminium necessitates distinct cutting forces, thereby resulting in varied signal features. This variance can costs additional computation and lead to inaccuracies in the model if the information regarding process incidences is absent. Consequently, it is feasible to incorporate the predictions of process incidence that exhibits high certainty into the prognosis of tool wear, thereby augmenting predictive accuracy and enhancing practical applicability of tool condition monitoring for drilling of hybrid stacks. To achieve this aim, a knotted structure that integrates process incidence information explicitly into tool wear prediction is proposed and illustrated in Figure 3.

In the knot architecture, two forks containing fully connected layer (dense) are positioned subsequent to the ultimate feature map, corresponding to the outputs pertaining to process incidence and tool wear. The structure is aptly named due to the interconnection of the process incidence with the tool wear, resembling the configuration of a knot. The prediction of process incidence follows the methodologies established in prior research: a tensor representing the probabilities of each case is outputted in the dense layer, subsequently activated by the SoftMax function into a one-hot format of n dimensions to indicate the specific class, where n denotes the number of process incidence classes predicted in this study [16].

Similarly to process incidence, the prediction of tool wear begins with a dense layer, generating tensor which is shaped in n-dimension and indicates tool wear value for each process incidence. Subsequently, the tensor is transposed and subjected to a cross product with the one-hot encoded tensor representing process incidence, culminating in the generation of the tool wear prediction. This operation is inspired by Deep Convolutional Generative Adversarial Networks (DCGAN), wherein the information pertaining to the conditional label is transmitted to image generation via a cross product operation with a one-hot encoded tensor [25]. Given that only a single element is equal to one while all others remain at zero, the cross product operation ensures that only the element corresponding to the specific process incidence is rendered into the final prediction. Consequently, the contributions of other elements are rendered negligible, as any element multiplied by zero inherently equals zero. Hence, this operation enables the adjustment of parameters for tool wear prediction based on the corresponding prediction of process incidence within this architectural framework, thereby facilitating a unified predictive outcome for this investigation.

2.3. Knot TPP Model for Unified Prediction

To fulfil the objective of enabling a deep learning model to predict two distinct outcomes, a knot–TPP architecture, as depicted in Figure 4, is proposed. The entire network takes the machining signal as an input, while two outputs are produced in the later layers. While typically Residual Neural Network (ResNet) is utilised as backbone of the network, the TPP layer is introduced after all convolutional layers, removing the constraints of input shape and fitting the needs for both tool wear and process incidence. Apart from sampling to reduce computational load from high dimensionality, no additional preprocessing is needed, aligning with standard deep learning practices that minimise human bias and enhance generalisability. Furthermore, given the high classification accuracy achievable for process incidence, the predictions related to process incidences are conditionally multiplied with tool wear tensor within the knot structure, thereby facilitating the transfer of process incidence information to tool wear predictions and enhancing the overall prediction accuracy [16]. The parameters in convolutional layers are the same, meaning that the identifications of process incidence and prediction of wear value use the same features.

Within the ResNet backbone, all convolutional layers have a filter length of $16k$ and $32k$, where k starts at 1 and then increases incrementally after every fifth residual block. Every other block subsamples its input by a factor of 2. When a block subsamples its input, the convolutional layer at the corresponding shortcut follows the same subsample operation with the same factor. The size of the kernel in the initial convolutional layer is five, providing an expanded receptive field conducive to channel fusion and the extraction of coarse features. In contrast, the kernel size for all subsequent convolutional layers is three, optimising the focus on local feature extraction.

Following the extraction of hierarchical features within the residual blocks, the flattened layer transforms the tensor into an one-dimensional vector while preserving its original dimensionality. This vector is subsequently fed into a dense layer, where activation via the Softmax function is utilised to convert the input into a probability distribution. In the prediction of tool wear, however, the dense layer predict the tool wear through this knot structure. The computation of gradients and Back Propagation (BP) iteration for both objectives adheres to the total loss, which is the aggregate of process incidence classification and tool wear regression. The loss associated with process incidence is determined by the cross-entropy function, and all samples contributing to the total loss are assigned equal weights. For the regression of tool wear, MAE is utilised as the loss function, and solely the samples recorded during the drilling of CFRP and aluminium are employed in gradient calculations due to their stable signal characteristics. The Adam algorithm was adopted as the optimiser which updates the model using the gradient descending method, making the model learn the patterns embedded in signal and, thereby, predict the corresponding process incidence and wear [26].

3. Experiment

The drilling experiments were carried out on a Haas V2SS three-axis machining centre, using three tungsten carbide twist drills (Walter, A1263-8).

Table 1. Configuration and cutting parameters utilised in this drilling experiment.

Tool diameter	8 mm
Point geometry	4-facet with notches
Tool substrate	WC/Co, uncoated
Point angle	118 degrees
Spindle speed	4000 rpm
Feed velocity	200 mm/min
Cooling	Dry machining

provides the main characteristics of the drills and the corresponding cutting parameters. The stacked workpiece was supplied in the form of coupons measuring 50 mm by 50 mm. The stack consisted of a CFRP layer on the top with a thickness of 10.5 mm and an aluminium 7010-T651 bottom layer with a thickness of 6.25 mm. The CFRP-Al workpieces were stacked and clamped inside a custom-made vice, which was then mounted on top of a Kistler 9271A 2-axis piezoelectric dynamometer. The dynamometer was used to measure the thrust force and torque during the drilling process. To prevent signal saturation during the drilling process, a single-axis accelerometer (Kistler 8640A) and an energy wave sensor (Kistler 8152B) were attached to the side face of a baseplate positioned between the dynamometer and the machine tool table. This ensured that both sensors were sufficiently far away from the drilling location. Additionally, the dynamometer, when mounted on a rigid base, exhibits a natural frequency of 3.1 kHz, which is significantly higher than the spindle rotation frequency of 66 Hz. This substantial frequency separation ensures that signal acquisition remains unaffected by resonance effects. The dynamometer was connected to a charge amplifier (Kistler 5006), and the energy wave sensor and accelerometer were connected to couplers (Kistler 5108A and 5125B, respectively). The charge amplifier and coupler outputs were recorded using a data acquisition card (NI 6356), which was connected to a PC. The sampling frequency was set to 100 kHz. The drilling jig used in the study is shown in Figure 5.

Nine holes arranged in a 3 × 3 matrix were drilled into each CFRP/Al coupon while recording thrust force, torque, energy wave, and Y-axis acceleration. After drilling a row of three holes, additional holes (6 mm deep) were drilled into a larger CFRP dummy plate placed next to the main drilling jig to increase tool wear without consuming more CFRP/Al stack coupons. For the first twist drill, after drilling a row of three holes into the CFRP/Al stack coupon, 10 holes were drilled into the dummy plate. For tools two and three, due to low tool wear with the first drill, this was increased to 20 holes. As a result, the first tool drilled a total of 117 holes, while tools two and three drilled 207 holes each. After each row of three holes drilled into the coupon stack clamped on top of the dynamometer, the tool’s flank wear was measured using a digital microscope (Jenoptik Progress C10 Plus). Flank wear was quantified at five distinct locations along each of the two cutting edges, and these measurements were subsequently averaged, see Figure 6. The resultant tool wear curve for the three utilised tools are depicted in Figure 7. It shows that tools two and three reached an average flank wear of around 360 microns, which according to ISO 3685 is considerably higher than the 0.3 mm average and should be scrapped [27].

To reduce the computation burden on signal processing and model inference during training process, the original signal was subsampled to reduce the size and thereby the load in model’s memory and computation. The training process involved generating samples from the collected signal at a sample frequency ranging from 200 Hz to 2000 Hz and a sample duration from 0.1 to 0.5 s, which includes four channels: thrust, torque, energy wave and y-axis acceleration. Sample frequency is how often samples are taken (Hz), and sample duration is the total time recorded. The model was trained using a supervised learning approach, where a deep learning network learns to predict the drilling stages and tool wear based on the input data and the corresponding labels. The model was trained through iterations, where the loss between model’s predictions and actual data was minimised, thereby improving the model’s accuracy in classify drilling stages and predicting tool wear with a same input and one model. During the training process, the model with the highest accuracy score was selected and saved to the hard drive for future use, ensuring the best model was available to accurately classify drilling stages and predict tool wear in new data.

4. Result

4.1. Process Incidence Classification

Figure 8 shows thrust force, torque, AE, and y-axis acceleration recorded during three drilling cycles at different tool live stages. At the start of each drilling cycle, thrust force and torque rise sharply as the tool contacts the workpiece. Once fully engaged in the CFRP top layer, both signals stabilise with minor oscillations due to fibre removal. Entering the aluminium layer causes another increase, with thrust force rising faster than torque due to the twist drill’s chisel edge generating about 70% of the thrust [5], while torque builds gradually along the cutting edges. As the drill penetrates deeper into aluminium, friction with the borehole and chips further raises both force and torque, along with their fluctuations. During tool breakthrough at the aluminium’s bottom, both signals drop sharply. Noisy signals here stem from burr formation and poor chip evacuation, complicating detection of tool exit. The AE signal initially rises during CFRP cutting, drops near zero at the CFRP–aluminium interface, then spikes with strong oscillations during disengagement. Y-axis acceleration fluctuates throughout, peaking during tool exit, and showing lower amplitudes during aluminium drilling than CFRP.

Table 2. Classification report of sample in 0.128 s and 1000 Hz for process incidences in the test dataset.

	Precision	Recall	F1
Engagement	0.9974	0.9925	0.9949
Cutting CFRP	0.9895	0.9977	0.9936
Material transition	0.9956	0.9845	0.9900
Cutting Al	0.9868	0.9928	0.9898
Disengagement	0.9905	0.9923	0.9914
Accuracy	0.9919

presents the three indices: precision, recall, and F1 score, quantifying the classification outcomes of individual drilling stages. The accuracy score is provided subsequently, illustrating the overall hit rate for all classes. The sample duration is 0.128 s, with a sampling frequency of 1000 Hz. The model attains remarkably high scores, all nearing 1 for every incidence, thereby demonstrating the classification accuracy of process incidences in stack drilling. Furthermore, the scores for all five incidences exhibit notable similarity, reflecting the consistency and uniformity of the identification results. Overall, the model’s prediction outcomes are accurate and precise, ensuring a reliable identification of process incidences in the drilling of CFRP/Al stacks.

Figure 9 shows the normalised confusion matrix of the classification results where CFRP and Al in both x and y axis mean the second and fourth stages: Cutting CFRP and Al, respectively. Transition is the stage of material transition.

The diagonal values of the matrix, which indicate the hit rate of individual classes, approach one, illustrating the knot–TPP model’s efficacy in categorising machining signals into their respective incidences with a maximum error margin of two percentages. Additionally, the short sample duration (0.128s) allows for the prompt identification of each process incidence. The ‘engagement’ incidence is the easiest to identify, as it is the preliminary occurrence and can be rejected based on their temporal sequence. A minor proportion of the ‘drilling CFRP’ incidence is incorrectly identified as ‘engagement’, which constitutes a typical Type II error, signifying that the system tends to delay the identification of drilling CFRP. Regarding the remaining three incidences, namely ‘material transition’, ‘drilling Al’, and ‘tool disengagement’, no distinct error type is discernible, as they are equally likely to occur as type I and II errors. Notwithstanding these misclassifications, the error rate is minimal, suggesting that the developed model remains both reliable and precise in identifying the five process incidences throughout the drilling cycle.

Table 3. Accuracy and macro F1 score of machine learning and deep learning model in test dataset with all signals.

Classifier	Accuracy	F1
SVM [5]	0.9766	0.9766
RF [5]	0.9709	0.9709
GB [5]	0.9718	0.9718
ResNet [16]	0.9837	0.9837
Knot-TPP	0.9961	0.9961

shows the accuracy and F1 score of Support Vector Machine (SVM), Random Forest (RF), Gradient Boosting (GB) and proposed knot–TPP models while the sample duration is set to 0.128 s and frequency of 1 kHZ. In comparison to these commonly employed machine learning models, which depend on manually engineered signal features, the proposed model exhibits superior accuracy and F1-score. This discrepancy underscores their inadequate capability to precisely identify process incidents within a constrained temporal window. In contrast to the model documented in ResNet by Zhang et al. [16], which solely focuses on monitoring process incidence, the proposed model demonstrates superior accuracy, benefiting from the additional information potentially derived from predicting tool wear.

In order to evaluate the efficacy of the trained model in accurately identifying the five process incidences in different combinations of sample duration and frequency, data samples varying in duration and frequency were input into the model. As shown in Figure 10, the impact of sampling frequency and duration on the model’s accuracy is illustrated in the form of Accuracy Response Topography Map (ARTM) [5].

As the sampling frequency increases from 200 Hz to 600 Hz, the accuracy score increases noticeably, followed by a sudden jump from 0.8 to 0.95 when increasing the sampling frequency further to 800 Hz. Thereafter, the accuracy score stabilises across a wide range from 800 Hz to 1500 Hz. Increasing the sampling frequency even further (to up to 2000 Hz) then causes the accuracy score to decline slightly. The initial improvement in accuracy is due to the inclusion of more frequency components, in accordance with the Shannon–Nyquist theorem, which allows the samples to carry more information, making it easier for the model to distinguish signals into different classes. However, after all the frequencies that are necessary to extract relevant features to the model to accurately identify the desired process incidences have been included, any further increase in sampling frequency will not have a significant impact on the model’s performance, causing saturation, as observed in the study of Zhang et al. [16]. When the sample frequency continues to rise, the input size becomes larger and unnecessary details are included, which slightly lowers the model’s accuracy score. The wide frequency stabilisation range demonstrates knot–TPP’s ability to process signals at varying sample frequencies carrying different frequency information, while maintaining robustness.

Like sampling frequency, the duration of the sample significantly influences the accuracy score of the trained model, as demonstrated in Figure 10, such that an increase in sample duration can always enhances the accuracy score, following the CCEA. As the sample duration is lengthened, the model receives a greater volume of data and, consequently, more information from which it can extract features to determine whether a particular process incidence occurs. It is noteworthy that the improvement in accuracy score is more pronounced when the initial score is lower. Thus, supplying sample data that span a longer duration could yield considerable benefits for the model’s classification performance, particularly in instances where accuracy scores are notably low. It is, however, important to mention that extending the sample duration incurs the cost of a reduced responsiveness, as additional time is required to obtain the longer sample. Furthermore, processing the longer sample will necessitate additional time, thereby further delaying the model’s final determination. For instance, adopting a sample duration of 0.5 s renders it impossible to detect the incidences of material transition or disengagement, both of which last approximately 0.7 s, and to initiate a response, such as a reduction in feed rate, at the commencement or even during the occurrence of the incident. Consequently, the response is likely to be completed at the end of or even following the incidence. As a result, an excessively prolonged sample duration causes a mismatch between the process incidence and the cutting parameters used, as the adaptive system changes the cutting parameters when the incidences is nearing its conclusion or has already concluded, thus rendering the entire system ineffective. Therefore, selecting an appropriate sample duration is vital for the adaptive drilling system. The adaptability of the proposed approach, which allows for accommodating arbitrary sample durations, enables the system to detect incidences using short sample durations, thereby assuring promptness, while also delivering accurate predictions with high certainty.

4.2. Tool Wear Prediction

The assessment of tool wear is suggested to rely solely on the signals captured during the drilling of the CFRP and aluminium layers, as previously discussed. A vital condition for the success of this strategy is the system’s ability to precisely and reliably distinguish between the drilling of CFRP and aluminium. The efficacy of this approach is substantiated by the confusion matrix and ARTM, which illustrate the high accuracy and reliability in identifying process instances related to drilling CFRP and aluminium.

The prediction of tool wear constitutes a regression analysis task, as quantified in MAE. The MAE of the prediction medium for tool wear on the test data is determined to be 0.010 mm. Figure 11 illustrates the box plot of the predicted results compared to the actual values.

The figure demonstrates the performance of the deep learning model in predicting tool wear during drilling through the CFRP layer. Every box in the figure is constructed by two value: first quartile and third quartile, respectively. The size of it in all tool wear level is narrow, which means the two values are close to each other which suggests the high precision of the prediction result. The green lines within each box represent the median value, and the fact that these are close to the actual value suggests that the prediction gives an accurate indication of tool wear. It also indicates that enhancement of prediction accuracy could be achieved through the extension of sampling duration, utilising the statistical median as a method of analysis. Moreover, outlined lines, called whiskers, extend from the box and indicate the variability outside upper and lower quartiles. As the amount of tool wear increases, the length of the whiskers becomes longer, and more outliers, i.e., isolated points beyond the whisker, appear. This indicates the rise in prediction variation and, consequently, a decrease in precision. It can be attributed to signal oscillation from a short sequence and the model’s limitation in dealing with excessive noise. Nonetheless, the median still lies in the vicinity of the actual value, and a correct prediction could be obtained by counting the middle from a set of predictions. Furthermore, the fixed and short duration of the samples also restricts the amount of information available to the model, which makes it challenging to predict the tool wear precisely, especially in cases of excessive tool wear. Thus, additional measures ought to be implemented to address the variations in prediction when handling noisy signals under significant tool wear conditions. Extending the sampling duration while employing the minimum viable sampling frequency can enhance the accuracy of tool wear prediction.

Table 4. The error metrics and comparison of tool wear prediction in drilling CFRP and aluminium.

Metrics	Knot-TPP	Cyber-Physical Adaptive Control System [28]
MAE	10 μm	-
RMSE	5 μm	6 μm

shows the metrics compared with the methods proposed by Sadek et al. [28]. Compared with their approach, the Root Mean Square Error (RMSE) of knot–TPP is relatively lower, indicating the effectiveness of proposed methods in monitoring tool wear in drilling of hybrid stacks. Furthermore, tool wear progression in our experiment as shown in Figure 7 exhibits a stronger three-segmented features and becomes more challenging, which further indicates the effectiveness of proposed method.

The efficacy of the knot–TPP model in predicting tool wear across various combinations of sample duration and frequency is illustrated in ARTM, as presented in Figure 12. Analogous to the classification of process incidence, the proposed model demonstrates its capability to accurately predict tool wear across an extensive range of sampling combinations, thereby underscoring the model’s reliability in predicting tool wear. Contrary to process incidence, the size of the input data exerts a greater influence on the tool wear prediction. In scenarios where the sample duration is short, maintaining a small input size despite high sampling frequency, an increase in sampling frequency facilitates the reconstruction of more informative frequency components without incurring aliasing, thereby enhancing prediction accuracy. However, as the sampling duration is extended, the input size, the product of sampling frequency and duration, can become excessive, posing a challenge for the knot–TPP model in predicting tool wear and potentially leading to increased prediction errors.

Consequently, the approach to enhancing the precision of tool wear prediction focuses on reducing the dimensionality of signal inputs while preserving all informative frequency components. As examined by Zhang et al. [16] and highlighted in Figure 12, it is essential to encompass all harmonic components for an accurate representation of tool condition through signal analysis. Therefore, in the context of predicting tool wear, it is incumbent to select a sampling frequency proximate to the frequency delineated in MSU, thereby achieving dimensionality reduction while ensuring the retention of all pertinent signal information. At a frequency of 1000 Hz which approaches the frequency of MSU, the signal size remains manageable even with extended sampling durations, thereby enabling increased accuracy as the sampling duration is lengthened. This approach aligns with the objectives outlined in the introduction, which propose that prolonging the sampling duration enhances the certainty of tool wear prediction. Therefore, although knot–TPP model can be achieve high accuracy across various sampling configurations, it is optimal to adopt the sampling frequency specified in MSU to effectively manage input size and exploit the advantages of prolonged sampling durations.

5. Conclusions

In this paper, a knot–TPP model is proposed to achieve a unified prediction for process incidence and tool wear during the drilling of a typical aerospace stack comprising CFRP and aluminium. Based on the observation made, the following conclusion can be drawn:

• By incorporating TPP and knot structure within the deep learning framework, the knot–TPP model exhibits substantial accuracy in the classification of process incidence and the prediction of tool wear using one set of parameters.
• The knot–TPP model proposed in this study possesses the capability to process signals sampled at varying durations, thus rendering it adaptable for both brief and extended sampling periods. This flexibility permits immediate processing with a satisfactory level of accuracy for monitoring process incidences and enables extended sampling durations to enhance the reliability of predictions concerning progressive tool wear.
• The model can accurately identify incidences using signals sampled at frequencies above 800 Hz and up to 1500 Hz, without the need for creating and training multiple models. Using sampling frequencies below 800 Hz results in a significant loss in the model’s accuracy, whilst a much smaller but still noticeable decline in accuracy is observed in the case that the sampling frequency is increased above 1500 Hz.
• Increasing the length of the sample duration always improves the classification accuracy for process incidence regardless of sampling frequency. However, it also increases the response delay, which in extreme cases can lead to the model failing to match the parameters in adaptive drilling.
• The integration of process incidence into tool wear predictions contributes significantly to the enhancement of predictive accuracy. A more reliable and precise estimation of tool wear can be attained by computing the median value from a sequence of predictions generated throughout the process.
• To efficiently predict tool wear, reduce input dimensions while retaining key frequency components to avoid aliasing. Employing the frequency detailed in MSU can reduce the input size, facilitating extended sampling durations without significantly augmenting the input, thereby leveraging the advantages of the extension process.
• As tool wear becomes more pronounced, the variability in predictive accuracy increases, presenting difficulties in accurately monitoring tool wear due to marked signal fluctuations and substantial noise interference.

Nevertheless, additional limitations inherent to the methodology necessitate further investigation. The finite duration of samples, along with oscillations and excessive noise caused by increased tool wear, can lead to fluctuations in the precision of tool wear predictions, particularly under conditions of significant wear. Such circumstances present substantial challenges to the model’s accuracy and applicability. Furthermore, due to the lack of research on the minimum sufficient sampling condition for tool wear, the heightened sensitivity of the model to input size remains unexplained. Although the optimal condition has been identified, further exploration could enhance the comprehension and optimisation of deep learning models in predicting tool wear.