# Material Detection by Stack Drilling Monitoring and Reservoir Computing

Luc Gerber, Pierre-André Rey, Mathieu Ritou, Mehdi Cherif

► To cite this version:

Luc Gerber, Pierre-André Rey, Mathieu Ritou, Mehdi Cherif. Material Detection by Stack Drilling Monitoring and Reservoir Computing. Procedia CIRP, 2025, 133, pp.489 - 494. 10.1016/j.procir.2025.02.084. hal-05509938

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20th CIRP Conference on Modeling of Machining Operations

Material Detection by Stack Drilling Monitoring and Reservoir Computing

Luc GERBER<sup>a,b*</sup>, Pierre-André REY<sup>a</sup>, Mathieu RITOU<sup>b</sup>, Mehdi CHERIF<sup>a</sup>

Abstract

The multi-material stack drilling process is subjected to numerous possible defects such as tool wear, tool breakage, burr or delamination. It has been proposed to develop a monitoring system based on a digital twin of the process to validate the hole quality. This digital twin will first need to robustly identify the steps of the drilling process in order to monitor relevant process features despite signals distortions induced mainly by tool wear.

In this study, two approaches based on the Gaussian mixture model and reservoir computing are compared to a state-of-the-art analytical method. These data-driven models are improved with the integration of expert knowledges.

These models are tested on a series of CFRP/Al drilling which encompass the tool wear. The presented methods achieved an accuracy score over 95 % despite signals variability.

© 2025 The Authors. Published by Elsevier B.V.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Peer-review under responsibility of the scientific committee of the 20th CIRP Conference on Modeling of Machining Operations in Mons

Keywords: smart drilling; multi-material drilling; reservoir computing; machine learning

1. Introduction

The weight reduction in the aeronautical field has led to an
increasing use of composites materials that need to be fastened
to the metallic parts of the structure. In order to be fastened
together, the metallic and composite parts of the structure are
often riveted together. To put in place these rivets the parts need
to be drilled together to guarantee the holes alignment.

Ideally, optimized cutting condition for each material should
be used, but traditional machining technics do not allow that
[1], [2], [3]. To improve the quality of the holes, new drilling
strategies have been developed such as the use of Automatic
Drilling Units (ADU) with vibration assistance [4], [5] or
orbital drilling [6].

The multi-material stack drilling process is subjected to
numerous defects such as burr, delamination or interlayer gap.
All these defects reduce the fatigue performance of the
assembly [2], [3], [7], [8], [9].

Because of that, the ANR project SHAIR aims to build a
digital twin of the multi-material stack drilling with ADU to be
able to guarantee the quality of the drilled holes and to integrate
this technology with the human operator.

The first function of this digital twin is to be able to
recognize the process steps to monitor relevant features. In
other words, it needs to detect the material drilled. Traditionally
this kind of detection is performed knowing the process
 material thickness, tool geometry, ...) [10], [11], but this
approach lacks reliability against tool wear or defects such as
inter-layer gaps. Other approaches are limited to the
differentiation between metallic and composite materials [12].
Most of the time, transitions phases identification is also
disregarded.

In this article, material detection methods, that also detect
the transitions phases despite signals distortions induced
mainly by tool wear, are proposed and compared for axial
drilling application.

<footnote><sup>a</sup>Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, Hesam Universite, I2M, UMR 5295, F-33400 Talence, France</footnote>

<footnote><sup>b</sup>Nantes Université, LS2N, UMR CNRS 6004, 1 Rue de Noë, Nantes 44321, France</footnote>

<footnote>* Corresponding author. E-mail address: luc.gerber@ensam.eu</footnote>
## 2. Methods tested

In order to build the detections methods, it was assumed that the signals used can be associated with the simplified signal presented in figure 1. This simplified signal shape can be observed on most of the monitored signals during the process such as axial cutting force and torque or engine current. In this figure, it is also assumed that the position of the tool in the stack can be determined based on the points when the signal alternates between stable and transitional state, as detailed in [11], [13], [14]. Thus, the objective is to reliably identify these points. To do so, three approaches will be tested. The first one is based on a state-of-the-art analytic approach, the second is based on a Gaussian Mixture Model (GMM) and the last one is based on reservoir computing.

### 2.1. Analytical method

The analytical method used is inspired by Jallageas and Pardo [12], [13]. As shown in figure 1, the moment when the tool is fully engaged in a material is associated with a horizontal line. So, unlike transient phases, stable cutting phases should be characterized by a near zero derivative.

To implement this approach, the signal is first normalized and denoised using a rolling mean with a window of 0.1 s. Then, as suggested by Pardo [13], a three-points derivative is calculated. As the transitional phases are significantly shorter than the stable one, they appear as outliers. In order to differentiate the residual noise around zero from the points of interest, a one component GMM is used to allow us to determine the threshold out of which the points are considered to be part of a transitional step. Once a class is attributed to all the points a linear regression is performed between each class changing point. The slope of the line is compared to the threshold and the class of the points is reattribute.

During the first runs, false detections have been observed. In order to get rid of it, two rules based on expert knowledges have been implemented. First: "if a step last less than half the time of a transition and is preceded and followed by the same step class, then it is noise, thus it is removed", second: "if two steps of the same class follow each other, then it is the same step, thus they are merged".

The material detection proposed by Pardo [13] is based on the value of the slope calculated, but in this case the tool wear made this method unusable. Thus, the material detection is made knowing the stack order.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Simplified two materials drilling signal shape</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2: Stable steps detection with GMM method</figcaption></figure>

### 2.2. GMM based method

The GMM method is also based on the assumption that the stable cutting phases are associated with a horizontal line in the signal. It was assumed that each line can be assimilated to a gaussian distribution.

The first step of this method is to fit a GMM on the normalized signal. The number of components that the GMM has to find is determined with expert knowledges as the number of materials drilled plus one for the moments when the tool is out of the stack. Once the GMM is fitted, it can attribute a class to every point (Fig. 2), but to be able to use these classes it requires to incorporate expert knowledges.

The first step is to determine which class has been attributed to which material. Because of tool wear, it is not possible to directly use the average value of each gaussian, but it has been showed in [14] that the specific cutting pressure is constant, that is to say, that the order in which the materials cut produce the most important effort is always the same. So, the ascending order of the average value of each gaussian distribution is used to identify the material.

The second step is to identify the transitional part of the process, but the GMM is only capable of identifying the nearest stable phase. Advantage is taken out of that because the only points that will cross the thresholds are contained in the transitional steps. In other words, every time a class change is observed, the point is part of a transitional step. Knowing the tool point height and the feed rate it is possible to estimate the transition time and put a window around the class changing point to introduce transitional classes. Since, as a first assumption, the exact position of the point in the transitional phase is unknown, a window of two transitional times centered around the point has been used (Fig. 3). In this study, it has been observed that the position of the transition point is in fact rather stable in the transitional step, but different for each type

<figure><img src="image_4.png" /><figcaption>Fig. 3: Transition steps identification with GMM method</figcaption></figure>
of transition. So, the window width has been reduced to a transition time + 20 %. The transitional class label is attributed knowing the previous and next stable class so, this method is not sensitive to the stack order.

It is important to note that several thresholds can be crossed during a transition, thus multiple class changes can be observed during the same transition step. Thus, if several changes are observed within a transition time, they are discarded.

## 2.3. Reservoir computing based method

Reservoir computing is a supervised machine learning paradigm suited for time series prediction and classification. This paradigm has emerged independently two times in the early 00's, once in the machine learning field with the Echo State Network (ESN) [15] and once in the neuroscience field with the Liquid State Machine (LSM) [16]. Both methods have been assimilated to reservoir computing in the late 00's [17], [18]. Reservoir computing should be particularly well suited for machining monitoring application because it should be able to work with a small amount of training data and should be computationally inexpensive which is appreciable for online and edge computing [19]. To the best of the author's knowledge, this paradigm has not yet been used for machining monitoring.

In this article, an ESN will be used. This network is composed of two main elements: the reservoir and the readout. On the one hand, the reservoir is a dynamical system with “echo state properties” which mainly implies that the state of the reservoir is not related to its initial state and a given input will always induce the same output [20]. It is possible to use a physical object as a reservoir [19], [20], but a Recurrent Neural Network (RNN), with a Tanh activation function, will be used. On the other hand, the readout is made to translate the reservoir states. In the original description of the ESN [15], in an important part of literature and in this article, the readout is a single layer neural network fully connected to the reservoir (Fig. 4).

It is possible to use complex architectures with several reservoirs or readout, or by introducing feedback or direct connections between the input and readout. But, in this study, the best results are obtained with a basic ESN (Fig. 4).

The most important feature of the ESN is that the reservoir is randomly initialized, within a space described by hyperparameters, and only the readout is train linearly using the Tikhonov regression.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Architecture of the ESN</figcaption></figure>

The ESN hyperparameters are subject to optimization to obtain the best performances possible [21]. It is important to keep in mind that these hyperparameters influence the behavior of the ESN, but they also interact with one another. So, it is important to optimize a set of parameters and not just one. In order to optimize these parameters, the loss function used was the accuracy metric. During the optimization process several reservoir topologies are tested to limit its effect on the results. The number of neurons in the reservoir have been chosen with the best ration between the loss value after optimization and the number of neurons (elbow method). In this study, the most significant hyperparameters and their optimized values are summarized in table 1.

<table><caption>Table 1: Main hyperparameters used in this study</caption><thead><tr><td>Hyperparameter and description</td><td>Optimized value</td></tr></thead><tbody><tr><td>The number of neurons in the reservoir</td><td>500</td></tr><tr><td>The leak rate; characterize the importance of the new state compared to the previous states</td><td>0.1755</td></tr><tr><td>The spectral radius; the greatest eigenvalue of the connection matrix in the reservoir</td><td>1.3388</td></tr><tr><td>The input scaling; linear adjustment of the input value</td><td>0.9731</td></tr><tr><td>The Tikhonov coefficient; meant to avoid overfitting</td><td>2.4413*10<sup>-8</sup></td></tr></tbody></table>

The leak rate (LR) and the spectral radius (SR) are the best describers of the reservoir itself. The low value of the LR indicates that the input has a long-term effect on the state of the reservoir. Whereas the high value of the SR indicates that the reservoir has fast dynamics close to chaotic, which is appropriate for classification.

Once the architecture of the ESN is chosen and the hyperparameters optimized, the readout needs to be trained with normalized and labeled signals. The network is then ready to classify normalized input signals from the process (Fig. 4).

The implementation of reservoir computing has been performed using the “ReservoirPY” python library [22].

## 2.4. Online monitoring tests

Reservoir computing works by sequentially feeding the input signal in the reservoir, which is suitable for online monitoring. On the other hand, the GMM and analytical methods need the entire signal to be able to estimate their thresholds, they both were meant for offline monitoring. To be able to compare these methods for an online application it is proposed to train the GMM and analytical methods on the previous signal in the set to set their thresholds while minimizing the impact of tool wear on the signal.

As online monitoring is considered, it will not be possible to correct previously made mistakes. So, parts of the knowledges based rules in the analytical and GMM methods will not be usable for online monitoring. Thus, an increased number of misclassified points is expected.

# 3. Data used for the study

## 3.1. Nature of the data

For this article signals acquired during a tool wear test campaign available at the laboratory are used [10]. For this campaign, an ADU with a 6.35 mm in diameter tool was used
to drill in an 11 mm thick Al7175 Aluminum alloy and 16 mm thick T800/M21 carbon fiber reinforced polymer (CFRP) stack, with minimum quantity lubrication (MQL) and low frequency (2.5 * the spindle speed), high amplitude (0.1 mm) vibration assistance module provided by MITIS [4]. Three different cutting conditions were tested, according to the tool manufacturer recommendations, as summarized in table 2.

<table><caption>Table 2: Cutting Conditions available in the dataset</caption><thead><tr><th>Set of cutting conditions</th><th>1</th><th>2</th><th>3</th></tr></thead><tbody><tr><td>Number of trials</td><td>27</td><td>177</td><td>3</td></tr><tr><td>Spindle speed (RPM)</td><td>6000</td><td>6000</td><td>6000</td></tr><tr><td>Feed (mm/rev)</td><td>0.06</td><td>0.08</td><td>0.1</td></tr></tbody></table>

The ADU is equipped with two electric engines, one for feed motion and the other for spindle rotation. Since they are both DC motors, the current is an image of the torque delivered by each motor and by extension an image of the torque and trust force induced on the tool. The ADU records both currents at 100 Hz [23] which is, according to Shannon criteria, too low to observe phenomena related to the cut but high enough to distinguish the process steps. In addition, this 100 Hz setting is the default setting for industrial machines so the work performed on this data could be replicated to an industrial scale.

It is important to note that the average value of the current during the stable phase has been multiplied by more than 3 because of tool wear. Thus, the lowest value of the average current in the Aluminum is smaller than the maximum average current in the CFRP (fig. 5). So, it is not possible to identify materials based on the average value of the current observed.

## 3.2. Datasets construction

Preliminary testing and expert knowledges have demonstrated that the best performances are obtained using only the feed current so the datasets will only include this data

In this article, results obtained with two datasets are presented. The first uses one signal out of three in every cutting condition as a training set for the reservoir computing, and the rest as the test set. The second one uses one signal out of nine in every cutting condition as a training set for the reservoir and the rest as a test set. They are called respectively “Set 3” and “Set 9”. This choice allows us to keep the same unbalances in the data.

For the online application, the first signal of the test series has been removed since it is used as the initial training of the analytic and GMM methods. Trainings and tests sets contents are summarized in table 3.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Average current in the stable phases</figcaption></figure>

<table><caption>Table 3: Training and testing set distribution</caption><thead><tr><th>Set of cutting conditions</th><th>1</th><th>2</th><th>3</th><th>Total</th></tr></thead><tbody><tr><td>Training Set 3 Offline</td><td>9</td><td>59</td><td>1</td><td>69</td></tr><tr><td>Test Set 3 Offline</td><td>18</td><td>118</td><td>2</td><td>138</td></tr><tr><td>Training Set 9 Offline</td><td>3</td><td>20</td><td>1</td><td>24</td></tr><tr><td>Test Set 9 Offline</td><td>24</td><td>157</td><td>2</td><td>183</td></tr><tr><td>Training Set 3 Online</td><td>9</td><td>59</td><td>1</td><td>69</td></tr><tr><td>Test Set 3 Online</td><td>18</td><td>118</td><td>1</td><td>137</td></tr><tr><td>Training Set 9 Online</td><td>3</td><td>20</td><td>1</td><td>24</td></tr><tr><td>Test Set 9 Online</td><td>24</td><td>157</td><td>1</td><td>182</td></tr></tbody></table>

## 3.3. Normalization of the signal

Because part of this article aimed to work online, it was not possible to normalize the signal between its maximum and minimum values. Instead, the normalization was performed according to the maximum current allowable by the feed engine.

## 3.4. Labeling of the dataset

The reservoir computing method needs a labeled dataset because its training is supervised, and a labeled database is needed to be capable of comparing the results obtained with each method.

This dataset was originally not labeled, so an early version of the analytic method was used to pre-label the data. This dataset has then been given to an expert who corrected the labels.

# 4. Results

## 4.1. Metrics used in the study

In order to compare the performances of the three methods, three metrics have been put in place, the complement of the accuracy metric, “delay” and “error”. Computation time is also reported. All the metrics presented are computed over the all test set, not over individual signal.

### 4.1.1. Complement of the accuracy metric

Accuracy is defined as the ratio between the number of points correctly classified and the total number of points. In this work, the complement of the accuracy is used, which could be considerate as the error rate, because its magnitude is closer to the two other metrics used.

### 4.1.2. The “Delay” metric definition

As this work is carried out on time series, the classes follow one another in an order defined by the process. Initially, it was found that an important proportion of errors were in fact due to class changes that happened either too early or too late. Those errors may not be harmful to the system, thus it is interesting to differentiate this type of error from the others. In this article, early and late detections are both classified as “delay”. Delay is defined as the ratio of points misclassified in a class just before or just after the reference labeled class and the total number of points.
It is important to note that because of the manual expert labeling, there is a remaining uncertainty around the exact class transition point of about 0.02s. Considering the average signal duration, this uncertainty represents about 2.4 % of delay. So, it will certainly not be possible to fall under this value of delay.

### 4.1.3. The "Error" metric definition

The error metric describes all the points that are misclassified but not delayed. It is defined as the ratio of the points that are misclassified but not delayed and the total number of points.

It is noteworthy that, the sum of the “error” and “delay” is equal to the overall number of misclassified points, which corresponds to the complement of the accuracy. Thus, our metrics are easy to compare to an existing metric.

### 4.1.4. Computation time

As online monitoring is tested, the computation time will be compared. The results presented are obtained using a laptop running on Windows 10, with an Intel Core i7-12700H processor, 16 Go of RAM at 4800MHz and an SSD NVMe 7000 MB/s sequential reading and 5200 MB/s sequential writing. The reported value is the average time measured over 10 consecutive runs. Only the time needed to execute the previously mentioned algorithms has been measured. It excludes the time needed to import the data and exports the results. For information purposes, the training time for the reservoir computing is also indicated.

## 4.2. Offline tests results

The results obtained for offline calculation with Set 3 and Set 9 are summarized in table 4.

<table><caption>Table 4: Offline results</caption><thead><tr><th>Method</th><th>Data</th><th>Error (%)</th><th>Delay (%)</th><th>1-Accuracy (%)</th><th>Computation Time (s)</th></tr></thead><tbody><tr><td rowspan="2">Analytic</td><td>Set 3</td><td>3.37</td><td>1.57</td><td>4.94</td><td>8.38</td></tr><tr><td>Set 9</td><td>2.99</td><td>1.51</td><td>4.50</td><td>10.88</td></tr><tr><td rowspan="2">GMM</td><td>Set 3</td><td>0.50</td><td>2.81</td><td>3.31</td><td>7.01</td></tr><tr><td>Set 9</td><td>0.65</td><td>2.76</td><td>3.42</td><td>8.96</td></tr><tr><td rowspan="2">Reservoir Computing</td><td>Set 3</td><td>0.28</td><td>2.57</td><td>2.85</td><td>7.08</td></tr><tr><td>Set 9</td><td>0.28</td><td>2.73</td><td>3.01</td><td>9.36</td></tr></tbody></table>

The training time of the reservoir computing method is 3.85s for Set 3 and 1.41s for Set 9.

All the methods tested achieved an accuracy score over 95 %, which indicates that all these methods can be suitable for offline material detection, even with a significant evolution due to the tool wear.

The best method according to the delay metric is the analytical one, but it is important to keep in mind that an early version of this method has been used to pre-label the data which may favor this method. This fact may also explain why this method is the only one that has an error superior to its delay.

In terms of error and accuracy the best method is reservoir computing. The results obtained with the GMM method are close to the reservoir computing but the fact that the transitional

window is 20 % larger than it should introduce a delay that can not be reduced.

The computation time of all the methods is in the same order of magnitude. The fastest is GMM then reservoir computing and the slowest is the analytical method. It is also interesting to note that the training time of the reservoir computing is short enough to allow testing on a large number of training sets.

## 4.3. Online tests results

The results obtained for online calculation with Set 3 and Set 9 are summarized in table 5.

<table><caption>Table 5: Online results</caption><thead><tr><th>Method</th><th>Data</th><th>Error (%)</th><th>Delay (%)</th><th>1-Accuracy (%)</th><th>Computation Time (s)</th></tr></thead><tbody><tr><td rowspan="2">Analytic</td><td>Set 3</td><td>10.28</td><td>6.31</td><td>16.58</td><td>6.93</td></tr><tr><td>Set 9</td><td>8.56</td><td>6.29</td><td>14.79</td><td>9.14</td></tr><tr><td rowspan="2">GMM</td><td>Set 3</td><td>7.80</td><td>6.00</td><td>13.80</td><td>6.97</td></tr><tr><td>Set 9</td><td>6.38</td><td>5.79</td><td>12.18</td><td>9.57</td></tr><tr><td rowspan="2">Reservoir Computing</td><td>Set 3</td><td>0.28</td><td>2.57</td><td>2.85</td><td>6.83</td></tr><tr><td>Set 9</td><td>0.29</td><td>2.72</td><td>3.01</td><td>9.04</td></tr></tbody></table>

The training time of the reservoir computing method is 3.82s for Set 3 and 1.40s for Set 9.

As anticipated, the number of misclassified points increased for the GMM and analytical methods.

The increased error rate for both the analytical and the GMM methods is imputed to the tool wear. Even if the training is done with the previous signal in the series, the current in the two materials may be close, thus for the next drilling, the threshold determined may not offer enough margin to distinguish the two materials properly.

The increase in delay from the GMM was expected since it is already the “weak point” of this method, and it was anticipated that it would not be able to detect a transition step before one to two third of the transition step has passed.

The reservoir computing method was already running in an online manner that is why the results did not change to the nearest rounding.

The computation time mainly changes because the set is composed of one less signal. In this configuration reservoir computing is the fastest and the most accurate.

## 4.4. Discussion

The analytical method is well suited to distinguish the stable and the transitional steps, but it is sensitive to noise and wear, which makes it difficult to identify each material properly.

The GMM method is well suited to identify stable steps but is not capable of recognizing transitional steps. By introducing expert knowledges, it can recognize the material in an unsupervised manner and estimate the position of transitions steps.

For offline applications with unlabeled data, the GMM and analytical methods give particularly good results. Using a combination of the two methods (GMM for stable steps identification and analytical method for transition steps delimitation) could outperform the current results, if computation time is not a major concern.
If labeled data are available, the reservoir computing method has demonstrated the best results for offline and online detection. This method has proven to be lightweight in terms of computational resources, and to give satisfactory results with a small amount of training data which are two interesting features for machining monitoring. On the other hand, the need for labeled data and the fact that it is based on a neural network might not allow its use for critical applications.

Other tests, that are not presented in this article, have shown that reservoir computing performance is strongly related to the training dataset and the hyperparameters, as expected from neural network-based method. For example, if an event happens always at the same time in the training set, it is prone to overfit the moment when the event happens and not its features.

## 5. Conclusion

In this article, three material detection methods in stacks drilling have been presented and tested on a drilling series that encompass tool wear. A method based on the well-known GMM and a method based on the original reservoir computing paradigm are compared to a state-of-the-art analytical method for an offline and online monitoring application.

Although the analytical method works well in this case study, the GMM method demonstrated better results, but it has been outperformed by the reservoir computing method. These three methods seemed equivalent in terms of computation complexity because they need similar time to work on the same dataset.

For offline and unsupervised applications, the GMM based method will be preferred, whereas reservoir computing is more suited for online applications with labelled training data.

Since the presented methods mainly focus on the shape of the signal, they are expected to be usable to monitor other processes.

Future works will focus on using the strength of each of the presented methods to build a reliable digital twin of the process.

## Acknowledgements

This work was carried out within the research project SHAIR no.ANR-22-CE10-0009-01, funded by the French National Research Agency (ANR), and officially stamped by the Aerospace Valley and EMC2 competitiveness clusters.

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