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Ink transfer rate (ITR) is a reference index to measure the quality of 3D additive printing. In this study, an ink transfer rate prediction model is proposed by applying the least squares support vector machine (LSSVM). In addition, enhanced garden balsam optimization (EGBO) is used for selection and optimization of hyperparameters that are embedded in the LSSVM model. 102 sets of experimental sample data have been collected from the production line to train and test the hybrid prediction model. Experimental results show that the coefficient of determination (^{2}) for the introduced model is equal to 0.8476, the root-mean-square error (RMSE) is 6.6 × 10 (−3), and the mean absolute percentage error (MAPE) is 1.6502 × 10 (−3) for the ink transfer rate of 3D additive printing.

The quality of the vamp printed by the traditional running table depends entirely on the using experiences of the printer, so the printing quality stability is poor when different people use the printer. A good way to get better quality and stability of printing is intelligent parameter adjusting of the 3D additive printing machine. In the practical production, squeegee angle, printing pressure, squeegee speed, ink viscosity, and screen mesh thickness affect the adhesion of ink from screen to sneaker surface and then directly affect the printing quality of vamp [

In the case of unchanged printing screen, there are four adjustable parameters of the printing machine, such as the squeegee angle, printing pressure, squeegee speed, and ink viscosity [

Based on the above analysis, the process parameter optimization problem of 3D additive printing can be described as the mathematical model as following. The squeegee angle, printing pressure, squeegee speed, and ink viscosity are four input parameters in the model, ITR is the output of the printing effect index, and the goal of the model is finding out the relationship between the input parameters and output index [

Because of the importance of the research topic, the production staff tried to do a lot of work on the experiment of improving the printing quality by the combination of process parameters. Machine learning as an advanced modeling tool has been used effectively in engineering applications [

According to the literature review, the application of advanced machine learning-based model to estimate printing quality remains a rarity. Although other methods such as ANN and gene expression programming (GEP) can also be used for printing quality modeling, these methods also have certain difficulties [

In this study, the least squares support vector machine (LSSVM) is used to construct a functional mapping to solve the above difficult printing quality prediction problem [

The chapters of this paper are organized as follows: the next part reviews the calculation methods used by LSSVM and GBO to build the hybrid prediction model. The third part describes the proposed model. The fourth part reports the experimental results. The concluding remarks are provided in the last section.

This section describes the LSSVM method used to construct a mapping function between the ITR and technological parameters. The LSSVM is a powerful nonlinear function approximation method that can effectively process multivariable and small-scale datasets [

In addition, the radial basis function (RBF) kernel is commonly used in LSSVM [

LSSVM is a mature technology, and I will not go into details here. The model for the LSSVM method requires setting two hyperparameters, such as the regularization coefficient (

Garden balsam optimization (GBO) is a recent swarm-based evolutionary algorithm that is inspired by the seed transmission mode of garden balsam. Garden balsam randomly ejects the seeds within a certain range by virtue of mechanical force originating from cracking of mature seed pods, which is different from natural expansion of most species of plants. The seeds scattered to suitable growth area will have greater reproductive capacity in the next generation, followed by iteration until the most suitable point for growth in a particular space is eventually found. Like other evolutionary algorithms, GBO is a numerical random search algorithm that simulates natural behavior. However, it also shows some deficiencies in the experiment. In the iteration process of the basic GBO algorithm, there is no cooperative mechanism between individuals; furthermore, there is lack of utilization of optimal individual information.

In the algorithm improvement, the balance between the early global exploration capability and the later local development capability should be considered. Enhanced garden balsam optimization (EGBO) uses flower pollination strategy for the population [

In the global pollination step, flower pollens are carried by pollinators such as insects, and pollens can travel over a long distance. This ensures the pollination and reproduction of the most fit, and thus, we represent the most fit as

The local pollination and flower constancy can be represented as follows:

The above two key steps plus the switch condition can be summarized in the pseudocode shown in Algorithm

Draw a (d-dimensional) set vector

Global pollination via

Draw

Randomly choose

Do local pollination via

Evaluate new solutions

If new solutions are better, update them in the population

Find the current best solution

Based on the strategy, the EGBO algorithm flowchart is given in Figure

Framework of the EGBO algorithm.

This section describes the framework of the hybrid model used to predict the final ink transfer rate. The hybrid model combines EGBO and LSSVM. It is worth noting that LSSVM is used to build a functional map that calculates the final ink transfer rate value based on four input variables. Since the regularization coefficient and kernel function parameters need to be determined in the training phase of the LSSVM model, the EGBO clustering intelligent algorithm is adopted to set these two hyperparameters automatically.

Therefore, the hyperparameters of the LSSVM model are randomly generated within the above boundary, and their expressions are as follows:

Figure

Hybrid EGBO-LSSVM model used for ink transfer rate prediction.

In order to determine the most appropriate LSSVM’s hyperparameter set, _{k} denotes root-mean-square error (RMSE) of LSSVM.

RMSE is calculated as follows:_{A} denotes actual value, _{P} denotes predicted value, and _{K} denotes the number of samples.

After calculating the cost function for each member of the population, the EGBO algorithm performs mechanical and secondary propagators to explore the search space and find a better solution, and then updates the positions of all population members based on the elitist-random selection operator. The EGBO optimization continues until the number of iterations reaches the value of iter_{max}. The optimized LSSVM model can be used to predict the ink transfer rate of new data samples when the appropriate set of hyperparameters is determined.

This section will present and analyze the experimental results of the hybrid EGBO-LSSVM model in the ink transfer rate prediction experiment. Four variables, including printing pressure (

The three variables of printing pressure (

Table

Statistical description of variables.

Variables | Notation | Max | Min | Mean | Std | Kurt | Skew |
---|---|---|---|---|---|---|---|

Printing pressure (N) | 5000 | 2600 | 3913.73 | 586.79 | −0.55 | −0.67 | |

Squeegee angle (°) | 20 | 5 | 10.49 | 6.66 | −1.46 | 0.63 | |

Squeegee speed (mm/s) | 900 | 400 | 658.82 | 159.26 | −0.60 | −0.47 | |

Ink viscosity (cP) | 180000 | 110000 | 141568.63 | 25581.29 | −1.52 | 0.25 | |

ITR | 0.44 | 0.21 | 0.35 | 0.05 | −0.41 | −0.41 |

Scatter plots of ink transfer rate w.r.t. different variables.

The experimental dataset.

NU | Printing pressure (N) | Squeegee angle (°) | Squeegee speed (mm/s) | Ink viscosity (cP) | Ink transfer rate |
---|---|---|---|---|---|

1 | 4000 () | 20 | 400 | 170000 | 0.267 |

2 | 4000 | 10 | 400 | 170000 | 0.314 |

3 | 4000 | 10 | 400 | 170000 | 0.287 |

4 | 4000 | 5 | 700 | 110000 | 0.316 |

5 | 4000 | 5 | 700 | 110000 | 0.312 |

6 | 4500 | 5 | 700 | 110000 | 0.323 |

7 | 4500 | 5 | 700 | 120000 | 0.324 |

8 | 4000 | 5 | 700 | 120000 | 0.323 |

9 | 4000 | 5 | 700 | 120000 | 0.323 |

10 | 4000 | 5 | 700 | 120000 | 0.323 |

11 | 5000 | 5 | 700 | 120000 | 0.317 |

12 | 4500 | 5 | 700 | 120000 | 0.421 |

13 | 4500 | 20 | 400 | 150000 | 0.344 |

14 | 4500 | 20 | 400 | 150000 | 0.362 |

15 | 4500 | 20 | 400 | 150000 | 0.375 |

16 | 4000 | 5 | 400 | 150000 | 0.417 |

17 | 4000 | 5 | 700 | 150000 | 0.428 |

18 | 4500 | 5 | 700 | 150000 | 0.349 |

19 | 4500 | 5 | 700 | 120000 | 0.349 |

20 | 5000 | 5 | 700 | 120000 | 0.432 |

21 | 4500 | 5 | 700 | 120000 | 0.379 |

22 | 4500 | 5 | 700 | 140000 | 0.379 |

23 | 4300 | 5 | 700 | 140000 | 0.383 |

24 | 4000 | 20 | 400 | 180000 | 0.413 |

25 | 4000 | 20 | 400 | 180000 | 0.427 |

26 | 4000 | 20 | 400 | 180000 | 0.431 |

27 | 4000 | 5 | 700 | 170000 | 0.346 |

28 | 4300 | 5 | 700 | 170000 | 0.386 |

29 | 4000 | 20 | 400 | 170000 | 0.356 |

30 | 3800 | 20 | 400 | 110000 | 0.345 |

31 | 3800 | 20 | 400 | 110000 | 0.298 |

32 | 4000 | 20 | 400 | 110000 | 0.213 |

33 | 4300 | 20 | 400 | 120000 | 0.425 |

34 | 3000 | 5 | 700 | 120000 | 0.321 |

35 | 3800 | 5 | 700 | 120000 | 0.318 |

36 | 3300 | 5 | 700 | 120000 | 0.316 |

37 | 3000 | 10 | 700 | 120000 | 0.394 |

38 | 2800 | 5 | 700 | 120000 | 0.296 |

39 | 2600 | 5 | 700 | 150000 | 0.265 |

40 | 2600 | 5 | 700 | 150000 | 0.265 |

41 | 3000 | 5 | 900 | 150000 | 0.323 |

42 | 4500 | 20 | 700 | 150000 | 0.442 |

43 | 4500 | 20 | 500 | 150000 | 0.443 |

44 | 4200 | 20 | 500 | 150000 | 0.435 |

45 | 4000 | 20 | 400 | 120000 | 0.298 |

46 | 2800 | 10 | 700 | 120000 | 0.334 |

47 | 3000 | 10 | 700 | 170000 | 0.367 |

48 | 3000 | 5 | 700 | 170000 | 0.385 |

49 | 3500 | 5 | 700 | 170000 | 0.412 |

50 | 2800 | 10 | 700 | 110000 | 0.254 |

51 | 3000 | 10 | 700 | 110000 | 0.296 |

52 | 3000 | 5 | 700 | 110000 | 0.227 |

53 | 4000 | 5 | 400 | 180000 | 0.413 |

54 | 4000 | 5 | 700 | 180000 | 0.412 |

55 | 4500 | 5 | 700 | 180000 | 0.374 |

56 | 4500 | 5 | 700 | 180000 | 0.353 |

57 | 4500 | 5 | 700 | 180000 | 0.353 |

58 | 4500 | 5 | 700 | 170000 | 0.427 |

59 | 4500 | 5 | 700 | 170000 | 0.353 |

60 | 4500 | 5 | 700 | 170000 | 0.341 |

61 | 4500 | 5 | 700 | 110000 | 0.327 |

62 | 4000 | 20 | 400 | 110000 | 0.389 |

63 | 4000 | 20 | 400 | 110000 | 0.365 |

64 | 4000 | 5 | 400 | 120000 | 0.337 |

65 | 4000 | 5 | 700 | 120000 | 0.323 |

66 | 4000 | 5 | 700 | 170000 | 0.395 |

67 | 4500 | 5 | 700 | 170000 | 0.385 |

68 | 4500 | 5 | 700 | 170000 | 0.385 |

69 | 4500 | 5 | 700 | 110000 | 0.376 |

70 | 4500 | 5 | 700 | 110000 | 0.369 |

71 | 4000 | 5 | 700 | 110000 | 0.329 |

72 | 4300 | 5 | 700 | 120000 | 0.375 |

73 | 4300 | 20 | 400 | 120000 | 0.369 |

74 | 4300 | 20 | 400 | 120000 | 0.407 |

75 | 4500 | 20 | 400 | 120000 | 0.421 |

76 | 4500 | 5 | 700 | 120000 | 0.254 |

77 | 4000 | 5 | 700 | 150000 | 0.297 |

78 | 4000 | 20 | 700 | 120000 | 0.324 |

79 | 4500 | 20 | 700 | 120000 | 0.315 |

80 | 4200 | 20 | 700 | 120000 | 0.382 |

81 | 4300 | 20 | 700 | 120000 | 0.378 |

82 | 4500 | 20 | 700 | 120000 | 0.368 |

83 | 3000 | 10 | 900 | 120000 | 0.304 |

84 | 3000 | 10 | 900 | 150000 | 0.297 |

85 | 3000 | 5 | 900 | 150000 | 0.245 |

86 | 4000 | 5 | 900 | 150000 | 0.392 |

87 | 3000 | 10 | 900 | 150000 | 0.327 |

88 | 3000 | 10 | 900 | 150000 | 0.33 |

89 | 3500 | 5 | 900 | 150000 | 0.329 |

90 | 4000 | 5 | 900 | 120000 | 0.414 |

91 | 4000 | 5 | 900 | 120000 | 0.432 |

92 | 3800 | 20 | 700 | 120000 | 0.423 |

93 | 3800 | 20 | 700 | 140000 | 0.41 |

94 | 3800 | 20 | 700 | 140000 | 0.411 |

95 | 3800 | 20 | 700 | 180000 | 0.411 |

96 | 3800 | 20 | 700 | 180000 | 0.411 |

97 | 3000 | 10 | 900 | 180000 | 0.312 |

98 | 2800 | 10 | 900 | 180000 | 0.289 |

99 | 3500 | 10 | 900 | 180000 | 0.389 |

100 | 3300 | 10 | 900 | 180000 | 0.431 |

101 | 2800 | 10 | 900 | 180000 | 0.218 |

102 | 3500 | 20 | 800 | 170000 | 0.3945 |

The experimental work for all problems is done on DELL Inspiron computer with Intel(R) Core (TM) i7-4500U, 2.4 GHz processor and 8 GB of memory running Windows 10. The implementation of experiment is done in MATLAB R2014a tool. EGBO and LSSVM parameters are shown in Table

The parameter values of the EGBO algorithm.

Symbol | Quantity | Value |
---|---|---|

_{init} | Number of initial population | 5 |

iter_{max} | Maximum number of iterations | 100 |

Problem dimension | 2 | |

_{max} | Maximum number of plant population | 50 |

_{max} | Maximum number of seeds | 5 |

_{min} | Minimum number of seeds | 1 |

Nonlinear modulation index | 3 | |

_{sec} | Number of second transmission | 5 |

Zoom factor | 2 | |

_{init} | Initial value of diffusion amplitude | 10 |

Switch probability | 0.8 |

The model optimization process by EGBO is shown in Figure

Convergence of the EGBO-LSSVM model.

After further analysis, the data set containing 102 samples is divided into training set (81 samples) and test set (21 samples). After the model is stabilized, the training set samples and test set samples are predicted to obtain the prediction results of ink transfer rate and the real value comparison. Figures

Comparison between estimated and measured ink transfer rate in training and testing phases.

Error between estimated and measured ink transfer rate in the testing phase: (a) absolute error and (b) absolute percentage error.

Scatter plot of estimated and measured ink transfer rate in training and testing phases.

Histograms of the model prediction error in training and testing phases.

In order to further analyze the performance of the prediction model, another analysis method is used. Figure

In order to better verify the capability of the EGBO-LSSVM model, the performance of the hybrid model is compared with that of BPANN, MARS, and RegTree [

As mentioned earlier, the data set containing 102 samples is divided into a training set (81) and a test set (21).

In order to offset the randomness of data selection, the EGBO-LSSVM model is executed 20 times and the average results obtained are compared with the other models for the same number of runs. To evaluate the performance of the EGBO-LSSVM model, relative percentage error (MAPE) and determination coefficient (^{2}) are used in addition to the RMSE described above [

The experimental results of ink transfer rate prediction of the four models are reported in Table ^{2} = 0.8476), followed by MARS (RMSE = 0.0080, MAPE = 2.0296%, and ^{2} = 0.7941), RegTree (RMSE = 0.0084, MAPE = 2.0915%, and ^{2} = 0.7563), and BPNN (RMSE = 0.0097, MAPE = 2.3631%, and ^{2} = 0.7467). It is worth noting that these results are the average of 20 repeated data samples used for model predictions. In addition, the prediction error boxplot of all models is shown in Figure

Comparative results of various methods averaged over 20 runs.

Phase | Metrics | EGBO-LSSVM | BPANN | MARS | RegTree | ||||
---|---|---|---|---|---|---|---|---|---|

Mean | Std | Mean | Std | Mean | Std | Mean | Std | ||

Training | RMSE | 0.0047 | 0.04 | 0.0110 | 0.53 | 0.0073 | 0.12 | 0.0088 | 0.19 |

MAPE (%) | 1.0247 | 0.45 | 3.7913 | 7.82 | 2.1734 | 2.11 | 3.1429 | 2.82 | |

^{2} | 0.9470 | 0.03 | 0.7908 | 0.06 | 0.8982 | 0.03 | 0.8591 | 0.03 | |

Testing | RMSE | 0.0066 | 0.42 | 0.0097 | 0.67 | 0.0080 | 0.61 | 0.0084 | 0.75 |

MAPE (%) | 1.6502 | 2.83 | 2.3631 | 5.28 | 2.0296 | 4.17 | 2.0915 | 5.41 | |

^{2} | 0.8476 | 0.14 | 0.7467 | 0.16 | 0.7941 | 0.14 | 0.7563 | 0.21 |

Box plots of prediction models.

It is also important to find out statistical significance of EGBO-LSSVM over other comparative models. To quantify the performance of the models statistically, the Wilcoxon symbolic rank test is used to better confirm the statistical significance of the superiority of EGBO-LSSVM. The ^{2} values.

Wilcoxon signed-rank test for the “RMSE,” “MAPE,” and the “^{2}” values obtained.

Test for RMSE | Test for MAPE | Test for ^{2} | |||
---|---|---|---|---|---|

Algorithm | Algorithm | Algorithm | |||

1-2 | 3.07 | 1-2 | 0.0050142 | 1-2 | 0.001481 |

1–3 | 0.07204543 | 1–3 | 0.0478682 | 1–3 | 0.000129 |

1–4 | 3.29 | 1–4 | 0.0016747 | 1–4 | 0.009786 |

In addition, to assess the sensitivity of input variables to the performance of the EGBO-LSSVM model, the Fourier amplitude sensitivity test (FAST) [

First-order sensitivity index (FOSI) of variables.

As can be seen from Figure

In this study, a model is developed and proposed in order to predict ink transfer rate in 3D additive printing by printing pressure, squeegee angle, squeegee speed, and ink viscosity as influential parameters. The conclusion can be summarized as follows:

The high viability and capability of LSSVM approach with RBF kernel to calculate ink transfer rate in 3D additive printing are proven based on the available experimental data.

Hyperparameters, including

A hybrid model of LSSSVM and EGBO provides an appropriate tool to predict ink transfer rate in 3D additive printing. The outputs of the model had good agreement with the experimental data. The determination coefficients, the root-mean-squared errors, and the mean absolute percentage errors of the model are 0.8476, 6.6 × 10 (−3), and 1.6502 × 10 (−3), respectively.

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was partially supported by the Natural Science Foundation of China (5147509) and the National Key R&D Program of China (2018YFB1308800).

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