# A Two-Phased Approach to Energy Consumption Prediction for Fused Filament Fabrication of CFR-PEEK

Heena Noh, Kijung Park, Gül E. Kremer

► To cite this version:

Heena Noh, Kijung Park, Gül E. Kremer. A Two-Phased Approach to Energy Consumption Prediction for Fused Filament Fabrication of CFR-PEEK. IFIP International Conference on Advances in Production Management Systems (APMS), Sep 2022, Gyeongju, South Korea. pp.274-281, 10.1007/978-3-031-16407-1_33. hal-05386062

HAL Id: hal-05386062

https://inria.hal.science/hal-05386062v1

Submitted on 27 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>
<figure><img src="image_2.png" /></figure>

ifip

International Federation for Information Processing

This document is the original author manuscript of a paper submitted to an IFIP
conference proceedings or other IFIP publication by Springer Nature. As such, there
may be some differences in the official published version of the paper. Such
differences, if any, are usually due to reformatting during preparation for publication or
minor corrections made by the author(s) during final proofreading of the publication
manuscript.
# A Two-Phased Approach to Energy Consumption Prediction for Fused Filament Fabrication of CFR-PEEK

Heena Noh<fnref n="1" /> Ⓒ, Kijung Park<fnref n="1" />(✉) Ⓒ, and Gül E. Kremer<fnref n="2" />

**Abstract.** With increasing attention on fused filament fabrication (FFF) applica-
tions for high-performance polymers, understanding the energy characteristics of
FFF is critical to pursue a sustainable additive manufacturing system. In this regard,
this study proposes a two-phased energy prediction approach to FFF. A full facto-
rial design of experiments for FFF is planned to collect data for build time, filament
volume, and energy consumption by varying major process parameters (i.e., layer
thickness, infill density, and printing speed). Carbon fiber reinforced polyether-
ether-ketone (CFR-PEEK), which is an emerging high-performance polymer for
advanced engineering applications, is used for a material of the experiments. In
the first phase, two machine learning methods (i.e., decision tree and random for-
est) are employed to estimate the material addition rate (MAR) of FFF, which
indicates the amount of deposited material volume per unit time. Then, a statis-
tical regression model of energy consumption on the estimated MAR is built to
predict the energy consumption of FFF for CFR-PEEK. The results show that
the decision tree model has better prediction performance to predict the MAR of
FFF than the random forest model. In addition, the energy consumption model
through the predicted MAR shows that an increase in the MAR reduces energy
consumption. The two-phased prediction approach based on the MAR provides
better performance than the direct energy prediction from process parameters
through a machine learning technique. The findings of this study provide a basis
to characterize energy dynamics in FFF for CFR-PEEK.

**Keywords:** Fused filament fabrication · CFR-PEEK · Material addition rate · Energy consumption · Machine learning

<footnote n="1">¹ Department of Industrial and Management Engineering, Incheon National University, Incheon 22012, Republic of Korea
{nhn, kjpark}@inu.ac.kr</footnote>

<footnote n="2">² School of Engineering, University of Dayton, Dayton OH 45469, USA

[gkremer2@udayton.edu](mailto:gkremer2@udayton.edu)</footnote>
# 1 Introduction

Additive manufacturing (AM) implements layer-by-layer fabrication using various materials to produce components from computer aided design (CAD) models [1]. Fused filament fabrication (FFF) is a representative AM technique, which is widely used in practice due to its cost-effectiveness, ease of use, and compatibility with various thermoplastic materials [1]. In particular, FFF for carbon fiber reinforced polyether-ether-ketone (CFR-PEEK) has received attention in various domains such as aerospace, automobile engineering, and medical devices due to its superior strength and mechanical stability [2]. The FFF of CFR-PEEK requires higher energy consumption than common polymers due to the high temperature and resultant long fabrication time of CFR-PEEK required for material extrusion [3]. Therefore, estimating the energy consumption of FFF using CFR-PEEK is critical to manage the energy intense AM process for CFR-PEEK in practice. However, most studies relevant to FFF not only relied on common polymers such as acrylonitrile-butadiene-styrene (ABS) and polylactide (PLA) but also mainly focused on the effects of process parameters on energy consumption [4–8].

This study proposes a two-phased approach to effectively predict the energy consumption of FFF for CFR-PEEK. A machine learning algorithm is employed first to estimate a material addition rate (MAR), the amount of deposited material volume per time, from major process parameters of FFF. Then, resultant energy consumption is predicted based on the estimated MAR through a regression model. For this, a full factorial experimental design for all combinations of major process parameters (i.e., layer thickness, infill density, and printing speed) is performed to collect the build time, filament volume, and energy consumption of FFF for CFR-PEEK. Then, two popular machine learning techniques (i.e., decision tree and random forest) are used to build models to predict the MAR of FFF, and the best MAR prediction model is selected. Through the predicted MAR, the energy consumption is fitted by a linear regression model.

# 2 Literature Review

Existing studies for the energy consumption of FFF have employed analysis of variance (ANOVA) to identify the effects of process parameters on energy performance. For example, Al-Ghamdi [5] performed ANOVA and multi-response optimization to identify the best parameter combination of FFF for ABS in energy consumption, product mass, and build time. Elkaseer et al. [6] examined the effects of process parameters (i.e., infill density, layer thickness, printing speed, extruder temperature, and surface inclination angle) on the energy consumption, dimensional accuracy, surface roughness, and productivity of FFF for PLA. Galetto et al. [7] employed ANOVA for the impact of FFF parameters (i.e., layer thickness, infill density, printing speed, extruder temperature, number of shells, and retraction speed) on the build time, energy consumption, surface roughness, and dimensional accuracy of FFF for PLA. Although the above studies suggest optimal parameter settings for energy consumption based on their ANOVA results, the resultant process parameters are difficult to be generalized due to different machine specifications and specific process parameter settings in each study. On the other hand, recent studies have employed the MAR of FFF to generalize energy characteristics in FFF. Liu et al.
[9] examined the relationship between the MAR and the energy consumption of different AM processes. Lunetto et al. [1] suggested regression models based on the MAR to characterize the specific energy consumption of FFF using ABS and polycarbonate ABS. They found that the specific energy consumption decreases as the MAR increases.

Despite the effectiveness of using the MAR measure to develop a general energy consumption model for FFF, a high-performance polymer such as CFR-PEEK that requires a much higher energy demand than other polymers has not been sufficiently investigated in the literature. Indeed, the prediction of energy consumption in the FFF of an advanced polymer is essential in practice not only to achieve environmental sustainability but also to save the total energy cost.

From this point of view, this study proposes a two-phased approach to estimate the energy consumption of FFF for CFR-PEEK. In the first phase, two machine learning algorithms (i.e., decision tree and random forest) are respectively employed to estimate the MAR from major FFF parameters (i.e., layer thickness, infill density, and printing speed). A machine learning model that shows better prediction performance for the MAR is selected to estimate the energy consumption of FFF for CFR-PEEK. Then, a linear regression model is built for energy prediction based on the estimated MAR. Finally, this study compares the energy prediction performance between the proposed approach and a machine learning approach to direct energy prediction from FFF process parameters.

# 3 Methodology

## 3.1 Experimental Settings

This study used a seat buckle design (volume = 3 cm³) (see Fig. 1), which was collected from the Thingiverse online CAD sharing platform [10], for experiments. The stereolithography (STL) file of the CAD was imported to the Simplify 3D slicing software [11] to generate a G-code file that reflects parameter settings for FFF. Experimental samples were fabricated by Apium P220 [12], which is an industrial FFF-machine for high-performance polymers. The fabrication of each experiment was performed using Apium PEEK CFR, which has the density of 1.38 g/cm³ and the tensile strength of 190 MPa [13]. The extruding nozzle and printing bed of the machine was set up to maintain 510 °C and 120 °C, respectively, during the FFF process. In addition, a brim was generated for each fabrication to ensure part quality (see Fig. 1b).

## 3.2 Design of Experiments (DOE)

The DOE of this study aims to collect energy consumption data from the FFF of CFR-PEEK given varied parameter settings. For this, three major FFF parameters (i.e., layer thickness, infill density, and printing speed) were selected as input variables for experiments. These factors have been examined as parameters significantly affecting the energy consumption of FFF in the existing literature [4–8]. Each input parameter has three levels as shown in Table 1.
<figure><img src="image_3.png" /><figcaption>Fig. 1. Sample design and its fabricated output.</figcaption></figure>

<table><caption>**Table 1.** Process parameters for DOE.</caption><thead><tr><th>Process parameter</th><th>Unit</th><th>Level 1</th><th>Level 2</th><th>Level 3</th></tr></thead><tbody><tr><td>Layer thickness</td><td>mm</td><td>0.1</td><td>0.15</td><td>0.2</td></tr><tr><td>Infill density</td><td>%</td><td>20</td><td>60</td><td>100</td></tr><tr><td>Printing speed</td><td>mm/min</td><td>1000</td><td>1100</td><td>1200</td></tr></tbody></table>

A full factorial design was planned to fabricate samples for all possible parameter combinations; a total of 27 experiments (3 levels × 3 levels × 3 levels) were randomly ordered to fabricate samples with different parameter settings. For each fabrication, the build time, filament volume, and energy consumption of each sample were collected for analysis. The energy consumption (Wh: Watt-hour) of each experiment was measured by Wattman HPM-100A Power Analyzer [14] during the FFF process. For calculating MAR values, build time (s: seconds) and consumed filament volume (cm³) were recorded for each fabrication using the machine data system. The MAR value of each experiment is computed through Eq. (1).

$$MAR = \frac{\text{filament volume (cm}^3\text{)}}{\text{build time (s)}} \quad (1)$$

## 3.3 Two-Phased Energy Consumption Prediction

A two-phased prediction approach to energy consumption was proposed to effectively estimate the energy consumption of FFF for CFR-PEEK. In the first prediction phase, a machine learning method was used to estimate the MAR of FFF for CFR-PEEK that is resulted from process parameter settings. Herein, two representative machine learning techniques, decision tree (DT) [15] and random forest (RF) [16] were examined to select the best model for prediction. The process parameters and the MAR were considered as predictor variables at the root node of a DT and a target variable at the leaf node of a DT, respectively. The minimum number of samples needed to split each internal node was set to two, and that of samples required to be at the leaf node was restricted to one. In
the RF method, a meta estimator fits multiple decision trees on various sub-samples of the dataset, and then combines the results to improve the predictive accuracy [16]. The number of trees in the forest was set to ten. The minimum number of samples needed to split each internal node and that of samples required to be at the leaf node were set to two and one, respectively.

Two-thirds of all the experiment data were used as a training dataset to build a model, and the remaining dataset was used to test the model in each machine learning technique. The DT and RF models used the same datasets for training and testing. Each machine learning method was examined by the mean squared error (MSE), the mean absolute error (MAE), and the coefficient of determination (R²) to identify the best prediction model for the MAR. The DT and RF models used for the first phase were implemented using the scikit-learn library in Python [18].

In the second phase, the energy consumption of FFF was fitted by a regression model using the estimated MAR as a predictor. The regression model was adopted from a general model of energy consumption in the previous studies [3, 19]. The regression model of energy consumption on the MAR is expressed by Eq. (2):

$$EC = \beta_{0}(EC) + \beta_{1}(EC) \cdot MAR_{inv}, \quad (2)$$

where EC (unit: Wh) is the energy consumption of FFF, MARinv (unit: s/cm³) is the inverse value of a material addition rate (= 1/MAR), β₀(EC) represents an intercept, and β₁(EC) represents a coefficient of the energy consumption model. The statistical significance of the regression model was tested by β₁(EC) at the *p*-value of 0.05. The regression model was derived using Minitab 21 [17].

Finally, the effectiveness of the proposed two-phased prediction approach was verified by comparing the proposed approach and energy prediction directly derived from the process parameters through a machine learning technique selected in the first phase.

# 4 Results

Table 2 shows the performance measures of the MAR estimation models. The DT method has better prediction performance than the RF method in all the measures. Thus, the DT model was selected to estimate the MAR of FFF for CFR-PEEK in this study.

<table><caption>**Table 2.** Estimation of MAR.</caption><thead><tr><td>Measure</td><td>Decision Tree</td><td>Random Forest</td></tr></thead><tbody><tr><td>MSE</td><td>4.9276</td><td>9.3187</td></tr><tr><td>MAE</td><td>2.0780</td><td>2.8849</td></tr><tr><td>R<sup>2</sup></td><td>0.9912</td><td>0.9834</td></tr></tbody></table>
The MAR of each parameter combination predicted by the decision tree model was transformed into 1/MAR to build a linear regression model in Eq. (2). Figure 2(a) and Table 3 show the linear regression results. The *p*-value shows that MAR is a statistically significant predictor of energy consumption (see Table 3). In addition, the derived regression model has a high prediction power (*R*² = 0.958). As shown in Fig. 2(b), the decrease in the energy consumption of FFF for CFR-PEEK is accelerated as the MAR increases.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Fitted regression plot (a) and energy consumption plot (b) on MAR.</figcaption></figure>

<table><caption>**Table 3.** Fitted energy consumption model on MAR.</caption><tr><td>Equation</td><td>EC = 52.13 + 0.126 · MAR</td></tr><tr><td>F-value</td><td>159.79</td></tr><tr><td>p-value</td><td>0.00 (p < 0.05)</td></tr><tr><td>R<sup>2</sup></td><td>0.958</td></tr></table>

Table 4 shows the performance measures of the decision tree model of energy consumption, which directly uses the process parameter values for the model. The DT model shows a lower prediction performance (*R*² = 0.898) than that of the final energy prediction model from the two-phased approach (*R*² = 0.958).

<table><caption>**Table 4.** Estimation of energy consumption on process parameters through decision tree.</caption><thead><tr><td>Measure</td><td>Decision Tree</td></tr></thead><tbody><tr><td>MSE</td><td>281.8005</td></tr><tr><td>MAE</td><td>15.0489</td></tr><tr><td>R<sup>2</sup></td><td>0.898</td></tr></tbody></table>
# 5 Conclusions

This study proposed a two-phased prediction approach to estimate the energy consumption of FFF for CFR-PEEK, which can have a better prediction power than the direct prediction of energy consumption based on process parameters. For this, the DOE considering three process parameters (i.e., layer thickness, infill density, and printing speed) was planned to collect data for build time, filament volume, and energy consumption from experimental samples. This study employed the MAR of FFF to represent the process efficiency resulted from process parameter settings. In the first phase, two machine learning methods (i.e., decision tree and random forest) were examined to estimate the MAR of FFF for CFR-PEEK. Then, a linear regression model was derived to estimate energy consumption from the MAR obtained from the best machine learning method for the MAR estimation in the first phase.

The results showed that the decision tree model for the MAR estimation has better prediction performance than the random forest model. The linear regression model of energy consumption on the estimated MAR in the second phase also showed good prediction performance. The two-phased prediction approach provided better final performance ($R^2 = 95.8\%$) than the direct energy prediction using the DT model directly using process parameters ($R^2 = 89.8\%$). Thus, it can be concluded that the proposed energy prediction approach for the FFF of CFR-PEEK is more effective in estimating energy consumption for the FFF of CFR-PEEK. The findings from this study also demonstrate that the MAR provides a basis to characterize energy dynamics in FFF; the MAR of FFF can effectively explain the energy performance of FFF depending on parameter settings.

Nonetheless, this study should be further extended to reflect the following tasks. First of all, the replicates of each experiment should be employed to derive more statistically significant results that consider possible experimental noises. Second, the proposed energy consumption approach should be improved by a meta-optimization process for parameter tuning of each machine learning method to ensure the best prediction condition of the model. Moreover, different part designs and other high performance materials should be jointly considered to develop a more reliable and general energy prediction approach for various FFF applications in practice.

**Acknowledgement.** This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1C1C1012140) for Kijung Park.

# References

1. Lunetto, V., Priarone, P.C., Galati, M., Minetola, P.: On the correlation between process parameters and specific energy consumption in fused deposition modelling. J. Manuf. Process. **56**, 1039–1049 (2020). https://doi.org/10.1016/j.jmapro.2020.06.002

2. Park, K., Kim, G., No, H., Jeon, H.W., Okudan Kremer, G.E.: Identification of optimal process parameter settings based on manufacturing performance for fused filament fabrication of CFR-PEEK. Appl. Sci. **10**(13), 4630 (2020). https://doi.org/10.3390/app10134630
3. Kim, K., Noh, H., Park, K., Jeon, H.W., Lim, S.: Characterization of power demand and energy consumption for fused filament fabrication using CFR-PEEK. Rapid Prototyp. J. **28**(7), 1394–1406 (2022). https://doi.org/10.1108/rpj-07-2021-0188

4. Mognol, P., Lepicart, D., Perry, N.: Rapid prototyping: energy and environment in the spotlight. Rapid Prototyp. J. **12**(1), 26–34 (2006). https://doi.org/10.1108/13552540610637246

5. Al-Ghamdi, K.A.: Sustainable FDM additive manufacturing of ABS components with emphasis on energy minimized and time efficient lightweight construction. Int. J. Lightweight Mater. Manuf. **2**(4), 338–345 (2019). https://doi.org/10.1016/j.ijlmm.2019.05.004

6. Elkaseer, A., Schneider, S., Scholz, S.G.: Experiment-based process modeling and optimization for high-quality and resource-efficient FFF 3D printing. Appl. Sci. **10**(8) (2020). https://doi.org/10.3390/app10082899. Article 2899

7. Galetto, M., Verna, E., Genta, G.: Effect of process parameters on parts quality and process efficiency of fused deposition modeling. Comput. Ind. Eng. **156**, 107238 (2021). https://doi.org/10.1016/j.cie.2021.107238

8. Peng, T., Yan, F.: Dual-objective analysis for desktop FDM printers: energy consumption and surface roughness. Procedia CIRP **69**, 106–111 (2018). https://doi.org/10.1016/j.procir.2017.11.084

9. Liu, Z., et al.: Investigation of energy requirements and environmental performance for additive manufacturing processes. Sustainability **10**(10), 3606 (2018). https://doi.org/10.3390/su10103606

10. Thingiverse. https://www.thingiverse.com

11. Simplify 3D. www.simplify3d.com/software/release-notes/version-4-1-2

12. Apium. https://apiumtec.com/download/apium-p220-datasheet

13. Apium. https://apiumtec.com/download/apium-cfr-peek-datasheet

14. Adpower. https://bit.ly/3LOZm3S

15. Wei, Y., et al.: A review of data-driven approaches for prediction and classification of building energy consumption. Renew. Sustain. Energy Rev. **82**, 1027–1047 (2018). https://doi.org/10.1016/j.rser.2017.09.108

16. Zhang, W., Wu, C., Li, Y., Wang, L., Samui, P.: Assessment of pile drivability using random forest regression and multivariate adaptive regression splines. Georisk Assessment Manage. Risk Eng. Syst. Geohaz. **15**(1), 27–40 (2021). https://doi.org/10.1080/17499518.2019.1674340

17. Minitab. https://www.minitab.com/en-us/products/minitab

18. Scikit-learn. https://scikit-learn.org/stable/supervised-learning.html#supervised-learning

19. Gutowski, T.G., Branham, M.S., Dahmus, J.B., Jones, A.J., Thiriez, A., Sekulic, D.P.: Thermodynamic analysis of resources used in manufacturing processes. Environ. Sci. Technol. **43**(5), 1584–1590 (2009). https://doi.org/10.1021/es8016655