Multi criteria optimization of FDM process parameters for NylonAF80 filaments using CRITIC CoCoSo and machine learning approaches

Abstract

This study aimed to optimize the fused deposition modeling (FDM) process parameters for an 8% aramid fiber-reinforced polyamide filament (NylonAF80) to enhance the quality of printed parts. Six parameters were varied: the slice height, nozzle temperature, bed temperature, deposition speed, raster orientation, and build orientation. Cuboid samples with a central circular hole were printed using Taguchi’s L18 orthogonal array, and evaluated for volumetric error, average roughness, and Shore D hardness. The CRITIC-CoCoSo technique identified optimal settings of 0.1 mm slice height, 255 °C nozzle temperature, 100 °C bed temperature, 40 mm/s deposition speed, 90° raster orientation, and on-edge build orientation to maximize the multi-response performance index. Sensitivity analysis using different weighting schemes and MCDM methods showed strong correlations (> 0.93) between rankings. The decision tree algorithm exhibited superior performance to k-nearest neighbor, stochastic gradient descent, and logistic regression in classifying output responses, achieving 88.9%, 94.4%, and 100% accuracies for hardness, volumetric error, and roughness, respectively, at an 80:20 split ratio. Slice height was the most influential factor for all responses. FESEM microstructural analysis revealed pores and voids in the samples printed under extreme conditions and at high slice heights. These findings provide valuable insights for optimizing FDM parameters to improve the quality of NylonAF80 parts for industrial applications.

Introduction

In recent decades, industrial sectors have witnessed a dramatic change in the way prototypes and end-user products are manufactured, owing to the advent of additive manufacturing techniques^1,2. Additive Manufacturing (AM) is a fascinating technology that began its journey as a toy-making process in the mid 1980’s, by building solid objects from a digital model by adding layers in a successive form^3,4. This process has substantial benefits compared to traditional manufacturing techniques, such as mass customization, high design freedom and flexibility, low waste, and cost minimization, by eliminating the need for tools, process planning, and highly skilled labor⁵. The attractive advantages of AM have benefited various sectors, such as aerospace, automotive, engineering, medical, and food systems⁶. AM can be classified into seven major categories: vat photopolymerization (VP)⁷, material jetting (MJ)⁸, binder jetting (BJ)⁹, material extrusion (ME)^10,11, sheet lamination (SL)^12,13, powder bed fusion (PBF)¹⁴, and directed energy deposition (DED)¹⁵. Fused deposition modeling (FDM)^16,17 is the preferred AM process owing to its notable process characteristics, such as fabrication simplicity, low cost, ability to produce more complicated parts, and wider material choice¹⁸. FDM creates solid objects by extruding a thin filament through a heated nozzle in a molten state and depositing layers one over the other. The extruded filament is heated below its melting point and undergoes cooling to solidify and form the desired object shape after deposition over a heated or non-heated bed¹⁹. Despite their significant advantages, AM-processed parts suffer from certain shortcomings, such as low surface quality, poor mechanical properties, energy wastage, and long manufacturing time²⁰. The selection of appropriate process parameters is vital for obtaining products with the desired quality and excellent mechanical properties for peak performance. Many researchers^21–25 have discussed different issues pertinent to the FDM process, which has gained momentum in recent years to enhance the ability of the process to address the prevailing global demand for efficient and economical products. Rajmohan et al.²⁶ reported the density, microhardness, surface roughness, and processing time of ABS samples prepared using the FDM process by varying the infill percentage, layer thickness, and bed temperature. Higher infill percentages and bed temperatures led to a significant increase in both surface roughness and microhardness. Ramesh and Panneerselvam²⁷ optimized the FDM parameters for nylon filaments to enhance their mechanical properties such as tensile strength, impact strength, and flexural strength. The authors varied the fill density, slice height, and print speed to understand their influence and found that the fill density was the dominant factor affecting the properties studied. Elena et al.²⁸ conducted a comparative study on the mechanical properties of FDM-printed and injection-molded parts and reported that the former had considerably inferior mechanical properties. Ouballouch et al.²⁹ evaluated the dimensional accuracy and mechanical properties of fiber-reinforced polyamide parts processed using FDM and concluded that the dimensional accuracy of Kevlar-reinforced parts is significantly affected by the process parameters compared to that of glass fiber-reinforced polyamide parts. Shakeri et al.³⁰ focused on controlling the shape deviation of PA 6 parts processed using the FDM through the Taguchi method and observed cylindricity and circularity. A low layer thickness results in fewer geometrical deviations. Ailing et al.³¹ studied the porosity of aramid fiber-reinforced composite filaments using micro-CT by varying the printing speed, layer thickness, and spacing. The authors developed a 0° fiber orientation mathematical model, and an absolute error of 0.26% was reported in the validation trials. Mohammed Raffic et.al.³² assessed the dimensional accuracy of nylon composite filaments reinforced with 8% aramid fiber and reported that layer thickness was the influencing parameter.

The FDM process has different limitations associated with printed parts, such as poor dimensional accuracy and surface finish, inferior mechanical properties, higher processing time, and anisotropic nature, which hinder their adoption for end-use product manufacturing. Conflicting and challenging output responses need to be considered for optimization when combined using multi-response optimization techniques. Abas et al.³³ employed the WASPAS technique to optimize the FDM parameters for PLA materials and reported the optimal level of input parameters for controlling the dimensional deviations. Sakthivel and Vinod³⁴ adopted the grey Taguchi and TOPSIS techniques to optimize the FDM parameters for developing an automotive component. The optimal process parameters obtained using the GRA method were verified using the TOPSIS and AHP methods, and a similarity of 27% was observed in the ranking. Saeed et al.³⁵ integrated techniques such as response surface methodology, grey relational analysis, and grey wolf optimization to optimize the FDM process parameters for carbon fiber-reinforced PA12 parts. The optimal process parameters led to a decrease in the surface roughness and an enhancement of the mechanical properties. Selvam et al.³⁶ deployed response surface methodology (RSM) and particle swarm optimization (PSO) to optimize the FDM process parameters for ABS to minimize the surface roughness and printing time. The optimal process parameter levels obtained were validated through the WASPAS method, and the optimum levels recommended through the PSO method were highly beneficial. Raja and John³⁷ selected an appropriate FDM machine using the fuzzy TOPSIS technique by evaluating different criteria. This study explored the Cube Pro Duo machine as the optimal machine for a non-government organization. Towaiq et al.³⁸ applied the preference selection index (PSI) technique to optimize the FDM process parameters, such as layer thickness, infill density, and infill pattern, to reduce the time cost and enhance the mechanical properties. The study involved analyzing the experimental outcomes under three different cases and concluded that the PSI method is efficient for multi-objective optimization.

Machine learning techniques are effective algorithms that can learn a dataset to identify underlying patterns and make accurate predictions of future outcomes. Lalitha et al.³⁹ considered the NIST benchmark for evaluating dimensional accuracy and its prediction using machine-learning algorithms. The predictions of the machine learning algorithms were 97% accurate and regression equations were developed. Feng et al.⁴⁰ combined the capabilities of machine learning and numerical simulations to optimize the FDM process parameters for PEEK materials. The authors reported that the combination has excellent potential for optimizing the FDM process parameters, and that the XGBoost model performed better.

The cited literature from past studies^41–47 reveals the significant effects of FDM control factors on the part quality and properties of the end product. The selection of the optimal FDM control factor and its level are of utmost importance to attain the desired part quality. Based on this context, the current research considered six different FDM control factors, namely slice height, nozzle temperature, bed temperature, deposition speed, raster orientation, and build orientation, to maximize shore D hardness and minimize the volumetric error and roughness average. Cuboid samples from polyamide filaments with 8% aramid fiber reinforcement were prepared according to Taguchi’s L₁₈ orthogonal array, and the experimental outcomes were analyzed using the CRITIC-CoCoSo technique for optimal factor levels towards combined objectives. Sensitivity analysis was performed by applying different weight values to the responses and different MCDM techniques to observe the changes in the alternative ranking. In addition, classification-based machine learning algorithms were deployed to analyze the experimental outcomes, and the decision tree structure represented the significant input factors. The FESEM analysis of the printed samples revealed the presence of pores and voids. Figure 1 shows the proposed research methodology for improving the quality of parts printed using the FDM process.

Fig. 1.

Proposed Research Methodology for FDM part quality improvement.

Research materials and methods

The filament material considered for this research and the proposed methodology for performing the experimental work are described in detail in this section.

Filament material

A polyamide 12 filament with 8% short-cut aramid fiber reinforcement was used to prepare the experimental samples. The filament was manufactured and distributed by Filamentum Industrial (Czech Republic) and is known for its hardness, wear, creep, and heat resistance under high loads. Filament material was used to make the bearings and cogwheels.

Experimental design layout

The current study varied six different FDM factors: slice height, nozzle temperature, bed temperature, deposition speed, raster orientation, and build orientation. The slice height was varied at six levels and all other parameters were fixed at three levels. According to the fractional factorial design, 18 experimental trials were recommended by Minitab 17.0, using Taguchi’s orthogonal array. Table 1 lists the different FDM parameters considered as control factors and their corresponding levels. Table 2 presents the experimental design layout for the sample preparation and experimentation.

Table 1.

FDM parameters and levels.

S. No	Control factors	Symbol	S.I Unit	Level 1	Level 2	Level 3	Level 4	Level 5	Level 6
1	Slice height	A	mm	0.1	0.14	0.18	0.22	0.26	0.3
2	Nozzle Temperature	B	°C	235	245	255	–	–	–
3	Bed Temperature	C	°C	90	100	110	–	–	–
4	Deposition Speed	D	mm/s	30	40	50	–	–	–
5	Raster Orientation	E	°	0	45	90	–	–	–
6	Build Orientation	F	–	Horizontal	On-edge	Vertical	–	–	–

Table 2.

Constant FDM parameters.

S. No	Fixed Parameters	Value / Characteristic
1	Nozzle diameter	0.4 mm
2	Filament diameter	1.75 mm
3	Filament colour	Natural
4	Shell thickness	0.4 mm
5	Infill density	66%
6	Infill pattern	Grid

The layer thickness was varied across six levels due to its significant influence on the dimensional accuracy, surface quality, and mechanical performance of FDM-fabricated parts. In the present study, a hardened steel nozzle with a diameter of 0.4 mm was employed; accordingly, the minimum and maximum layer thicknesses were selected as 0.1 mm and 0.3 mm, respectively. In accordance with established FDM processing guidelines, the upper limit of the layer thickness was restricted to approximately 80% of the nozzle diameter to ensure stable material deposition and adequate interlayer bonding⁴⁸. The manufacturer’s data were used to fix the range of parameters such as extrusion temperature, print bed temperature, and printing speed. Determining the critical values of extrusion temperature and speed is crucial for the structural formation of the printed part because the process involves subsequent cycles of heating and cooling. Both the first layer and successive layers deposited on top of it were supported by the bed temperature. The levels of the raster angle and part orientation factor parameters were set to the standard values used in the majority of previous studies^49–52. Support structures are formed when the parts are oriented at an angle. A typical part orientation without necessity has negative impacts, such as increasing printing time, material consumption, and the need for post-processing treatment. Table 2 shows that the FDM parameters remained constant during the printing of the experimental samples, and Table 3 presents the design plan.

Table 3.

Experimental design plan.

Trial No	A	B	C	D (mm/s)	E	F
	(mm)	(°C)	(°C)		(°)
1	1	1	1	1	1	1
2	1	2	2	2	2	2
3	1	3	3	3	3	3
4	2	1	1	2	2	3
5	2	2	2	3	3	1
6	2	3	3	1	1	2
7	3	1	2	1	3	2
8	3	2	3	2	1	3
9	3	3	1	3	2	1
10	4	1	3	3	2	2
11	4	2	1	1	3	3
12	4	3	2	2	1	1
13	5	1	2	3	1	3
14	5	2	3	1	2	1
15	5	3	1	2	3	2
16	6	1	3	2	3	1
17	6	2	1	3	1	2
18	6	3	2	1	2	3

FDM control factor definitions

1. Slice height: The thickness of an individual layer is deposited one over the other to obtain a 3D object. It is also known as the layer height and is represented in millimeters (mm).

2. Nozzle temperature: The temperature at which the filament is extruded through the nozzle. The nozzle must be preheated to the required temperature before the extrusion of the filament. The nozzle temperature was varied from one filament to another. Its unit is °C.

3. Bed temperature: The temperature that must be maintained in the print bed to attain better adhesion between the initially deposited layers. The NylonAF 80 bed temperature ranges from to 90 to 110 °C.

4. Deposition speed: The speed at which the filament is deposited using an extrusion nozzle. Every material had a nominal speed range for the optimal results, represented in mm/s.

5. Raster orientation: The angle at which the raster is deposited inside the part and its angle with respect to the horizontal axis are considered as a reference. Its unit is degrees (angular).

6. Build orientation: The style in which the part is built in a 3D printer, which can be considered based on the part to be printed. Horizontal, on-edge, and vertical are the basic strategies available, and inclined deposition with respect to the print bed is also possible at the cost of support structures, which increases the printing time.

Experimental works

This section details the preparation of the experimental samples and methodology used to evaluate the output responses for further analysis.

Sample preparation

A cuboid sample with dimensions of 30 × 25 × 10 mm was printed as per the experimental plan using an Ultimaker S3 professional FDM printer. The sample consists of a full-depth circular hole at its center. The rationale for considering a circular hole is that the proposed sample material, nylonAF80, is used to fabricate gears and bearings employed in potential industrial applications. The sample was filled with 66% material, and a grid pattern was used. Figure 2 shows the samples prepared using FDM printing. Figure 3 shows the different orientations adopted in this study. Table 4 lists the specifications of the FDM machine used in this study.

Fig. 2.

NylonAF80 Samples.

Fig. 3.

Different orientation of samples during printing (a) Flat (b) Onedge and (c) Upright.

Table 4.

Ultimaker S3 FDM machine specifications.

S. No	Machine Particulars	Value / Characteristic
1	Build volume	230 × 190 × 200 mm
2	Feeder type	Dual geared feeder
3	Extrusion head	Dual extrusion head
4	Build speed	< 24 mm3/s
5	Nozzle heatup time	< 2 min
6	Maximum power output	350 W

The reason behind considering grid infill patterns in the current research is that they strike a good balance between the strength and efficiency of the materials. Its crossed structure permits even load distribution, which makes the printed parts more stable. Compared to unidirectional infill patterns, the pattern exhibits fairly isotropic mechanical behavior in the XY plane. In the same way, using an infill density of 66% reduces the amount of material used, thermal stresses, and the time it takes to print the part. The main benefit of FDM printing is that it makes parts with custom filling of material, which gives an insight into the performance of printed parts in load- and non-load-bearing applications.

Measurement of output responses

The current study evaluated three different output responses: volumetric error (VE), face hardness, and surface roughness of the prepared sample using standard equipment. The volumetric error resulting from the workpiece was measured using a digital Vernier caliper, and the dimensional variations in the individual dimensions and deviations in the volume were calculated. The face hardness of the sample was evaluated using a Shore D hardness durometer by plunging three different regions of the sample, and the average value was considered for further analysis. The surface roughness of the sample was recorded at three different regions using a Marsurf VD280 surface roughness tester, and the average value was considered for evaluation and minimization.

Face hardness

The hardness of a printed sample is an important property that is crucial for materials to resist wear and abrasion. Similarly, to withstand higher mechanical loads without deformation, the maximum Shore D hardness is vital. Table 5 lists the specifications of the Shore D hardness dynamometer used in this study.

Table 5.

Shore D hardness durometer specifications.

S. No	Particulars	Value / Characteristic
1	Measurement Scale	Shore D hardness (0 – 100 HD)
2	Measuring Range	0 – 100 Shore D
3	Resolution	0.5 HD
4	Accuracy	± 1 Shore D (approx.)
5	Measuring Force	44.5 N (5 kgf) typical for Shore D
6	Indenter Type	Conical point, 30° angle, tip radius = 0.1 mm

Volumetric error

A higher volumetric error resulting in a part could lead to misalignment, which has a severe impact on the performance of the individual parts; therefore, the entire system may fail to meet the desired function. The individual dimensions of the sample were measured separately and also the volumetric deviation. Table 6 represents the specifications of the digital Vernier caliper were used to measure the dimensions and evaluate the volumetric error of the sample.

Table 6.

Digital vernier caliper specifications.

S. No	Particulars	Value / Characteristic
1	Measuring Range	0 to 150 mm
2	Resolution	0.01 mm
3	Accuracy	± 0.02 mm
4	Sensor Type	AOS (Advanced Onsite Sensor)
5	Material	Hardened stainless steel

Roughness average

The average roughness is an important quality characteristic that affects the aesthetic quality of the final product and acts as a stress concentrator. Table 7 lists the specifications of the surface roughness tester used in the current study, which has a severe impact on the tensile strength, impact resistance, and fatigue resistance of the printed samples.

Table 7.

Marsurf VD280 surface roughness tester specifications.

S. No	Particulars	Value / Characteristic
1	Resolution (roughness probe)	7.6 nm and 0.76 nm (dual range)
2	Probe arm length (roughness)	45 mm – 135 mm
3	Measuring speed	Up to 10 mm/s
4	Traversing length (X)	0.1 mm – 280 mm
5	Measuring force	Roughness probe: 0.7 mN

Prior to experimentation, all the measurement tools utilized in this study were calibrated using traceable standards. A digital Vernier caliper was calibrated using certified gauge blocks and precision standards to measure the dimensions. A calibrated roughness tester with traceable roughness reference specimens and probing artifacts was used to evaluate the surface roughness, and a calibrated Shore D durometer that was validated against certified hardness blocks was used to measure hardness. Each measurement was repeated thrice at several specimen sites to ensure repeatability.

Results and discussions

The calculated and measured values of the output responses were analyzed to understand the effects of the FDM control factors. Table 8 presents the experimental outcomes for the individual trials.

Table 8.

Experimental outcomes.

Trial No	A	B	C	D (mm/s)	E	F	Hf	VE	Ra
	(mm)	(°C)	(°C)		(°)			(mm3)	(μm)
1	1	1	1	1	1	1	46.33	− 172.73	16.59
2	1	2	2	2	2	2	56.67	− 101.33	13.94
3	1	3	3	3	3	3	51.67	− 148.29	17.44
4	2	1	1	2	2	3	49.67	− 185.15	15.35
5	2	2	2	3	3	1	49.33	− 106.47	25.14
6	2	3	3	1	1	2	60.67	− 135.79	16.49
7	3	1	2	1	3	2	54.00	− 235.92	13.93
8	3	2	3	2	1	3	52.67	− 389.17	14.51
9	3	3	1	3	2	1	54.67	527.24	27.54
10	4	1	3	3	2	2	48.00	− 377.29	15.07
11	4	2	1	1	3	3	43.67	− 260.21	11.44
12	4	3	2	2	1	1	48.33	− 285.53	14.32
13	5	1	2	3	1	3	29.67	− 515.46	16.15
14	5	2	3	1	2	1	43.00	− 426.11	26.98
15	5	3	1	2	3	2	57.67	− 176.07	16.31
16	6	1	3	2	3	1	41.67	− 277.46	18.46
17	6	2	1	3	1	2	53.33	− 553.52	22.60
18	6	3	2	1	2	3	45.67	− 146.61	18.24

According to the experimental results, the sixth experimental trial using the factor combination of A2B3C3D1E1F2 (0.14 mm slice height, 255° nozzle temperature, 110° bed temperature, 30 mm/s deposition speed, 0° raster orientation, and on-edge positioned printing) shows the highest face hardness of 60.67. Although the current study only considered a 66% infill density (2/3 of the part volume) to save printing time and material consumption, the hardness obtained was 87% of the hardness suggested by the filament manufacturer. According to the manufacturer data, the Shore D hardness of the NylonAF80 filament material is 70. 29.67 A5B1C2D3E1F3 had the lowest face hardness (0.26 mm slice height, 235° nozzle temperature, 100° bed temperature, 50 mm/s deposition speed, 0° raster orientation, and vertical mounted printing).

The volumetric error measured in the sample indicated that the sample underwent severe warping and shrinkage during printing. The transition of the filament material after flowing through the nozzle during extrusion from a higher temperature to room temperature induces thermal stresses and distortions, which promote warping and material shrinkage. Most samples had negative values, indicating warpage and shrinkage. Moreover, another main cause of the negative volumetric error in the aramid-reinforced nylon composite is the thermal shrinkage of the polymer matrix during cooling, which is further affected by the fiber–matrix interactions. It is known that, depending on processing conditions and cooling pace, nylon-based materials can shrink by 1% to 2%. Anisotropic shrinkage and warpage are encouraged by the presence of aramid fibers, which limits in-plane contraction and lowers the overall measured volume. The lowest volumetric error of 101 mm³ (negative) was obtained with A2B1C2D2E2F2—0.14 mm slice height, 235° nozzle temperature, 100° bed temperature, 40 mm/s deposition speed, 45° raster orientation, and edge-mounted printing. The maximum volumetric error of 527.24 mm³ (positive) was obtained with an A3B3C1D3E2F1 of 0.18 mm slice height, 255° nozzle temperature, 90° bed temperature, 50 mm/s deposition speed, 45° raster orientation, and flat oriented printing.

The 11th experimental trial (A4B2C1D1E3F3), corresponding to a slice height of 0.22 mm, nozzle temperature of 245 °C, print bed temperature of 90 °C, deposition speed of 30 mm/s, raster orientation of 90°, and upright build orientation, exhibited the minimum average surface roughness of 11.44 µm. In contrast, the 9th experimental trial (A3B3C1D3E2F1), characterized by a slice height of 0.18 mm, nozzle temperature of 255 °C, print bed temperature of 90 °C, deposition speed of 50 mm/s, raster orientation of 45°, and flat build orientation, resulted in the maximum average roughness value of 27.54 µm. Elevated surface roughness is generally associated with inappropriate combinations of slice height and nozzle temperature, which promote insufficient interlayer fusion and non-uniform material deposition during printing.

Effect of FDM control factors on face hardness

Figure 4 shows the surface plot generated for the interaction of slice height with the other parameters involved in the study. In most cases, a nonlinear relationship existed between the factors considered. From Fig. 4a, it can be understood that lower to moderate nozzle temperatures should be considered with lower slice height values to increase the hardness values. Similarly, as shown in Fig. 4b, lower bed temperatures and higher slice heights must be avoided to increase the hardness values. As shown in Fi. 4c, lower deposition speeds should be considered to avoid fast cooling of the layer after deposition, as fast cooling prevents the previously deposited layer from better bonding to the next layer, which ultimately reduces adhesion and induces poor hardness. Figure 4d At higher slice heights and lower raster angles, poor hardness may result as it impacts the stress distribution and interlayer contact between the rasters. Better hardness can be attained at a low slice height combined with a flat orientation, resulting in superior hardness values, as shown in Fig. 4e.

Fig. 4.

Face Hardness (a) Slice height x Nozzle temperature (b) Slice height x Bed temperature (c) Slice height x Deposition speed (d) Slice height x Raster orientation (e) Slice height x Build orientation.

Effect of FDM control factors on volumetric error

The interaction of the slice height with other control factors over the volumetric error is presented as surface plots in Fig. 5a–e. Figure 5a shows that the adoption of a higher slice height and lower nozzle temperature led to a higher volumetric error owing to the improper melting and fusion of the layers. A low slice height with a moderate to high nozzle temperature is preferable for reducing the volumetric errors. Figure 5b indicates that the volumetric error increases when a low bed temperature and a high layer temperature are considered, and at a low bed temperature, the initial adhesion of the printed layer is low, which promotes volumetric error.

Fig. 5.

Volumetric Error (a) Slice height x Nozzle temperature (b) Slice height x Bed temperature (c) Slice height x Deposition speed (d) Slice height x Raster orientation (e) Slice height x Build orientation.

At higher deposition speeds and slice heights, the volumetric error increased because of the reduced cooling and bonding time of the layers, as shown in Fig. 5c. The interaction between the slice height and raster orientation is crucial, as shown in Fig. 5d, and considering that low or high raster orientation could impact the volumetric error, it causes poor overlap between rasters. At a higher slice height and vertically oriented printing, the volumetric error is higher owing to the layer-by-layer error stacking, as shown in Fig. 5e.

Effect of FDM control factors on roughness average

Figure 6 shows the interaction of the slice height with other control factors in the form of surface plots for the roughness average. Figure 6a recommends adopting a lower slice height and higher extrusion temperature to minimize the average roughness, as a high slice height and low extrusion temperature leads to the production of stepped layers with incomplete fusion between them.

Fig. 6.

Roughness Average (a) Slice height x Nozzle temperature (b) Slice height x Bed temperature (c) Slice height x Deposition speed (d) Slice height x Raster orientation (e) Slice height x Build orientation.

From Fig. 6b, the impact of considering lower bed temperatures at higher slice heights is evident, as it leads to issues such as warping, poor first-layer adhesion, and layer lifting. The selection of higher deposition speeds for thicker layers generally causes fast cooling and produces uneven layers, which promotes surface roughness, as shown in Fig. 6c. The higher slice heights in the horizontal and vertical orientations led to the formation of ridges and gaps, which increased the surface roughness, as shown in Fig. 6d. Figure 6e recommends the adoption of a flat orientation for printing with a low slice height to reduce the pronounced stair-stepping effect.

The observations performed for the different output responses investigated in this study recommended different combinations of control factors to minimize or maximize the output response. The study needs to be extended to identify the optimal control factor settings that can address all three output responses combined and enhance the printed part quality in all aspects, which stimulates the application of multicriteria decision-making methods for optimizing the control factors.

Multi response optimization

Multi-response optimization is an effective method for optimizing input variables when multiple conflicting output variables are present. This technique facilitates the identification of an optimal solution for the combined objectives. The current research evaluated the weight values of the output responses through CRITIC, equal weightage, and principal component analysis, and ranked the alternatives through methods such as CocoSo, WASPAS^41,42, and TOPSIS^43–45.

Criteria importance through intercriteria correlation (CRITIC)

Criteria Importance Through Intercriteria Correlation (CRITIC) is a systematic approach for objectively determining the weights of output responses by initially normalizing the experimental data^46,47. The methodology involves computing the standard deviation of the normalized data, followed by the construction of the correlation matrix, evaluation of the conflict among criteria, and estimation of the information content. The quantified information content is subsequently used as the basis for calculating the relative weights of the output responses. The governing equations employed for weight determination are presented below in accordance with the standard CRITIC procedure⁵³.

Step 1: normalization of the decision matrix

1

Table 9 presents the normalized output response values obtained using Eq. (1).

Table 9.

Normalized output response values.

Trial No	A	B	C	D (mm/s)	E	F	Hf	VE	Ra
	(mm)	(°C)	(°C)		(°)			(mm3)	(μm)
1	1	1	1	1	1	1	0.5376	0.8421	0.6802
2	1	2	2	2	2	2	0.8710	1.0000	0.8444
3	1	3	3	3	3	3	0.7097	0.8962	0.6275
4	2	1	1	2	2	3	0.6452	0.8146	0.7570
5	2	2	2	3	3	1	0.6344	0.9886	0.1489
6	2	3	3	1	1	2	1.0000	0.9238	0.6864
7	3	1	2	1	3	2	0.7849	0.7023	0.8456
8	3	2	3	2	1	3	0.7419	0.3634	0.8094
9	3	3	1	3	2	1	0.8065	0.0587	0.0000
10	4	1	3	3	2	2	0.5914	0.3897	0.7746
11	4	2	1	1	3	3	0.4516	0.6486	1.0000
12	4	3	2	2	1	1	0.6022	0.5927	0.8208
13	5	1	2	3	1	3	0.0000	0.0842	0.7072
14	5	2	3	1	2	1	0.4301	0.2818	0.0349
15	5	3	1	2	3	2	0.9032	0.8347	0.6974
16	6	1	3	2	3	1	0.3871	0.6105	0.5640
17	6	2	1	3	1	2	0.7634	0.0000	0.3067
18	6	3	2	1	2	3	0.5161	0.8999	0.5776

Step 2: calculate the standard deviation for each criterion

Table 10 presents the standard deviation of the output responses.

Table 10.

Standard deviation values.

S. No	Hf	VE (mm3)	Ra (μm)
1	0.2318	0.3331	0.2904

Step 3: Evaluate the symmetric matrix of n x n with element , which is the linear correlation coefficient between the vectors and

Table 11 presents a symmetric matrix of the output responses.

Table 11.

Symmetric matrix.

Symmetric Matrix	Hf	VE (mm3)	Ra (μm)
Hf	1.0000	0.3441	0.0013
VE (mm3)	0.3441	1.0000	0.3703
Ra(μm)	0.0013	0.3703	1.0000

Step 4: Calculate the measure of conflict created by criterion j with respect to the decision situation defined by the other criteria

2

The measure of conflict for output responses is shown in Table 12.

Table 12.

Measure of conflict.

Measure of Conflict	Hf	VE	Ra
		(mm3)	(μm)
Hf	0.0000	0.6558	0.9987
VE (mm3)	0.6558	0.0000	0.6297
Ra (μm)	0.9987	0.6297	0.0000

Step 5: Evaluating the quantity of information in relation for each criterion

3

The quantity of information for the output responses according to Eq. (3) is shown in Table 13.

Table 13.

Quantity of information.

Output Responses	Cj
Hf	0.3835
VE (mm3)	0.3055
Ra (μm)	0.3831
Total	1.072

Step 6: Determining the objective weights

4

Based on the CRITIC methodology, the calculated weights for the output responses were 0.36 (36%) for face hardness, 0.28 (28%) for volumetric error, and 0.36 (36%) for surface roughness. Consequently, equal importance was assigned to face hardness and surface roughness in the multi-criteria evaluation. The corresponding weight values derived using Eq. (4) are summarized in Table 14.

Table 14.

Weightage of output responses.

Output responses	Wj
Hf	0.36
VE (mm3)	0.28
Ra (μm)	0.36
Total	1

CoCoSo

The Combined Compromise Solution (CoCoSo) method is a hybrid multi-criteria decision-making approach³², that integrates the principles of simple additive weighting and weighted product models. The step-by-step procedure adopted in the present study is outlined below,

Step 1: The initial decision matrix was constructed in accordance with Eq. (5) by considering m alternatives, representing the number of experimental trials, and n criteria, corresponding to the evaluated output responses.

5

Step 2: Normalization of the decision matrix

Depending on the nature of the evaluation criterion, the initial decision matrix was normalized using Eqs. (6) and (7). As the present study aims to minimize dimensional inaccuracy and related quality deviations in the printed components, all the considered output responses were treated as non-beneficial (lower-the-better) criteria.

For the beneficial (higher-the-better) criterion

6

For the non-beneficial (lower-the-better) criterion:

7

where n_ij is the normalized value of x_ij, and.

Step 3: The power-weighted comparability sequence (Pᵢ) and the sum-weighted comparability sequence (Sᵢ) were calculated for each alternative using Eqs. (8) and (9), respectively. These metrics quantify the weighted performance of each alternative across all evaluated criteria.

8

9

Step 4: Estimation of the appraisal scores

The appraisal score for each alternative was determined using three distinct aggregation strategies, as defined by Eqs. (10), (11) and (12).

10

11

12

The current study considers value as 0.5 (0< 1).

Step 5: The final appraisal score (Aᵢ) for each alternative was computed using Eq. (13).

13

Table 15 presents the normalized output response values weighted according to the CRITIC method.

Table 15.

Normalized output response values as per CRITIC weight values.

Trial No	A	B	C	D (mm/s)	E	F	Hf	VE (mm3)	Ra (μm)
1	1	1	1	1	1	1	0.54	0.84	0.68
2	1	2	2	2	2	2	0.87	1.00	0.84
3	1	3	3	3	3	3	0.71	0.90	0.63
4	2	1	1	2	2	3	0.65	0.81	0.76
5	2	2	2	3	3	1	0.63	0.99	0.15
6	2	3	3	1	1	2	1.00	0.92	0.69
7	3	1	2	1	3	2	0.78	0.70	0.85
8	3	2	3	2	1	3	0.74	0.36	0.81
9	3	3	1	3	2	1	0.81	0.06	0.00
10	4	1	3	3	2	2	0.59	0.39	0.77
11	4	2	1	1	3	3	0.45	0.65	1.00
12	4	3	2	2	1	1	0.60	0.59	0.82
13	5	1	2	3	1	3	0.00	0.08	0.71
14	5	2	3	1	2	1	0.43	0.28	0.03
15	5	3	1	2	3	2	0.90	0.83	0.70
16	6	1	3	2	3	1	0.39	0.61	0.56
17	6	2	1	3	1	2	0.76	0.00	0.31
18	6	3	2	1	2	3	0.52	0.90	0.58

Tables 16 and 17 summarize the corresponding weighted comparability sequences and the resulting appraisal scores for all alternatives.

Table 16.

Power of weighted, sum of weighted and compatibility score values.

Trial No	A	B	C	D (mm/s)	E	F	Si	Pi	Kia	Kib	Kic
	(mm)	(°C)	(°C)		(°)
1	1	1	1	1	1	1	0.67	2.62	0.06	4.64	0.87
2	1	2	2	2	2	2	0.90	2.89	0.07	5.74	1.00
3	1	3	3	3	3	3	0.73	2.70	0.06	4.93	0.91
4	2	1	1	2	2	3	0.73	2.70	0.06	4.94	0.91
5	2	2	2	3	3	1	0.56	2.35	0.05	3.97	0.77
6	2	3	3	1	1	2	0.87	2.85	0.07	5.59	0.98
7	3	1	2	1	3	2	0.78	2.76	0.07	5.19	0.94
8	3	2	3	2	1	3	0.66	2.58	0.06	4.55	0.85
9	3	3	1	3	2	1	0.31	1.38	0.03	2.25	0.44
10	4	1	3	3	2	2	0.60	2.51	0.06	4.26	0.82
11	4	2	1	1	3	3	0.70	2.64	0.06	4.77	0.88
12	4	3	2	2	1	1	0.68	2.63	0.06	4.66	0.87
13	5	1	2	3	1	3	0.28	1.38	0.03	2.13	0.44
14	5	2	3	1	2	1	0.25	1.74	0.04	2.26	0.52
15	5	3	1	2	3	2	0.81	2.79	0.07	5.32	0.95
16	6	1	3	2	3	1	0.51	2.40	0.05	3.82	0.77
17	6	2	1	3	1	2	0.39	1.56	0.04	2.70	0.51
18	6	3	2	1	2	3	0.65	2.58	0.06	4.49	0.85

Table 17.

Appraisal score and alternative rankings as per CRITIC weights.

Trial No	A	B	C	D (mm/s)	E	F	Ai	Rank
	(mm)	(°C)	(°C)		(°)
1	1	1	1	1	1	1	2.47	9
2	1	2	2	2	2	2	2.99	1
3	1	3	3	3	3	3	2.61	6
4	2	1	1	2	2	3	2.61	5
5	2	2	2	3	3	1	2.13	13
6	2	3	3	1	1	2	2.91	2
7	3	1	2	1	3	2	2.73	4
8	3	2	3	2	1	3	2.42	10
9	3	3	1	3	2	1	1.22	17
10	4	1	3	3	2	2	2.28	12
11	4	2	1	1	3	3	2.53	7
12	4	3	2	2	1	1	2.48	8
13	5	1	2	3	1	3	1.17	18
14	5	2	3	1	2	1	1.29	16
15	5	3	1	2	3	2	2.79	3
16	6	1	3	2	3	1	2.08	14
17	6	2	1	3	1	2	1.44	15
18	6	3	2	1	2	3	2.4	11

The alternative ranking follows the order: 2 > 6 > 15 > 7 > 4 > 3 > 11 > 12 > 1 > 8 > 18 > 10 > 5 > 16 > 17 > 14 > 9 > 13.

The ranking of the alternatives is based on the highest value of multi response performance index (MRPI), which is also the appraisal score in the current study. The 2nd alternative was ranked as the best parameter combination, which enhanced the face hardness of the sample and minimized volumetric error and surface roughness. In contrast, the 13th alternative was considered the worst combination, as it reduced the face hardness value and maximized the volumetric error and surface roughness.

Sensitivity analysis

Sensitivity analysis is a key element in the MCDM approach to understand the influence of changes on the existing outcomes of a decision model. Two major approaches, changing the weight values of the output responses and applying different MCDM concepts to understand the changes in alternative ranking, were carried out in the current research.

The experimental outcomes were analyzed using principal component analysis to evaluate their weight values. face hardness was assigned a weightage of 23% (0.23), volumetric error 50% (0.50), and roughness average value 27% (0.27). The equal weight or average weight method assigns an equal weight, such as 33% (0.33), to all three responses studied in the research. The weight values obtained through the different methods were applied to the normalized values to understand their impact on the alternative ranking and correlation. Table 18 presents the alternative rankings obtained using different weight values assigned using diverse techniques.

Table 18.

Alternative rankings – different weight values (CRITIC, Equal and PCA).

Trial No	CRITIC	Equal	PCA
1	9	8	7
2	1	1	1
3	6	5	4
4	5	6	6
5	13	13	11
6	2	2	2
7	4	4	5
8	10	11	12
9	17	17	18
10	12	12	14
11	7	7	9
12	8	9	10
13	18	18	17
14	16	16	15
15	3	3	3
16	14	14	13
17	15	15	16
18	11	10	8

Figure 7 shows the ranking of alternatives by applying different criteria weight values evaluated through CRITIC equal and PCA techniques. Figure 7 visually corroborates the ranking trends reported in Table 18. The rankings obtained using the different methods were correlated with each other, and a strong positive correlation ranging from 95 to 99% was observed between the different weighting methods employed for ranking the alternatives, as shown in Table 19.

Fig. 7.

Comparison of alternative ranking – Different MCDM methods (CRITIC, Equal and PCA).

Table 19.

Correlation matrix for alternative ranking – different weight values.

Criteria assessment methods	CRITIC	Equal	PCA
CRITIC	1.00	0.99	0.95
Equal	0.99	1.00	0.97
PCA	0.95	0.97	1.00

Similarly, MCDM methods, such as WASPAS and TOPSIS, have been employed to rank alternatives using CRITIC weight values. Table 20 presents the rankings of the alternatives using the different MCDM methods.

Table 20.

Alternative ranking – different MCDM methods (CoCoSo, WASPAS and TOPSIS).

Trial No	CoCoSo	WASPAS	TOPSIS
1	9	10	7
2	1	1	1
3	6	4	5
4	5	6	4
5	13	7	11
6	2	2	2
7	4	5	6
8	10	12	13
9	17	16	17
10	12	13	14
11	7	8	9
12	8	11	10
13	18	17	15
14	16	18	18
15	3	3	3
16	14	14	12
17	15	15	16
18	11	9	8

Alternative rankings obtained using different MCDM techniques were compared and correlated with each other. A strong positive correlation of 93% to 95% was observed between the different MCDM methods employed for ranking alternatives. Figure 8 shows a comparison of the alternative rankings using different MCDM methods.

Fig. 8.

Comparison of alternative ranking – Different MCDM methods (CoCoSo, WASPAS and TOPSIS).

The CoCoSo alternative rankings had a good correlation of 93% with WASPAS-based alternative rankings and 94% correlation with TOPSIS-ranked alternatives. Regarding the correlation between the WASPAS and TOPSIS rankings, a correlation of 95% was obtained.

Table 21 shows the correlation matrix obtained for the alternative ranking according to different MCDM methods.

Table 21.

Correlation matrix for alternative ranking – different MCDM methods (CoCoSo, WASPAS and TOPSIS).

Alternative ranking methods	CoCoSo	WASPAS	TOPSIS
CoCoSo	1.00	0.93	0.94
WASPAS	0.93	1.00	0.95
TOPSIS	0.94	0.95	1.00

The optimal factor combination that enhanced the multi-response performance was a 0.1 mm slice height, 255 °C nozzle temperature, 100 °C nozzle temperature, 40 mm/s deposition speed, 90° raster orientation, and on-edge orientation. Slice height ranked top as per response (Table 22), followed by deposition speed, build orientation, raster orientation, nozzle temperature, and bed temperature. Figure 9 shows the main effect plot of the MRPI values.

Table 22.

Response table ranking for MRPI values.

Level	A	B	C	D	E	F
1	9.144	7.516	6.860	7.825	6.991	5.731
2	8.385	6.609	7.649	8.806	6.51	8.367
3	6.569	7.750	7.365	5.244	8.374	7.777
4	8.643
5	4.832
6	6.175
Delta	4.311	1.14	0.789	3.562	1.865	2.636
Rank	1	5	6	2	4	3

Fig. 9.

Main effect plot for MRPI values.

ANOVA results shown in Table 23 indicate that p-values for the input factors are not less than 0.05, and F-value has indicated that both slice height and deposition speed have a strong influence on the multi-response performance index, with contributions of 32.18% and 33.32%, respectively. In addition, the build orientation had an influence of 19.90% on the multi-response performance index values. The error was 3.18%, which was acceptable in this study. Table 18 presents the ANOVA results for the MRPI values.

Table 23.

ANOVA results for MRPI values.

Source	DF	Adj SS	Adj MS	F-Value	P-Value	Contribution %
A	5	2.30105	0.46021	4.04	0.210	32.18
B	2	0.24301	0.1215	1.07	0.484	3.40
C	2	0.07962	0.03981	0.35	0.741	1.11
D	2	2.38246	1.19123	10.47	0.087	33.32
E	2	0.49404	0.24702	2.17	0.315	6.91
F	2	1.42329	0.71165	6.25	0.138	19.90
Error	2	0.22757	0.11378			3.18
Total	17	7.15103				100.00

Predictions through classification machine learning algorithms

Machine learning algorithms are a subset of artificial intelligence that can learn a dataset and perform various tasks such as predicting future outcomes, discovering underlying patterns, and recommending optimal strategies by interacting with an environment to tackle complex problems. These algorithms can solve both regression- and classification-based problems by repeating the learning of a dataset and acquiring a better understanding of the nature of the relationship between the input and output variables. The output responses were labeled as classes 1 and 2 with respect to the average values and were analyzed using four different machine learning techniques: k-nearest neighbor, decision tree, stochastic gradient descent, and logistic regression. The reason behind considering the mean of the experimental dataset as the threshold for label assignment is that it represents the central tendency of the data, providing an objective and data-driven cutoff to separate lower and higher values. This approach often results in reasonably balanced class distributions, which improve model learning and stability, and serves as a simple, interpretable baseline when no domain-specific threshold is available. The rationale behind adopting classification-based algorithms is to provide a decision-support system under limited data conditions. The application of such classifiers identifies parameter combinations that may yield above-average performance, as the mean value serves as a neutral benchmark.

All the algorithms considered can analyze a dataset in the form of labels and make predictions about future outcomes. The performance of the algorithms was evaluated using different metrics, such as the area under the curve, classification accuracy, F1 score, precision, and recall. Table 24 shows the range of values and labeled data information for the different output responses.

Table 24.

Range values and labeled data information.

S. No	Response	Range	Label	No of Class 1 labelled data	No of Class 2 labelled data
1	Face Hardness	0 – 49.26	Class 1	8	10
		> 49.26	Class 2
2	Volumetric error	0 – 278.90	Class 1	11	7
		> 278.90	Class 2
3	Roughness average	0 – 17.81	Class 1	12	6
		> 17.81	Class 2

The input data for analyzing the experimental dataset in the form of labels were stored in. csv format and input into the Orange data mining software version 3.11.0. The dataset consisted of 18 different instances labeled as Class 1 and Class 2, which were connected to different algorithms to understand their performance in understanding the pattern of the labeled data. The accuracies of the algorithms were observed by varying the training and testing ratios, such as 70:30, 75:25 and 80:20. The performance of the algorithms improved when the split ratio was maintained at 80:20. Table 25 presents the output responses in labeled mode.

Table 25.

Output responses in labeled mode.

A	B	C	D	E	F	Hf	VE (mm3)	Ra (µm)
1	1	1	1	1	1	Class 1	Class 1	Class 1
1	2	2	2	2	2	Class 2	Class 1	Class 1
1	3	3	3	3	3	Class 2	Class 1	Class 1
2	1	1	2	2	3	Class 2	Class 1	Class 1
2	2	2	3	3	1	Class 2	Class 1	Class 2
2	3	3	1	1	2	Class 2	Class 1	Class 1
3	1	2	1	3	2	Class 2	Class 1	Class 1
3	2	3	2	1	3	Class 2	Class 2	Class 1
3	3	1	3	2	1	Class 2	Class 2	Class 2
4	1	3	3	2	2	Class 1	Class 2	Class 1
4	2	1	1	3	3	Class 1	Class 1	Class 1
4	3	2	2	1	1	Class 1	Class 2	Class 1
5	1	2	3	1	3	Class 1	Class 2	Class 1
5	2	3	1	2	1	Class 1	Class 2	Class 2
5	3	1	2	3	2	Class 2	Class 1	Class 1
6	1	3	2	3	1	Class 1	Class 1	Class 2
6	2	1	3	1	2	Class 2	Class 2	Class 2
6	3	2	1	2	3	Class 1	Class 1	Class 2

The face hardness of the prepared sample was classified into eight class 1 labeled data and ten class 2 labeled data with respect to the average value of the response obtained. The decision tree algorithm exhibited a maximum classification accuracy of 88.9%, followed by the stochastic gradient descent algorithm, with an accuracy of 83.3%. By contrast, both kNN and logistic regression achieved an accuracy of 72.2%. Table 26 presents the evaluation metrics for the face hardness-labeled data.

Table 26.

Evaluation metrics for face hardness.

ML Model	AUC	CA	F1	Precision	Recall
kNN	0.831	0.722	0.720	0.722	0.722
Tree	0.912	0.889	0.886	0.907	0.889
SGD	0.838	0.833	0.834	0.840	0.833
Logistic Regression	0.875	0.722	0.720	0.722	0.722

The volumetric error of the prepared sample was classified into 11 class 1 labeled data and 7 class 2 labeled data with respect to the average value of the obtained response. A classification accuracy of 94.4% was obtained for the decision tree, stochastic gradient descent, and logistic regression algorithms, and kNN resulted in an accuracy of 83.3%. Table 27 presents the evaluation metrics for the surface-roughness labeled data.

Table 27.

Evaluation metrics for surface roughness.

ML Model	AUC	CA	F1	Precision	Recall
kNN	0.922	0.833	0.831	0.833	0.833
Tree	0.981	0.944	0.945	0.951	0.944
SGD	0.929	0.944	0.944	0.949	0.944
Logistic Regression	1.000	0.944	0.944	0.949	0.944

The average roughness of the sample was classified into 12 class 1 labeled data and 6 class 2 labeled data with respect to the average value of the obtained response. The decision tree showed 100% accuracy in classifying the labeled data, and 83.3% classification accuracy was achieved using the stochastic gradient descent algorithm. Both kNN and logistic regression achieved a classification accuracy of 77.8%. Table 28 presents the evaluation metrics for the average roughness.

Table 28.

Evaluation metrics for roughness average.

ML Model	AUC	CA	F1	Precision	Recall
kNN	0.944	0.778	0.738	0.833	0.778
Tree	1.000	1.000	1.000	1.000	1.000
SGD	0.833	0.833	0.836	0.844	0.833
Logistic Regression	0.917	0.778	0.778	0.778	0.778

The proposed factors and levels (6¹ × 5³) led to a total of 1458 experimental trails per full factorial design. From the vast input dataset, random input parameter combinations were considered and validated for the prediction of machine-learning models with higher accuracy. Table 29 presents the results obtained for the validation dataset using the decision tree algorithm.

Table 29.

Validation test results – decision tree algorithm.

A	B	C	D	E	F	Hf	VE (mm3)	Ra (µm)
1	1	2	3	1	3	Class 1	Class 1	Class 1
3	2	3	3	3	3	Class 2	Class 1	Class 2
6	1	3	2	1	3	Class 2	Class 1	Class 1
4	3	2	3	1	2	Class 1	Class 2	Class 1
6	1	2	1	2	2	Class 1	Class 2	Class 2
1	3	3	1	2	1	Class 2	Class 1	Class 1

Decision tree structure

A decision tree is a hierarchical structure that provides a detailed idea for attaining a particular outcome by adopting recommended criteria. The structure consists of a root node from which the data are split and further extended with decision nodes, and finally terminated with the leaf node.

The decision tree structure for the face hardness value consisted of five nodes and three leaves, with slice height (A) as the root node. The targeted labeled data is class 2, as the face hardness value should be higher, and as per the tree structure, adopting the slice height values from 0.1 to 0.18 mm will lead to a higher face hardness value of the material. In addition, if the slice height value is preferred to be more than 0.18 mm, then the bed temperature (C) while printing the part should be maintained at less than or equal to 100 °C. Figure 10 shows the decision tree structure for improving the face hardness values. Both the slice height and bed temperature were highlighted as significant parameters that affect the face hardness value of the sample.

Fig. 10.

Decision tree structure for face hardness.

The volumetric error decision tree consisted of nine nodes and five leaves with a slice height at the root node position. The volumetric error must be reduced to enhance the quality of the printed parts, and the targeted labeled data should be class 1. To attain a low volumetric error, the factor of slice height (A) must be fixed at values less than or equal to 0.14 mm. In contrast, when the slice height values are fixed at more than 0.14 mm, other factors, such as deposition speed (D), need to be maintained at values less than or equal to 40 mm/s and nozzle temperature (B) to be maintained less than or equal to 235 °C; when the nozzle temperature is fixed at more than 235 °C, then the bed temperature (C) values should be less than or equal to 90 °C. Figure 11 shows the decision tree structure for minimizing the volumetric error.

Fig. 11.

Decision tree structure for volumetric error.

The roughness average decision tree structure consists of seven nodes and four leaves, with the factor slice height as the root node and other factors such as raster orientation (E) and build orientation at the decision nodes. The targeted class label is class 1 because the roughness average must be reduced to enhance the quality of the printed part. The factor slice height (A) must be maintained at values ranging from 0.1 to 0.22 mm to reduce the roughness average. Other factors, such as build orientation (F), must be considered either on-edge or upright. If the build orientation is considered flat and the average roughness needs to be reduced, the raster orientation should be maintained at 0°. Figure 12 represents the decision tree structure for the roughness average, and the factors of slice height, build orientation, and raster orientation are considered significant.

Fig. 12.

Decision tree structure for roughness average 7 nodes and 4 leaves.

According to the decision tree structures developed for the experimental outcomes, it was observed that the slice height (A) is a highly influential parameter affecting the mechanical properties and quality characteristics of the final product. The slice height acts as the steering factor over other control factors involved in printing a sample with the desired quality.

Morphological studies

The surface morphologies of the printed specimens were analyzed using a CARL ZEISS FESEM analyzer at magnifications of 100 × , 1000 × , 2500 × , and 50,000 × to observe the surface irregularities and structural porosities of the samples.

The microstructural investigation of the printed structure provides insight into the effect of changing the FDM input process parameters to understand the void distribution, layer bonding, and raster orientation, which significantly influence the mechanical performance of the printed part. This facilitates the understanding of process-induced defects, such as porosity, incomplete fusion, and thermal degradation in the printed part. The microstructural investigation was performed using parameter combinations that were ranked as the best and worst alternatives through the MCDM methods. The parameter combination 0.1 mm layer thickness, 245° nozzle temperature, 100° bed temperature, 40 mm/s deposition speed, 45° raster angle, and on-edge orientation was considered and 0.26 mm layer thickness, 235° nozzle temperature, 100° bed temperature, 50 mm/s deposition speed, 0° raster angle, and upright orientation were used to prepare samples with dimensions of 8 mm × 8 mm.

Figure 13a shows the pores formed on the sample surface in elliptical and round forms owing to poor layer bonding and insufficient interlayer adhesion owing to poor temperature control. This induced a weak spot in the sample and ultimately reduced its hardness and other associated mechanical properties. Figure 13b shows a highly porous structure with an irregular void distribution and rough texture owing to poor material, which occurs at low extrusion temperatures and higher slice heights. The structural formation owing to a faster cooling rate at layers printed at a higher slice rate and high deposition speed promotes delamination between adjacent layers and accumulates material at an unintended position, as shown in Fig. 13c, which corresponds to the sample produced from the best alternative. A surface with wavy edges or partially melted filament material protrudes over the surface and promotes surface roughness owing to the overlap between adjacent layers during deposition, as shown in Fig. 13d.

Fig. 13.

FESEM micrographs of NylonAF80 samples printed under (a, b) worst-ranked and (c, d) best-ranked MCDM parameter combinations showing pores, poor interlayer fusion, material accumulation, and surface stringing.

Conclusions

The present research focused on optimizing the FDM process parameters to enhance part quality by maximizing the Shore D hardness and minimizing the volumetric error and surface roughness. Techniques, such as multi-criteria decision-making methods and machine learning algorithms, have been employed to achieve these objectives. The study found that the maximum hardness (60.67) was obtained at optimal settings, including a 0.14 mm slice height and on-edge positioning, while the lowest hardness (29.67) resulted from a 0.26 mm slice height and vertical mounting. The minimum volumetric error (101 mm³) was observed under conditions involving a 0.14 mm slice height and on-edge mounting, whereas the maximum error (527.24 mm³) occurred with a flat orientation. Similarly, the smoothest surface (11.44 µm roughness) was achieved with a 0.22 mm slice height and upright positioning, whereas the roughest surface (27.54 µm) was achieved with a flat orientation at a 0.18 mm slice height. The CRITIC technique assigned equal weightage to hardness and volumetric error, while CoCoSo ranked the second trial as the best and the thirteenth as the worst, showing strong correlations with other MCDM methods such as WASPAS and TOPSIS. The ANOVA results highlighted the slice height and print speed as the most influential parameters, contributing 32.18% and 33.32%, respectively, to the multi-response performance. Among the machine learning models, the decision tree algorithm achieved the highest classification accuracy for all the three responses. Slice height emerged as the dominant factor affecting all the outcomes, and microstructural analysis confirmed that poor layer formation and porosity contributed to lower hardness and higher surface roughness. The parts produced through optimal printing parameters may find applications in functional prototypes, jigs, fixtures, and interior components in automotives and aircraft, where rigidity, dimensional stability, and wear resistance are highly demanding. The expansion of the experimental dataset by including more control factors and the interaction effects of the control factors on the mechanical properties and part characteristics will be extensively studied in future work. The limited dataset size restricts the statistical reliability and generalization capability of the trained machine learning models. Future work will focus on expanding the dataset to enable robust validation and reduce overfitting.

Abbreviations

AI

Artificial intelligence

AM

Additive manufacturing

ANOVA

Analysis of variance

ABS

Acro nitrile butadiene styrene

CRITIC

Criteria importance through intercriteria correlation

CoCoSo

Combined compromise solution

DSC

Differential scanning calorimetry

EDAX

Energy dispersive X-ray

FDM

Fused deposition modeling

MCDM

Multi-criteria decision making

PLA

Poly lactic acid

PCA

Principal component analysis

TGA

Thermogravimetric analysis

TOPSIS

Technique for order of preference by similarity to ideal solution

WASPAS

Weighted aggregated sum product assessment

Author contributions

Nashmi H. Alrasheedi: *Conceptualization, Investigation, Writing—original draft.* P. Manoj Kumar: *Conceptualization, Writing—review and editing, Supervision.* Gokulkumar Sivanantham: *Formal analysis, Validation, Visualization, Writing—original draft.* Dawit Tafesse Gebreyohannes: *Methodology, Project administration, Writing—review and editing.*

Funding

This work was supported and funded by the Deanship of Scientific Research at the Imam Mohammad Ibn Saud Islamic University (IMSIU) (grant number IMSIU-DDRSP2602).

Data availability

All data is provided within the article.

Declarations

Competing interests

The authors declare no competing interests.

Informed consent

Not applicable.