# Comparative Analysis of Multivariate Time Series Forecasting Methods for Modeling Plastic Extruder Behavior

Amira Souilah, Jérôme Rocheteau, Benoit Lardeux, Christian Attiogbé

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Amira Souilah, Jérôme Rocheteau, Benoit Lardeux, Christian Attiogbé. Comparative Analysis of Multivariate Time Series Forecasting Methods for Modeling Plastic Extruder Behavior. 13th International Conference on Model and Data Engineering - Naples - November 18 - 20, 2024, Elio Masciari; Ladjel Bellatreche, Nov 2024, Naples, Italy. pp.229-237, 10.1007/978-3-031-87719-3. hal-05109732

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# Comparative Analysis of Multivariate Time Series Forecasting Methods for Modeling Plastic Extruder Behavior

Amira Souilah<sup>1,2</sup>, Jérôme Rocheteau<sup>1,2</sup>, Benoit Lardeux<sup>3</sup>, and Christian Attiogbé<sup>2</sup>

<sup>1</sup> Icam Ouest campus of Nantes, 44470 Carquefou
amira.souilah@icam.fr, jerome.rocheteau@icam.fr

<sup>2</sup> Nantes Université, Ecole Centrale Nantes, CNRS, LS2N, UMR 6004, Nantes
christian.attiogbe@univ-nantes.fr

<sup>3</sup> L@bISEN, Usine du Futur, ISEN Yncra Ouest, 44470, Carquefou, France
benoit.lardeux@isen-ouest.yncrea.fr

**Abstract.** The extrusion process stands as one of the most important technology of polymer processing in the industry. The inclusion of recycled plastic introduces material property variations, challenging the assumption of stability and fixed setpoints. Therefore, it becomes crucial to dynamically adapt parameters such as the motor speed and heating temperatures based on factors such as material output pressure, temperature and motor torque. Modelling the plastic extruder becomes valuable, offering insights into the its behavior, serving as a valuable asset to maintain consistent product quality despite variations in input material properties. Additionally, the model enables accurate evaluation of the extruder performance under different conditions and contexts. We have conducted an analysis of various virgin polypropylene plastic extruder behavior, treating the adaptation of its parameters as multivariate time series data. This allowed us to gain a comprehensive understanding of how the extruder parameters vary over time, specifically during the move from special grades of virgin polypropylene to another, wherein dealing with recycled plastics turns manageable and an intelligent forecasting model able to autonomously guiding both virgin and recycled plastic extrusion process can be developed.

**Keywords:** Plastic Extrusion · Multivariate Time Series · Deep Forecasting · Recurrent Neural Network · Linear Regression

## 1 Introduction

Predictive models and their implementation are used in several area to help in understanding or controlling industrial processes for instance. Plastics are produced in large quantities due to their advantageous features, including being lightweight, possessing high impact resistance, malleability for shaping into multiple forms. However, when exposed to heat, plastics can melt and lose their original shape. Polypropylene (PP) stands out as thermoplastics with widespread usage owing to its excellent chemical resistance and its ability to be processed
through various methods like injection molding and extrusion. However the gen-
eration of plastics for different purposes leads definitely to a significant waste.
Consequently, the importance of recycling solutions becomes obvious. The ex-
trusion process can be considered among the best solutions to reduce the use
of *virgin plastic*, with the extruder serving as its key component. But what will
happen if there are mixtures of different types of polypropylene or when contin-
uously extruding and reextruding the same polypropylene types or mixtures for
a specific number of recycling. The question then arises: is it possible to main-
tain this level of adjustment in the extrusion process parameters under recycling
conditions automatically? This motivates our work on modeling the behaviour
of the plastic extruder. Our work is undertaken in the **Recyplast-Demo** project
which aims to develop a real-time manufacturing unit capable of controlling the
properties of recycled material and adjusting manufacturing parameters. Fore-
casting the future based on historical data presents a noteworthy challenge [16]
but this does not prevent the existence of several methods used for this purpose,
each of which has its strengths and limitations. Our main objective is to prove
that it is possible to predict the plastic extruder parameters using multivariate
time series forecasting methods even amidst fluctuations in plastic properties
during the manufacturing process.

The contributions of our work are: i) the production of public datasets, which are used to predict the process supervision parameters through previously unexplored multivariate time series; ii) the construction and a comparison of statistical and artificial intelligence forecasting models to determine the most effective one. The paper is structured as follows: Section 2 delves into the background and related work. Section 3, deals with a case study with the used datasets, the preprocessing steps, the training and validation procedures, the hyperparameter tuning and the introduction of dedicated evaluation metrics. We then discuss the experimental results in Section 4 and finally, Section 5 gives conclusions and future work. The remaining data and code can be accessed via the following link: RecyPlast-MEDI2024 Repository.

## 2 Background and Related Work

*Time series* are a sequence of data points that occur in successive order over time. It is all the dataset that comprises insights about one or more variables in the case of *multivariate time series* [7]. The art of exploiting the optimal combination of time delay and the input dimension from historical data to be used to develop predictive models for future data is known as *time series forecasting* [10]. Forecasting methods can be categorized into linear and non-linear modeling approaches. Linear modeling approaches assume a direct, straight-line relationship between input variables and the output variable while the non-linear approaches are considered when comprehending the relationships and the dependencies among multiple variables becomes challenging. The challenges come from that the prediction values not only rely on its own past values but also on past values of other interdependent variables, a scenario often come upon multivariate time series [12]. Hence, statistical methods like VAR are commonly used in finan-
cial and economics forecasting. Each variable is assumed to impact every each other variable in the system [2,9]. Stationarity in time series data is a condition for VAR models, indicating that throughout time, their statistical characteristics like mean, variance, and autocovariance do not change. MLR model is used as well to understand the relationships between one dependent value and more than two dependent variables [6] while the Prophet model is used to capture trends and seasonality in the data while combining between statistical models and ML techniques [11]. To overcome these issues, particularly those related to handling non-linear problems, Deep Learning (DL) techniques may appear to be a significant undertaking for forecasting time series data more accurately given their proficiency in processing long sequences of data to predict future events and their ability to identify complex relationships that might be difficult to identify with statistical models. Among DL forecasting models, we have Recurrent Neural Networks (RNN) and their variants Long Short Term Memory (LSTM) [3,13] and Gated Recurrent Unit (GRU) that have been revealed as efficient for modeling sequential data with a temporal link between them [14]. In [3] the authors proposed RNN model using LSTM techniques for weather forecasting system while compiling data on temperature, humidity, pressure, dew point, wind speed, precipitation, and visibility. The task involves preprocessing data collected from the Small Wild Goose Pagoda and utilizing LSTM neural networks to estimate tourism flow citing their ability to capture intricate patterns and evaluating their performance against traditional methods using metrics such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) [1]. In [4] the authors argue that data collection is becoming more feasible and there could be a multitude of related sequences, where altering one sequence may impact the changes of other sequences. That prompted their searching for elaborating the attention mechanism [15] incorporated into the LSTM to predict multivariate functions. This innovative model improved the predictive capacity of LSTM. In this paper, we compare the forecasting performance using the LSTM network, MLR, VAR and the Prophet models.

## 3 Plastic Extrusion Modelling and Prediction

We consider a plastic extrusion process where plastic materials such as solid plastic pellets, chips, beads or powder are placed into hoppers. Subsequently, a motorized endless screw compresses and propels the pellets, guiding them through a heating zones where the undergo melting. Once a molten state, the plastic is extruded through a die, ultimately acquiring its final shape. The variation of polypropylene pellets during each extrusion test over time necessarily requires an adequate adjustment of parameters such as motor speed and temperature of heating among 5 zones in order to guarantee the desirable quality of the extruded plastics. This adjustment is needed to ensure the desired quality of the end product. Such fine-tuning can be easily managed when dealing with distinct types of polypropylene accompanied by technical data sheets detailing their chemical and energetic properties.
*The proposed method* Our method involves the following steps.

**Step 1. Producing datasets for training** Due to the lack of public datasets in plastic's field, we generate the whole dataset from experiment. We designed a specific data acquisition protocol for the extrusion process as part of the Recyplast-Demo project. This experimental protocol was came up to understand the behavior of the extruder, particularly how its settings evolve over time, while processing both virgin and recycled polypropylene (PP) chosen for its excellent chemical resistance and capability to withstand high temperatures, allowing it to be processed through various methods such as injection molding and extrusion. Our protocol implicated operating virgin polypropylene, specifically PP30, PP40, and PP89, separately and in different mixtures. Our underlying approach is to fine-tune the five heating zone settings after maintaining a constant motor speed. For example, we varied the motor speed within the range of [5-60] rotations of the motor while adjusting the temperatures zone from [160-230] degrees Celsius, aiming to achieve optimal extruded polypropylene quality, qualified by the operator (rated 1 if good, otherwise 0). This protocol will also be tailored for recycled polypropylene, with adjustments made over an infinite number of cycles. However, we primarily focus on the inspection of virgin polypropylene in this study. The results of this acquisition protocol are structured as CSV files for later manipulations.

**Step 2. Data preprocessing for training and forecasting** The collected CSV files include data from the virgin polypropylene extrusion process during experiments in the ICAM School of Engineering. Each dataset, recorded at a frequency of 0.5 Hz, contains over 103 variables, including but not limited to:

1. timestamps: of the recorded data converted to datetime type.

2. cgn_mot_spe: the motor speed setpoint.

3. cgn_temp_zx: the temperature setpoints for five different zones and its recording measurements: mes_temp_zx where $x \in 1, 2, 3, 4, 5$.

4. cgnProp_pp_30, cgnProp_pp_40, cgnProp_pp_89: instructions for the proportions of polypropylene.

5. mes_pre Mat: the plastic pressure as is passes through the barrel heat.

6. mes_temp Mat: the plastic temperature as is passes through the barrel heat.

7. qual_indic: a quality indicator feature given by the operator.

The main preprocessing steps are as follows:

1. Determining whether our variables exhibit stable behaviors over time, we apply the Augmented Dickey-Fuller (ADF) test [8], which assesses the presence of nonstationary behavior: by comparing the original time series with its lagged version. We then select the optimal lag order by analyzing the Akaike Information Criterion (AIC) [5].

2. Normalizing the data: we used Min Max Scaler to ensure the values are scaled within the range of 0 to 1, such as: for every feature, the minimum value $X_{min}$ of that feature gets transformed into a 0, the maximum value $X_{max}$ gets transformed into a 1, and every other value gets transformed into a decimal between 0 and 1.
3. Splitting into training and test data: we divided the dataset using a specific ratio. The first 80% is used for training, while the remaining 20% is used for testing in the experiments.

*Metrics for predictive capabilities* To assess and contrast the predictive capabilities of various models, three fundamental evaluation metrics for regression problems are used: mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination *R*² [1]. Lower MAE and RMSE values are thought to increase the effectiveness of a model, and if *R*² is closer to 1, it is considered more effective.

**Step 3. Training, hyper-parameters tuning and validation** We now apply four forecasting models to a dataset comprising all experiments with virgin PP extrusion, which include various material proportion instructions (cgnProp_pp), following the data acquisition protocol outlined in subsection 3. The objective is to predict the extruder's setpoints. To illustrate, we will showcase the performance of these models on datasets representing various polypropylene mixtures.

(a) *Vector Autoregressif Model* Before applying the VAR model, some variables in our dataset underwent differencing to ensure stationarity of the series. The model requires the specification of the order, which represents the number of included lagged historical observations, determined with information criterion.

(b) *Prophet Model* We leverage the Prophet forecasting model with additional regressors recognizing the multifactorial nature of plastic extrusion control. These regressors were added without standardization to preserve their original scales. We then initialized the Prophet model with a 90% prediction interval and renamed the target variable to 'y' to ensure compatibility with the Prophet model.

(c) *Multiple Regression Model* we applied train_test_split in the scikit-learn library to divide the data into training and testing sets, We then initialized a separate Linear Regression model for each column in the dataset and fitted it to our training data. The model obtained from training makes prediction and the scores is calculated.

(d) *Forecasting based on deep-learning based models (LSTM Model)* We prepared the plastic extrusion dataset for the LSTM model by framing it as a supervised learning task. However, as the extruder's behavior does not change significantly over time, we set the time steps to 1, meaning the model is designed to process each input independently without relying on past states. The LSTM model was built using Keras with a three-layer LSTM architecture. The first two LSTM layers use 30 neurons with ReLU activation and recurrent dropout, followed by a dense output layer with 17 neurons for the forecast. The model hyperparameters have been computed from the Adam optimizer and trained according to MSE loss function. A training process involving 100 epochs and a batch size of 32 have been performed, with early stopping based on validation performance. The model's output has been evaluated by monitoring the training and testing loss curves, ensuring that the final model configuration achieved stable and robust forecasting results without overfitting. The last step is about comparing the results obtained and selecting the most performant one.
## 4 Results, Comparison and Discussion

In Table 1 we compare between the performance of MLR, VAR and Prophet models for forecasting extruder's parameters; they are used as baseline models for assessing the performance of the LSTM model. For most variables cgn_temp_z3, cgn_temp_z4, MLR tends to perform better, with lower MAE and higher $R^2$ values, indicating that MLR generally provides a better fit to the data. However, for certain variables like cgn_temp_z1 and cgn_temp_z5, Prophet shows better performance in terms of lower MAE and RMSE, indicating it can be more accurate in some cases. In general, MLR appears to have a slight advantage in overall accuracy and consistency, especially in explaining the variability ($R^2$) (0.95), but Prophet performs comparably, with marginally better average MAE (1.76) despite being more sensitive to large errors (higher RMSE = 2.87). In the case of the VAR model, although it produces very small errors, the results are not reliable due to the negative $R^2$ values, which indicates that the model fails to capture much of the variability in the data. This suggests the model's inadequacy for this specific forecasting task.

<table><caption>**Table 1.** Comparison of Results from VAR, MLR and Prophet Models</caption><thead><tr><th rowspan="2">Variables</th><th colspan="3">VAR</th><th colspan="3">MLR</th><th colspan="3">Prophet</th></tr><tr><th>MAE</th><th>RMSE</th><th>$R^2$</th><th>MAE</th><th>RMSE</th><th>$R^2$</th><th>MAE</th><th>RMSE</th><th>$R^2$</th></tr></thead><tbody><tr><td>cgn_temp_z1</td><td>0.00</td><td>0.09</td><td>0.00</td><td>1.65</td><td>2.59</td><td>0.95</td><td>1.43</td><td>2.44</td><td>0.96</td></tr><tr><td>cgn_temp_z2</td><td>0.01</td><td>0.16</td><td>0.00</td><td>1.08</td><td>1.47</td><td>0.98</td><td>0.94</td><td>1.63</td><td>0.97</td></tr><tr><td>cgn_temp_z3</td><td>0.01</td><td>0.19</td><td>0.00</td><td>0.76</td><td>1.20</td><td>0.98</td><td>0.96</td><td>1.59</td><td>0.96</td></tr><tr><td>cgn_temp_z4</td><td>0.01</td><td>0.09</td><td>0.00</td><td>0.95</td><td>1.23</td><td>0.97</td><td>1.04</td><td>1.83</td><td>0.95</td></tr><tr><td>cgn_temp_z5</td><td>0.00</td><td>0.00</td><td>0.00</td><td>2.25</td><td>3.09</td><td>0.86</td><td>1.69</td><td>2.49</td><td>0.91</td></tr><tr><td>cgn_mot_spe</td><td>0.06</td><td>0.78</td><td>0.00</td><td>4.86</td><td>6.30</td><td>1.00</td><td>4.53</td><td>7.27</td><td>0.77</td></tr></tbody></table>

Moving towards the performance of the LSTM model that was evaluated based on the same metrics. The test data provided the model's performance with an average $R^2$ of 96.07%, an average RMSE of 1.42, and an average MAE of 0.97. In Table 2 we compare the performance of three forecasting models: LSTM, Prophet and MLR across various datasets representing different mixtures of virgin polypropylene. In the fourth dataset, MLR stands out with a notably low MAE of 0.32, the smallest among all models for this dataset, indicating strong performance in minimizing the average prediction error. When considering the RMSE (0.74), which emphasizes larger errors more heavily, MLR's performance is exceptional compared to other cases. Additionally, the $R^2$ value of 0.80 suggests that while MLR predicts with a small average error, its overall fit to the data is somewhat weaker, as it explains less variance in the dataset compared to other cases where $R^2$ values are closer to 0.98. On the other hand, Prophet delivers the best performance with the lowest MAE (0.21), RMSE (0.36), and the highest $R^2$ (0.98), indicating the most accurate predictions for the first, second, third and fifth mixture. It is followed by MLR and then LSTM that performs moderately well, with low MAE and RMSE, though its $R^2$ (0.67) is
notably lower. An important observation from our experiments is that while LSTM performs well with merged datasets, capturing broader patterns across merged datasets, its performance declines when applied to individual datasets. This suggests that LSTM benefits from larger data pools but has difficulty capturing finer details specific to smaller datasets. In contrast, Prophet and MLR often outperform LSTM on individual datasets due to their simpler structure. As far as the plastic extrusion process is concerned, we observed that as the viscosity of the polypropylene decreases, the extrusion process becomes more challenging. Specifically, PP89, which has a low viscosity, creates significant difficulties during extrusion when it makes up a large percentage of the mixture. This difficulty may introduce greater variability into the data, potentially contributing to the poorer performance of models like LSTM and MLR in datasets with high proportions of PP89. The inherent instability in the extrusion process with lower-viscosity materials makes it harder for models to make accurate predictions, leading to higher errors in metrics like MAE and RMSE. In contrast, PP30 is more viscous than PP40, and their mixture proves to be a more stable combination for the extrusion process. This stability is reflected in the improved performance of all models across the datasets that contain these mixtures, where prediction errors are lower and $R^2$ values are higher. The balanced viscosity between PP30 and PP40 reduces the challenges in the extrusion process, allowing the models to capture patterns more effectively and produce more accurate predictions.

<table><caption>**Table 2.** Results of LSTM, MLR and Prophet models for different plastic mixtures</caption><thead><tr><th colspan="3">Datasets</th><th colspan="3">LSTM</th><th colspan="3">Prophet</th><th colspan="3">MLR</th></tr><tr><th>PP30</th><th>PP40</th><th>PP89</th><th>MAE</th><th>RMSE</th><th>R<sup>2</sup></th><th>MAE</th><th>RMSE</th><th>R<sup>2</sup></th><th>MAE</th><th>RMSE</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>0.25</td><td>0.50</td><td>0.25</td><td>0.49</td><td>1.13</td><td>0.72</td><td>0.21</td><td>0.36</td><td>0.98</td><td>0.65</td><td>0.29</td><td>0.99</td></tr><tr><td>0.33</td><td>0.33</td><td>0.33</td><td>2.55</td><td>4.49</td><td>0.66</td><td>1.16</td><td>1.71</td><td>0.95</td><td>1.21</td><td>1.16</td><td>0.95</td></tr><tr><td>0.75</td><td>0.00</td><td>0.25</td><td>1.13</td><td>1.63</td><td>0.68</td><td>0.42</td><td>0.71</td><td>0.94</td><td>1.01</td><td>0.47</td><td><span style="color:red;">0.80</span></td></tr><tr><td>0.00</td><td>0.50</td><td>0.50</td><td>2.00</td><td>3.42</td><td>0.69</td><td>1.17</td><td>2.82</td><td>0.91</td><td><span style="color:red;">0.32</span></td><td>0.74</td><td>0.98</td></tr><tr><td>0.50</td><td>0.50</td><td>0.00</td><td>0.74</td><td>1.31</td><td>0.67</td><td>0.24</td><td>0.46</td><td>0.97</td><td>0.39</td><td>0.39</td><td>0.98</td></tr><tr><td colspan="3">conc. dataset</td><td><span style="color:blue;">0.97</span></td><td><span style="color:blue;">1.42</span></td><td><span style="color:blue;">0.96</span></td><td><span style="color:blue;">1.77</span></td><td><span style="color:blue;">2.88</span></td><td><span style="color:blue;">0.92</span></td><td><span style="color:blue;">1.12</span></td><td><span style="color:blue;">1.60</span></td><td><span style="color:blue;">0.95</span></td></tr></tbody></table>

## 5 Conclusion

We designed a specific experimental protocol to collect data for both virgin and recycled polypropylene extrusion. Such data were not available before in the plastic extrusion field. Moving on to the forecasting step, acknowledging the lack of a universally perfect model that fits all data, we experimented with linear modeling approaches (Prophet and VAR) which leverage time series decomposition techniques. Additionally, we employed the nonlinear modelling approaches such as recurrent neural networks with LSTM cells. These nonlinear models demonstrated enhanced capabilities in capturing relationships within multivariate time series data, showcasing accurate predictions. An important observation from our experiments is that LSTM performs well with several merged datasets, capturing broader patterns, but struggles with smaller, individual datasets although
Prophet and MLR are better due to their simpler structure and trend focus. We plan to evaluate the most effective model ability to forecast the settings of the extruder when it processes recycled plastics. We will refine the model accuracy, possibly by incorporating additional descriptive features including the implementation of quality and viscosity sensors and exploring various setting scenarios. Then, we opt to keep the model updates dynamically by using transfer learning and reinforcement learning to ensure the implementation of a system that continuously adapts and improves the model's performance over time.

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