Adaptive Neuro-Fuzzy Inference System-Based Predictive Modeling of Mechanical Properties in Additive Manufacturing

Abstract

Predicting the mechanical properties of Additive Manufacturing (AM) parts is a complex task due to the intricate nature of the manufacturing processes. This study presents a novel application of the Adaptive Neuro-Fuzzy Inference System (ANFIS) to predict the mechanical properties of PLA specimens produced using Fused Filament Fabrication (FFF). The ANFIS model integrates the strengths of neural networks and fuzzy logic to establish a mapping between the inputs and the output mechanical properties, specifically maximum stress, strain, and Young’s modulus. Experimental data were collected from three-point bending tests conducted on FFF samples fabricated from PLA material with different manufacturing parameters, such as infill pattern, infill, layer thickness, printing speed, extruder and bed temperature, printing orientation (along each axis and twist angle), and raster angle. These data were used to train, check, and validate the ANFIS model. The results reveal that the proposed predictive model can effectively predict the mechanical properties of FFF-printed PLA samples, demonstrating its potential for broader applications across various AM technologies and materials, ultimately enhancing the efficiency and effectiveness of the AM fabrication process.

1. Introduction

Within the context of the fourth industrial revolution, several science sections merge with each other in order to lead industry to new horizons. Fuzzy modeling, a tool which can impressively represent nonlinear relations between the parameters of a system [1], along with adaptive Artificial Neural Network (ANN) results in the Adaptive Neuro-Fuzzy Inference System (ANFIS). ANFIS can establish input–output systems based on both “if–then” rules and specified input–output data pairs [2]. This combination takes advantage of both tools in a single framework.

Additive Manufacturing is a rapidly expanding technology, applied to a wide range of industrial sectors, transforming design files to functional products as well as parts and assemblies. The main advantages of AM are the freedom of design, sustainability in energy and materials, the ability for complex structures to be manufactured, and the affordability in fast prototyping. However, AM still faces low productivity and uncertainty of the parts, regarding their mechanical properties. The main reason is the multifactorial process parameters that influence the manufacturing procedure.

Several studies have been made to propose new methods and materials in AM, offering solutions and further development on the AM, as it is one of the four manufacturing pillars. In 1986, Charles Hull presented a new technology in which successive layers of materials are formed on top of each other creating three-dimensional parts. This new process was named stereolithography (SLA). Since then, new methods are being developed, and novel materials are being applied, allowing new applications and industry fields to continuously merge with AM.

ASTM classifies Additive Manufacturing into seven major categories [3]: Material Extrusion, Powder Bed Fusion, Sheet Lamination, Binder Jetting, Material Jetting, VAT Photopolymerization, and Direct Energy Deposition. Among these, Material Extrusion is the most widely used AM process. In this method, the material is selectively dispensed through a heated nozzle following a layer-by-layer path to create a physical model.

The large variety of materials, used in AM, can be categorized [4] into four groups: Metals and Alloys, Polymers and Composites, Ceramics, and finally Concrete, most of which can be used in Material Extrusion processes.

New Additive Manufacturing (AM) technologies are continually being developed, and the variety of materials utilized in these processes is expanding rapidly. Moreover, AM, also known as 3D printing, is experiencing rapidly growth due to its facilitation capabilities, having a key role in industries, such as aerospace, oil and gas, automotive, energy, medical, tool and die, and other consumer goods [5]. As Artificial Intelligence (AI) tools can be applied to control the factors that affect the mechanical properties of the materials [6,7], this study will explore the convergence of AM and ANFIS. The aim is to develop a tool that can predict the mechanical properties of specimens, taking into consideration most of the manufacturing parameters of AM processes, thereby enhancing the efficiency of AM applications.

Although Additive Manufacturing is gaining popularity, due to its reduced product cycle time and the lack of need for expensive tools, the commercialization of this technology is still limited because of several shortcomings. One significant issue is the difficulty in determining the strength of the parts, which arises from the anisotropic and heterogeneous microstructure of the fabricated parts. The most critical material characteristics are the mechanical properties, as they determine the product’s ability to meet the designed requirements. These properties, which include stress, strain, and Young’s modulus, depend on various parameters, such as the applied AM method, material, infill pattern and percentage, layer thickness, the existence of wall and its thickness, temperature, building orientation, curing conditions, and many more.

Previous studies [8,9,10,11,12,13,14,15,16,17,18,19,20] in the field have usually focused on a limited number of the most significant parameters, within the strict boundaries of the conducted experiments, using several experimental, numerical, and statistic methods.

This research is triggered by the need to develop a unified tool for predicting the mechanical properties of AM parts, adaptable to AM technology and material, while accounting for the various process parameters that impact the final product. The mechanical properties to be approached are maximum stress, strain, and Young’s modulus.

With the rapid evolution of AM technologies and the range expansion of used materials, the application of AM structures is continuously widening. Therefore, Artificial Intelligence (AI) can be employed to control the factors that affect the mechanical properties of the materials [4].

This study examines the synergy between Additive Manufacturing (AM) and Artificial Intelligence (AI) to develop an AI tool aimed at enhancing the understanding and efficient use of materials in AM. This tool will be used to predict the mechanical properties of the specimens, considering the majority of setting parameters during the AM process, thereby benefiting research and practical applications.

2. The Adaptive Neuro-Fuzzy Inference System (ANFIS)

The modeling of processes and system identification using input–output data has attracted many research efforts. The main components of soft computing, such as fuzzy logic and neural networks, have shown great ability in solving complex nonlinear system identification and control problems. The Adaptive Neuro-Fuzzy Inference System (ANFIS) model [2] is a hybrid predictive model that combines the learning capabilities of Artificial Neural Networks (ANNs) with the reasoning capabilities of fuzzy logic. ANFIS uses input–output sets and a series of if–then fuzzy rules to incorporate the human-like reasoning style of fuzzy inference systems (FISs). The ANFIS model is especially effective in a variety of engineering applications [21,22,23,24,25,26], when data are inconsistent or nonlinear, where conventional methods fail or are too complicated to employ.

A typical ANFIS structure consists of five layers, wherein each layer is constructed by several nodes. The outputs of the previous layer are used as input nodes for the current layer. Considering a first-order Sugeno fuzzy model with two inputs x and y and one output f, a typical rule set with two fuzzy if–then rules can be expressed as follows:

• Rule 1: if (x is A₁) and (y is B₁), then (f₁ = p₁x + q₁y + r₁).
• Rule 2: if (x is A₂) and (y is B₂), then (f₂ = p₂x + q₂y + r₂).

Where x, y are inputs, A_i, B_i are membership functions and p_i, q_i, r_i are consequent parameters, and i is the node number. The corresponding equivalent ANFIS architecture is shown in Figure 1. The entire system architecture consists of five layers, namely, the fuzzy layer (Layer 1), product layer (Layer 2), normalized layer (Layer 3), consequence layer (Layer 4), and total output layer (Layer 5). The number of nodes in other layers (layer 2–4) relates to the number of fuzzy rules (R).

The basic idea behind using neuro-adaptive learning techniques is that it is very simple and allows implementation of multi-input–single-output first-order Sugeno-type FIS. This technique provides a method for the fuzzy modeling procedure to learn information about a dataset, in order to compute the membership function parameters that best allow the associated fuzzy inference system to track the given input/output data. This learning approach takes place prior to the operation of the control system. The ANFIS methodology can be decomposed into four steps:

Step 1: A set of input–output data, to be used as training data, is obtained from the sewing process. Another optional dataset can be used as test data after training.

Step 2: The initial Sugeno-type FIS structure, regarding antecedent membership functions, number of rules, and consequence parameters, is created.

Step 3: The learning process is carried out using the training data to adjust the membership functions, to create the interference rules, and to determine the consequent parameters.

Step 4: The model is validated using the testing data, which have not been used during the training. The objective of this validation is to validate its generalization capability.

3. Experimental Results and Validation

Through a literature review and experiments [9], many factors that influence the mechanical properties of the AM specimens were gathered. By the use of Taguchi methodology and sensitivity analysis, these factors were classified according to their impact on the mechanical properties of the specimens. These factors and their values were selected as an input to the ANFIS model. Bending, tension, and torsion experiments were conducted on various materials with the use of many AM technologies, such as SLA, FFF, SLS, etc. All experiments were conducted according to ASTM standards such as ASTM D638, D695, D7791, D790, and D5279 [27,28,29,30,31,32].

3.1. Gathering Experimental Data

The challenge was to produce a tool capable of predicting the mechanical properties (stress, strain, and Young’s modulus) of as many AM technologies and materials as possible. Thus, a model with twenty-one inputs and three outputs was created. A total of twenty-one parameters are presented, namely, (1) AM Technology, (2) Testing Method, (3) Material, (4) Infill Pattern, (5) Infill Percentage, (6) Layer Thickness, (7) Wall Thickness, (8) Speed, (9) Extruder Temperature, (10) Laser Power Ratio, (11) Bed Temperature, (12) Position on Printer Bed, (13) Incline against Printer Bed, (14) Twist around Axis of Centre of Gravity, (15) Raster Angle, (16) Layers for Alternating Raster Angle, (17) Percentage of First Material, (18) Curing Time, (19) Curing Power, (20) Layer Composition, and (21) Cross-Section. All selected inputs are presented in

Table 1. All initial parameters/model inputs of ANFIS generic model.

Input/Factor	Number of Levels	Levels	Level Code
Input 1 */AM Technology	4 discrete values	FFF/FDM	1
		SLA	2
		SLS	3
		DED	4
Input 2 */Testing Method	3 discrete values	Bending	1
		Tensile	2
		Torsion	3
Input 3 */Material	8 discrete values	ABS + PLA	1
		PLA	2
		ABS	3
		Resin Pro CR	4
		ABS +	5
		PETG	6
		SUS316L	7
		Ti	8
Input 4 */Infill Pattern	6 discrete values	Rectilinear	1
		Triangle	2
		Honeycomb	3
		Spiral	4
		Cross	5
		Diamond	6
Input 5 */Infill Percentage	Continuous (Range values)	Lower Level 0% Higher Level 100%	As input
Input 6 */Layer Thickness	Continuous (Range values)	Lower Level Higher Level	As input
Input 7 */Wall Thickness	Continuous (Range values)	Lower Level Higher Level	As input
Input 8/Speed	Continuous (Range values)	Lower Level Higher Level	As input
Input 9/Extruder Temperature	Continuous (Range values)	Lower Level Higher Level	As input
Input 10/Laser Power Ratio	Continuous (Range values)	Lower Level 0% Higher Level 100%	As input
Input 11/Bed Temperature	Continuous (Range values)	Lower Level 0 °C Higher Level 100 °C	As input
Input 12 */Position on Printer Platform	6	X	1
		X + 30°	2
		X + 45°	3
		X + 60°	4
		X + 90°	5
		Y	6
Input 13 */Inclination against Printer Platform	6	On table	1
		On table +30°	2
		On table +45°	3
		On table +60°	4
		On table +90°	5
		Vertical	6
Input 14 */Twist Angle around Center of Gravity axis	2	On table	1
		On table +90°	2
Input 15 */Raster Angle	7	0°	1
		90°	2
		0°/90°	3
		90°/0°	4
		30°/0°/−30°	5
		45°/−45°	6
		0°/120°/240°	7
Input 16/Layers for Altering Raster Angle (Block)	7	Per 1 layer	1
		Per block—2 layers	2
		Per block—3 layers	3
		Per block—4 layers	4
		Per block—5 layers	5
		Per block—6 layers	6
		Per block—7 layers	7
Input 17/Percentage of First Material	Continuous (Range values)	Lower Level 0% Higher Level 100%	As input
Input 18/Curing Time	Continuous (Range values)	Lower Level Higher Level	As input
Input 19/Curing Power	4 discrete values	0	0
		UT1	1
		UT2	2
		UT3	3
Input 20/Layer Composition	2	Sandwich	1
		Wave	2
Input 21/Cross-Section	3 discrete values	Rectangle	1
		Dogbone	2
		Circle	3

* Mandatory input.

, along with their values and the code given to each value for use within the model.

All AM processes and materials presented in this study were used in the AM Laboratory Mechanical Engineering Department, University of West Attica.

3.2. The ANFIS Generic Model

Such predictive models require a high quantity of input data to produce accurate outputs. During the development of the methodology and tool creation, there was a sufficient amount of data on the FFF technology, bending test method, and PLA material. Thus, all predictions were based on such data, which are presented in

Table 2. Three-point bending experimental data—printing parameters.

S/N	Infill Pattern	Infill (%)	Layer Thickness (mm)	Speed (mm/s)	Temperature (°C)	Bed Temperature (°C)	Position on Bed	Twist Angle (°)	Inclination (°)
1	2	50	0.07	50	200	60	1	1	5
2	2	75	0.07	50	200	60	3	1	5
3	3	100	0.18	50	200	60	5	1	7
4	2	75	0.18	50	200	60	5	1	5
5	2	100	0.18	50	200	60	1	1	5
6	3	50	0.18	50	200	60	3	1	7
7	2	100	0.3	50	200	60	3	1	5
8	2	50	0.3	50	200	60	5	1	5
9	3	75	0.3	50	200	60	1	1	7
10	1	60	0.18	25	215	55	1	1	6
11	3	60	0.18	38	215	55	5	1	7
12	2	60	0.18	50	215	55	1	5	5
13	3	60	0,18	25	230	55	1	5	7
14	2	60	0.18	38	230	55	1	1	5
15	1	60	0.18	50	230	55	5	1	6
16	2	60	0.18	25	245	55	5	1	5
17	1	60	0.18	38	245	55	1	5	6
18	3	60	0.18	50	245	55	1	1	7
19	1	15	0.18	25	215	55	1	1	6
20	3	15	0.18	38	215	55	5	1	7
21	2	15	0.18	50	215	55	1	5	5
22	3	15	0.18	25	230	55	1	5	7
23	2	15	0.18	38	230	55	1	1	5
24	1	15	0.18	50	230	55	5	1	6
25	2	15	0.18	25	245	55	5	1	5
26	1	15	0.18	37.5	245	55	1	5	6
27	3	15	0.18	50	245	55	1	1	7
28	1	15	0.18	25	180	25	1	1	6
29	3	15	0.18	38	180	25	5	1	7
30	2	15	0.18	50	180	25	1	5	5
31	3	15	0.18	25	195	25	1	5	7
32	2	15	0.18	37.5	195	25	1	1	5
33	1	15	0.18	50	195	25	5	1	6
34	2	15	0.18	25	210	25	5	1	5
35	1	15	0.18	38	210	25	1	5	6
36	3	15	0.18	50	210	25	1	1	7
37	1	60	0.18	25	180	60	1	1	6
38	3	60	0.18	37.5	180	60	5	1	7
39	2	60	0.18	50	180	60	1	5	5
40	3	60	0.18	25	195	60	1	5	7
41	2	60	0.18	37.5	195	60	1	1	5
42	1	60	0.18	50	195	60	5	1	6
43	2	60	0.18	25	210	60	5	1	5
44	1	60	0.18	37.5	210	60	1	5	6
45	3	60	0.18	50	210	60	1	1	7

. Some of the specimens used for the bending test are visually presented in Figure 2. Figure 3 illustrates the bending test (a) conducted according to ASTM D790 [29] and the specimen after the test (b).

Each experiment was repeated five times, according to the ASTM standard. In

Table 3. Three-point bending experimental data—results.

S/N	Stress Average (MPa)	Stress Standard Deviation	Strain Average (%)	Strain Standard Deviation	Young’s Modulus (GPa)
1	14.00	1.10	5.80	0.62	6.03
2	12.00	0.67	7.00	0.52	4.29
3	13.00	0.66	5.00	0.71	6.50
4	13.00	0.60	8.50	0.72	3.82
5	8.50	0.41	5.00	0.45	4.25
6	18.00	0.62	6.00	0.77	7.50
7	8.50	0.34	5.00	0.24	4.25
8	8.00	0.78	2.50	0.49	8.00
9	6.00	0.73	4.50	0.58	3.33
10	3.20	0.45	2.50	0.42	3.20
11	4.00	0.41	3.40	0.64	3.02
12	1.00	0.35	0.82	0.68	3.20
13	2.00	0.35	1.50	0.49	3.59
14	3.00	0.42	2.45	0.74	3.38
15	4.00	0.42	3.00	0.66	3.76
16	2.00	0.57	1.50	0.62	3.85
17	1.50	0.24	1.00	0.42	4.43
18	4.00	0.44	3.45	0.32	3.51
19	3.75	0.70	2.50	0.64	4.64
20	4.00	0.55	2.50	0.47	5.06
21	2.50	0.47	1.60	0.56	5.05
22	2.00	0.23	1.20	0.38	5.51
23	4.00	0.40	2.60	0.44	5.20
24	3.00	0.51	1.95	0.59	5.31
25	4.00	0.48	2.50	0.57	5.64
26	1.50	0.33	1.05	0.47	5.14
27	4.00	0.53	2.55	0.54	5.77
28	4.08	0.75	4.78	0.49	2.14
29	5.09	0.62	4.51	0.77	2.82
30	4.03	0.80	1.86	0.83	5.41
31	4.27	0.52	1.85	0.42	5.77
32	4.53	0.79	4.44	0.55	2.55
33	4.45	0.67	4.33	0.65	2.57
34	3.96	1.04	4.28	0.98	2.32
35	3.13	0.75	1.90	0.53	4.12
36	5.29	0.54	4.70	0.62	2.81
37	2.73	0.83	5.18	0.92	0.74
38	2.64	0.76	3.75	0.81	0.99
39	2.66	0.48	2.77	0.39	1.35
40	1.69	0.52	2.80	0.64	0.85
41	3.03	0.62	4.63	0.52	0.92
42	2.98	0.62	4.80	0.58	0.87
43	3.36	0.83	3.82	0.78	1.24
44	1.98	0.40	2.53	0.37	1.10
45	3.01	0.70	4.90	0.69	0.86

, the three-point bending results are presented as average values along with their standard deviations. Stress and strain (Figure 4) produced by the experimental data and the Young’s modulus were calculated based on Equation (1):

$$w_0=\frac{P L^3}{48 E I}$$

(1)

where w₀ is the deflection (mm), P is the concentrated load (N) applied on the center of the beam, L is the distance between the two supports of the beam (mm), I is the second moment of area (mm⁴), and E is the Young’s modulus. The calculation of the I is based on Equation (2).

$$I={\displaystyle \frac{a^3 b}{12}}$$

(2)

where a is the beam’s depth (mm), and b the beam’s width (mm). All bending specimens were square sections (□8 mm). Thus, by knowing the beam dimensions, experimentally measuring the central deflection and the applied force, it is possible to calculate the Young’s modulus E.

Considering that ANFIS models have a single output, three separate models were developed, each corresponding to one of the outputs.

The fuzzy inference system (FIS) is generated following the Subtractive Clustering method [33], as suggested for systems with more than six input parameters. The training process for the ANFIS model involved preparing the experimental data by randomly splitting the data into training and validation sets. Figure 5 shows the scattering of the output values. Specifically, the training dataset is depicted as circles, and the checking dataset is depicted as pluses. For the generation of the initial model for ANFIS training, Subtractive Clustering is applied. Subtractive Clustering method groups the data in clusters based on the given range of influence. The system locates the center of each cluster and defines its effect according to that range.

The model structure, combining fuzzy logic and neural networks, was trained using a hybrid learning algorithm that adjusts membership function parameters through least-squares and backpropagation gradient descent methods. Training continued for a specified number of epochs until the error converged to a relatively low value. The training error is calculated as the difference between the predicted output of the ANFIS model and the actual experimental value for each data point in the training set. The error calculation was performed using the Root Mean Square Error (RMSE) for both training and validation sets, providing a measure of the model’s performance and generalization capability. Figure 6 illustrates this process, showing the reduction in RMSE over successive epochs, indicating the model’s successful training and validation. Figure 6 shows the checking error as dots on top and the training error as asterisks on the bottom. The FIS test against the training data (Figure 7) revealed a well-trained system, but the test against the checking data (Figure 8) showed low performance. The RMSE of the model equals to 9.17, 20% within the range of the outputs, caused probably by the high number of the examined factors compared to the low number of the entries. Regarding the RMSE for strain and Young’s modulus, the values for the index error were correspondingly high (51% and 41% within the range of the data for each one, respectively).

3.3. The ANFIS Bending Model

Based on the analysis of the generic ANFIS model, a reduced focus on bending and PLA material was produced. This decision was motivated by the relatively higher number of experimental available data of these two inputs (PLA and bending).

The proposed bending model was based on the experimental data of FFF technology, bending test method, and PLA material. Thus, nine inputs were used, i.e., (1) Infill Pattern, (2) Infill Percentage, (3) Layer Thickness, (4) Speed, (5) Extruder Temperature, (6) Bed Temperature, (7) Position on Printer Bed, (8) Incline against Printer Bed, and (9) Raster Angle, as presented in

Table 4. Datasheet of the ANFIS bending model.

Infill Pattern	Infill (%)	Layer Thickness (mm)	Speed (mm/s)	Temperature (°C)	Bed Temperature (°C)	Position on Bed	Twist angle (°)	Inclination (°)
2	50	0.1	50	200	60	1	1	5
2	75	0.1	50	200	60	3	1	5
3	100	0.1	50	200	60	5	1	7
2	75	0.2	50	200	60	5	1	5
2	100	0.2	50	200	60	1	1	5
3	50	0.2	50	200	60	3	1	7
2	100	0.3	50	200	60	3	1	5
2	50	0.3	50	200	60	5	1	5
3	75	0.3	50	200	60	1	1	7

.

A further examination of the data revealed three areas where the responses vary from low to quite accurate. Taking this into account, a higher level of investigation on the settings of the FIS is conducted. Figure 9 illustrates the five processing layers and the connections between them within the structure of the ANFIS model. The dataset is divided into training (circles) and checking datasets (pluses), as depicted in Figure 10. Figure 11 shows that the system achieves the best convergence since the first epoch due to limited inputs, with the checking error depicted as dots on top and the training error as asterisks on the bottom.

For a better understanding of Sugeno-type fuzzy rules, a pictorial view of fuzzy rules is presented in Figure 12. Figure 13 illustrates the surface plots that represent the mapping from the inputs to the outputs. Each surface plot indicates the correlation between two inputs and the output (maximum stress) expressed by different colors. Warmer colors like yellow indicate higher activation levels, while cooler colors like blue indicate lower activation levels. Finally, Figure 14 represents the experimental and predicted values for the maximum stress against the checking data. The maximum stress is equal to 1.17, which is compared to the range of the checking outputs equal to 9.75%.

Similarly, two ANFIS models are developed for the strain and the Young’s modulus based on the same experiments. For both models, the training error equals to zero. Figure 15 and Figure 16 depict the experimental and predicted values for the two cases, respectively. Regarding the Young’s modulus, it equals to 3049 MPa, which reflects 40% of the data range. However, the strain equals to 2.21, reduced by 20% within the data range.

4. Analysis of Model Performance

The ANFIS generic model, developed for 21 inputs, showed inadequate performance, as expected, in achieving satisfactory results for the analyzed properties of the specimens. Although the training process showed excellent recognition of the correlations of the 3D printing parameters with the output values, the test against the checking data proved that the entries in the dataset are few to support the method. The resultant RMSE against checking data is 20%, 41%, and 51% within the range of data for maximum stress, Young’s modulus, and strain, respectively.

The ANFIS bending model, consisting of nine inputs, exhibited improved RMSE for maximum stress and strain, equal to 9.75% and 20%, respectively. The fact that the index for the Young’s modulus was 40% seems to be illusory. It could be evidence that the quantity of the available data was not adequate.

The observed difference in the modeling accuracy of stresses compared to Young’s modulus and strain can be explained by several factors. Firstly, stresses, particularly maximum stress, are more directly influenced by key input parameters such as infill density, layer height, and printing speed, which directly affect the load-bearing capacity and stress distribution within the material. In contrast, Young’s modulus and strain percentage are more sensitive to microstructural variations and intrinsic material properties, which may not be as effectively captured by the input parameters used. Additionally, the experimental measurement of maximum stress is typically more straightforward and less prone to error compared to Young’s modulus and strain, which can be influenced by small experimental errors and noise. The variability in the experimental data for Young’s modulus and strain can be higher due to the complex interactions between material properties and the printing process, introducing noise into the training data and making it more challenging for the model to learn accurate patterns. Lastly, the ANFIS model might be more adept at capturing the relatively simpler relationship between input parameters and maximum stress, whereas the relationships for Young’s modulus and strain might be more complex, leading to potential overfitting or underfitting issues. These considerations underscore the importance of refining input parameters and model structures to improve predictions for Young’s modulus and strain percentage.

As a concluding remark, the performance increases when using 9 input parameters compared to 21 input parameters. This is explained by the fact that two distinct models are developed in this study: one with 21 inputs designed to be more general, and another with 9 inputs specifically focused on bending. The general model with 21 inputs aims to capture a wide range of physical effects and is therefore applicable to a broader spectrum of AM technologies and materials. However, the data available for this model are less comprehensive, which can limit its performance. In contrast, the bending model with nine inputs is customized for specific parameters that directly influence the bending behavior of the samples. The data used for the bending model are more extensive, allowing for a more precise training process.

While it is true that reducing the number of input parameters may exclude certain physical effects, the selected parameters in the bending model are those most critical to capturing the mechanical behavior under bending conditions. This approach strikes a balance between model simplicity and accuracy, demonstrating that a focused, well-trained model can outperform a more general one with fewer but more relevant input parameters.

5. Conclusions

The main focus of this research aimed at establishing a novel, flexible method for predicting the mechanical properties of Additively Manufactured parts through Artificial Neural Networks and fuzzy logic. Two ANFIS models were developed, i.e., a generic model that requires additional experimental data from various AM technologies, materials, and mechanical tests, and a focused model specifically designed for predicting the mechanical properties of PLA specimens produced using FFF in bending tests.

In line with the objective of optimizing the AM fabrication process, the majority of the relevant studies typically focus and examine a limited number of parameters within the strict boundaries of the experiments. The innovative aspect of this research is the development of a predictive model capable of adapting to any AM technology and material, while considering the various process parameters that affect the maximum stress and strain and Young’s modulus of the final product.

The study highlights the performance improvement achieved by using 9 input parameters compared to 21 input parameters. This is due to the development of two distinct models: one with 21 inputs designed to be more general, and another with 9 inputs specifically focused on bending. The general model with 21 inputs aims to capture a wide range of physical effects and is therefore applicable to a broader spectrum of AM technologies and materials. However, the data available for this model are less comprehensive, which can limit its performance. In contrast, the bending model with nine inputs is customized for specific parameters that directly influence the bending behavior of the samples. The data used for the bending model are more extensive, allowing for a more precise training process.

Comparing the experimental results with the numerically modeled mechanical parameters, we observe a good correlation in certain aspects while identifying areas that require further refinement. The numerically predicted maximum stress and strain showed reasonable agreement with the experimental values, with RMSE values within 20% and 9.75%, respectively, suggesting that the model is fairly accurate for these parameters. However, the prediction for Young’s modulus exhibited a higher RMSE of approximately 40%, primarily due to one outlier with a significant deviation. This indicates that, while the model captures the general trend, the accuracy for Young’s modulus can be improved with additional data and potential refinement of the model.

The results of the developed systems revealed the potential of the method to provide successful predictions, highlighting the necessity for more input data. This would enable an accurate initial estimation of the applied AM process (including AM technologies, materials, structure settings, and process parameters), thereby avoiding the waste of crucial resources.

Despite the potential of this novel approach, it is clear that further experiments are necessary to enhance the model. Future experiments will enrich the dataset with results from different AM technologies, materials, and experimental studies. Given ANFIS’s proven capability to identify nonlinear relationships in the field of mechanical properties, it can be applied to other areas of research. For example, examining the surface quality of AM parts using ANFIS, while integrating the knowledge gained from this study, would be particularly interesting.

In conclusion, the developed ANFIS model shows great promise for predicting the mechanical properties of FFF-printed PLA specimens with high accuracy. The findings highlight the importance of optimizing input parameters to enhance model performance, providing a valuable tool for researchers and practitioners in the field of additive manufacturing. Future research will further validate the model with diverse datasets and investigate ways to include additional relevant parameters without sacrificing model simplicity and performance along with continuous addition of experimental data on all available AΜ technologies, materials, and types of experimental tests in mechanics.