# Cognitive Digital Twin in Manufacturing: A Heuristic Optimization Approach

Atiq Ur Rehman, Mobyen Uddin Ahmed, Shahina Begum

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Atiq Ur Rehman, Mobyen Uddin Ahmed, Shahina Begum. Cognitive Digital Twin in Manufacturing: A Heuristic Optimization Approach. 19th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2023, León, Spain. pp.441-453, 10.1007/978-3-031-34107-6_35. hal-05498096

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# Cognitive Digital Twin in Manufacturing: A Heuristic Optimization Approach

Atiq ur Rehman(✉) ID, Mobyen Uddin Ahmed ID, and Shahina Begum ID

Artificial Intelligence and Intelligent Systems Research Group, School of Innovation, Design and Engineering, Mälardalen University, Västerås, Sweden
{atiq.ur.rehman,mobyen.uddin.ahmed,shahina.begum}@mdu.se

**Abstract.** Complex systems that link virtualization and simulation platforms with actual data from industrial processes are vital for the next generation of production. Digital twins are such systems that have several advantages, notably in manufacturing where they can boost productivity throughout the whole manufacturing life-cycle. Enterprises will be able to creatively, efficiently, and effectively leverage implicit information derived from the experience of current production processes, thanks to cognitive digital twins. The development of numerous technologies has made the digital twin notion more competent and sophisticated throughout time. This article proposes a heuristic approach for cognitive digital twin technology as the next development in a digital twin that will aid in the realization of the goal of Industry 4.0. In creating cognitive digital twins, this article suggests the use of a heuristic approach as a possible route to allowing cognitive functionalities. Here, heuristic optimization is proposed as a feature selection tool to enhance the cognitive capabilities of a digital twin throughout the product design phase of production. The proposed approach is validated using the use-case of Power Transfer Unit (PTU) production, which resulted in an improvement of 8.83% in classification accuracy to predict the faulty PTU in the assembly line. This leads to an improved throughput of the PTU assembly line and also saves the resources utilized by faulty PTUs.

**Keywords:** Cyber-Physical Systems · Cognitive Digital Twins · Heuristic Optimization · Industrial Manufacturing

## 1 Introduction

The fourth industrial revolution is referred to mostly as Industry 4.0, connected industries, Smart Manufacturing, Made in China (MIC) 2025, and a few other terms [1]. Utilizing the potential of computation in manufacturing processes is frequently at the core of this wave of future manufacturing visions. The majority of these visions aim to combine cloud computing, cybersecurity, smart sensors, cyber-physical systems, wireless (and wired) communications, advanced robotics,

© IFIP International Federation for Information Processing 2023

Published by Springer Nature Switzerland AG 2023

I. Maglogiannis et al. (Eds.): AIAI 2023, IFIP AICT 676, pp. 441–453, 2023.

https://doi.org/10.1007/978-3-031-34107-6_35
advanced data analytics, simulation and high-performance computing, additive manufacturing, internet of things (IoT), and the machine learning. The fourth industrial revolution aims to produce products and production across decentralized factories and supply networks that are personalized, inexpensive, efficient, resilient, adaptive, and sustainable [2,3].

One of the many technologies that will influence how manufacturing is done in the future is Digital Twins (DTs). Through the integration of the digital and physical worlds, DTs enable seamless communication between digital simulations and real production systems. Manufacturing has been proven to benefit significantly from these DTs [4,5]. Digital twin technology makes use of a variety of auxiliary systems and technologies, including modelling and simulation, IoT sensors, standards for interoperability between digital technologies, computation, and data from various product lifecycle stages. The use of this technology in manufacturing may have an influence on the whole product life cycle, and much like many other contemporary computer research areas, the number of applications for DTs in manufacturing is growing quickly.

Fundamental cognitive processes like perception (having formed useful pre-cepts from raw sensory data), attention, memory, reasoning (drawing inferences from observations, beliefs, and models), problem-solving, and learning (from experiences, and observations) have been incorporated into DTs in order to further their evolution [6]. Cognitive Digital Twins (CDTs) are the result of this evolution through the incorporation of these cognitive processes into the Digital Twin [7-9]. Through the incorporation of cognition-enabling services, CDTs provide the capability to track the present condition of the corresponding manufacturing components, recognise (or even anticipate) production anomalies, investigate their root cause, and then compute, evaluate, and assist in making decisions about potential courses of action for the best (optimised) prevention against the impacts of the associated interruptions [10]. In this article, a CDT based on a heuristic approach is proposed, utilizing a use case from the manufacturing industry. The all-wheel drive (AWD) transfer case used in automobiles and sport utility vehicles is called the Power Transfer Unit (PTU). It enables power to be sent to all four wheels intermittently or continuously, and it also adjusts how much power is sent to the front and back depending on the circumstances of the road. A faulty produced PTU during manufacturing brings a huge economic loss to the manufacturing industry [11]. Prediction of faulty PTUs before the End-of-Line (EOL), during the production phase, can lead to saving resources and helping the manufacturing industry cope with losses incurred due to the production of faulty PTUs. There are certain parameters in the lapping and assembly line which are considered important by human experts to predict faulty PTUs. However, these parameters are manually inspected by the experts in the industry and mostly there is no guarantee to associate the fault with a certain set of parameters. At the same time, the inspection of several parameters through hundreds of sensors manually is not feasible. In order to solve such issues and propose an innovative solution, a heuristic optimization approach is added to the digital twin technology to provide cognitive activities.

Metaheuristic approaches have the capability to solve the NP-hard combinatorial optimization problems [12]. Due to the effective search strategy, these
metaheuristics can be utilized to optimize the large feature spaces and increase the prediction accuracy of machine learning algorithms [13]. Moreover, these approaches are computationally more efficient compared to the gradient-based approaches. Therefore, a recently proposed Jumping Particle Swarm Optimization method [14] is incorporated in the Digital twin architecture to optimize its feature space. The proposed approach is validated using a use-case of the PTU manufacturing process to optimize the fault detection process [15]. The proposed architecture is tested on the real data taken from the PTU manufacturing industry and the results show a significant increase in the fault detection accuracy of the system. The rest of the article is organized as follows: Sect. 2 (Methodology) Sect. 3.1 (Results), and Sect. 4 (Conclusion).

## 2 Methodology

As a use case for this work, the overall PTU manufacturing process is depicted in Fig. 1. Pinion and Ring Gear are the two main components of a PTU. After machining, these two components are passed for lapping and assembly, and from there towards the EOL. The Pinion and Ring Gear are processed as a pair in the lapping and assembly line and during this processing, a lot of data is collected using different sensors. Human experts observe the process closely to avoid any faulty PTU. However, it is not feasible for human experts to monitor a huge amount of data produced by the sensors. To facilitate the prediction of a faulty unit during lapping and assembly lines, this study proposes a CDT based on a heuristic approach. The Pinion and Ring Gear pair is depicted in Fig. 2 (a), whereas, Fig. 2 (b) shows a PTU. The heuristic approach used for the proposed CDT technology is explained next.

<figure><img src="image_4.png" /><figcaption>Fig. 1. PTU manufacturing process.</figcaption></figure>

### 2.1 Metaheuristic for Cognitive Digital Twin

Sophisticated optimization problems are addressed using computational intelligence paradigms such as metaheuristic algorithms. A heuristic method is one that repeatedly tries to make a candidate solution better in terms of a specified quality metric. Without being able to guarantee either feasibility or optimality, or even in many circumstances to indicate how close to optimality a specific
<figure><img src="image_5.png" /><figcaption>Fig. 2. (a) Pinion and Ring Gear pair, (b) PTU.</figcaption></figure>

viable solution is, heuristics can explore enormous areas of candidate solutions in pursuit of optimal or nearly optimal solutions at a reasonable computing cost. These algorithms have the ability to solve NP-hard optimization problems. Particle Swarm Optimization (PSO) is a metaphor-based metaheuristic optimization algorithm developed initially based on the inspiration from the behaviour of birds and fish folks. During the past few decades, different researchers have worked on the development of PSO, and the algorithm has proved itself as a powerful tool in solving complex optimization problems [16,17]. The main drawback of PSO is its possibility of getting stuck in the local minima while searching in high dimensions. This drawback is solved recently by proposing a Jumping strategy in PSO [14,18]. Complex and large feature spaces are mostly associated with a well-known phenomenon called *curse of dimensionality*. Data produced from the lapping and assembly line during PTU production is usually large in size. Some of these data parameters could predict a faulty PTU in advance. However, if the entire data is used for training machine learning algorithms, the model's performance is not optimum due to redundancy and irrelevance in the feature space. Therefore, to utilize the abilities of machine learning models in an optimum level, optimization of feature space is usually required. PSO has proved to be a powerful tool in optimizing the feature space for different industrial applications [19,20]. Therefore, in this study, Jumping PSO with an ability to skip local minima is adopted to optimally select the best-performing sensor values from lapping and assembly line to predict the faulty PTU units. The proposed framework is explained in the next subsection.

## 2.2 Cognitive Digital Twin for PTU Manufacturing

The overall concept of the proposed CDT for PTU manufacturing is depicted in Fig. 3. The data from the lapping and assembly lines are utilized to analyze the future prediction of faulty PTUs. The sensor data received from the lapping and assembly lines are quite large in number, and different sensor values define different manufacturing parameters. Most of these parameters have no influence on the prediction of faulty PTUs as described by human experts, while some of these are believed to have an impact on the prediction of faulty PTUs. To analyze all the manufacturing parameters in an optimized way, Jumping PSO is wrapped with machine learning algorithms. The algorithm evolves the feature
space in an optimized way to select the best combination of parameters for faulty PTU predictions. The three basic optimization steps carried by PSO are:

<figure><img src="image_6.png" /><figcaption>Fig. 3. Overall concept for the proposed CDT for PTU manufacturing.</figcaption></figure>

1. Evaluation of particles against a fitness function.

2. Keeping record of best position and fitness values.

3. Velocity and position update of particles.

The velocity and position update of particles in a classical PSO is done as:

$$v_i(t + 1) = wv_i(t) + c_1rand(g(t) - x_i(t)) + c_2rand(p_i(t) - x_i(t)) \quad (1)$$

$$x_i(t + 1) = x_i(t) + v_i(t) \quad (2)$$

here, $v_i$ is the velocity of $i^{th}$ particle, $x_i$ is the position, $c_1, c_2$ are the exploration and exploitation constants, $p_i(t)$ and $g_i(t)$ are the personal and global best positions at time $t$. By introducing a jumping strategy, the velocity update equation is modified as [14]:

$$v_i(t + 1) = wv_i(t) + c_1rand(g(t) - x_i(t)) + c_2rand(p_i(t) - x_i(t)) + J_i(CJ) \quad (3)$$

where, $J_i(CJ)$ is the jumping value given to $i^{th}$ searching particle. The amount of jump is defined as:

$$J_i(CJ) = \left( \log\left( \frac{\left( \frac{CJ}{0.1 \times \text{acceptance}} \right)^{\alpha}}{\left( \frac{CJ}{0.1 \times \text{acceptance}} \right)^{\alpha} + 1} \right) + \epsilon \right) \times rand^N \quad (4)$$

$$CJ_i = v_i(t) + (g(t) - x_i(t)) + (p_i(t) - x_i(t)) \quad (5)$$

The whole optimization process is iterative and based on the successive iterations $t$, the swarm of particles evolves towards convergence. Once the algorithm converges, either by reaching a maximum number of successive iterations or by reaching a certain value of fitness value, the global best position of the algorithm defines the best combination of features (manufacturing parameters) for
prediction. The process is explained visually in Fig. 4. The binary numbers in a single row represent the position of a particle, where 0's represent the feature not being selected and 1's show the feature being selected. Combination of particles (rows) form a swarm, and each particle in the swarm is tested for its performance against different machine learning algorithms. The personal best position $p(t)$ of a particle is the combination of features (represented by 1's) at which the machine learning algorithm achieved the highest classification accuracy at particle level. The global best position $g(t)$ is the combination of features in the whole swarm achieving highest classification accuracy.

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Proposed process of selecting best manufacturing parameters for the prediction of faulty PTUs.</figcaption></figure>

# 3 Results and Discussion

The dataset used for the evaluation of the proposed Heuristic Digital Twin is taken from the database of *GKN Automotive*, a global leader in eDrive technologies. The actual data had 41776 observations of PTU manufacturing samples, with 47 important parameters provided by human experts. However, the problem of class imbalance existed in the dataset because there were only 60 observations out of 41776 observed as faulty, the rest of all the observations were standard PTUs. Therefore, to deal with the class imbalance problem in the data, downsampling of the majority class (standard PTU) is done. After the downsampling, the class with Standard PTUs has 72 samples, while the faulty PTUs class has 60 samples.

## 3.1 Results

To evaluate the power of the proposed heuristic digital twin architecture, some of the standard machine learning algorithms are tested in a wrapper framework. The results are computed for two different scenarios: (i) performance of machine learning algorithms using the important variables identified by human experts, and (ii) performance of machine learning algorithms with optimized feature space using the proposed architecture. All the results are reported after 5-fold cross-validation. The performance of different machine learning algorithms using the
<table><caption>**Table 1.** Performance of different algorithms with all the parameters.</caption><thead><tr><td>Model</td><td>Accuracy(%)</td></tr></thead><tbody><tr><td>SVM (RBF)</td><td>57.35</td></tr><tr><td>Random Forest</td><td>55.88</td></tr><tr><td>KNN</td><td><b>66.17</b></td></tr><tr><td>Nive Bayes</td><td>50.00</td></tr><tr><td>Discriminant Analysis</td><td>53.63</td></tr><tr><td>Generalized additive model</td><td>58.08</td></tr><tr><td>Decision Tree</td><td>55.14</td></tr></tbody></table>

important parameters identified by human experts is provided in Table. 1. Here, it can be seen that the performance of different machine learning algorithms in the prediction of faulty PTUs is quite weak using all the features identified by human experts. The best performance achieved is 66.17% using the KNN model with Euclidean distance and 3 nearest neighbours. The results reported in Table. 1 are the best-achieved results after hyperparameter tuning of all the machine learning models. The results achieved using the proposed heuristic digital twin model are reported in Table. 2. From the results in Table. 2, it can be concluded that the proposed framework has the ability to perform better. The best accuracy using an optimized subset of feature space is 75.00%, which is significantly greater than the accuracy achieved by all the features without optimization. It clearly signifies the importance of optimizing the large feature space and identifies the important manufacturing parameters for predicting faulty PTUs in advance. Therefore, the proposed framework has two major advantages: (i) ability to improve the prediction accuracy, and (ii) ability to identify the important prediction parameters.

There are different subsets of features provided in Table. 2, these subsets are the best-performing combination of features for prediction using the specified model. The experiment is repeated with different swarm sizes of Jumping PSO to see its influence on the performance. The results with different swarm sizes on two best-performing classifiers are reported in Table. 3. Here, different results reported for the same model indicate the influence of swarm size. The details of different Jumping PSO hyperparameters used for the experimentation are provided in Table. 4, and the details of features taken from the PTU manufacturing are provided in Appendix A, Table. 7.

## 3.2 Analysis of Results

The results are further analyzed using some of the common evaluation parameters such as Sensitivity, Specificity, Precision, False Positive Rate, F1 score, Matthews Correlation Coefficient, Kappa, and Receiver Operating Characteristic (ROC) curve. The results of these evaluation parameters are reported in Table. 5 and Fig. 5. It can be seen from the results in Table. 5 that the sensitivity
<table><caption>**Table 2.** Performance of different algorithms with optimized feature space.</caption><thead><tr><th>Model</th><th>#Features</th><th>Features</th><th>Accuracy(%)</th></tr></thead><tbody><tr><td>SVM (RBF)</td><td>12</td><td><b>3,4,5,18,26,28,29,30,33,39,43,46</b></td><td><b>75.00</b></td></tr><tr><td>Random Forest</td><td>10</td><td>4,7,11,16,20,22,27,45,46,47</td><td>72.79</td></tr><tr><td>KNN (k=1, cosine)</td><td>11</td><td><b>3,4,9,11,18,29,34,38,39,41,44</b></td><td><b>75.00</b></td></tr><tr><td>Nive Bayes</td><td>6</td><td>4,5,9,21,27,45</td><td>66.18</td></tr><tr><td>Discriminant Analysis</td><td>8</td><td>4,11,15,18,26,28,36,37,38</td><td>68.38</td></tr><tr><td>Generalized additive model</td><td>12</td><td>5,9,11,16,19,20,30,33,40,41,42,43</td><td>69.85</td></tr><tr><td>Decision Tree</td><td>12</td><td>3,5,8,11,13,14,16,19,21,29,42,47</td><td>73.53</td></tr></tbody></table>

<table><caption>**Table 3.** Influence of Jumping PSO's swarm size.</caption><thead><tr><th>Model</th><th>swarm size</th><th>#Features</th><th>Features</th><th>Accuracy(%)</th></tr></thead><tbody><tr><td>SVM</td><td>150</td><td>12</td><td><b>3,4,5,18,26,28,29,30,33,39,43,46</b></td><td><b>75.00</b></td></tr><tr><td>SVM</td><td>100</td><td>12</td><td>4,5,6,12,15,18,21,23,39,43,44,45</td><td>71.32</td></tr><tr><td>SVM</td><td>50</td><td>8</td><td>5,10,18,22,29,30,39,47</td><td>69.85</td></tr><tr><td>SVM</td><td>150</td><td>9</td><td>3,5,11,18,23,29,30,41,47</td><td>72.05</td></tr><tr><td>SVM</td><td>100</td><td>8</td><td>10,11,14,22,23,31,34,39</td><td>71.32</td></tr><tr><td>KNN</td><td>150</td><td>11</td><td><b>3,4,9,11,18,29,34,38,39,41,44</b></td><td><b>75.00</b></td></tr><tr><td>KNN</td><td>100</td><td>14</td><td>5,10,11,14,18,19,21,27,29,30,31,32,39,41</td><td>69.85</td></tr><tr><td>KNN</td><td>50</td><td>2</td><td>35,47</td><td>66.17</td></tr><tr><td>KNN</td><td>150</td><td>13</td><td>3,8,13,18,19,22,27,36,38,39,41,43,44</td><td>71.32</td></tr><tr><td>KNN</td><td>100</td><td>13</td><td>2,3,4,5,7,18,24,29,30,35,36,39,44</td><td>68.38</td></tr></tbody></table>

<table><caption>**Table 4.** Hyperparameters for Jumping PSO.</caption><thead><tr><th>Hyperparameter</th><th>Value</th></tr></thead><tbody><tr><td>swarm size</td><td>50,100,150</td></tr><tr><td>Max. iterations</td><td>2000</td></tr><tr><td>c<sub>1</sub>, c<sub>2</sub></td><td>2</td></tr><tr><td>α</td><td>30</td></tr><tr><td>ε</td><td>0.0001</td></tr><tr><td>ω</td><td>exponential decrease from 0.9 to 0.1</td></tr><tr><td>acceptance</td><td>0.1</td></tr></tbody></table>

of the models is low, this shows that the faulty PTU samples are miss-classified as the standard PTU samples. Furthermore, it is also observed that the machine learning models are able to classify the faulty PTUs with a maximum of 75% accuracy. One possibility of these results could be the challenging and complex data that has low discriminatory powers. Secondly, as there are only limited data samples available for faulty PTUs in the real scenarios, therefore, the training samples of faulty PTU's might be limited for sufficient models training. To guar-
<table><caption>**Table 5.** Performance evaluation on different metrics.</caption><thead><tr><th>Evaluation</th><th>SVM</th><th>RF</th><th>KNN</th><th>NB</th><th>DA</th><th>GAM</th><th>DT</th></tr></thead><tbody><tr><td>Accuracy</td><td><strong>0.75</strong></td><td>0.72</td><td><strong>0.75</strong></td><td>0.66</td><td>0.68</td><td>0.69</td><td>0.73</td></tr><tr><td>Error</td><td><strong>0.25</strong></td><td>0.27</td><td><strong>0.25</strong></td><td>0.33</td><td>0.31</td><td>0.30</td><td>0.26</td></tr><tr><td>Sensitivity</td><td>0.58</td><td>0.65</td><td><strong>0.68</strong></td><td>0.63</td><td>0.51</td><td>0.66</td><td>0.60</td></tr><tr><td>Specificity</td><td><strong>0.88</strong></td><td>0.78</td><td>0.80</td><td>0.68</td><td>0.81</td><td>0.72</td><td>0.84</td></tr><tr><td>Precision</td><td><strong>0.79</strong></td><td>0.70</td><td>0.73</td><td>0.61</td><td>0.68</td><td>0.65</td><td>0.75</td></tr><tr><td>False Positive Rate</td><td><strong>0.11</strong></td><td>0.21</td><td>0.19</td><td>0.31</td><td>0.18</td><td>0.27</td><td>0.15</td></tr><tr><td>F1 score</td><td>0.67</td><td>0.67</td><td><strong>0.70</strong></td><td>0.62</td><td>0.59</td><td>0.66</td><td>0.66</td></tr><tr><td>Matthews Correlation Coefficient</td><td><strong>0.49</strong></td><td>0.44</td><td><strong>0.49</strong></td><td>0.31</td><td>0.35</td><td>0.38</td><td>0.45</td></tr><tr><td>Kappa</td><td>0.47</td><td>0.44</td><td><strong>0.48</strong></td><td>0.31</td><td>0.34</td><td>0.38</td><td>0.45</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** ROC curves for Machine Learning Models.</figcaption></figure>

ensure the best performance, sufficient training samples of faulty PTUs must be provided, and as the current study is based on the limited available data, the performance of the models could be further enhanced after the availability of more training samples. The selected subset of optimized features is also analyzed in terms of the frequency of selection of a particular feature in different experiments. The higher frequency of selection shows a higher chance of importance because the feature is selected repeatedly during different experiments. The frequency of selection of features is shown in Fig. 6. It is observed that the feature (i) Cover Dimension D2 mm is selected the maximum number of times, followed by (ii) Press Ball Bering To Housing Force kN, and (iii) Press Shim Head Outer Race To Housing Force kN. Besides these parameters, the frequency of selection of the following parameters is also high: (iv) Press Shim Outer Race To BPA Force kN, (v) Press Inner Ring Upper To Tubular Shaft Length mm, (vi) Press Inner Ring Upper To Tubular Shaft Force kN, (vii) Housing Dimension H3 mm, (viii) Housing Dimension D1 mm, and (ix) Press Shim Head Outer Race To Housing Length mm. Therefore, these features are deemed important to build a CDT model for PTU manufacturing process.
<figure><img src="image_9.png" /><figcaption>Fig. 6. Feature's selection frequency in different experiments.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. All features accuracy Vs heuristically selected features.</figcaption></figure>

<table><caption>**Table 6.** Comparison of proposed heuristic approach with PCA and LDA.</caption><thead><tr><th>Model</th><th>PCA</th><th>LDA</th><th>Proposed</th></tr></thead><tbody><tr><td>SVM (RBF)</td><td>66.17</td><td>63.97</td><td><strong>75.00</strong></td></tr><tr><td>Random Forest</td><td>56.61</td><td>59.55</td><td><strong>72.79</strong></td></tr><tr><td>KNN (k=1, cosine)</td><td>59.55</td><td>59.55</td><td><strong>75.00</strong></td></tr><tr><td>Nive Bayes</td><td>59.55</td><td>58.82</td><td><strong>66.18</strong></td></tr><tr><td>Discriminant Analysis</td><td>57.35</td><td>60.29</td><td><strong>68.38</strong></td></tr><tr><td>Generalized additive model</td><td>59.55</td><td>61.76</td><td><strong>69.85</strong></td></tr><tr><td>Decision Tree</td><td>64.70</td><td>65.44</td><td><strong>73.53</strong></td></tr></tbody></table>

Furthermore, the importance of adopting a metaheuristic approach for optimizing the feature space in a Digital Twin is shown in Fig. 7. It can be clearly seen from Fig. 7 that the accuracy of selected features is higher than the accuracy of all features for all the tested models. Moreover, the comparison of proposed heuristic approach with PCA and LDA which are conventional feature reduction approaches is provided in Table. 6. The comparison reveals that the proposed approach is better as compared to the state-of-art feature reduction techniques. Furthermore, the use of lesser features makes the model more computationally efficient and less prone to over-fitting. Therefore, a heuristically optimized cognitive digital twin model for PTU manufacturing is recommended.
# 4 Conclusions

The role of implementing a heuristic approach for designing a CDT in manufacturing is evaluated and recommended in this article. A use case of PTU manufacturing is utilized to evaluate the proposed heuristic CDT model. From the results, it is observed that the use of a heuristic approach for optimizing the feature space is important for CDTs. It not only helps in improving the performance of machine learning models but also provides information about the key parameters. Along with increasing decision-making and control autonomy, the proposed model has the capability to enhance the enterprise's performance (at scale). Therefore, it is recommended to utilize such frameworks while developing the CDT models for the manufacturing industry. Future work involves increasing the availability of a number of faulty PTU samples and improving the classification accuracy of the system.

**Acknowledgment.** This work was supported in part by the project DIGICOGS project which is financed by Vinnova (Vinnovas Diarien: 2019-0532) and the innovation program Process Industrial IT and Automation (PiiA) at Mälardalen University.

The authors would like to thank Michael Osbakk, Mikael Eriksson, Jonathan Widén, Jimmy Vesa, and 'GKN Drive line' for all the help and support during this study.

# A Details of Features Taken from the PTU Manufacturing Process

<table><caption>Table 7. Features from the PTU manufacturing process utilized for experimentation.</caption><tr><td>1</td><td>Housing Dimension H1 mm</td><td>2</td><td>Housing Dimension H2 mm</td></tr><tr><td>3</td><td>Housing Dimension H3 mm</td><td>4</td><td>Housing Dimension D1 mm</td></tr><tr><td>5</td><td>Press Ball Bering To Housing Force kN</td><td>6</td><td>Press Ball Bering To Housing Length mm</td></tr><tr><td>7</td><td>Press Snapping Length mm</td><td>8</td><td>Press Input Shaft To Housing Force kN</td></tr><tr><td>9</td><td>Press Input Shaft To Housing Lenth mm</td><td>10</td><td>Cover Dimension C1 mm</td></tr><tr><td>11</td><td>Cover Dimension D2 mm</td><td>12</td><td>Bearing Plate Adapter Dimension C2 mm</td></tr><tr><td>13</td><td>Bearing Plate Adapter Dimension D3 mm</td><td>14</td><td>Pinion Head Bearing Height Dimension mm</td></tr><tr><td>15</td><td>GMD</td><td>16</td><td>Shim Pinion Calculated mm</td></tr><tr><td>17</td><td>Shim Pinion Actual mm</td><td>18</td><td>Press Shim Head Outer Race To Housing Force kN</td></tr><tr><td>19</td><td>Press Shim Head Outer Race To Housing Length mm</td><td>20</td><td>Press Tail Outer Race To Housing Force kN</td></tr><tr><td>21</td><td>Press Tail Outer Race To Housing Length mm</td><td>22</td><td>Press Collapsible Spacer Tail Inner Race To Pinion Force kN</td></tr><tr><td>23</td><td>Press Collapsible Spacer Tail Inner Race To Pinion Length mm</td><td>24</td><td>Press Companion Flange Force kN</td></tr><tr><td>25</td><td>Pinion Torque To Turn 80 Nm</td><td>26</td><td>Pinion Nut Torque 80 Nm</td></tr><tr><td>27</td><td>Pinion Height mm</td><td>28</td><td>Pinion Height Real mm</td></tr><tr><td>29</td><td>Press Inner Ring Upper To Tubular Shaft Force kN</td><td>30</td><td>Press Inner Ring Upper To Tubular Shaft Length mm</td></tr><tr><td>31</td><td>Press Inner Ring Lower To Tubular Shaft Force kN</td><td>32</td><td>Press Inner Ring Lower To Tubular Shaft Length mm</td></tr><tr><td>33</td><td>Measure Tubular Shaft Dimension R2 mm</td><td>34</td><td>Measure Tubular Shaft Dimension R3 mm</td></tr><tr><td>35</td><td>Shim Backlash Calculated mm</td><td>36</td><td>Shim Back lash Actual mm</td></tr><tr><td>37</td><td>Shim Preload Calculated mm</td><td>38</td><td>Shim Preload Actual mm</td></tr><tr><td>39</td><td>Press Shim Outer Race To BPA Force kN</td><td>40</td><td>Press Shim Outer Race To BPA Length mm</td></tr><tr><td>41</td><td>Press Shim Outer Race To Cover Force kN</td><td>42</td><td>Press Shim Outer Race To Cover Length mm</td></tr><tr><td>43</td><td>Measure Final Torque To Turn Nm</td><td>44</td><td>Measure Back lash 180 M1 Degree</td></tr><tr><td>45</td><td>Measure Backlash 180 M2 Degree</td><td>46</td><td>Measure Backlash 180 Avarage Degree</td></tr><tr><td>47</td><td>Serial</td><td></td><td></td></tr></table>
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