I. Abstract of the Paper’s Core Research

This study employs silver nanoparticle conductive ink and a polyimide (PI) flexible substrate as the experimental platform, establishing a hybrid machine-learning–based process optimization framework. It systematically quantifies the coupled effects of sheath gas flow rate (SHGFR), carrier gas flow rate (CGFR), and printing speed on two key quality metrics—line width roughness and material overflow—and presents the following core findings:

Latin Hypercube Sampling (LHS) for global sampling, ensuring complete coverage of the parameter design space.

By abandoning traditional single-factor gradient experiments, we uniformly sample the multidimensional parameter space, comprehensively capturing printing defects arising from parameter interactions and thereby avoiding misjudgments due to local optima.

K-means unsupervised clustering partitions the print morphology into four classes.

Automatic grouping based on two key quality attributes—surface roughness and flash—yields distinct zones: the wire‑break defect zone, the high‑roughness–high‑flash zone, the single‑sided roughness zone, and the high‑quality molding zone, enabling intuitive identification of the parameter ranges associated with each type of process defect.

SVM: Support Vector Machine Automatically Generates the Optimal Process Boundary

A classification algorithm is used to plot the decision boundary, thereby identifying a stable printing window characterized by low surface roughness and minimal material overflow, and delineating the optimal sheath‑gas flow‑rate ranges for each printing speed.

Multi-source transfer learning significantly reduces the number of experiments required for new operating conditions.

Knowledge from the 1/4/7 mm/s datasets has been successfully transferred to the new printing speeds of 2.5 and 5.5 mm/s, enabling the construction of a highly accurate model with only a small number of additional samples, thereby reducing the experimental sample size by more than 60%.

Three-dimensional incremental classification for constructing a full-domain process window.

By integrating three key variables—gas flow, velocity, and deposition rate—an optimal 3D operating window is established, clearly demonstrating that high-speed printing requires enhanced carrier-gas‑assisted deposition. This provides comprehensive parameter guidance for customized micro‑circuit fabrication, while enabling silver traces to withstand thousands of bends with controllable resistance variation.

II. Aerosol + Machine Learning: A Complete Experimental Workflow

1) Silver nanoparticle ink formulation, ultrasonic atomization aerosol equipment, 150 μm nozzle, with a fixed spray distance of 4 mm;

2) A Latin hypercube is used to generate full‑dimensional experimental parameter points, enabling batch printing of conductive traces.

3) Optical imaging algorithms extract two key quality metrics: line-edge roughness and overflow area.

4) K-means clustering is used for morphological partitioning, and SVM is employed to delineate the optimal two-dimensional process window.

5) Transfer learning leverages low-speed experimental data to predict high-speed operating conditions, and an incremental iterative approach is employed to construct a three-dimensional, full-domain parameter model.

6) Optimal window parameter printing process, with conductivity and flexural durability testing conducted.

Five Key Advantages of Aerosol-Related Processes (Compared with Traditional Trial-and-Error Approaches)

Machine learning significantly shortens the debugging cycle and reduces ink and substrate waste.

Traditionally, manual trial-and-error required dozens of experimental runs, whereas algorithm-driven approaches can pinpoint the optimal parameter range with just a small number of samples, significantly reducing R&D material and time costs.

Global parameter coverage to avoid getting stuck in local optima.

Univariate experiments can easily overlook high-quality parameter combinations, whereas LHS uniform sampling fully captures the airflow–velocity coupling effect.

The model is transferable and reusable, enabling rapid adaptation to new devices and new inks.

The existing process knowledge base has been migrated to accommodate different printing speeds and ink systems, eliminating the need to conduct full-scale experiments from scratch.

Three-dimensional, full‑domain parameter guidance, tailored to customize high‑precision microcircuits.

It simultaneously controls sheath gas, carrier gas, and printing speed, balancing fine-line precision with film‑thickness‑dependent current‑carrying capability.

Quantify quality standards to establish replicable, mass‑production specifications.

Roughness and flash are assessed digitally, eliminating subjective visual judgments and facilitating the standardized implementation of production-line processes.

III. Five Core Technological Innovations of This Study

Innovation 1: An Integrated Aerosol Optimization Framework for Hybrid Machine Learning

An end-to-end algorithm integrating sampling, clustering, classification, and transfer learning—driving AJP process development through data, as opposed to the traditional trial-and-error approach based solely on experimentation.

Innovation 2: Automated Morphology Classification Mechanism

Using roughness and flash as distinguishing features, K-means unsupervised clustering automatically identifies four defect categories within the molding process window without manual labeling, enabling reverse traceability of defect causes to specific process parameters.

Innovation 3: Transfer Learning Addresses the Pain Point of Repeated Experiments Across Multiple Speed Conditions

The low-speed, mature model enables knowledge transfer to high-speed, new operating conditions, significantly reducing the need for experimental data and accelerating process‑iteration efficiency.

Innovative 4D Incremental Classification Full-Range Process Window Model

Breaking free from the limitations of a two-dimensional window of fixed printing speeds, we construct a three-dimensional global parameter space of airflow–velocity and comprehensively elucidate the compensation mechanisms underlying high-speed printing.

Innovation 5: A Digitalized, Quantitative Evaluation System for Product Quality

An image‑processing algorithm has been developed to automatically extract metrics for line roughness and material overflow, enabling an objective, quantitative assessment of print quality.

IV. Current Industry Challenges and Corresponding Solutions for Overcoming Them

Challenge 1: The sheath gas, carrier gas, and printing speed are strongly coupled across multiple variables, resulting in extremely low efficiency when relying on manual trial-and-error.

✅ Latin Hypercube Sampling combined with machine learning–based automated optimization enables you to pinpoint a stable process window using just dozens of data sets.

Challenge 2: Replacing the printing speed requires extensive re‑testing, resulting in a lengthy R&D cycle.

✅ Multi-source transfer learning reuses historical experimental data, significantly reducing the need for new-condition samples.

Challenge 3: Assessing circuit quality solely by visual inspection lacks a standardized quantitative metric, resulting in poor reproducibility during mass production.

✅ Optical image processing algorithms quantify surface roughness and flash‑over metrics, enabling objective assessment of circuit‑formation quality.

Challenge 4: A two-dimensional fixed-speed window cannot guide a variable-speed mass-production line.

✅ A three-dimensional, full‑domain process model that comprehensively characterizes airflow‑matching patterns across varying speeds, enabling compatibility with roll‑to‑roll dynamic printing.

Challenge 5: Process optimization yields only locally optimal solutions, leaving high-quality parameter combinations unexplored.

✅ Uniform sampling across the entire parameter space ensures comprehensive coverage, avoiding the bias inherent in single-variable experiments.

V. Future Diversified Industrial Application Scenarios

1 Rapid Process Calibration for Flexible Electronics Mass-Production Lines

When switching inks or substrates on a roll-to-roll aerosol production line, machine learning rapidly calibrates the optimal airflow velocity parameters, thereby reducing line‑setup downtime.

2 MEMS Microelectrode R&D Platform

Micro‑interdigitated electrodes with varying line widths and printing speeds are used, and an algorithm rapidly identifies processes that yield low surface roughness with no material overflow, thereby accelerating sensor prototype development.

3 Standardized R&D Tools for Aerosol Processes in Higher Education Institutions

The accompanying algorithms rapidly establish process libraries tailored to various conductive and dielectric inks, thereby reducing students’ need for repetitive trial-and-error experiments.

4 Foldable-screen precision metal wiring mass production

High-speed, high-precision micrometer-scale silver‑line fabrication, with a three-dimensional process window that enables real-time airflow matching under dynamic printing speeds.

5 Customized Printing of Aerospace Micro-Sensors

Rapid process development for small-batch, custom-shaped microcircuits reduces R&D waste associated with precious-metal inks.

Image and Text Guide

• The ultrasonic atomizer nebulizes a functional ink (silver ink mixed with water at a 1:1 ratio, at 20 °C) into an aerosol, which is then… Carrier gas (nitrogen) Carry it into the print head.
• Annular Sheath gas The aerosol stream is enclosed within the nozzle, then pneumatically focused and ejected at high velocity through a 150 μm nozzle, enabling the deposition of fine lines onto a moving polyimide substrate positioned on a heated stage.
• Experimental parameters: sheath gas flow rate (SHGFR) 15–150 sccm, carrier gas flow rate (CGFR) 15–50 sccm, and printing speed 1–10 mm/s.

• Edge roughness Rₘ : The deviation of the actual line edge from the average line (reference line), expressed as an upper/lower δ, reflects the line’s uniformity.
• Line Splash Oₛₚ : The average distance from the edge of the line to the discrete spatter points (upper/lower θ), reflecting the degree of overspray.
• The total quality Lq = wᵣ·Rₘ + w₀·Oₛₚ, after normalization, serves as a quantitative metric for print quality.

• (a) : Three-dimensional distribution of normalized line mass within the design space—significant mass variations across different regions.
• (b) K-means clustering partitions the line morphology into four subspaces: I—broken lines (low CGFR with insufficient ink transfer); II—high roughness plus high spattering (high SHGFR and high CGFR); III—high roughness plus low spattering (high CGFR with excessive buildup and spreading); IV—normal lines (low CGFR).
• (c–f) : Microscopic images of four types of line morphologies.

• SVM is used to determine the decision boundary in the SHGFR–CGFR design space, separating normal lines (blue) from abnormal lines (red) and defining the operational process window.
• After increasing the threshold α, the optimal window converges to SHGFR 40–85 sccm — Printing within this window can simultaneously reduce line roughness and overspray.

• (a) : Distribution of linear conductivity within the design space—Type I is predominantly open-circuit, while Type IV‑1 (within the improved window) exhibits optimal conductivity.
• (b) : Type III wire resistance varies nonlinearly with length (high non-uniformity), while Type IV is linear and optimal.
• (c) : After 1,000 bending cycles, the relative resistance remains nearly unchanged for r = 12 mm, while for r = 6 mm it increases to 1.4 times—demonstrating excellent mechanical flexibility of the wire within the window.

• After accelerating to 4 mm/s, subspace I expands (at high speeds, ink supply remains insufficient even at higher CGFR); the area of subspace IV (the normal line zone) decreases significantly.
• Quality is more sensitive to process parameters near the process window; therefore, after densifying the experimental points around the window, a support vector machine (SVM) is used to determine the decision boundary.

• Use the labeled line samples at 1/4/7 mm/s as the source domain, and apply Inductive Transfer Learning Transferring knowledge to the target speeds (2.5 and 5.5 mm/s) requires only a very small number of newly annotated samples to recognize new windows.
• Arrow direction: As printing speed increases, the normal line window shifts toward higher CGFR and lower SHGFR.

• In the three-dimensional space of SHGFR–CGFR–printing speed, the classifier is trained using the initial data plus 300 3D-LHS incremental samples, with iterations continuing (adding 30 points each time when the error exceeds ε) until convergence.
• Three-dimensional Separating Hyperplane Define the 3D process window; its cross-section is essentially consistent with the 2D window at 2.5/5.5 mm/s, and this has been verified as valid.
• Conclusion: Higher printing speeds require lower SHGFR and higher CGFR to produce normal lines, providing guidance for customized printing.