Machine learning-aided jet lag prediction for high-accuracy fabrication of melt electrowriting fibrous scaffolds

2.1. Material preparation

PCL (Mw = 50 kDa, Capa® 6500, Perstorp AB) pellets were sourced from Dongguan KXL Plastic Raw Material Co., Ltd. Prior to experimental use, the PCL pellets were loaded into a custom alumina syringe (Guangdong Blue Whale Ceramic Technology Co., Ltd.) and subjected to vacuum drying at 90 °C for 12 hours to remove residual moisture and eliminate entrapped air. Following this treatment, the syringe was equilibrated to room temperature (23.5±1 °C) and stored in a desiccator to minimize moisture uptake. For each printing experiment, the syringe was thermally conditioned within the MEW system at 90 °C for 30 minutes to attain a uniform molten phase with desired fluidity. All procedures were carried out in a controlled environment (temperature: 23.5±1 °C, relative humidity: 35±5%) to ensure process repeatability. After each printing, residual PCL was retained in the syringe and stored in a desiccator for subsequent experiments.

2.2. MEW system configuration

The MEW system comprised four functionally integrated units, as depicted in Figure 2: (a) Material feeding: A customized 5-mL alumina ceramic syringe was loaded with molten PCL and fitted with a 24-gauge stainless steel nozzle (inner diameter: 0.27 mm). The syringe’s upper port was linked to an air compressor (Hong Run Compressor Technology Co., Ltd.) via a pressure regulator (0–0.4 MPa range) to ensure controlled extrusion. (b) Thermal regulation: A dual-layer heating assembly enclosed the syringe, with a PID-controlled heating pad placed between the ceramic walls to maintain temperature control. (c) High-voltage generation: A high-voltage DC power supply (Teslaman Technology Co., Ltd.) provided an adjustable electric field (0–20 kV range), where the nozzle is connected to the positive terminal and a circular copper collector plate (150 mm diameter × 0.5 mm thickness) to the negative terminal. The nozzle-to-collector distance was fixed at 7 mm using a Z-axis slide (Suzhou Zhide Automation Co., Ltd.). (d) Motion control: The collector plate, mounted on a polylactic acid (PLA)-insulated base, was driven by a computer-controlled XY translational stage (Suzhou Zhide Automation Co., Ltd.) with a positional resolution of 1 μm, enabling programmable movements.OPEN IN VIEWER

2.3. Image acquisition and toolpath design

To systematically capture jet images under varying process parameters, an industrial camera (MIchrome 20, Shenzhen SANOTID Optical Instrument Co., Ltd.) was fixed at a position aligned horizontally with the nozzle, ensuring a clear view of the nozzle and jet at the same angle and distance. Illumination was provided by an LED light panel positioned behind the collector to enhance the contrast of the jet (Figure 3(a)). For each combination of process parameters, 50 images were acquired to ensure that enough clear and stable jet images were available for subsequent analysis and computation and to reduce the influence of incomplete or low-quality images. Additionally, the printed samples were imaged using a scanning electron microscope (KYKY-EM6200, KYKY Technology Co., Ltd.).OPEN IN VIEWER

To ensure accurate measurement of the jet lag length from the captured images, reciprocating toolpaths along the X-axis were designed and programmed (with minimal offset in the Y-axis direction). These toolpaths ensured that the platform moved parallel to the camera’s focal plane, allowing the camera to continuously and fully capture the jet lag with acceptable clarity (Figure 3(b)). Each segment exceeded 50 mm in length, with a minimum printing duration of 5 seconds, ensuring that a steady-state jet was captured for analysis.

2.4 Image processing algorithm for jet lag length computation

Raw images captured by the industrial camera were first converted to grayscale to facilitate feature extraction. An adaptive thresholding method was applied to binarize the images. In the binarized image, the contours of the objects in the image can be identified, sequentially representing the nozzle, jet, and collector from top to bottom. (Figure 4(a)).OPEN IN VIEWER

Based on the extracted contours, the jet lag length can be calculated as follows. First, the pixels are scanned from left to right for each row for the index of the first white pixel. When this index keeps invariant for five consecutive rows, it is identified as the location of the left edge of the nozzle. The horizontal distance between the first and last white pixels in these rows defines the outer diameter of the nozzle ( D n oz ).

The midpoints between these edge pixels are calculated for each row, and connected to form a vertical reference line ( L ve r ) perpendicular to the X-axis, which indicates the location of the centerline of the nozzle.

Subsequently, scanning resumes downward from the nozzle edge until the index of the first white pixel starts to change, which indicates the uppermost location of the jet.

Scanning continues until a row exceeds a predefined jet diameter threshold ( D j et ), which indicates the identification of the lowermost location of the jet. The midpoint between the first and last white pixels in the last row is identified as the jet contact point with the collector, namely the jet deposition point ( P je t ).

Finally, the horizontal offset between P je t and L ve r is measured ( D ho r ), and the jet lag length is calculated using Equation (1):

L = 0.70 D ho r D noz ( mm )

(1)

2.5 Single-factor experiments

To systematically evaluate the independent effect of the selected process parameters on the jet lag length, single-factor experiments were conducted for each of the parameters. The parameter ranges were carefully chosen in order to maintain a relatively constant jet lag length within the field of view of the camera, i.e. to avoid instabilities such as electrostatic sparking, fiber pulsing, or jet deformation. The conditions of single-factor experiments were set according to Table 1(denoted as set levels), and the reference levels indicate the levels at which the other parameters were maintained when the set level of the study factor was varied.

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Table 1.

Parameter ranges and reference levels for single-factor experiments.

Process parameter	Set level	Reference level
		Material temperature (°C)	Collector speed (mm/s)	Nozzle-to-collectordistance (mm)	Voltage (kV)	Air pressure (MPa)
Material temperature (°C)	125/130/135/140/145/150	/	5	0.8	4.0	0.25
Collector speed (mm/s)	3/5/7/9/11/13	140	/	0.8	4.0	0.25
Nozzle-to-collector distance (mm)	0.6/0.7/0.8/0.9/1.0/1.1	140	5	/	4.0	0.25
Voltage (kV)	2.5/3.0/3.5/4.0/4.5/5.0	140	5	0.8	/	0.25
Air pressure (MPa)	0.15/0.20/0.25/0.30/0.35/0.40	140	5	0.8	4.0	/

2.6 Data processing

For each combination of parameters, 10 representative images were selected from the 50 acquired images for quantitative measurement, and the results are expressed as the mean ± standard deviation. As shown in Table 1, data collection was performed for 6 levels of each parameter while the remaining parameters were kept at their reference levels, resulting in a total of 300 data points (6 levels × 5 parameters × 10 images). This dataset was designed as a controlled first-step dataset for jet lag prediction, with emphasis on physically interpretable single-factor trends rather than full coverage of the multidimensional parameter space. The statistical significance between process parameter levels was assessed using one-way analysis of variance (ANOVA) followed by Tukey’s post hoc test (α=0.05). Group differences were annotated in figures using lowercase letters, where distinct letters denote statistically significant deviations (p<0.05).

2.7 Model development and performance evaluation

To evaluate the effects of process parameters on the jet lag length and to develop predictive models, two supervised learning models were employed: multiple linear regression and random forest. Multiple linear regression was used as an interpretable baseline model to show the first-order effects of the five process parameters on the jet lag length, whereas random forest was used as a more flexible model to account for potential nonlinear dependencies in the dataset. In this way, the comparison between the two models allowed both interpretability and predictive performance to be considered.

Explicit interaction and quadratic terms were not included in the present multiple linear regression model. This is because the current dataset was mainly generated from single-factor experiments, which are suitable for identifying first-order trends but do not fully cover the multidimensional parameter space needed to robustly estimate higher-order terms. In addition, including such terms would substantially increase model complexity and could lead to unstable coefficients under the current dataset structure. Therefore, a relatively simple multiple linear regression model was used as the baseline model in this study.

Prior to model development, the dataset was assessed for suitability. The dataset was then randomly divided into a training set (80%) and a test set (20%), using a fixed random seed (42) for reproducibility. Because the data were collected under a controlled single-system experimental setting rather than across clearly separable experimental batches, no batch grouping was applied. The training set was used for model fitting, and the test set was used for model evaluation. Model performance was assessed using the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). Given the modest dataset size and the structured single-factor design, the predictive results should be interpreted within the scope of the present dataset.

3.1 Single-factor experimental analysis of process parameters on jet lag length

In the single-factor experimental analysis, we investigated the individual effects of five key process parameters on the jet lag length: material temperature, collector speed, nozzle-to-collector distance, voltage, and air pressure. These process parameters were chosen due to their ease of dynamic control during experiments and their significant effects on jet lag based on our previous attempts. Other potential process parameters, such as the thermal conductivity, viscosity, density, relative permittivity, and electrical conductivity of PCL, as well as nozzle inner diameter and ambient temperature and humidity, were not considered.

The corresponding single-factor results are shown in Figure 5. Overall, Figure 5 shows clear correlations between jet lag length and each parameter. Specifically, jet lag length decreases with increasing material temperature and voltage, indicating negative correlations, whereas it increases with increasing collector speed, nozzle-to-collector distance and air pressure, indicating positive correlations. These trends provide the basis for the following mechanistic interpretation.OPEN IN VIEWER

These results are consistent with the fundamental principles of the MEW process. During MEW, the high voltage at the nozzle injects positive charges into the melt through two mechanisms: field emission and charge dissociation, forming the physical basis for the electrostatic stretching of the jet. The viscoelastic resistance opposing this stretching primarily stems from the viscosity of the melt, which decreases with higher material temperature. This reduction in viscosity allows for faster jet acceleration and results in a smaller jet lag length (Figure 5(a)). An increase in collector speed elevates the mechanical drag on the jet, causing it to deviate more from the nozzle’s projection on the collector and thus increasing jet lag length (Figure 5(b)). Nozzle-to-collector distance affects the electric field intensity. When voltage is fixed, increasing nozzle-to-collector distance weakens the electric field, slowing jet deposition and increasing jet lag length (Figure 5(c)). Higher voltage increases both charge density and electric field intensity. The greater electrostatic force accelerates jet deposition, thereby reducing jet lag length (Figure 5(d)). Lastly, air pressure influences the melt flow rate. Higher air pressure boosts the flow rate. Under the same electric field conditions, this reduces the charge density per unit mass of the melt, diminishing the electrostatic force per unit mass and leading to a larger jet lag length (Figure 5(e)).

3.2 Model selection for multiple linear regression and random forest

As described in Section 2.7, multiple linear regression and random forest were employed as complementary models to evaluate both first-order trends and potential nonlinearities.

For the multiple linear regression model, the main assumptions, including linearity, residual normality, homoscedasticity, independence of observations, and absence of multicollinearity, were checked before further analysis. The detailed results are provided in the Supporting Information (Figure S1 and Table S1). Compared with multiple linear regression, random forest requires fewer assumptions about data distribution and is more flexible in handling potentially complex relationships. Therefore, multiple linear regression and random forest were used here as complementary models for comparing interpretability and predictive capability in jet lag prediction.

3.3 Qualitative comparison of feature importance rankings between multiple linear regression and random forest

Understanding how different process parameters influence jet lag length is important for both model interpretation and process optimization. In the multiple linear regression model, the standardized coefficients (β) were used to indicate the linear contribution of each process parameter to jet lag length. For a given parameter, β was calculated using Equation (2)

β = B * S x S y

(2)

L = 27.152 − 0.136 * T + 0.414 * V + 6.261 * D − 3.741 * U + 9.080 * P .

(3)

A larger absolute value of β (i.e., | β | ) indicates a stronger linear relationship with the target variable. As shown in Table 2, according to | β | from the multiple linear regression model, the process parameters are ranked in the following order of importance: voltage > collector speed > material temperature > nozzle-to-collector distance > air pressure.

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Table 2.

| β | and feature importance (FI) for different process parameters in the multiple linear regression and random forest models.

​	Material temperature	Collector speed	Nozzle-to-collectordistance	Voltage	Air pressure
| β |	0.290	0.433	0.266	0.795	0.193
FI	0.078	0.218	0.073	0.565	0.066

On the other hand, random forest assesses feature importance through the mean decrease in impurity denoted by FI, which quantifies how much a feature contributes to reducing prediction uncertainty. For a specific parameter, FI can be calculated using Equation (4):

FI = 1 N ∑ j = 1 N ( I j − N jL N j I jL − N jR N j I jR ) ,

(4)

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Figure 6.

Comparison of feature importance rankings, predictive performance, and model interpretability. (a) Feature importance rankings identified by the multiple linear regression and random forest models, shown as orange and green bars, respectively. (b) Comparison of predicted and actual jet lag length values on the test set using 20 randomly selected data points, where orange triangles and green circles denote the multiple linear regression and random forest models, respectively. (c) Schematic diagram of the random forest model. (d) Distribution of Shapley additive explanations (SHAP) values for each feature in the random forest model. The color gradient from blue to red indicates low to high feature values. In Figure 6, U, V, T, D, and P denote voltage, collector speed, material temperature, nozzle-to-collector distance, and air pressure, respectively.

3.4 Comparison of predictive performance and practical implications of multiple linear regression and random forest

Commonly used metrics for evaluating predictive performance include the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). As shown in Table 3, the random forest model outperformed the multiple linear regression model across all three metrics on the test set. To provide a more intuitive comparison, the predicted and actual values of jet lag length are plotted in Figure 6(b). The random forest predictions are generally closer to the actual values, further indicating its higher predictive accuracy under the present dataset.

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Table 3.

Comparison of predictive metrics for multiple linear regression and random forest models.

Model	R2	RMSE	MAE
Multiple linear regression	0.934	0.507	0.365
Random forest	0.992	0.174	0.137

Random forest is an ensemble learning method based on decision trees, as schematically illustrated in Figure 6(c). Compared with multiple linear regression, random forest is better suited to representing potential nonlinear dependencies within the current dataset, whereas multiple linear regression is restricted to first-order linear effects. This distinction is relevant because the MEW process is governed by multiple physical mechanisms, including extrusion, electrostatic stretching, and solidification, which may give rise to nonlinear dependencies among process parameters. However, this result should be interpreted with appropriate caution. The present findings should not be regarded as definitive evidence of multidimensional interaction learning, because the current dataset was mainly generated from single-factor experiments and does not fully cover the coupled parameter space of MEW. Stronger validation of such effects will require future experiments involving deliberately coupled multi-parameter conditions or testing under previously untested parameter combinations.

From an interpretability perspective, multiple linear regression provides clear information on the direction and relative magnitude of first-order parameter effects, which is useful for understanding how individual process parameters relate to jet lag length. Random forest, in contrast, offers greater flexibility in prediction but requires additional tools for interpretation. Therefore, SHAP values were used to interpret the random forest model internally. As shown in Figure 6(d), SHAP values quantify the direction and magnitude of each feature’s contribution to the random forest prediction of jet lag length. Values on the right side of zero contribute to a higher predicted jet lag length, whereas values on the left side contribute to a lower predicted jet lag length. The wider spread observed for voltage, collector speed, and material temperature suggests that these features exert relatively stronger effects on the prediction, while nozzle-to-collector distance and air pressure play comparatively smaller roles.

From a practical perspective, the comparison between multiple linear regression and random forest suggests different use scenarios for the two models in MEW. Multiple linear regression is useful when interpretable first-order parameter trends are of primary interest, whereas random forest is more suitable when accurate jet lag prediction is needed to support nonlinear printing. Therefore, the value of random forest in this study lies not only in its higher predictive accuracy, but also in its practical utility for improving printing accuracy in MEW.

3.5 Experimental validation of the predictive framework

To further evaluate the practical usefulness of the predictive framework, nonlinear printing was implemented with the circle curve used as the toolpath. As reported in our previous research, if the jet lag length is kept constant and the printed fiber pattern is a circle, the toolpath will be a concentric circle with a larger radius. To be specific, the radius of the fiber pattern (r) and the toolpath (R) follow r 2 = R 2 − L 2 (Figure 7(a)). In this section, R was kept at 6 mm, and the corresponding calculated r are shown in Figure 7(b) at different jet lag length values (jet lag length = 1, 2, 3, 4, and 5 mm). Using process parameters from our existing dataset that were predicted to produce jet lag length values of 1, 2, 3, 4, and 5 mm, we proceeded to print and obtained the actual fiber pattern (Figure 7(c)). Subsequently, the actual r was compared with the calculated r as shown in Figure 7(d). These results provide experimental validation of the predictive framework and demonstrate its practical value for improving printing accuracy in MEW.OPEN IN VIEWER

3.6 Printing of complex nonlinear fibrous scaffolds and the limitation of residual charge effects

Building upon the validated predictive performance, we further applied the jet lag prediction to the fabrication of complex nonlinear fibrous scaffolds. As shown in Figure 8, by adjusting process parameters based on the predicted jet lag length, the resulting fibrous scaffolds exhibit well-ordered fiber stacking and high accuracy, highlighting the positive impact of jet lag prediction on both printing stability and accuracy.OPEN IN VIEWER

However, we observed a phenomenon where the jet lag length tended to increase as printing progressed to higher layers, even with unchanged process parameters. This is attributed to the gradual accumulation of positive charges injected into the polymer on the collector. This accumulation creates repulsion with the similarly positively charged jet, weakening the electric field’s acceleration effect on the jet and thereby increasing the jet lag length. It should be noted that the current predictive models were trained using data collected under single-factor, effectively low-layer printing conditions. Therefore, although the models show high predictive accuracy under the present conditions, their performance may decrease in higher-layer printing, where residual charge effects become more pronounced. Addressing this dynamic influence of residual charge remains an important challenge for future model development and for more accurate prediction in complex MEW fabrication.