A Method for Predicting Surface Finish of Polylactic Acid Parts Printed Using Fused Deposition Modeling

Abstract

Accurately predicting the surface finish of fused deposition modeling (FDM) parts is an important task for the engineering application of FDM technology. So far, many prediction models have been proposed by establishing a mapping relationship between printing parameters and surface roughness. Each model can work well in its specific context; however, existing prediction models cannot meet the requirements of multi-factor and multi-category prediction of surface finish and cope with imbalanced data. Aiming at these issues, a prediction method based on a combination of the adaptive particle swarm optimization and K-nearest neighbor (APSO-KNN) algorithms is proposed in this paper. Seven input variables, including nozzle diameter, layer thickness, number of perimeters, flow rate, print speed, nozzle temperature, and build orientation, are considered. The printing values of each specimen are determined using an L27 Taguchi experimental design. A total of 27 specimens are printed and experimental data for the 27 specimens are used for model training and validation. The results indicate that the proposed method can achieve a minimum classification error of 0.01 after two iterations, with a maximum accuracy of 99.0%, and high model training efficiency. It can meet the requirements of predicting surface finish for FDM parts with multiple factors and categories and can handle imbalanced data. In addition, the high accuracy demonstrates the potential of this method for predicting surface finish, and its application in actual industrial manufacturing.

1. Introduction

Currently, additive manufacturing (AM) technologies are increasingly being used in various fields [1,2,3,4]. Compared with traditional manufacturing technologies [5], they improve production efficiency, reduce manufacturing costs, and enable personalized production, further promoting the progress of Industry 4.0. Fused deposition modeling (FDM) is a widely used AM technology due to its low manufacturing cost, fast molding speed, and simple process [6]. However, the poor surface finish of printed parts limits their application in practical engineering [7]. For example, when using FDM technology to manufacture molds in casting and injection molding processes, or when printed parts are in contact with human skin, surface finish is crucial and can affect the product’s performance to meet its assembly and functional requirements [8,9]. Accurately predicting the surface finish of printed parts is one of the important tasks of FDM technology in engineering applications [10].

In recent years, the influence of FDM printing parameter settings on surface finish, including layer thickness, temperature, print speed, flow rate, build orientation, number of perimeters, etc., has been reported [11,12,13,14,15]. Layer thickness refers to the thickness of each layer printed by the printer nozzle along the Z-axis, which affects the details and printing speed of the finished product. Print speed refers to the moving speed of the printer nozzle, which affects the printing time and quality of the finished product. Wall thickness refers to the thickness of the printed model shell after the removal of the infill, which can also be understood as the number of times the nozzle passes over the outer layer, or the number of perimeters. Print temperature determines the melting point and fluidity of the printing material. Flow rate compensation, also known as flow rate, mainly corrects errors in the actual extrusion amount caused by internal factors. Build orientation is the molding direction of the part and is closely related to the surface shape of the part. Currently, mainstream prediction methods aim to establish a mapping relationship between part printing parameters and part surface roughness, with printing parameters as input and predicted roughness parameters as output. Researching different mapping relationship models to improve prediction accuracy is an important direction in the prediction of surface smoothness of FDM-printed parts.

Some researchers attempted to establish models for fitting the contours of printed parts. Taufik et al. [16], Buj-Corral et al. [17], Xu et al. [18], Perez et al. [19], and Pandey et al. [20] constructed geometric models of surface contours to predict surface roughness (Ra) by studying the relationship between surface contours of different types of FDM-printed parts and printing parameters. Other researchers, such as Vahabli et al. [21], Wu et al. [22], Boschetto et al. [23], and Reddy et al. [24], generated models using machine-learning-based algorithms. The common features of these studies are threefold: First, they use commonly used printing materials such as ABS or PC. Second, the main factors considered in their models are only layer thickness and build orientation. Third, the output of their models is the surface roughness values, obtained by solving a regression problem.

Predicting the surface roughness of a part may be meaningful for certain purposes, such as accurately modeling the surfaces of printed parts. However, in actual engineering manufacturing, it is only necessary to know whether the surface finish level of the part meets the required manufacturing requirements (classification problem) [25]. In fact, the standards used until a few years ago in the industry used classes when defining surface roughness [26]. For example, N11 is a class that corresponds to a surface roughness between 12.5 and 25 μm; N12 is a class that corresponds to a surface roughness between 25 and 50 μm. Studies can be found in the literature that use classification algorithms to determine the surface finish levels of parts manufactured by other printing technologies [27]. Molero et al. [28], Barrios et al. [29], and Cerro et al. [30] compared different machine learning algorithms to verify their performance by dividing the range of the surface roughness dataset of parts into different categories. The input factors, data types, and number of classifications used by each model are shown in

Table 1. Summary of current classification models.

Authors	Method	Data Balance	Factor	Classification
Molero et al. [28]	ML	√	LT, T, PS, PA, F	2
Barrios et al. [29]	DT	√	LT, T, PS, PA, F	2
Cerro et al. [30]	ML	√	LT, PS, NP, T, BO	2

Note: ML stands for machine learning; DT stands for decision tree; Layer thickness (LT), mm; Temperature (T), °C; Print speed (PS), mm/s; Print acceleration (PA), mm/s²; Flow rate (F), %; Build orientation, (BO), °; Number of perimeters (NP); “√” represents data balance.

.

Each of the existing classification models can work well in its specific context. However, they still have the following shortcomings: first, they do not consider imbalance in the data, resulting in low prediction accuracy for categories with fewer individuals. Second, they consider limited types of input factors. In the literature, you can find previous work in which the influence of different printing parameters on the surface roughness of 3D printed parts has been studied (

Table 2. Previous studies on the surface roughness of FDM PLA parts.

Authors	Layer Thickness	Temperature	Print Orientation	Print Speed	Nozzle Diameter	Filling Density	Wall Thickness
García Plaza et al. [31]	√	–	√	√	–	–	–
Taşcıoğlu et al. [32]	√	√	–	√	–	–	–
Ramli et al. [33]	√	–	–	–	–	√	–
Alsoufi et al. [34]	√	–	–	–	√	–	–
Cerro et al. [30]	√	√	√	√	–	–	√

Note: “√” represents that the study involves this factor, while “–” represents that the study don’t involve this factor.

). Third, they cannot meet the demand for multi-factor and multi-category prediction of surface finish. Category expansion will reduce prediction accuracy and the model will be complex, difficult to tune, and difficult to understand, making it unsuitable for practical engineering applications.

The K-nearest neighbor algorithm (KNN) is simple, robust, and highly interpretable, and is suitable for multi-classification, nonlinear, and imbalanced data problems [35]. The basic principle of the K-nearest neighbor algorithm is to classify the k-closest labels to the target distance, where distance is the main factor affecting classification accuracy. However, different weights of the input variables inevitably lead to biases in distance calculation and classification errors. In [36,37,38], the particle swarm optimization (PSO) algorithm was used to optimize the data features and the number of neighbors of the KNN algorithm, which was applied to specific tasks such as perception, recognition, and diagnosis, and achieved good performance.

In the population-based optimization algorithms, the PSO algorithm has the advantages of simple principles, few adjustable parameters, low computational complexity, and strong global optimization capability [39]. The optimization method has been widely used in various fields and effectively solved corresponding problems in specific fields [40,41,42]. However, the fast convergence speed of the PSO algorithm can easily cause the parameter search to fall into a local optimum, leading to premature convergence. To address this issue, we use clustering to adaptively divide the particle swarm into different populations and guide the populations by applying different update strategies [43]. This enhances the diversity of particles and helps particles jump out of a local optimum.

Based on the above considerations, this paper introduces the adaptive particle swarm optimization algorithm into the K-nearest neighbor classification algorithm and proposes a method for predicting the surface finish of FDM PLA parts based on this. By introducing the adaptive particle swarm optimization algorithm into the distance formula of the K-nearest neighbor algorithm, random weight values are generated for each input variable to adjust the distance calculation deviation. This method reduces the impact of data imbalance on the prediction results and meets the needs of multi-factor and multi-category prediction of surface finish in engineering practice, providing a powerful reference for the surface finish of FDM-printed parts in engineering manufacturing.

The remainder of this paper is organized as follows: Section 2 explains the details of the proposed method. Section 3 presents the experimental design, dataset, and model framework. Section 4 shows the results and discussions. Finally, Section 5 provides a conclusion, including future directions for further work.

2. Materials and Methods

This method introduces the adaptive particle swarm optimization algorithm into the distance formula of the K-nearest neighbor algorithm, generating optimal weights for each input variable to adjust the calculation bias of the distance formula. Its framework diagram is shown in Figure 1. The principles are analyzed in detail below.

2.1. K-Nearest Neighbors

The K-nearest Neighbor (KNN) algorithm is an instance-based machine learning algorithm and one of the simplest and least parameterized classification algorithms [44]. The KNN algorithm is simple, robust, and highly interpretable, and is suitable for multi-classification, nonlinear, and imbalanced data problems. The idea behind the KNN algorithm is to find the k closest labels to the label to be classified in the training set, and to determine the classification of the label to be classified by counting the categories of these k labels [45]. Distance is the main factor affecting classification accuracy.

The neighbors of a label can be defined based on the Euclidean distance, assuming all labels are in m-dimensional space, and any set x can be represented as a feature vector x = (x₁, x₂, ⋯, x_m), where $x_i^l$ represents the feature value of the i-th example. The distance between example x_i and set x_j is defined as the Euclidean distance d(x_i,x_j), as shown in the following formula.

$$d(x_i,x_j)=\sqrt{{\displaystyle \sum _{l=1}^m{(x_i^l-x_j^l)}^2}}$$

(1)

However, different weights of the input variables inevitably lead to biases in distance calculation and classification errors. To address this issue, a weight α is assigned to each feature value used in the distance formula, adjusting the calculation bias. The above formula can be written as:

$$d(x_i,x_j)=\sqrt{{\displaystyle \sum _{l=1}^m{\left(\alpha \left(x_i^l-x_j^l\right)\right)}^2}}$$

(2)

2.2. Adaptive Particle Swarm Optimization

Adaptive Particle Swarm Optimization (APSO) is an evolutionary algorithm [46,47]. Based on the Basic Particle Swarm Optimization algorithm, APSO introduces adaptive mechanisms and polynomial mutation strategies. The updated rules for particle velocity and position are the same as those in the Basic Particle Swarm Optimization algorithm, but the algorithm dynamically adjusts the inertia weights by introducing an adaptive mechanism to improve the search efficiency and convergence performance and avoid getting trapped in local optima.

The updated rules for particle velocity and position are as follows:

$$\left\{\begin{array}{c}{x}_{i,j}(t+1)=x_{i,j}(t)+v_{i,j}(t+1) j=1,2,3,\cdots ,d\\ v_{i,j}(t+1)=\omega \cdot v_{i,j}(t)+c_1{r}_1[p_{i,j}-x_{i,j}(t)]+c_2{r}_2[p_{g,j}-x_{i,j}(t)]\end{array}\right.$$

(3)

In Equation (3), x_i,j and v_i,j represent the numerical values of particle displacement and velocity; ω is the inertia weight; c₁ and c₂ are the learning factors; r₁ and r₂ are uniformly distributed random numbers within [0, 1]; p_i,j is the individual best value of the particle; p_g,j is the global best value of the particle.

The adaptive mechanism is expressed as follows:

$$\omega =\left\{\begin{array}{cc}{\omega }_{\mathit{min}}-\frac{({\omega }_{\mathit{max}}-{\omega }_{\mathit{min}})\times (f-f_{\mathit{min}})}{f_{avg}-f_{\mathit{min}}}& f\le f_{avg}\\ {\omega }_{\mathit{max}}& f>f_{avg}\end{array}\right.$$

(4)

In Equation (4), f represents the real-time objective function value of the particle; f_avg and f_min represent the average value and the minimum target value of all particles at present; ω_max and ω_min represent the maximum and minimum values of the inertia weight, and the value range is 0.4–0.8.

2.3. APSO-KNN

In this study, the APSO algorithm is incorporated into the KNN algorithm to search the weight of each feature value in Formula (2). Additionally, the selection of fitness function in APSO is crucial. The KNN classification accuracy function is chosen as the fitness function.

$$acc=\frac{N\mathrm{C}}{NT}$$

(5)

In Equation (5), acc represents the accuracy, and its value range is 0–1; NC represents the number of correct classifications; NT represents the total number of classification labels.

By learning the weight value “α”, the fitness function value can be maximized to the greatest extent possible. The workflow of the APSO-KNN algorithm is shown in Figure 2.

Step 1: Standardize the dataset. Standardizing the dataset can reduce the differences between certain attributes and decrease the errors in the classification accuracy of the dataset.

Step 2: Initialize particle swarm. Using the weight α for each feature value as the optimization variable, the position and velocity of each particle in the population are randomly initialized.

Step 3: Calculate the distance between each label and the predicted label vector using Formula (2) and calculate the fitness value using Formula (5).

Step 4: Evaluate the fitness of each particle, store the particle’s position and fitness value in its personal best p_best, and save the position and fitness value of the best individual from p_best in the global best g_best.

Step 5: Update each particle using the updated Formulas (3) and (4) and evaluate the fitness of each particle.

Step 6: Compare the fitness value of each particle with its personal best position, and if they are close, update the personal best position with the current value. Compare all p_best and g_best, and update g_best.

Step 7: Stop the search and output the results if the termination condition is met; otherwise, return to Step 5 to continue the search.

3. Experiments

An industrial-grade FDM BM345 (Blue Maker, China) printer (Figure 3) was used for 3D printing. It is equipped with nozzles with diameters of 0.4 mm, 0.6 mm, and 0.8 mm, and the maximum molding size is 350 × 350 × 450 mm. The recommended printing speed is 60 mm/s, with a maximum of 150 mm/s. A blower fan is installed next to the extruder for accelerated cooling of the printed object. The recommended slicing software is BlueMaker3D (version 18.10), which allows the use of STL and G-code standards.

Polylactic Acid (PLA) was used as the base material. Its main properties are density, temperature, diameter, and color [48]. These properties have an impact on the FDM printing parameter settings, as well as the quality and strength of printed parts. The specific parameters are shown in

Table 3. Material properties.

Chemical Name	Composition	Density (g/mm³)	Printing Temperature (°C)	Diameter (mm)	Color
Polylactic Acid	PLA (Polylactide Resin) 99%	1.24	220 ± 20	1.75 ± 0.03	white

. The material is provided by Smart Materials 3D company (Alcalá la Real, Spain) with a diameter of 1.75 mm and a diameter variation range of ±0.03 mm. The material has stable performance and is expected not to warp.

Surface roughness measurement is defined in ISO 21920-2:2021 [49] and has different parameters. Ra is the most commonly used parameter in determining the surface texture state, as it provides the most general and adequate information about surface roughness. The surface shapes of 27 samples were observed and the surface roughness (Ra) was measured using OLS40-SU laser confocal microscope (Figure 4a). It can magnify at a range of 108×–17,280×, with a display resolution of 1 nm. The highest precision of the X/Y axis is 0.12 μm, and the optimal measurement range is 1 μm–1.5 mm. The highest precision of the Z axis is 0.01 μm, and the optimal measurement range is 0.5 μm–3 mm. The roughness measurement range is above 0.1 μm, and it has a built-in Gaussian filter. The objective lens used is 10×. The samples shown in Figure 4b were measured using this technique. Each sample was placed horizontally with the surface to be measured facing upwards, and five positions were taken on the plane, four on the edge and one in the center (Figure 4c). The surface roughness value was the average roughness measured at the five points.

The Taguchi L27 experimental design [50] was used in this study to print 27 specimens with dimensions of 20 × 20 × 20 mm (Figure 4b), using 7 factors with 3 levels (

Table 4. Factors and levels in the design of experiments (DOE).

Factors	Level 1	Level 2	Level 3
Nozzle diameter, ND (mm)	0.40	0.60	0.80
Layer thickness, LT (mm)	0.10	0.25	0.35
Number of perimeters, NP	2	3	4
Flow rate, F (%)	90	100	110
Printing speed, PS (mm/s)	40	60	80
Temperature, T (°C)	190	210	230
Build orientation, BO (°)	30	45	75

). The factors studied were nozzle diameter (ND), layer thickness (LT), number of perimeters (NP), flow rate (F), print speed (PS), nozzle temperature (T), and build orientation (BO), with the number of perimeters associated with the layer width.

Table 5. Taguchi L27 experimental design.

No.	ND (mm)	LT (mm)	NP	F (%)	PS (mm/s)	T (°C)	BO (°)
1	0.40	0.10	2	90	40	190	30
2	0.40	0.10	2	90	60	210	45
3	0.40	0.10	2	90	80	230	75
4	0.40	0.25	3	100	40	190	30
5	0.40	0.25	3	100	60	210	45
6	0.40	0.25	3	100	80	230	75
7	0.40	0.35	4	110	40	190	30
8	0.40	0.35	4	110	60	210	45
9	0.40	0.35	4	110	80	230	75
10	0.60	0.10	3	110	40	210	75
11	0.60	0.10	3	110	60	230	30
12	0.60	0.10	3	110	80	190	45
13	0.60	0.25	4	90	40	210	75
14	0.60	0.25	4	90	60	230	30
15	0.60	0.25	4	90	80	190	45
16	0.60	0.35	2	100	40	210	75
17	0.60	0.35	2	100	60	230	30
18	0.60	0.35	2	100	80	190	45
19	0.80	0.10	4	100	40	230	45
20	0.80	0.10	4	100	60	190	75
21	0.80	0.10	4	100	80	210	30
22	0.80	0.25	2	110	40	230	45
23	0.80	0.25	2	110	60	190	75
24	0.80	0.25	2	110	80	210	30
25	0.80	0.35	3	90	40	230	45
26	0.80	0.35	3	90	60	190	75
27	0.80	0.35	3	90	80	210	30

shows the settings for each parameter.

4. Results and Discussion

4.1. Results of Surface Roughness Measurements

Following the measurement method shown in Figure 4c, the surface roughness (Ra) values were measured at five points, and the average value was calculated. However, due to the large variation in roughness values at different measurement points on the same plane, the results had high variability. This variability made it difficult to draw conclusions about surface roughness based on measurement location. Calculating the standard deviations for all test points can clearly show the measurement performance. The standard deviations (SD) and average values are listed in

Table 6. Results of surface roughness measurements.

Test	Ra1 (μm)	Ra2 (μm)	Ra3 (μm)	Ra4 (μm)	Ra5 (μm)	Ra (μm)	SD (μm)
1	15.43	14.24	16.50	18.32	15.22	15.94	1.55
2	16.93	12.60	12.63	15.21	15.50	14.58	1.90
3	10.90	10.67	9.89	10.72	11.73	10.78	0.65
4	44.53	44.61	44.25	45.79	44.11	44.66	0.66
5	34.19	31.29	32.69	34.22	29.11	32.30	2.15
6	24.58	24.91	26.7	28.17	21.46	25.17	2.52
7	52.91	49.05	54.76	51.82	48.08	51.32	2.75
8	43.75	41.16	43.25	48.18	41.05	43.48	2.89
9	37.76	34.28	35.22	35.29	36.61	35.83	1.35
10	9.03	8.92	7.97	9.88	7.98	8.76	0.80
11	18.74	14.19	15.40	19.86	14.64	16.57	2.56
12	11.23	12.48	13.81	10.90	11.56	11.99	1.17
13	25.71	21.30	21.67	23.15	24.35	23.24	1.84
14	37.56	43.28	42.84	43.96	39.59	41.45	2.74
15	34.02	29.64	32.96	30.23	31.59	31.69	1.83
16	31.66	30.21	31.80	28.21	32.16	30.81	1.62
17	52.47	50.76	53.15	49.82	52.84	51.81	1.44
18	38.20	37.42	39.64	43.37	41.49	40.02	2.43
19	18.01	17.81	16.59	16.67	16.07	17.03	0.83
20	7.30	8.11	7.43	8.83	7.41	7.81	0.65
21	24.90	22.98	23.81	25.22	24.16	24.21	0.89
22	29.83	28.42	30.70	29.89	28.89	29.55	0.90
23	20.02	16.33	20.91	21.98	22.95	20.44	2.55
24	33.60	33.57	34.31	33.90	34.87	34.05	0.54
25	41.54	40.78	41.91	41.96	40.38	41.31	0.70
26	30.42	32.67	29.87	30.30	28.26	30.30	1.57
27	59.04	58.72	55.41	52.35	52.88	55.68	3.14

in units of μm.

4.2. Experimental Data Classification

From the experimental data, it can be seen that the range of variation in Ra mean values is 7–55 μm. In order to achieve surface finish classification, the values of the arithmetic mean deviation Ra of the contours were divided into four levels according to the standard (ISO 1302:2002 [26]), namely N10, N11, N12, and N13, as shown in

Table 7. Classification ranges for surface roughness.

Roughness Value (μm)	Class Label
$Ra\le 12.5$	N10
$12.5<Ra\le 25$	N11
$25<Ra\le 50$	N12
$50<Ra$	N13

. Then, the 27 sets of experimental data were classified according to the grading ranges, as shown in

Table 8. Measurement values and category comparison table.

Test	Ra (μm)	Class Label	Sign
1	15.94	N11	2
2	14.58	N11	2
3	10.78	N10	1
4	44.66	N12	3
5	32.30	N12	3
6	25.17	N12	3
7	51.32	N13	4
8	43.48	N12	3
9	35.83	N12	3
10	8.76	N10	1
11	16.57	N11	2
12	11.99	N10	1
13	23.24	N11	2
14	41.45	N12	3
15	31.69	N12	3
16	30.81	N12	3
17	51.81	N13	4
18	40.02	N12	3
19	17.03	N11	2
20	7.81	N10	1
21	24.21	N11	2
22	29.55	N12	3
23	20.44	N11	2
24	34.05	N12	3
25	41.31	N12	3
26	30.30	N12	3
27	55.68	N13	4

.

4.3. Evaluation of Predictive Model Performance

In this section, the performance of APSO-KNN in predicting surface finish levels of FDM parts is evaluated and compared with existing mainstream classifiers, including Support Vector Machine (SVM), Artificial Neural Network (ANN), K-nearest neighbor (KNN), and Decision Tree. All models were developed using MATLAB R2021a [51].

Performance evaluation includes two aspects: comparing the accuracy of classification prediction and comparing model running time. First, the dataset was divided into a training set and a test set, with 70% of the dataset used for training the prediction model and 30% used for verifying the accuracy of the trained model. Then, the performance of each prediction model was examined through the minimum classification error chart and confusion matrix. The minimum error chart is a two-dimensional graph of classification error versus iteration number, showing the convergence speed of each algorithm, while the confusion matrix can show the predictive ability of each algorithm for each category. The results were divided into true positive rate (TPR) and false negative rate (FNR), where TPR represents the proportion of correctly predicted categories, while FNR represents the proportion of misclassified categories. Finally, the model running times were compared.

Comparative analysis was conducted using different classification indicators. The minimum prediction error of the APSO-KNN model is shown in Figure 5. Each model was trained using 19 data points (3-N10, 5-N11, 9-N12, and 2-N13) and tested using 8 data points (1-N10, 2-N11, 4-N12, and 1-N13) for surface finish prediction. The results showed that the APSO-KNN model converged after two iterations, with a minimum classification error of 0.01. The Decision Tree and ANN models achieved minimum classification errors of 0.32 and 0.32 after four and eight iterations, respectively. The number of layers of neurons in the ANN model is one of the important factors affecting its prediction accuracy. When the ANN model performs classification prediction, it optimizes the number of layers of neurons to search for the globally optimal number of layers that minimize the classification error. The model automatically adjusts the number of layers of neurons during iterations 19–30, but this is not the optimal number, which is why it jumps.

The optimal hyperparameter settings required for each model to achieve the minimum classification error are listed in

Table 9. Summary of the training of each model.

Model	Hyperparameter	Minimum Error	Training Accuracy	Training Time (s)
APSO-KNN	c1:2; c2:2; wmax:0.8; wmin:0.6; M:2; D:7; k:1	0.01	99.0%	14.40
Decision Tree	Maximum number of divisions: 1. Split criterion: Gini diversity index. Optimizer: Bayesian optimization	0.32	67.5%	14.18
SVM	Kernel function: linear. Box constraint level: 1. Multiple methods: one-to-one. Standardized data: true. Optimizer: Bayesian optimization	0.41	59.3%	36.63
KNN	k:1. Distance Metric: Euclidean. Distance weight: equidistant. Standardized data: true. Optimizer: Bayesian optimization	0.39	60.1%	24.88
ANN	Number of layers: 3. Activation function: ReLU. Iteration limit: 1000. Standardized data: true. Optimizer: Bayesian optimization	0.32	67.1%	39.92

.

Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10 display the confusion matrices of the test data for each model under the hyperparameter settings that resulted in the minimum classification error. The areas where the classifier performs poorly can be found by the percentage and color displayed within the cell, with orange representing predicted classes that do not match true classes. The higher the percentage, the darker the color inside the cell. It can be observed that only the APSO-KNN, SVM, and ANN models are capable of predicting the highest level of surface finish for class 1 (N10) with a small amount of data. However, the Decision Tree model predicts class 1 (N10) as a similar class 2 (N11), and the KNN model predicts it as class 3 (N12) with a larger amount of data. For class 2 (N11), only the APSO-KNN model can make accurate predictions, while the KNN model deviates completely by predicting the class with the largest amount of data, class 3 (N12). Other models have a TPR of 50%, and some will be predicted incorrectly (FNR is 50%). For class 3 (N12) with the largest amount of data, the SVM and ANN models are still affected by the excessive number of predicted categories, resulting in a large prediction error, with TPRs of 25% and 50%, respectively. The APSO-KNN model can accurately predict class 4 (N13), while other models predict it as class 3 (N12). Figure 11 shows the TPR of each model, with the APSO-KNN model having the best predictive performance. When the input variable weights are not searched using the APSO algorithm, the KNN model’s prediction results are biased toward the class with the largest amount of data (Figure 9). This problem is resolved by introducing the APSO algorithm, which accurately predicts and classifies imbalanced data with multiple factors and categories.

From Table 9, it can be observed that the training time of the APSO-KNN model is optimized compared to the KNN model, with a relative reduction of 10 s, which enhances the model’s predictive efficiency. The experiment results demonstrate that the proposed prediction model has good applicability in multi-factor and multi-class prediction and imbalanced data situations. It can provide instructive predictive data for the surface finish of FDM-printed parts in engineering practice.

5. Conclusions

In the current work, a method for predicting the surface finish of FDM PLA parts based on APSO-KNN is developed. The input attributes considered in this method include nozzle diameter, layer thickness, number of perimeters, flow rate, printing speed, nozzle temperature, and build orientation. The output variable is the discrete values of Ra measured on the sample surface: N10 (surface roughness value less than 12.5 μm), N11 (surface roughness value between 12.5 μm and 25 μm), N12 (surface roughness value between 25 μm and 50 μm), and N13 (surface roughness value greater than 50 μm). These values are taken from ISO 1302:2002 [26] and are commonly used in actual industrial production. The printing values of each sample were determined using the L27 Taguchi experimental design, and 27 samples were printed. The experimental data for the 27 samples were used to train and validate the method. The performance was compared with the most commonly used classifiers in existing research, including Decision Tree, SVM, KNN, and ANN. The actual classification accuracy and training time were used as comparison criteria for each model.

The comparative results show that the APSO-KNN prediction model performs the best, completing almost all predictions for the eight test datasets (1-N10, 2-N11, 4-N12, and 1-N13), with a TPR of 100% for N10, N11, N12, and N13. Moreover, the APSO-KNN model completed the prediction after only two iterations, and the training time of the model was only 14 s, indicating a satisfactory running efficiency. This model can solve the problems caused by data imbalance and multiple factors and multiple categories in predicting the surface finish of FDM-printed parts.

A limitation of the proposed method lies in the selection of the k value, which is a controversial issue in academia. Adjustments need to be made based on the actual situation, as too large or too small k values may affect classification accuracy, leading to a lack of uniformity in k value selection. In future work, deep learning methods will be explored to address this issue and increase the uniformity and robustness of the proposed method across different datasets. This would provide strong data support for the development of a surface finish prediction system for FDM-manufactured parts, improve the efficiency of actual engineering production, and reduce unnecessary material waste.