Electrofluid jet printing process parameter adjusting method based on Bayesian optimization

Abstract

The invention provides an electrofluid jet printing process parameter adjusting method based on Bayesian optimization, and belongs to the technical field of precision additive manufacturing. The process parameter adjustment method is realized through the following steps: firstly, constructing a parameter adjustment optimization model of electrofluid jet printing process parameters, and then establishing a historical data set by using multiple groups of set hyper-parameters and corresponding experimental observation objective function values; establishing a probability distribution model by using data in the historical data set, and constructing an acquisition function for calculation to obtain process parameters observed by next parameter adjustment; based on the idea of Bayesian optimization, adding a group of newly observed parameters and objective function values thereof into a historical data set, and correcting an original probability distribution model; the steps are repeated, loop iteration is achieved till the convergence criterion is reached, and an optimization result is obtained. The parameter adjusting method provided by the invention is high in result precision and low in parameter adjusting cost, shortens the process debugging process, and gets rid of the influence of human experience on the parameter adjusting effect and efficiency.

Description

Technical Field

[0001] This invention belongs to the field of additive precision manufacturing technology and relates to a method for adjusting the parameters of electrofluid inkjet printing process based on Bayesian optimization. Background Technology

[0002] Electrohydraulic inkjet printing is a high-resolution printing technology that uses an electric field to drive liquid out of a nozzle, spraying droplets or jets much smaller than the nozzle size. This allows common industrial fluids, such as inks, adhesives, silver paste, and solder paste, to be deposited onto a substrate, achieving high-precision additive manufacturing. Different jetting modes can be obtained within different process parameter ranges, including droplet, micro-droplet, spindle, and cone jet modes.

[0003] In major industrial manufacturing applications, such as fabricating silver circuits on circuit boards using electrohydraulic inkjet printing and creating light-shielding ink patterns on optical glass lenses, it is typically required to print patterns composed of straight lines, arcs, and spline curves on the substrate. The printed linewidth must meet design requirements, and the lines must be uniform in width with no wavy or burr-like edges. However, because electrohydraulic inkjet printing technology is highly precise and sensitive to process parameters, the parameter adjustment window is relatively narrow. If the selected process parameters are inappropriate, the printed line quality often fails to meet technical requirements. For example, improper selection of air pressure, needle inner diameter, or pulse voltage amplitude may result in a printed linewidth that does not meet design requirements. Inappropriate selection of pulse voltage parameters (amplitude, frequency, duty cycle) can create burrs and wavy patterns at the edges of the printed lines, causing the line profile to fail to meet design requirements and affecting the product's appearance and performance.

[0004] Because of the different properties of fluids and substrates, and the numerous process parameters affecting the printing effect, many of which have non-linear effects, it is difficult for those skilled in the art to quantitatively grasp the relationship between process parameters and printing results. Currently, adjusting process parameters mostly relies on the experience of technicians and process experiments, continuously adjusting parameters based on printing results, which may require a significant amount of debugging time and material resources. Conventional multi-factor mathematical statistical analysis and parameter tuning methods, such as orthogonal experimental design, grid search, and random search, can only grasp the general trend of parameter influence, making it difficult to achieve high-precision parameter tuning results, or requiring a large number of parameter tuning samples, resources, and time. Summary of the Invention

[0005] To address the technical problems of low accuracy, low efficiency, large sample requirements, and reliance on human experience in electro-hydraulic inkjet printing process parameter tuning in existing technologies, this invention provides a Bayesian optimization-based electro-hydraulic inkjet printing process parameter tuning method. The method uses the difference between the printed linewidth and the target linewidth, as well as the shape error of the printed linewidth, as evaluation indicators for the printing target result. Since the nonlinear influence between electro-hydraulic process parameters and printing effect is difficult to quantify, the printed linewidth and the shape error of the printed linewidth can be considered as "black box" functions. A parameter tuning optimization model function for electro-hydraulic inkjet printing process parameters is established. First, a probability distribution model is constructed using existing historical experimental observation data, and a data acquisition function is constructed to search for the next observation point. Based on the Bayesian optimization idea, newly obtained data is added to the historical data set to correct the probability model. Multiple iterations are performed to find the optimal solution. The parameter tuning method provided by this invention achieves high accuracy, low tuning cost, shortens the process debugging, eliminates the influence of human experience on the tuning effect and efficiency, and enables online parameter tuning.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] This invention provides a Bayesian-optimized method for tuning electrohydraulic inkjet printing process parameters, comprising the following steps:

[0008] S1. Set the electro-hydraulic inkjet printing process parameters to be optimized as a set of parameter vectors x, and construct a parameter tuning and optimization model for the electro-hydraulic inkjet printing process parameters:

[0009] x=(x1,x2,…x i …x n ) T

[0010] Let g(x) = [w(x) - w a ] 2 h(x)=[max(0, e(x)-t)] 2

[0011] min f(x)=g(x)+μ k ·h(x)

[0012] Where x represents the column vector of parameters to be optimized, x i (i=1,2,3……n) represents the i-th electrohydraulic inkjet printing process parameter to be optimized; T represents transpose; g(x) represents the linewidth error function; w(x) represents the electrohydraulic inkjet printing linewidth function; w a denoted as target linewidth; h(x) represents the penalty term function; e(x) represents the shape error function of the printing line; t is the tolerance corresponding to the shape error; f(x) is the objective function; k is the iteration number, μ kLet μ be the penalty factor for the k-th iteration; and set the initial penalty factor μ. 1 .

[0013] The electro-hydraulic inkjet printing process parameters x i (i=1,2,3……n), including one or more of the following electrohydraulic inkjet printing process parameters: air pressure, pulse voltage amplitude, pulse frequency, duty cycle, printing height, printing speed, nozzle inner diameter, fluid viscosity, fluid surface tension coefficient, and fluid conductivity.

[0014] Furthermore, for printed straight lines, e(x) represents the straightness error function of the printed straight line; for printed arcs, e(x) represents the roundness error function of the printed arc; and for printed spline curves, e(x) represents the line profile error function of the printed spline curve.

[0015] Furthermore, when the number of iterations k≥2, the method for determining the penalty function factor μ is as follows:

[0016] μ k+1 =c k+1 μ k

[0017] c k+1 =exp{[h(x k ) / (g(x k )+σ)]-1}

[0018] c is the growth factor of the penalty function factor μ, and σ is an infinitesimally small positive number. k+1 It is the growth factor of the penalty function factor in the (k+1)th iteration.

[0019] The core idea behind determining the growth factor c of the penalty function in this invention is as follows: Based on the characteristics of adjusting process parameters in electrohydraulic inkjet printing technology, it is necessary to first primarily adjust the linewidth, and then optimize the adjustment parameters in the vicinity of the target linewidth. In the initial stage of parameter optimization, since the linewidth usually deviates significantly from the target linewidth, the penalty factor is typically small, between 0 and 1, allowing for rapid searching and approximation of the target linewidth. In the later stages of parameter optimization, the penalty factor increases, exceeding 1, and significantly increases in the later stages, rapidly reducing the shape error of the printed lines. Therefore, an exponential function of the natural constant e is constructed, so that the growth factor has a small value in the initial optimization stage (usually between 0 and 1). After the linewidth is optimized to the vicinity of the target linewidth, if the shape error of the printed lines is large in the later stages of optimization, [h(x k ) / (g(x k A large ratio of [)+σ] allows the penalty term to grow exponentially, rapidly reducing shape error and achieving convergence quickly. σ is taken as an infinitesimally small positive number to prevent the denominator from being zero.

[0020] S2. Set m sets of hyperparameters X j (j=1,2,3……m), the hyperparameter X was observed experimentally. j The corresponding objective function value f(X) j (q=1,2,3……m), and establish a historical data set H=(X 1：m ,f(X 1：m )); where X 1：m This indicates the first set of hyperparameters X. 1 Up to the m-th group of hyperparameters X m f(X) 1：m ) represents the first set of objective function values ​​f(X) corresponding to the hyperparameters obtained through experimental observation. 1 From the m-th objective function value f(X) to the m-th group m );

[0021] Furthermore, the method for setting hyperparameters in step S2 includes Latin hypercube sampling or orthogonal experimental sampling.

[0022] S3. Use the data in the historical dataset H to build a probability distribution model M;

[0023] The methods for constructing the probability distribution model in step S3 include Gaussian process regression or double Parzen window estimator modeling.

[0024] S4. Construct an acquisition function based on the probability distribution model M, and calculate the observed electrofluid inkjet printing process parameters x for the next parameter tuning step based on the acquisition function. k+1 Specifically:

[0025] The acquisition function EI f (x) is:

[0026] EI f (x)= max[y*-f(x), 0]p M (f(x)|x)d[f(x)]

[0027] The next step is to observe the electrohydraulic inkjet printing process parameters x. k+1 for:

[0028] x k+1 =argmax x EI f (x)

[0029] Where y* is the set optimization threshold, and f(x) is the objective function; p M (f(x)|x) represents the conditional probability density function of f(x) based on the probability model M; argmax x This makes the acquisition function EIf (x) retrieves the parameter value of x corresponding to the maximum value.

[0030] The formula EI f (x) represents an expectation that measures the average improvement of f(x) relative to y*. The set of parameters that yields the largest expected improvement is the set of parameters to be searched in the next iteration. M (f(x)|x) can be calculated using data from the probability distribution model M and / or Bayes' theorem; the Bayes' theorem is:

[0031] p M (f(x)|x)=p M (x|f(x))p M (f(x)) / p M (x)

[0032] Where, p M (x|f(x)) represents the conditional probability density function of x based on the probability model M, p M (f(x)) represents the probability density function of f(x) based on the probability model M, p M (x) represents the probability density function of x based on the probability model M.

[0033] Furthermore, the value of the optimization threshold y* includes the best observation value minf(X) in the historical data set H. j (j=1,2……, m+k-1);

[0034] S5. The parameter value x is obtained through experimental observation. k+1 The observed value of the objective function f(x) under the given conditions k+1 ), and the newly observed (x) k+1 ,f(x k+1 Add it to the historical data set H;

[0035] S6. Determine if the convergence criterion is met: If the convergence criterion is met, stop the iterative calculation and obtain the optimal solution for the electrohydraulic inkjet printing process parameters x*=x k+1 If the convergence criterion is not met, repeat steps S3 to S6 in a loop until the convergence criterion is met.

[0036] Furthermore, the convergence criterion includes: f(x) k+1 )-f(x k The condition is that the error of the printed line is less than ε, and h(x) = 0, where ε is the convergence accuracy term. It is also necessary to verify whether the shape error of the printed line is within the tolerance band, i.e., whether the penalty term h(x) is 0. If not, the penalty factor needs to be increased iteratively to search for an optimal solution that meets the conditions.

[0037] The beneficial effects of this invention are:

[0038] The solution provided by this invention achieves high accuracy in process parameter tuning, requires a small number of test samples, shortens the process tuning process, has low tuning costs, eliminates the influence of human experience on the tuning effect and efficiency, and enables online parameter tuning. Attached Figure Description

[0039] Figure 1 This is a flowchart of the parameter adjustment method for electrofluid inkjet printing process. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0041] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0042] In this embodiment, electrohydraulic inkjet printing technology is used to print silver ink onto a PCB substrate to prepare a silver circuit. The target printing linewidth is w. a =200μm, with a printing straightness tolerance of t=10μm. Among them, air pressure, pulse voltage amplitude, and printing speed are three process parameters to be optimized, while pulse frequency, duty cycle, printing height, nozzle inner diameter, fluid viscosity, fluid surface tension coefficient, and fluid conductivity are other process parameters as known constants.

[0043] S1. Construct a parameter tuning and optimization model for electrohydraulic inkjet printing process:

[0044] Let g(x) = [w(x) - w a ] 2 h(x) = [max(0, e(x) - t)] 2

[0045] min f(x)=g(x)+μ k ·h(x)

[0046] Where x represents the column vector of parameters to be optimized, x i(i=1,2,3) represents the i-th electro-hydraulic inkjet printing process parameter to be optimized; T represents transpose; g(x) represents the linewidth error function; w(x) represents the electro-hydraulic inkjet printing linewidth function; w a denoted as target linewidth; h(x) represents the penalty term function; e(x) represents the shape error function of the printing line; t is the tolerance corresponding to the shape error; f(x) is the objective function; k is the iteration number, μ k Let μ be the penalty factor for the k-th iteration; set the initial penalty factor μ. 1 =1;

[0047] Define a set of column vectors of parameters to be optimized, x = (x1, x2, x3). T Where x1 represents air pressure, x2 represents pulse voltage amplitude, and x3 represents printing speed.

[0048] S2. Using a 3-factor, 3-level orthogonal experimental sampling design, 9 hyperparameters X were set. 1 ~X 9 The corresponding objective function value f(X) is observed through experiments. 1 )~f(X 9 ), and establish a historical data set H=(X 1：9 ,f(X 1：9 Among them, X 1：9 This represents the first set of hyperparameters X obtained through sampling. 1 Up to the 9th group of hyperparameters X 9 f(X) 1：9 ) represents the first set of observed values ​​of the objective function f(X) obtained through experimental observation. 1 The objective function observations from group 9 to group 9 are f(X). 9 );

[0049] S3. Using the data in the historical data set H, establish a probability distribution model M based on the Gaussian process regression process.

[0050] S4. Calculate the observed electrofluid inkjet printing process parameters x based on the acquisition function for the next parameter tuning step. k+1 The acquisition function is:

[0051] EI f (x)= max[y*-f(x), 0]p M (f(x)|x)d[f(x)]

[0052] The next step in parameter tuning involves observing the printing process parameters x. k+1 for:

[0053] x k+1 =argmax x EIf (x)

[0054] The values ​​in the formula can be obtained and calculated using the probability distribution model M and Bayes' theorem, where y* is the best observation minf(X) in the historical data set H. j (j=1,2……, m+k-1);

[0055] S5. The parameter value x is obtained through experimental observation. k+1 The observed value of the objective function f(x) under the given conditions k+1 ), and the newly observed (x) k+1 ,f(x k+1 Add it to the historical data set H;

[0056] S6. Determine if the convergence criterion is met: If the convergence criterion is met, stop the iterative calculation and obtain the optimal solution for the electrohydraulic inkjet printing process parameters x*=x k+1 If the convergence criterion is not met, repeat steps S3 to S6 in a loop until the convergence criterion is met.

[0057] The convergence criterion in this embodiment is: f(x) k+1 )-f(x k The condition is that the error of the printed line is less than ε, and h(x) = 0. Here, ε is the convergence accuracy term, which is 0.1 in this embodiment. It is also necessary to verify whether the shape error of the printed line is within the tolerance zone, that is, whether the penalty term h(x) is 0. If not, the penalty factor needs to be increased and iterated to search for an optimal solution that meets the conditions.

[0058] When the number of iterations k≥2, the method for determining the penalty function factor μ is as follows:

[0059] μ k+1 =c k+1 μ k

[0060] c k+1 =exp{[h(x k ) / (g(x k )+σ)]-1}

[0061] Where c is the growth factor of the penalty function factor μ, and σ is an infinitesimally small positive number (taken as 0.1 in this embodiment), c k+1 It is the growth factor of the penalty function factor in the (k+1)th iteration.

[0062] After running the algorithm and conducting subsequent experiments, a total of 8 iterations were performed, and the output result was f(x*) = 0.0097. The optimized result was x* = (x1, x2, x3). T=(25.1234, 3.5012, 3.5678) T Including the initial nine historical data experiments, a total of 17 experimental observations were conducted, ensuring high parameter tuning accuracy while significantly improving tuning efficiency and eliminating the influence of human experience on the tuning effect and efficiency.

[0063] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A parameter tuning method for electrohydraulic inkjet printing process based on Bayesian optimization, characterized in that, The electrohydraulic inkjet printing process parameter adjustment method includes the following steps: S1. Set the electro-hydraulic inkjet printing process parameters to be optimized as a set of parameter vectors x, and construct a parameter tuning and optimization model for the electro-hydraulic inkjet printing process parameters: x=(x1,x2,…x i …x n ) T 4 Let \(g(x)=[w(x)-w a 2 , h(x)=[\max(0, e(x)-t)] 2 ;\​ min f(x)=g(x)+μ k ·h(x); Where x represents the column vector of parameters to be optimized, x i (i=1,2,3……n) represents the i-th electrohydraulic inkjet printing process parameter to be optimized; T represents transpose; g(x) represents the linewidth error function; w(x) represents the electrohydraulic inkjet printing linewidth function; w a denoted as target linewidth; h(x) represents the penalty term function; e(x) represents the shape error function of the printing line; t is the tolerance corresponding to the shape error; f(x) is the objective function; k is the iteration number, μ k Let μ be the penalty factor for the k-th iteration; and set the initial penalty factor μ. 1 ; S2. Set m sets of hyperparameters X j (j=1,2,3……m), the hyperparameter X was observed experimentally. j The corresponding objective function value f(X) j (q=1,2,3……m), and establish a historical data set H=(X 1：m ,f(X 1：m )); where X 1：m This indicates the first set of hyperparameters X. 1 Up to the m-th group of hyperparameters X m f(X) 1：m ) represents the first set of objective function values ​​f(X) corresponding to the hyperparameters obtained through experimental observation. 1 From the m-th objective function value f(X) to the m-th objective function value m ); S3. Use the data in the historical dataset H to build a probability distribution model M; S4. Construct an acquisition function based on the probability distribution model M, and calculate the observed electrofluid inkjet printing process parameters x for the next parameter tuning step based on the acquisition function. k+1 ; S5. The parameter value x is obtained through experimental observation. k+1 The observed value of the objective function f(x) under the given conditions k+1 ), and the newly observed (x) k+1 ,f(x k+1 Add it to the historical data set H; S6. Determine if the convergence criterion is met: If the convergence criterion is met, stop the iterative calculation and obtain the optimal solution for the electrohydraulic inkjet printing process parameters x*=x k+1 If the convergence criterion is not met, repeat steps S3 to S6 in a loop until the convergence criterion is met.

2. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 1, characterized in that, In S1, when the number of iterations k≥2, the method for determining the penalty function factor μ is as follows: m k+1 =c k+1 m k ; c k+1 =exp{[h(x k ) / (g(x k )+σ)]-1}; Where c is the growth factor of the penalty function factor μ, σ is an infinitesimally small positive number, and c k+1 It is the growth factor of the penalty function factor in the (k+1)th iteration.

3. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 1, characterized in that, In S1, the electrohydraulic inkjet printing process parameter x i (i=1,2,3……n), including one or more of the following electrohydraulic inkjet printing process parameters: air pressure, pulse voltage amplitude, pulse frequency, duty cycle, printing height, printing speed, nozzle inner diameter, fluid viscosity, fluid surface tension coefficient, and fluid conductivity.

4. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 1, characterized in that, In S1, for a printed straight line, e(x) represents the straightness error function of the printed straight line; for a printed arc, e(x) represents the roundness error function of the printed arc; and for a printed spline curve, e(x) represents the line profile error function of the printed spline curve.

5. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 1, characterized in that, The methods for setting hyperparameters in S2 include Latin hypercube sampling or orthogonal experimental sampling.

6. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 1, characterized in that, The methods for constructing the probability distribution model in step S3 include Gaussian process regression or double Parzen window estimator modeling.

7. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 1, characterized in that, In S4, the acquisition function is: EI f (x)= max[y*-f(x), 0]p M (f(x)|x)d[f(x)] ; The next step is to observe the electrohydraulic inkjet printing process parameters x. k+1 for: x k+1 =argmax x EI f (x) ; Where y* is the set optimization threshold, and f(x) is the objective function; p M (f(x)|x) represents the conditional probability density function of f(x) based on the probability model M; argmax x This makes the acquisition function EI f (x) retrieves the parameter value of x corresponding to the maximum value.

8. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 7, characterized in that, The acquisition function EI f In (x), p M (f(x)|x) is calculated using data from the probability distribution model M and / or Bayes' theorem, which is: p M (f(x)|x)=p M (x|f(x))p M (f(x)) / p M (x) ; Where, p M (x|f(x)) represents the conditional probability density function of x based on the probability model M, p M (f(x)) represents the probability density function of f(x) based on the probability model M, p M (x) represents the probability density function of x based on the probability model M.

9. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 1, characterized in that, In step S4, the value of the optimization threshold y* includes the best observation value minf(X) in the historical data set H. j (j=1,2……,m+k-1).

10. The method for parameter tuning of electrofluid inkjet printing process based on Bayesian optimization according to claim 1, characterized in that, In S6, the convergence criterion includes: f(x) k+1 )-f(x k )<ε, and h(x)=0, where ε is the convergence accuracy term.

Images