A method for synergistic optimization of process parameters for reactive silver ink in aerosol inkjet printing

Abstract

This invention discloses a method for synergistic optimization of process parameters for aerosol inkjet printing of reactive silver ink. It relates to the field of aerosol inkjet printing technology and addresses the technical problems of existing technologies that struggle to achieve synergistic optimization under multi-parameter coupling of ink formulation parameters and aerosol inkjet printing process parameters, failing to guarantee conductivity while simultaneously improving adhesion performance, and requiring numerous experiments and long optimization cycles. The method comprises: determining a parameter space; generating initial parameter combinations within the parameter space and conducting printing experiments; obtaining an initial experimental dataset; training two independent Gaussian process regression models; performing multi-objective optimization search to obtain the Pareto front solution set; determining the first and second combinations and conducting printing verification to obtain experimental data; retraining the Gaussian process regression models; and outputting the optimal parameter combination after meeting the convergence condition.

Description

Technical Field

[0001] This invention relates to the field of aerosol inkjet printing technology, and more specifically, to a method for synergistic optimization of process parameters for aerosol inkjet printing of reactive silver ink. Background Technology

[0002] Aerosol Jet Printing (AJP), a high-resolution direct-writing manufacturing technology, can deposit functional materials with linewidths in the micrometer or even sub-ten-micrometer range onto the surfaces of flexible polymers, glass, ceramics, and complex three-dimensional structures. It holds broad application prospects in flexible electronics, wearable electronics, and conformal electronic devices. Conductive ink is one of the key materials affecting AJP printing quality and device performance. Reactive Silver Ink uses silver complexes or silver precursors as its metal source, generating metallic silver in situ at lower temperatures through thermal decomposition or chemical reactions. It offers advantages such as low-temperature sintering and high metal utilization.

[0003] Currently, common methods for optimizing the formulation and process parameters of AJP reactive silver inks include single-factor experiments, orthogonal experimental design, and response surface methodology. These methods find optimal combinations by systematically changing some parameters and analyzing their impact on performance indicators, thus improving experimental efficiency to some extent. However, when there are many parameters to be optimized and there are obvious coupling relationships between them, the above methods often require a large number of experiments to obtain a better solution, and it is difficult to simultaneously consider the trade-offs between multiple performance indicators (such as conductivity and adhesion performance). In recent years, machine learning methods have been gradually introduced into the field of materials design and process optimization. By establishing predictive models between parameters and performance, they guide experimental design, thereby reducing the number of experiments and improving optimization efficiency. However, in existing research, most machine learning methods still mainly optimize a single performance indicator, or only optimize material formulation parameters or only a certain type of variable in the process parameters. Research on the synergistic optimization between ink formulation parameters and AJP process parameters remains relatively limited. Therefore, in the AJP reactive silver ink system, how to achieve synergistic optimization of ink formulation parameters and printing and sintering process parameters under multi-parameter coupling conditions, while ensuring that the conductivity of the conductive circuit meets the requirements, further improves the adhesion performance, and reduces the number of experiments and optimization cycle, remains a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0004] The purpose of this invention is to provide a method for synergistic optimization of process parameters for aerosol inkjet printing of reactive silver ink. This method addresses the technical problems of existing technologies, which struggle to achieve synergistic optimization under multi-parameter coupling conditions of ink formulation parameters and aerosol inkjet printing process parameters, failing to balance conductivity and adhesion properties, and requiring numerous experiments and long optimization cycles. Therefore, this invention achieves this through the following solution.

[0005] This invention provides a method for synergistic optimization of process parameters for aerosol inkjet printing of reactive silver ink, comprising: Determine the parameter space; the parameter space includes ink formulation parameters and printing and sintering process parameters. Initial parameter combinations are generated within the parameter space, and printing experiments are performed; the conductivity and interfacial shear strength corresponding to each initial parameter combination are obtained to obtain the initial experimental dataset; Using the initial parameter combination as input, and electrical conductivity and interfacial shear strength as outputs, two independent Gaussian process regression models are trained. A multi-objective optimization search is performed based on a Gaussian process regression model, with the search direction being to find a conductivity greater than or equal to 10. 7 Under the premise of S / m, increase the interfacial shear strength to obtain the Pareto front solution set; Determine the first and second parameter combinations, and verify them by printing to obtain experimental data; add this experimental data to the initial experimental dataset to retrain the Gaussian process regression model; repeat the subsequent process until the preset convergence condition is met, and output the optimal parameter combination; wherein: The first combination is the parameter combination with the highest predicted conductivity selected from the Pareto front solution set; the second combination is the parameter combination with the largest predicted variance of the Gaussian process regression model.

[0006] Compared with existing technologies, the co-optimization method for process parameters of aerosol inkjet printing active silver ink in this invention treats the formulation parameters of aerosol inkjet printing active silver ink (such as silver precursor concentration, volume fraction of low-boiling-point alcohol solvent, and polymer thickener concentration) and printing and sintering process parameters (such as substrate temperature, printing speed, nozzle diameter, sintering time, and aerosol focusing ratio) as a complete parameter space. Initial parameter combinations are generated and experiments are conducted (e.g., using Latin hypercube sampling) to obtain conductivity and interfacial shear strength data. Two independent Gaussian process regression models are then trained to predict conductivity and interfacial shear strength respectively, while simultaneously providing prediction uncertainties. Based on this, a multi-objective optimization algorithm is used to optimize conductivity to a value not less than 10. 7S / m is a hard constraint, and the Pareto front solution set is searched with the goal of maximizing the interface shear strength. In particular, in each iteration, the parameter combination with the highest predicted conductivity (using the current best prediction value) and the parameter combination with the largest prediction variance (using the model's cognitive uncertainty) are selected from the Pareto front solution set for actual printing verification. New data is added to the training set to retrain the model. This process is repeated until convergence, and finally the optimal parameter combination is output. Based on the above technical solution, a Gaussian process regression model is used to model the conductivity and interfacial shear strength. For example, combined with NSGA-II multi-objective optimization, it can effectively handle the complex nonlinear coupling relationship between substrate temperature, ethanol ratio, hydroxyethyl cellulose, and AJP printing parameters. Specifically, too low a substrate temperature will result in incomplete silver sintering and insufficient adhesion, while too high a substrate temperature will cause bubble defects due to intensified reaction. Insufficient ethanol ratio cannot suppress high-temperature bubbles, while too high an ethanol ratio dilutes the silver content. Too high a concentration of hydroxyethyl cellulose will affect the conductive network during low-temperature sintering, while too low a concentration will reduce adhesion. These factors are intertwined, making it almost impossible for traditional single-factor experimental methods to find the parameter combination that achieves the optimal adhesion performance while meeting the conductivity requirement. This invention uses Gaussian process regression to learn the mapping relationship between parameters and performance and quantifies the prediction uncertainty. Then, through multi-objective optimization, it automatically searches for the Pareto optimal solution of adhesion performance under the premise of satisfying the conductivity constraint, thereby stabilizing the conductivity to 10. 7 The parameters are above S / m, and the interfacial shear strength also reaches a high level. Furthermore, this invention achieves an automatic balance between exploration and utilization by simultaneously selecting two candidate parameter combinations—the predicted optimal and the one with the largest predicted variance—for experimental verification in each iteration. Specifically, the predicted optimal combination is used to find the optimal solution using the current model knowledge, while the combination with the largest predicted variance is used to explore parameter regions where the model's understanding is insufficient to accelerate model convergence. This active learning strategy significantly reduces the number of experiments required to reach the optimal parameter combination. Furthermore, since both conductivity and adhesion performance are considered simultaneously during the optimization process, and a lower limit for conductivity is set in the constraints, the final output optimal parameter combination not only meets the conductivity standard but also exhibits good repeatability. For example, in one embodiment of this invention, the standard deviation of conductivity in five repeated experiments is 0.03 × 10⁻⁶. 7The S / m ratio is less than 5% of the mean, and the standard deviation of the interfacial shear strength is 0.22 MPa, indicating that the low-temperature sintering process window of the reactive silver ink has been broadened, the tolerance to process fluctuations has been improved, and the process stability in industrial production has been enhanced. Furthermore, this invention can ensure that the optimization process can terminate within a reasonable number of iterations by setting the convergence condition to a change in conductivity of less than 1% in two consecutive iterations, or reaching the maximum number of iterations of 5, or actual verification that the conductivity has been stably met and the adhesion performance meets the requirements, thus outputting a stable and reliable parameter combination and avoiding excessive experimentation. Through the above technical solution of this invention, the technical problems of existing technologies that are difficult to achieve synergistic optimization under the multi-parameter coupling of ink formulation parameters and aerosol inkjet printing process parameters, cannot take into account both conductivity and adhesion performance, and have a large number of experiments and a long optimization cycle are solved.

[0007] Furthermore, in the method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink of the present invention, the ink formulation parameters include: a silver precursor concentration of 10~30wt%, an alcohol solvent volume fraction of 5~20vol%, and a polymer tackifier concentration of 0.1~1.0wt%. The printing and sintering process parameters include: substrate temperature of 70~110℃, printing speed of 2~8mm / s, nozzle diameter of 100~300μm, sintering time of 30~60min, and aerosol focusing ratio of 1.5~3.0; the aerosol focusing ratio is the ratio of sheath gas flow rate to carrier gas flow rate.

[0008] Furthermore, in the method for synergistic optimization of process parameters for aerosol inkjet printing active silver ink of the present invention, the alcohol solvent includes ethanol, isopropanol, or n-propanol; the polymer tackifier includes hydroxyethyl cellulose, polyethylene oxide, or polyvinylpyrrolidone.

[0009] Furthermore, in the aerosol inkjet printing reactive silver ink process parameter co-optimization method of the present invention, the convergence conditions include the predicted conductivity change of the optimal parameter combination obtained in two consecutive iterations being less than 1%, reaching a preset maximum number of iterations of 5, or the verification experimental results satisfying a conductivity greater than or equal to 10. 7 The S / m ratio is high, and the interfacial shear strength meets the application requirements.

[0010] Furthermore, in the aerosol inkjet printing reactive silver ink process parameter co-optimization method of the present invention, the Gaussian process regression model adopts a combination of squared exponential kernel function and noise kernel, and optimizes the signal variance, feature length scale and noise variance hyperparameters in the kernel function by maximizing marginal likelihood estimation.

[0011] Furthermore, in the aerosol inkjet printing reactive silver ink process parameter co-optimization method of the present invention, after outputting the optimal parameter combination, it further includes: At least five repeated printing experiments were conducted using the optimal parameter combination, and the mean and standard deviation of conductivity and interfacial shear strength were statistically analyzed; if the mean conductivity was greater than or equal to 10... 7 If the S / m value is less than or equal to 5% of the mean, then the parameter combination is considered to meet the process stability requirements.

[0012] Furthermore, in the aerosol inkjet printing reactive silver ink process parameter co-optimization method of the present invention, multi-objective optimization search is performed based on a Gaussian process regression model, including: Based on a trained Gaussian process regression model, a non-dominated sorting genetic algorithm with an elitist strategy is used for multi-objective optimization search.

[0013] Furthermore, in the method for collaborative optimization of process parameters of aerosol inkjet printing reactive silver ink of the present invention, a data acquisition function is introduced when selecting the first combination and the second combination; the data acquisition function is used to weight and combine the predicted mean and the predicted variance to achieve a balance between exploration and utilization.

[0014] Furthermore, in the aerosol inkjet printing reactive silver ink process parameter co-optimization method of the present invention, before training the Gaussian process regression model, it further includes: The bubble area ratio of the conductive line cross section is extracted. When the bubble area ratio exceeds 5%, the sample is marked as an outlier and assigned the first weight in the model training. The extraction of the bubble area ratio is automatically identified by a deep learning segmentation model based on the U-Net architecture.

[0015] Secondly, the present invention provides a collaborative optimization system for process parameters of aerosol inkjet printing reactive silver ink, comprising: The parameter space module is used to define the parameter space, which includes ink formulation parameters and printing and sintering process parameters. The dataset acquisition module is used to generate initial parameter combinations in the parameter space and to print experiments; it obtains the conductivity and interfacial shear strength corresponding to each initial parameter combination to obtain the initial experimental dataset. The model training module is used to train two independent Gaussian process regression models with initial parameter combinations as input and electrical conductivity and interfacial shear strength as outputs, respectively. The model update module is used for multi-objective optimization search based on the Gaussian process regression model. The search direction is to find the model with conductivity greater than or equal to 10. 7Under the premise of S / m, the interfacial shear strength is increased to obtain the Pareto front solution set; the first combination and the second combination are determined and printed to verify and obtain experimental data; the experimental data are added to the initial experimental dataset to retrain the Gaussian process regression model; wherein: the first combination is the parameter combination with the highest predicted conductivity selected from the Pareto front solution set; the second combination is the parameter combination with the largest predicted variance of the Gaussian process regression model; The results output module is used to output the optimal parameter combination.

[0016] Compared with the prior art, the beneficial effects of the aerosol inkjet printing active silver ink process parameter co-optimization system of the present invention are the same as the beneficial effects of the aerosol inkjet printing active silver ink process parameter co-optimization method described in the above technical solution, and will not be repeated here. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart illustrating a method for collaborative optimization of process parameters for aerosol inkjet printing of reactive silver ink according to the present invention. Figure 2 This is a schematic diagram illustrating the coupling effect of substrate temperature, the proportion of low-boiling-point alcohol solvents, and the concentration of polymer thickener on conductivity in this invention. Figure 3 This is a schematic diagram comparing the process windows before and after optimization in this invention. Detailed Implementation

[0018] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0019] It should be noted that when a component is referred to as being "fixed to" or "set on" another component, it can be directly on or indirectly on that other component. When a component is referred to as being "connected to" another component, it can be directly connected to or indirectly connected to that other component.

[0020] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. "Several" means one or more, unless otherwise explicitly specified.

[0021] Currently, common methods for optimizing the formulation and process parameters of AJP reactive silver inks include single-factor experiments, orthogonal experimental design, and response surface methodology. These methods find optimal combinations by systematically changing some parameters and analyzing their impact on performance indicators, thus improving experimental efficiency to some extent. However, when there are many parameters to be optimized and there are obvious coupling relationships between them, the above methods often require a large number of experiments to obtain a better solution, and it is difficult to simultaneously consider the trade-offs between multiple performance indicators (such as conductivity and adhesion performance). In recent years, machine learning methods have been gradually introduced into the field of materials design and process optimization. By establishing predictive models between parameters and performance, they guide experimental design, thereby reducing the number of experiments and improving optimization efficiency. However, in existing research, most machine learning methods still mainly optimize a single performance indicator, or only optimize material formulation parameters or only a certain type of variable in the process parameters. Research on the synergistic optimization between ink formulation parameters and AJP process parameters remains relatively limited. Therefore, in the AJP reactive silver ink system, how to achieve synergistic optimization of ink formulation parameters and printing and sintering process parameters under multi-parameter coupling conditions, while ensuring that the conductivity of the conductive circuit meets the requirements, further improves the adhesion performance, and reduces the number of experiments and optimization cycle, remains a technical problem that urgently needs to be solved in this field.

[0022] To address the aforementioned technical problems, this invention provides a method for synergistic optimization of process parameters for aerosol inkjet printing of reactive silver ink, comprising: Determine the parameter space; the parameter space includes ink formulation parameters and printing and sintering process parameters. Initial parameter combinations are generated within the parameter space, and printing experiments are performed; the conductivity and interfacial shear strength corresponding to each initial parameter combination are obtained to obtain the initial experimental dataset; Using the initial parameter combination as input, and electrical conductivity and interfacial shear strength as outputs, two independent Gaussian process regression models are trained. A multi-objective optimization search is performed based on a Gaussian process regression model, with the search direction being to find a conductivity greater than or equal to 10. 7 Under the premise of S / m, increase the interfacial shear strength to obtain the Pareto front solution set; Determine the first and second parameter combinations, and verify them by printing to obtain experimental data; add this experimental data to the initial experimental dataset to retrain the Gaussian process regression model; repeat the subsequent process until the preset convergence condition is met, and output the optimal parameter combination; wherein: The first combination is the parameter combination with the highest predicted conductivity selected from the Pareto front solution set; the second combination is the parameter combination with the largest predicted variance of the Gaussian process regression model.

[0023] In the above-mentioned technical solution, the method for collaborative optimization of process parameters of aerosol inkjet printing active silver ink of the present invention treats the formulation parameters of aerosol inkjet printing active silver ink (such as silver precursor concentration, volume fraction of low-boiling-point alcohol solvent, and polymer thickener concentration) and printing and sintering process parameters (such as substrate temperature, printing speed, nozzle diameter, sintering time, and aerosol focusing ratio) as a complete parameter space. Initial parameter combinations are generated and experiments are conducted (e.g., using Latin hypercube sampling) to obtain conductivity and interfacial shear strength data. Two independent Gaussian process regression models are then trained to predict conductivity and interfacial shear strength respectively, while simultaneously providing prediction uncertainties. Based on this, a multi-objective optimization algorithm is used to optimize conductivity to a value not less than 10. 7 S / m is a hard constraint, and the Pareto front solution set is searched with the goal of maximizing the interface shear strength. In particular, in each iteration, the parameter combination with the highest predicted conductivity (using the current best prediction value) and the parameter combination with the largest prediction variance (using the model's cognitive uncertainty) are selected from the Pareto front solution set for actual printing verification. New data is added to the training set to retrain the model. This process is repeated until convergence, and finally the optimal parameter combination is output. Based on the above technical solution, a Gaussian process regression model is used to model the conductivity and interfacial shear strength. For example, combined with NSGA-II multi-objective optimization, it can effectively handle the complex nonlinear coupling relationship between substrate temperature, ethanol ratio, hydroxyethyl cellulose, and AJP printing parameters. Specifically, too low a substrate temperature will result in incomplete silver sintering and insufficient adhesion, while too high a substrate temperature will cause bubble defects due to intensified reaction. Insufficient ethanol ratio cannot suppress high-temperature bubbles, while too high an ethanol ratio dilutes the silver content. Too high a concentration of hydroxyethyl cellulose will affect the conductive network during low-temperature sintering, while too low a concentration will reduce adhesion. These factors are intertwined, making it almost impossible for traditional single-factor experimental methods to find the parameter combination that achieves the optimal adhesion performance while meeting the conductivity requirement. This invention uses Gaussian process regression to learn the mapping relationship between parameters and performance and quantifies the prediction uncertainty. Then, through multi-objective optimization, it automatically searches for the Pareto optimal solution of adhesion performance under the premise of satisfying the conductivity constraint, thereby stabilizing the conductivity to 10. 7The parameters are above S / m, and the interfacial shear strength also reaches a high level. Furthermore, this invention achieves an automatic balance between exploration and utilization by simultaneously selecting two candidate parameter combinations—the predicted optimal and the one with the largest predicted variance—for experimental verification in each iteration. Specifically, the predicted optimal combination is used to find the optimal solution using the current model knowledge, while the combination with the largest predicted variance is used to explore parameter regions where the model's understanding is insufficient to accelerate model convergence. This active learning strategy significantly reduces the number of experiments required to reach the optimal parameter combination. Furthermore, since both conductivity and adhesion performance are considered simultaneously during the optimization process, and a lower limit for conductivity is set in the constraints, the final output optimal parameter combination not only meets the conductivity standard but also exhibits good repeatability. For example, in one embodiment of this invention, the standard deviation of conductivity in five repeated experiments is 0.03 × 10⁻⁶. 7 The S / m ratio is less than 5% of the mean, and the standard deviation of the interfacial shear strength is 0.22 MPa, indicating that the low-temperature sintering process window of the reactive silver ink has been broadened, the tolerance to process fluctuations has been improved, and the process stability in industrial production has been enhanced. Furthermore, this invention can ensure that the optimization process can terminate within a reasonable number of iterations by setting the convergence condition to a change in conductivity of less than 1% in two consecutive iterations, or reaching the maximum number of iterations of 5, or actual verification that the conductivity has been stably met and the adhesion performance meets the requirements, thus outputting a stable and reliable parameter combination and avoiding excessive experimentation. Through the above technical solution of this invention, the technical problems of existing technologies that are difficult to achieve synergistic optimization under the multi-parameter coupling of ink formulation parameters and aerosol inkjet printing process parameters, cannot take into account both conductivity and adhesion performance, and have a large number of experiments and a long optimization cycle are solved.

[0024] Further, please refer to Figure 2 and Figure 3 ; Figure 2 The study illustrates the coupled effects of substrate temperature, alcohol solvent ratio, and polymer tackifier concentration on conductivity. Substrate temperature primarily influences the thermal decomposition rate and sintering density of the silver precursor: too low a temperature results in insufficient silver particle formation and a discontinuous conductive network; too high a temperature leads to an excessively fast reaction rate, easily causing bubble defects. Alcohol solvents, as low-boiling-point components, can reduce the surface tension of the ink system and improve bubble defects during sintering, but excessively high concentrations reduce the silver content, thus affecting conductivity. Polymer tackifiers enhance the interfacial adhesion between the conductive lines and the substrate, but they are difficult to completely remove under low-temperature sintering conditions, and excessively high concentrations hinder conductive network formation. Therefore, a significant coupling relationship exists among these parameters, jointly determining the final conductivity. Figure 3 The comparison results of the process window before and after optimization are shown. Before optimization, the conductivity could only reach the preset threshold (10⁻⁶) within a relatively narrow parameter range. 7The conductivity of the circuit (S / m) indicates that the process is highly sensitive to changes in parameters such as substrate temperature and solvent ratio, resulting in poor process stability. After optimization using the method of this invention, the conductivity is not less than 10. 7 The parameter range of S / m is significantly expanded, indicating that the present invention can effectively identify better parameter combinations under multi-parameter coupling conditions and improve parameter fluctuation tolerance, thereby broadening the process window. The above results show that the method of the present invention can improve process robustness and reduce dependence on precise parameter control while ensuring that conductivity meets the standards.

[0025] To better understand the present invention, the following specific embodiments further illustrate the content of the present invention, but the content of the present invention is not limited to the following embodiments.

[0026] Example 1 This embodiment provides a method for synergistic optimization of process parameters for aerosol inkjet printing of reactive silver ink, including: Step 1, determine the parameter space; the parameter space includes ink formulation parameters and printing and sintering process parameters; Step 2: Generate initial parameter combinations in the parameter space and conduct printing experiments; obtain the conductivity and interfacial shear strength corresponding to each initial parameter combination to obtain the initial experimental dataset; Step 3: Using the initial parameter combination as input and electrical conductivity and interfacial shear strength as outputs, train two independent Gaussian process regression models. Step 4: Perform multi-objective optimization search based on the Gaussian process regression model, with the search direction being to achieve a conductivity greater than or equal to 10. 7 Under the premise of S / m, increase the interfacial shear strength to obtain the Pareto front solution set; Step 5: Determine the first and second combinations, and print them out to obtain experimental data; add the experimental data to the initial experimental dataset to retrain the Gaussian process regression model; repeat the subsequent process until the preset convergence condition is met, and output the optimal parameter combination; where: the first combination is the parameter combination with the highest predicted conductivity selected from the Pareto front solution set; the second combination is the parameter combination with the largest predicted variance of the Gaussian process regression model.

[0027] Example 2 This embodiment provides a method for synergistic optimization of process parameters for aerosol inkjet printing of reactive silver ink, including: Step 1: Determine the parameter space. The parameter space includes ink formulation parameters and printing and sintering process parameters. Specifically: Ink formulation parameters include: silver precursor concentration of 10-30 wt%, alcohol solvent volume fraction of 5-20 vol%, and polymer tackifier concentration of 0.1-1.0 wt%. Printing and sintering process parameters include: substrate temperature of 70-110℃, printing speed of 2-8 mm / s, nozzle diameter of 100-300 μm, sintering time of 30-60 min, and aerosol focusing ratio of 1.5-3.0. These parameter ranges are determined based on the stable printing window and low-temperature sintering characteristics of reactive silver ink. The aerosol focusing ratio is the ratio of sheath gas flow rate to carrier gas flow rate. Alcohol solvents include ethanol, isopropanol, or n-propanol. Polymer tackifiers include hydroxyethyl cellulose, polyethylene oxide, or polyvinylpyrrolidone.

[0028] Step 2: Generate initial parameter combinations in the parameter space and conduct printing experiments; obtain the conductivity and interfacial shear strength corresponding to each initial parameter combination to obtain the initial experimental dataset.

[0029] Step 3: Extract the bubble area ratio of the conductive line cross section. When the bubble area ratio exceeds 5%, the sample is marked as an outlier and assigned the first weight in the model training. The extraction of the bubble area ratio is automatically identified by a deep learning segmentation model based on the U-Net architecture. With the initial parameter combination as input and conductivity and interface shear strength as output, two independent Gaussian process regression models are trained. The Gaussian process regression model adopts a combination of squared exponential kernel function and noise kernel, and optimizes the signal variance, feature length scale and noise variance hyperparameters in the kernel function by maximizing the marginal likelihood estimation.

[0030] Step 4: Based on the trained Gaussian process regression model, a non-dominated sorting genetic algorithm with an elitist strategy is used for multi-objective optimization search. The search direction is to find models with conductivity greater than or equal to 10. 7 Under the premise of S / m, increase the interfacial shear strength to obtain the Pareto front solution set.

[0031] Step 5: Determine the first and second parameter combinations and print verification to obtain experimental data; add this experimental data to the initial experimental dataset to retrain the Gaussian process regression model; repeat the subsequent process until the preset convergence conditions are met, and output the optimal parameter combination; where: the first combination is the parameter combination with the highest predicted conductivity selected from the Pareto front solution set; the second combination is the parameter combination with the largest predicted variance of the Gaussian process regression model; a data acquisition function is introduced when selecting the first and second combinations; the data acquisition function is used to weight the predicted mean and predicted variance to achieve a balance between exploration and utilization; the convergence conditions include the predicted conductivity change of the optimal parameter combination obtained in two consecutive iterations being less than 1%, reaching the preset maximum number of iterations of 5, or verifying that the conductivity is greater than or equal to 10. 7 The S / m ratio is high, and the interfacial shear strength meets the application requirements.

[0032] Step 6: Conduct at least 5 repeated printing experiments using the optimal parameter combination, and statistically analyze the mean and standard deviation of conductivity and interfacial shear strength; if the mean conductivity is greater than or equal to 10... 7 If the S / m value is less than or equal to 5% of the mean, then the parameter combination is considered to meet the process stability requirements.

[0033] Example 3 In existing technologies, when optimizing the formulation and process parameters of AJP reactive inks, excessively low substrate temperatures lead to insufficient silver density, affecting conductivity, while excessively high substrate temperatures generate bubbles during printing, also impacting conductivity. Adding low-boiling-point alcohol solvents can suppress high-temperature bubbles but dilutes the silver content; adding polymer additives can improve adhesion, but they are difficult to completely remove during low-temperature sintering. Complex coupling relationships exist between these parameters and the AJP printing parameters, making it difficult to find the optimal parameter combination that ensures stable conductivity using traditional single-factor experimental methods. Therefore, in a first aspect, this embodiment provides a method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver inks, aiming to achieve a conductivity of not less than 10. 7 To maximize adhesion performance under the hard constraint of S / m, the collaborative optimization method in this embodiment includes: Step 1: Determine the parameter space to be optimized. The parameter space includes ink formulation parameters and printing and sintering process parameters. The ink formulation parameters include: silver precursor concentration (range 10–30 wt%); low-boiling-point alcohol solvent volume fraction (range 5–20 vol%); and polymer tackifier concentration (range 0.1–1.0 wt%). The printing and sintering process parameters include: substrate temperature (range 70–110 °C); printing speed (range 2–8 mm / s); nozzle diameter (range 100–300 μm); sintering time (range 30–60 min); and aerosol focusing ratio, defined as the ratio of sheath gas flow rate to carrier gas flow rate (range 1.5–3.0). These eight parameters constitute the complete parameter space to be optimized. The low-boiling-point alcohol solvent is ethanol, and the polymer tackifier is hydroxyethyl cellulose.

[0034] Step 2: Set optimization objectives and constraints; specifically, the optimization objectives include a primary optimization objective and a secondary optimization objective, wherein the primary optimization objective is that the conductivity of the conductive circuit after sintering is not less than 10. 7 The second optimization objective, S / m, is to maximize the interfacial shear strength between the printed lines and the substrate. The conductivity target is influenced by a combination of factors, including substrate temperature, ethanol ratio, and hydroxyethyl cellulose concentration. Specifically: too low a substrate temperature results in insufficient silver sintering and poor adhesion to the substrate; too high a temperature increases bubble defects. Insufficient ethanol ratio makes it difficult to suppress high-temperature bubbles, while excessive ethanol ratio dilutes the silver content. Excessive hydroxyethyl cellulose concentration may cause low-temperature sintering residues that affect the conductive network. Simultaneously, AJP printing parameters also influence conductivity by affecting the aspect ratio of the trace cross-section and overspray. These factors intertwine and collectively determine whether the conductivity target can be achieved.

[0035] Step 3: After defining the parameter space and optimization objective, this embodiment uses the Latin hypercube sampling method to generate 30-50 initial parameter combinations within the parameter space composed of the above eight parameters. AJP experiments are then conducted sequentially to measure and record the conductivity and interfacial shear strength corresponding to each parameter combination, thus forming the initial experimental dataset. Based on this, two independent Gaussian process regression models are trained, using the parameter combinations as input and conductivity and interfacial shear strength as outputs, respectively. The Gaussian process regression model uses a combination of a squared exponential kernel function and a noise kernel. By maximizing marginal likelihood estimation, it optimizes hyperparameters such as signal variance, feature length scale, and noise variance in the kernel function, enabling the model to not only provide predicted values ​​for conductivity and interfacial shear strength for any new parameter combination but also simultaneously provide an estimate of the prediction uncertainty.

[0036] Step 4: Based on the trained Gaussian process regression model, a non-dominated sorting genetic algorithm with an elitist strategy is further employed for multi-objective optimization search. In this step, the conductivity and interfacial shear strength predicted by the Gaussian process regression model are used as fitness functions to perform global optimization in the parameter space. The search direction is to find the optimal parameters where the conductivity is not less than 10. 7 To maximize interfacial shear strength under the premise of S / m, the initial population is generated in the parameter space. Individuals in the population are non-dominated and sorted according to the predicted conductivity and interfacial shear strength to divide the frontier level. Within the same frontier level, the crowding distance of individuals is calculated to maintain population diversity. The tournament selection operator is used to prioritize individuals with low frontier level and large crowding distance. Offspring individuals are generated through crossover and mutation operations. After merging the parent and offspring, the best individual is selected to enter the next generation. The above evolutionary process is repeated until the convergence condition is met, and finally a set of frontier solutions that satisfy the Pareto optimality condition is obtained. Each solution corresponds to a set of parameter combinations and its predicted conductivity and interfacial shear strength.

[0037] Step 5: After obtaining the Pareto front solution set, candidate parameter combinations are selected for actual printing verification. Two selection strategies are employed: one is to choose the parameter combination with the best predictive performance, i.e., the parameter combination with the highest predicted conductivity; the other is to choose the parameter combination with the largest prediction variance of the Gaussian process regression model, the latter aiming to explore regions where the model's understanding is insufficient to accelerate convergence. The selected candidate parameter combinations are applied to the actual AJP process to obtain the true conductivity and interface shear strength. The newly obtained experimental data is added to the initial dataset, and the Gaussian process regression model is retrained to update its kernel function hyperparameters. The above steps of multi-objective optimization search, candidate parameter combination selection, experimental verification, and model update are repeated until the preset convergence conditions are met. Convergence conditions include: the predicted conductivity change of the optimal parameter combination obtained in two consecutive iterations is less than 1%; the preset maximum number of iterations is reached (5); or the actual verification experimental results show that the conductivity has stabilized at 10. 7 The shear strength is above S / m and meets the application requirements.

[0038] Step 6: After the optimization process reaches convergence, select the parameter combination that performs optimally in the actual verification experiment from the Pareto front solution set obtained from the final iteration as the recommended ink formulation and process parameter scheme. Optimal performance means meeting the requirement that the conductivity is not less than 10. 7 Under the premise of S / m, the actual measured interfacial shear strength reaches its maximum; furthermore, at least 5 repeated printing experiments were conducted using the optimal parameter combination, and the mean and standard deviation of its conductivity and interfacial shear strength were statistically analyzed. If the mean conductivity is stable at 10... 7If the S / m value is above a certain level and the standard deviation does not exceed 5% of the mean, then the parameter combination is considered to have good process stability.

[0039] Furthermore, in this embodiment, the Gaussian process regression model can use multi-output Gaussian process regression instead of two independent single-output models to improve prediction accuracy by utilizing the correlation between conductivity and interface shear strength; the selection strategy for candidate parameter combinations can further introduce a collection function to weight the predicted mean and variance, for example, by using the expected improvement probability or confidence upper limit criterion to achieve an automatic balance between exploration and utilization; the extraction of the bubble area ratio can use a deep learning segmentation model based on the U-Net architecture to automatically identify and calculate the ratio of the bubble region to the cross-sectional area of ​​the conductive line. When the ratio exceeds 5%, the sample is marked as an outlier and given a lower weight in model training.

[0040] Secondly, this embodiment provides a collaborative optimization system for process parameters of aerosol inkjet printing reactive silver ink, including: The parameter space module is used to define the parameter space, which includes ink formulation parameters and printing and sintering process parameters. The dataset acquisition module is used to generate initial parameter combinations in the parameter space and to print experiments; it obtains the conductivity and interfacial shear strength corresponding to each initial parameter combination to obtain the initial experimental dataset. The model training module is used to train two independent Gaussian process regression models with initial parameter combinations as input and electrical conductivity and interfacial shear strength as outputs, respectively. The model update module is used for multi-objective optimization search based on the Gaussian process regression model. The search direction is to find the model with conductivity greater than or equal to 10. 7 Under the premise of S / m, the interfacial shear strength is increased to obtain the Pareto front solution set; the first combination and the second combination are determined and printed to verify and obtain experimental data; the experimental data are added to the initial experimental dataset to retrain the Gaussian process regression model; wherein: the first combination is the parameter combination with the highest predicted conductivity selected from the Pareto front solution set; the second combination is the parameter combination with the largest predicted variance of the Gaussian process regression model; The results output module is used to output the optimal parameter combination.

[0041] Example 4 Please see Figure 1 This embodiment utilizes the aerosol inkjet printing reactive silver ink process parameter synergistic optimization method of the present invention to synergistically optimize the reactive silver ink formulation and process parameters, specifically: First, the parameter space and optimization objective are defined. Ink formulation parameters include silver precursor concentration (10wt%~30wt%), ethanol volume fraction (5vol%~20vol%), and hydroxyethyl cellulose concentration (0.1wt%~1.0wt%). Process parameters include substrate temperature (70℃~110℃), printing speed (2mm / s~8mm / s), nozzle diameter (100μm~300μm), sintering time (30min~60min), and aerosol focusing ratio (1.5~3.0). The optimization objective is set as an electrical conductivity of not less than 10. 7 S / m, maximizing the interfacial shear strength under this premise.

[0042] Furthermore, the Latin hypercube sampling method was used to generate 40 initial parameter combinations for experiments, obtaining the initial dataset. Two independent Gaussian process regression models were trained using eight-dimensional parameters as input and conductivity and interfacial shear strength as output, with a kernel function combining a squared exponential kernel and a noise kernel. Based on the trained models, the NSGA-II algorithm (Non-dominated Sorting Genetic Algorithm II) was used for multi-objective optimization search, with a population size of 100 and 200 generations, to obtain the Pareto front solution set. The parameter combination with the highest predicted interfacial shear strength and the parameter combination with the largest predicted variance were selected from the solution set for experimental verification. New data was added to the training set to update the model. The above iterative process was repeated for 5 rounds until convergence was achieved.

[0043] The optimal parameter combination obtained in this embodiment is as follows: silver precursor concentration 25.7 wt%, ethanol volume fraction 12 vol%, hydroxyethyl cellulose concentration 0.5 wt%, substrate temperature 88℃, aerosol focusing ratio 1.8, printing speed 5 mm / s, nozzle diameter 150 μm, and sintering time 50 min. Five repeated printing experiments were conducted using this parameter combination, and the results are shown in Table 1.

[0044] Table 1. Repeatability verification results of Example 4

[0045] The results in Table 1 show that the average conductivity reaches 1.12 × 10⁻⁶. 7 S / m, satisfying a value not less than 10 7 The required S / m ratio is met, and the standard deviation is less than 5% of the mean, indicating good process stability; the average interfacial shear strength reaches 15.22 MPa, demonstrating good adhesion performance.

[0046] Example 5 The difference between this embodiment and embodiment 4 is that the initial experiment uses Latin hypercube sampling to generate 50 sets of parameter combinations, while the remaining steps are the same as in embodiment 4.

[0047] The optimal parameter combination obtained after 5 rounds of iterative optimization in this embodiment is: The concentrations of silver precursor (23.5 wt%), ethanol (13 vol%), and hydroxyethyl cellulose (0.4 wt%) were as follows: substrate temperature (85 °C), aerosol focusing ratio (2.0), printing speed (4 mm / s), nozzle diameter (150 μm), and sintering time (55 min).

[0048] Five repeated printing experiments were conducted using this parameter combination, and the average conductivity was 1.14 × 10⁻⁶. 7 S / m, standard deviation is 0.03×10 7 The mean shear strength of the interface was 15.19 MPa, and the standard deviation was 0.22 MPa. Compared with Example 4, increasing the number of initial sampling points had no significant impact on the optimization results, indicating that 40 initial experiments were sufficient to cover the main features of the parameter space.

[0049] Example 6 The difference between this embodiment and embodiment 4 is that the Gaussian process regression model uses the Matern kernel function instead of the squared exponential kernel function, while the remaining steps are the same as in embodiment 4.

[0050] The optimal parameter combination obtained after 5 rounds of iterative optimization in this embodiment is: The concentrations of silver precursor (22 wt%), ethanol (11 vol%), and hydroxyethyl cellulose (0.5 wt%) were as follows: substrate temperature (75 °C), aerosol focusing ratio (1.9), printing speed (4 mm / s), nozzle diameter (150 μm), and sintering time (40 min).

[0051] Five repeated printing experiments were conducted using this parameter combination, and the average conductivity was 1.09 × 10⁻⁶. 7 S / m, standard deviation is 0.05×10 7 The mean shear strength at the interface was 14.99 MPa, with a standard deviation of 0.30 MPa. The results indicate that the squared exponential kernel function slightly outperforms the Matern kernel function in this application scenario, exhibiting higher prediction accuracy.

[0052] Comparative Example 1 This comparative study uses traditional single-factor experimental methods for parameter optimization, without involving machine learning modeling or multi-objective optimization; specifically: In this comparative example, the baseline parameters were set as follows: silver precursor concentration 20 wt%, ethanol volume fraction 10 vol%, hydroxyethyl cellulose concentration 0.3 wt%, substrate temperature 90℃, aerosol focusing ratio 1.5, printing speed 5 mm / s, nozzle diameter 150 μm, and sintering time 40 min. The effects of each parameter on conductivity and interfacial shear strength were investigated one by one. Five levels were investigated for each parameter, and approximately 40 sets of experiments were conducted in total.

[0053] The optimal parameter combination determined after single-factor optimization was as follows: silver precursor concentration 25 wt%, ethanol volume fraction 10 vol%, hydroxyethyl cellulose concentration 0.3 wt%, substrate temperature 90℃, aerosol focusing ratio 2.0, printing speed 5 mm / s, nozzle diameter 200 μm, and sintering time 40 min. Five repeated printing experiments were conducted using this parameter combination, and the results are shown in Table 2.

[0054] Table 2. Repeatability verification results of Comparative Example 1

[0055] The results in Table 2 show that the average conductivity is 0.85 × 10⁻⁶. 7 S / m, not reaching 10 7 The S / m requirement was not met, and there were large fluctuations between batches. The average interfacial shear strength was 15.61 MPa, which was lower than that of Example 4. This indicates that the single-factor experimental method is difficult to handle the coupling relationship between substrate temperature, ethanol ratio, and hydroxyethyl cellulose concentration, and cannot find the optimal parameter combination to achieve the required conductivity.

[0056] Comparative Example 2 The difference between this comparative example and Example 4 is that the ethanol volume fraction was fixed at 5 vol% during the optimization process and was not adjusted further. Only the other seven parameters were optimized, and the single objective was to maximize electrical conductivity, without considering interfacial shear strength. Specifically: In this comparative example, the optimal parameter combination obtained after five rounds of iterative optimization is: silver precursor concentration 28 wt%, hydroxyethyl cellulose concentration 0.2 wt%, substrate temperature 70℃, aerosol focusing ratio 2.0, printing speed 4 mm / s, nozzle diameter 120 μm, and sintering time 40 min. Five repeated printing experiments were conducted using this parameter combination, and the average conductivity was 0.96 × 10⁻⁶. 7 S / m, standard deviation is 0.06×10 7 S / m; the mean interfacial shear strength is 11.20 MPa, and the standard deviation is 0.40 MPa.

[0057] The results of this comparative example show that when the ethanol ratio is fixed at 5 vol%, the low ethanol content cannot effectively suppress the bubbles generated by the reactive reaction during printing at higher substrate temperatures. To reduce bubble defects, the optimization process is forced to choose a lower substrate temperature for compensation. However, the lower substrate temperature leads to incomplete sintering of the silver precursor and insufficient formation of the conductive network. Although the final parameter combination controls bubbles to some extent by lowering the temperature, it sacrifices sintering density, and the electrical conductivity is still below 10. 7The S / m ratio indicates a strong coupling relationship between the ethanol ratio, substrate temperature, and hydroxyethyl cellulose concentration. Fixing any one of these parameters will disrupt the synergistic equilibrium, which cannot be fully compensated for by adjusting the other parameters. At the same time, the interfacial shear strength decreases significantly due to the low concentration of hydroxyethyl cellulose, indicating that the ethanol ratio, substrate temperature, and hydroxyethyl cellulose concentration must be optimized synergistically, and none of them can be omitted.

[0058] Comparative Example 3 The difference between this comparative example and Example 4 is that the training data of the Gaussian process regression model does not include samples showing the effect of hydroxyethyl cellulose concentration on conductivity, i.e., it is assumed that hydroxyethyl cellulose can be completely removed during the low-temperature sintering process.

[0059] In this comparative example, the optimal parameter combination obtained after five rounds of iterative optimization is: silver precursor concentration 25 wt%, ethanol volume fraction 15 vol%, hydroxyethyl cellulose concentration 0.8 wt%, substrate temperature 88℃, aerosol focusing ratio 1.6, printing speed 2 mm / s, nozzle diameter 150 μm, and sintering time 20 min. Five repeated printing experiments were conducted using this parameter combination, and the average conductivity was 0.77 × 10⁻⁶. 7 S / m, standard deviation is 0.07×10 7 S / m; the mean interfacial shear strength is 18.52 MPa, and the standard deviation is 0.34 MPa.

[0060] The results of this comparative example show that although the interfacial shear strength is high, the actual conductivity failed to meet the target due to neglecting the residual problem of hydroxyethyl cellulose during low-temperature sintering. This verifies that the negative impact of hydroxyethyl cellulose concentration on conductivity must be fully considered in the modeling.

[0061] Furthermore, the results of Examples 4 to 6, and Comparative Examples 1 to 3 are summarized and compared as shown in Table 3 below.

[0062] Table 3 Comparison of results between Examples 4-6 and comparative examples

[0063] As can be seen from the comparison results in Table 3, this invention, based on 40 initial experiments, achieved a stable conductivity of 10 after 5 rounds of iterative optimization. 7Achieving a conductivity of S / m or higher while simultaneously obtaining high interfacial shear strength; Comparative Example 1 shows that traditional single-factor experimental methods struggle to handle parameter coupling relationships, failing to achieve the required conductivity; Comparative Example 2 shows that the ethanol ratio must be incorporated into synergistic optimization, as fixing a single parameter disrupts the balance between parameters; Comparative Example 3 shows that the negative impact of hydroxyethyl cellulose concentration on conductivity must be fully considered, as ignoring this factor leads to substandard conductivity. As a further preferred embodiment of the invention, the Gaussian process regression model can employ multi-output Gaussian process regression instead of two independent single-output models to utilize the potential correlation between conductivity and interfacial shear strength to improve prediction accuracy. The selection strategy for candidate parameter combinations can further incorporate acquisition functions, such as the expected improvement probability or confidence upper limit criterion, to weight and combine the predicted mean and variance, achieving an automatic balance between exploration and utilization. The aerosol focusing ratio can be adjusted according to the specific structural characteristics of the printing equipment, becoming the ratio of sheath gas pressure to carrier gas pressure, or the ratio of sheath gas flow rate to atomized gas flow rate, as long as it characterizes the convergence characteristics of the aerosol beam.

[0064] In the description of the above embodiments, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0065] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for synergistic optimization of process parameters for aerosol inkjet printing of reactive silver ink, characterized in that, include: Determine the parameter space; The parameter space includes ink formulation parameters and printing and sintering process parameters; An initial parameter combination is generated within the parameter space, and a printing experiment is conducted. Obtain the conductivity and interfacial shear strength corresponding to each set of initial parameter combinations to obtain the initial experimental dataset; Using the initial parameter combination as input, and electrical conductivity and interfacial shear strength as outputs, two independent Gaussian process regression models are trained. A multi-objective optimization search is performed based on a Gaussian process regression model, with the search direction being to find a conductivity greater than or equal to 10. 7 Under the premise of S / m, increase the interfacial shear strength to obtain the Pareto front solution set; Determine the first and second parameter combinations, and verify them by printing to obtain experimental data; add this experimental data to the initial experimental dataset to retrain the Gaussian process regression model; repeat the subsequent process until the preset convergence condition is met, and output the optimal parameter combination; wherein: The first combination is the parameter combination with the highest predicted conductivity selected from the Pareto front solution set; the second combination is the parameter combination with the largest predicted variance of the Gaussian process regression model.

2. The method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink according to claim 1, characterized in that, The ink formulation parameters include: a silver precursor concentration of 10-30 wt%, an alcohol solvent volume fraction of 5-20 vol%, and a polymer tackifier concentration of 0.1-1.0 wt%. The printing and sintering process parameters include: substrate temperature of 70~110℃, printing speed of 2~8mm / s, nozzle diameter of 100~300μm, sintering time of 30~60min, and aerosol focusing ratio of 1.5~3.

0. The aerosol focusing ratio is the ratio of sheath gas flow rate to carrier gas flow rate.

3. The method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink according to claim 2, characterized in that, The alcohol solvents include ethanol, isopropanol, or n-propanol; The polymer thickener includes hydroxyethyl cellulose, polyethylene oxide, or polyvinylpyrrolidone.

4. The method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink according to claim 1, characterized in that, The convergence conditions include the predicted conductivity change being less than 1% after two consecutive iterations of the optimal parameter combination, reaching a preset maximum number of iterations (5), or verifying that the experimental results satisfy a conductivity greater than or equal to 10. 7 The S / m ratio is high, and the interfacial shear strength meets the application requirements.

5. The method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink according to claim 1, characterized in that, The Gaussian process regression model uses a combination of a squared exponential kernel function and a noise kernel, and optimizes the signal variance, feature length scale, and noise variance hyperparameters in the kernel function by maximizing the marginal likelihood estimation.

6. The method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink according to claim 1, characterized in that, The optimal combination of output parameters also includes: At least five repeated printing experiments were conducted using the optimal parameter combination, and the mean and standard deviation of conductivity and interfacial shear strength were statistically analyzed; if the mean conductivity was greater than or equal to 10... 7 If the S / m value is less than or equal to 5% of the mean, then the parameter combination is considered to meet the process stability requirements.

7. The method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink according to claim 1, characterized in that, Multi-objective optimization search based on Gaussian process regression model, including: Based on a trained Gaussian process regression model, a non-dominated sorting genetic algorithm with an elitist strategy is used for multi-objective optimization search.

8. The method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink according to claim 1, characterized in that, A data acquisition function is introduced when selecting the first and second combinations; the data acquisition function is used to weight the predicted mean and the predicted variance to achieve a balance between exploration and utilization.

9. The method for synergistic optimization of process parameters for aerosol inkjet printing reactive silver ink according to claim 1, characterized in that, Before training the Gaussian process regression model, the following steps are also included: The bubble area ratio of the conductive line cross section is extracted. When the bubble area ratio exceeds 5%, the sample is marked as an outlier and assigned the first weight in the model training. The extraction of the bubble area ratio is automatically identified by a deep learning segmentation model based on the U-Net architecture.

10. A collaborative optimization system for process parameters of reactive silver ink in aerosol inkjet printing, characterized in that, include: The parameter space module is used to define the parameter space. The parameter space includes ink formulation parameters and printing and sintering process parameters; The dataset acquisition module is used to generate initial parameter combinations in the parameter space and to print experiments; it obtains the conductivity and interfacial shear strength corresponding to each initial parameter combination to obtain the initial experimental dataset. The model training module is used to train two independent Gaussian process regression models with initial parameter combinations as input and electrical conductivity and interfacial shear strength as outputs, respectively. The model update module is used for multi-objective optimization search based on the Gaussian process regression model. The search direction is to find the model with conductivity greater than or equal to 10. 7 Under the premise of S / m, the interfacial shear strength is increased to obtain the Pareto front solution set; the first combination and the second combination are determined and printed to verify and obtain experimental data; the experimental data are added to the initial experimental dataset to retrain the Gaussian process regression model; wherein: the first combination is the parameter combination with the highest predicted conductivity selected from the Pareto front solution set; the second combination is the parameter combination with the largest predicted variance of the Gaussian process regression model; The results output module is used to output the optimal parameter combination.

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