A method and apparatus for optimizing the process parameters of light-absorbing coating preparation for photoacoustic transducers.

Abstract

This application discloses a method and apparatus for optimizing the process parameters of a light-absorbing coating for a photoacoustic transducer. The method includes: obtaining a dynamic weight allocation scheme; obtaining a parameter contribution dataset based on the dynamic weight allocation scheme; generating a subset of key process parameters based on the parameter contribution dataset; using a non-dominated sorting genetic algorithm to solve a bi-objective optimization model based on the subset of key process parameters to obtain a Pareto optimal parameter solution set covering different optimization priorities; setting interference conditions to conduct an anti-interference test on the Pareto optimal parameter solution set, and selecting parameter combinations whose performance fluctuation is less than a second preset threshold; the parameter combinations whose output is less than the second preset threshold are taken as the optimal combination of light-absorbing coating preparation process parameters. This application can solve the pain points of traditional methods such as parameter coupling ambiguity, poor optimization targeting, and weak adaptability to actual working conditions.

Description

Technical Field

[0001] This application relates to the field of photoacoustic transducer technology, specifically to a method and apparatus for optimizing the process parameters of a light-absorbing coating for a photoacoustic transducer. Background Technology

[0002] As a core component for calibrating 15-20MHz high-frequency hydrophones, the optimization of the light-absorbing coating fabrication process parameters of the photoacoustic transducer directly determines the sound pressure output amplitude, frequency band coverage, and operational stability, and is crucial for achieving accurate vibration acoustic measurement. Existing methods for optimizing the light-absorbing coating fabrication process parameters of photoacoustic transducers have several specific technical shortcomings, as follows: Inaccurate parameter correlation identification and lack of quantification of coupling strength: Existing technologies mostly use single parameter traversal or simple correlation analysis, without establishing a systematic parameter correlation identification mechanism. For example, it is impossible to accurately determine strongly correlated parameter pairs such as coating thickness-absorbance and laser pulse width-curing temperature through quantification methods. At the same time, there is a lack of a quantitative model for parameter coupling strength based on thermal expansion theory, and the interaction of parameters is judged only by experience. This leads to subsequent optimization not considering the synergistic effect of parameters, affecting the optimization's relevance.

[0003] Fixed weight allocation leads to insufficient sensitivity analysis: Traditional sensitivity analysis algorithms (such as the basic Sobol algorithm) use uniform weights to calculate the contribution of parameters without dynamically adjusting the weight allocation based on the coupling strength of parameters. This fails to highlight the influence of strongly coupled parameter pairs, resulting in biased identification of key parameters and making it difficult to match the dual-target optimization requirements of sound pressure and frequency band.

[0004] The lack of a basis for key parameter selection leads to low optimization efficiency: Existing technologies do not accurately select parameters based on their contribution to the dual objectives. The optimization process includes a large number of low-impact redundant parameters, resulting in a huge amount of numerical computation, low simulation optimization efficiency, and an inability to quickly focus on the core optimization object.

[0005] The parameter values ​​were not adjusted for gain, and the performance potential was not explored: The existing optimization process lacks a gain correction step for optical-thermal-acoustic multi-field coupling. It is only based on the original parameter values ​​and does not consider the synergistic gain effect between parameters. As a result, the parameter values ​​do not reach the optimal performance range, making it difficult to achieve the metrological requirements of sound pressure ≥0.9MPa and frequency band coverage of 15-20MHz.

[0006] Poor adaptability of optimization algorithms and insufficient quality of Pareto solution sets: The fitness function of traditional non-dominated sorting genetic algorithms does not incorporate parameter gain characteristics. The crossover mutation probability is fixed during iteration, which easily leads to premature convergence of the algorithm. This results in insufficient diversity of the generated Pareto optimal parameter solution sets, which cannot cover different priority requirements such as sound pressure priority, frequency band priority, and equalization optimization.

[0007] Lack of anti-interference verification and weak adaptability to actual working conditions: Existing technologies only focus on the parameter optimization results under ideal conditions, without systematically setting actual working condition interference conditions such as ambient temperature fluctuations, laser energy fluctuations, and coating rate fluctuations, and without quantifying the performance fluctuation threshold. As a result, the optimized parameter combination has poor stability in complex application scenarios, and the performance fluctuation exceeds the allowable range of metrological calibration.

[0008] Although relevant research has been conducted both domestically and internationally, a complete technical system covering "parameter correlation identification, coupling strength quantification, dynamic weight allocation, key parameter screening, gain correction, intelligent optimization, and anti-interference verification" has yet to be established. This results in the sound pressure output accuracy, bandwidth stability, and anti-interference capability of high-frequency photoacoustic transducers failing to meet the requirements of domestic metrological calibration. Therefore, it is urgent to address these technical deficiencies and establish a method for optimizing fabrication process parameters that balances parameter coupling characteristics, multi-field synergistic gain, and anti-interference capabilities, providing technical support for the precise development of high-frequency photoacoustic transducers. Summary of the Invention

[0009] The purpose of this invention is to provide a method for optimizing the absorbance of photoacoustic transducers and the light absorption of coating materials, as well as the process parameters for preparing photocoatings, to at least solve one of the above-mentioned technical problems.

[0010] One aspect of the present invention provides a method for optimizing the process parameters of the light-absorbing coating preparation for a photoacoustic transducer, the method comprising:

[0011] Step 1: Obtain the fabrication process parameters, structural parameters, excitation parameters, and dual target data of output sound pressure and frequency band for the light-absorbing coating of the photoacoustic transducer;

[0012] Step 2: Construct a parameter correlation table based on the preparation process parameters;

[0013] Step 3: Obtain the parameter coupling strength matrix;

[0014] Step 4: Generate a dynamic weight allocation scheme based on the parameter coupling strength matrix;

[0015] Step 5: Substitute the dynamic weight allocation scheme into the sensitivity analysis algorithm to calculate the contribution of each parameter and the parameter to the dual targets of output sound pressure and frequency band, thereby obtaining the parameter contribution dataset;

[0016] Step 6: Filter out parameters and parameter pairs whose influence contribution is greater than the first preset threshold from the parameter contribution dataset, thereby generating a subset of key process parameters;

[0017] Step 7: Obtain the dual-objective optimization model;

[0018] Step 8: Based on the subset of key process parameters, use a non-dominated sorting genetic algorithm to solve the bi-objective optimization model and obtain a Pareto optimal parameter solution set covering different optimization priorities;

[0019] Step 9: Set interference conditions, perform anti-interference tests on the Pareto optimal parameter solution set, and screen out parameter combinations with performance fluctuation less than the second preset threshold. The parameter combinations with output less than the second preset threshold are taken as the optimal combination of light-absorbing coating preparation process parameters.

[0020] Optionally, the preparation process parameters include the light absorbance of the coating material, the coating thickness, the curing temperature, the curing time, and the coating rate;

[0021] The step of constructing a parameter correlation table based on preparation process parameters includes:

[0022] Step 2.1: Using the Pearson correlation coefficient method, perform pairwise correlation analysis on any two preparation process parameters to calculate the correlation coefficient values ​​between each parameter pair;

[0023] Step 2.2: Set the correlation coefficient threshold to 0.7, determine parameter pairs with a correlation coefficient value greater than 0.7 as strongly correlated parameter pairs, and determine parameters with a correlation coefficient value less than or equal to 0.7 as uncorrelated parameters, thereby generating a parameter correlation table, which includes the correlation attributes of each parameter and the corresponding correlated parameters.

[0024] Optionally, obtaining the parameter coupling strength matrix includes:

[0025] Step 3.1: Extract the strongly correlated parameter pairs marked in the parameter correlation table;

[0026] Step 3.2: Obtain the physical property parameters corresponding to each strongly correlated parameter pair;

[0027] Step 3.3: Based on the theory of thermal expansion, construct a mathematical framework for the coupling strength calculation model. The mathematical framework uses physical property parameters as input variables and coupling strength coefficient as output variables, and introduces a correlation function between the thermal expansion coefficient and the parameter interaction term.

[0028] Step 3.4: Substitute the physical property parameters corresponding to each strongly correlated parameter into the mathematical framework of the coupling strength calculation model, determine the coefficient constants and constraints in the model, and form the coupling strength calculation model;

[0029] Step 3.5: Solve the coupling strength calculation model through numerical calculation to obtain the coupling strength coefficients of each strongly correlated parameter pair;

[0030] Step 3.6: Set the default coupling strength value of the non-associated parameters to 0.1. According to the classification order of preparation process parameters, structural parameters, and excitation parameters, arrange the coupling strength coefficients of each strongly correlated parameter pair with the default coupling strength values ​​of the non-associated parameters in sequence to construct a parameter coupling strength matrix corresponding to the dimension and the total number of parameters.

[0031] Optionally, the step of generating a dynamic weight allocation scheme based on the parameter coupling strength matrix includes:

[0032] Step 4.1: Extract the coupling strength coefficients corresponding to each parameter and strongly correlated parameter pair in the parameter coupling strength matrix;

[0033] Step 4.2: Classify the coupling level according to the coupling strength coefficient, which includes strong coupling, medium coupling and weak coupling;

[0034] Step 4.3: Design weight allocation rules for different coupling levels, and calculate the joint weight of each strongly correlated parameter pair and the independent weight of each uncorrelated parameter according to the weight allocation rules.

[0035] Step 4.4: Integrate all parameters and the weights of parameter pairs to generate a dynamic weight allocation scheme, which includes the weight attributes and specific weight values ​​of each parameter and parameter pair.

[0036] Optionally, the step of substituting the dynamic weight allocation scheme into the sensitivity analysis algorithm to calculate the contribution of each parameter and its influence on the dual targets of output sound pressure and frequency band, thereby obtaining a parameter contribution dataset, includes:

[0037] Step 5.1: Initialize the Sobol algorithm, determine the parameter sampling range, number of iterations, and convergence conditions;

[0038] Step 5.2: Generate a structured sensitivity analysis input dataset based on the dynamic weight allocation scheme;

[0039] Step 5.3: Substitute the sensitivity analysis input dataset into the initialized Sobol algorithm, use the dynamic weight value as the correction coefficient for the variance contribution calculation, and solve for each parameter and the first contribution of the parameter to the output sound pressure target and the second contribution of the parameter to the output frequency band target respectively.

[0040] Step 5.4: Set the dual-objective weighting coefficients, and calculate the comprehensive impact contribution of each parameter and parameter pair based on the dual-objective weighting coefficients;

[0041] Step 5.5: Integrate the parameter identifiers, first contribution, second contribution, and comprehensive impact contribution of each parameter and parameter pair to generate a structured parameter contribution dataset.

[0042] Optionally, the step of filtering parameters and parameter pairs with an impact contribution greater than a first preset threshold from the parameter contribution dataset to generate a subset of key process parameters includes:

[0043] Step 6.1: Extract the comprehensive impact contribution and parameter identification information of each parameter and parameter pair in the parameter contribution dataset;

[0044] Step 6.2: Compare the overall impact contribution of each parameter and parameter pair with the first preset threshold one by one, and select the parameters and parameter pairs whose overall impact contribution is greater than the first preset threshold.

[0045] Step 6.3: Integrate the selected parameters and parameter pairs, supplement their corresponding correlation attributes, weight values ​​and physical characteristic parameters, and generate a structured subset of key process parameters. The subset includes the correlation priority of each parameter and parameter pair with the output sound pressure-frequency band dual target.

[0046] Optionally, after step 6: selecting parameters and parameter pairs with influence contributions greater than a first preset threshold from the parameter contribution dataset to generate a subset of key process parameters, the optimization method for the photoacoustic transducer light-absorbing coating preparation process parameters further includes:

[0047] Obtain a multi-field coupling gain correction model;

[0048] A subset of key process parameters is input into a multi-field coupled gain correction model to obtain a parameter correction set with gain coefficients.

[0049] The non-dominated sorting genetic algorithm is used to solve the bi-objective optimization model, obtaining a Pareto optimal parameter solution set covering different optimization priorities, including:

[0050] Based on the parameter correction set with gain coefficients, a non-dominated sorting genetic algorithm is used to solve the bi-objective optimization model, obtaining a Pareto optimal parameter solution set covering different optimization priorities.

[0051] Optionally, the step of using a non-dominated sorting genetic algorithm to solve the bi-objective optimization model based on a subset of key process parameters to obtain a Pareto optimal parameter solution set covering different optimization priorities includes:

[0052] Step 8.1: Initialize the non-dominated sorting genetic algorithm, set the population size to 100-200, the number of iterations to 50-100, the initial crossover probability to 0.7-0.9, the initial mutation probability to 0.01-0.05, and determine the algorithm's convergence condition;

[0053] Step 8.2: Based on the parameter correction set with gain coefficients and combined with the constraints of the bi-objective optimization model, generate the initial population using real number encoding.

[0054] Step 8.3: Introduce a fitness function based on gain coefficient, embed the parameter gain coefficient as a weight in the fitness calculation, and calculate the fitness value of each individual in the population;

[0055] Step 8.4: Based on the results of the fitness quantification, select superior individuals, perform improved non-dominated sorting on the current population, divide Pareto levels through fast non-dominated sorting, retain population diversity by combining crowding degree calculation, and at the same time adopt an adaptive crossover and mutation strategy to dynamically adjust the crossover probability and mutation probability according to the population convergence degree, and output the new generation population after selection, sorting and genetic operations.

[0056] Step 8.5: Repeat steps 8.3-8.4 for fitness calculation, individual selection, non-dominated sorting, and crossover / mutation operations until the preset number of iterations is reached or the convergence condition is met, and output the final population after iterative convergence.

[0057] Step 8.6: Select all non-dominated solutions from the final population and classify them according to three priorities: sound pressure priority, frequency band priority, and equalization optimization, to form a Pareto optimal parameter solution set covering different optimization needs.

[0058] Optionally, the step of setting interference conditions and conducting anti-interference tests on the Pareto optimal parameter solution set to screen out parameter combinations with performance fluctuations less than a second preset threshold, wherein the parameter combinations with outputs less than the second preset threshold are selected as the optimal combination of light-absorbing coating preparation process parameters, including:

[0059] Step 9.1: Obtain ambient temperature fluctuation conditions, laser pulse energy fluctuation conditions, and coating rate fluctuation conditions;

[0060] Step 9.2: Obtain the preset multi-field coupling anti-interference test platform, import each parameter combination in the Pareto optimal parameter solution set into the preset multi-field coupling anti-interference test platform, simulate the entire process of light-absorbing coating preparation and photoacoustic conversion, and measure the output sound pressure value and frequency band coverage corresponding to each parameter combination under the interference-free reference state, and record it as the reference performance data.

[0061] Step 9.3: Apply ambient temperature fluctuation conditions, laser pulse energy fluctuation conditions, and coating rate fluctuation conditions one by one, keeping other parameters constant, measure the actual performance data under each interference condition, and obtain the comprehensive performance fluctuation amount of each parameter combination;

[0062] Step 9.4: Obtain the overall performance fluctuation of each parameter combination based on the baseline performance data and the actual performance data;

[0063] Step 9.5: Compare the overall performance fluctuation of each parameter combination with the second threshold, and select the parameter combination that is less than the second threshold as the optimal combination of light-absorbing coating preparation process parameters.

[0064] This application also provides an apparatus for optimizing the process parameters of the light-absorbing coating preparation for a photoacoustic transducer, the apparatus comprising:

[0065] The basic data acquisition module is used to acquire the preparation process parameters, structural parameters, excitation parameters, and output sound pressure-frequency band dual target data of the light-absorbing coating of the photoacoustic transducer.

[0066] A parameter association table acquisition module is used to construct a parameter association table based on the preparation process parameters.

[0067] A parameter coupling strength matrix acquisition module, wherein the parameter coupling strength matrix acquisition module is used to acquire the parameter coupling strength matrix;

[0068] A dynamic weight allocation scheme generation module is used to generate a dynamic weight allocation scheme based on the parameter coupling strength matrix.

[0069] The parameter contribution dataset acquisition module is used to substitute the dynamic weight allocation scheme into the sensitivity analysis algorithm, calculate the influence contribution of each parameter and the parameter on the dual targets of output sound pressure and frequency band, and thus obtain the parameter contribution dataset.

[0070] A key process parameter subset acquisition module is used to filter parameters and parameter pairs whose influence contribution is greater than a first preset threshold from the parameter contribution dataset, thereby generating a key process parameter subset.

[0071] A dual-objective optimization model acquisition module, wherein the dual-objective optimization model acquisition module is used to acquire a dual-objective optimization model;

[0072] The Pareto optimal parameter solution set acquisition module is used to solve the bi-objective optimization model based on a subset of key process parameters using a non-dominated sorting genetic algorithm, and obtain a Pareto optimal parameter solution set covering different optimization priorities.

[0073] The optimal combination acquisition module is used to set interference conditions, perform anti-interference tests on the Pareto optimal parameter solution set, and screen out parameter combinations with performance fluctuation less than a second preset threshold. The parameter combinations with output less than the second preset threshold are used as the optimal combination of light-absorbing coating preparation process parameters.

[0074] The core technological advantage of this application lies in constructing a closed-loop optimization system encompassing parameter coupling quantification, precise screening, intelligent optimization, and anti-interference verification, addressing the pain points of traditional methods such as fuzzy parameter coupling, poor optimization targeting, and weak adaptability to actual working conditions. By combining the Pearson correlation coefficient method with thermal expansion theory, it achieves quantitative characterization of parameter correlation and coupling strength, providing a precise basis for subsequent optimization. It innovatively employs the Sobol algorithm with embedded dynamic weights to accurately identify key parameters, eliminate redundant variables, and significantly improve optimization efficiency. A multi-field coupling gain correction stage is introduced to fully explore the performance potential of parameters. Combined with a non-dominated sorting genetic algorithm adapted to gain coefficients, it generates Pareto optimal solution sets covering different priorities to meet diverse metrological needs. By setting environmental and energy interference conditions, it quantifies performance fluctuations and screens out stable and reliable optimal parameter combinations, ensuring metrological requirements of ≥0.9MPa sound pressure level and full frequency band coverage in the 15-20MHz high-frequency band. The entire method not only ensures the accuracy and efficiency of the optimization results but also enhances stability in practical applications. Attached Figure Description

[0075] Figure 1 This is a schematic flowchart illustrating the optimization method for the preparation process parameters of the light-absorbing coating of a photoacoustic transducer according to an embodiment of this application. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0077] like Figure 1 The optimization methods for the light-absorbing coating preparation process parameters of the photoacoustic transducer shown include:

[0078] Step 1: Obtain the fabrication process parameters, structural parameters, excitation parameters, and dual-target data of output sound pressure and frequency band for the light-absorbing coating of the photoacoustic transducer; the fabrication process parameters include the light absorbance of the coating material, coating thickness, curing temperature, and coating rate; the structural parameters include the transducer curvature and coating coverage area; and the excitation parameters include the laser pulse energy and pulse width.

[0079] Step 2: Construct a parameter correlation table based on the preparation process parameters; the strongly correlated parameter pairs include coating thickness-absorbance and laser pulse width-curing temperature, characterizing the synergistic effect mechanism between parameters;

[0080] Step 3: Obtain the parameter coupling strength matrix; obtain the core parameters of the thermal expansion theory, including the volume expansion coefficient of water, underwater sound speed, and specific heat of water, and establish the parameter coupling strength matrix based on the thermal expansion theory;

[0081] Step 4: Generate a dynamic weight allocation scheme based on the parameter coupling strength matrix;

[0082] Step 5: Substitute the dynamic weight allocation scheme into the sensitivity analysis algorithm to calculate the contribution of each parameter and the parameter to the dual targets of output sound pressure and frequency band, thereby obtaining the parameter contribution dataset;

[0083] Step 6: Filter out parameters and parameter pairs whose influence contribution is greater than the first preset threshold from the parameter contribution dataset, thereby generating a subset of key process parameters;

[0084] Step 7: Obtain the dual-objective optimization model;

[0085] Step 8: Based on the subset of key process parameters, use a non-dominated sorting genetic algorithm to solve the bi-objective optimization model and obtain a Pareto optimal parameter solution set covering different optimization priorities;

[0086] Step 9: Set interference conditions, perform anti-interference tests on the Pareto optimal parameter solution set, and screen out parameter combinations with performance fluctuation less than the second preset threshold. The parameter combinations with output less than the second preset threshold are taken as the optimal combination of light-absorbing coating preparation process parameters.

[0087] In this embodiment, the preparation process parameters include the light absorbance of the coating material, the coating thickness, the curing temperature, the curing time, and the coating rate;

[0088] In this embodiment, structural parameters may include transducer curvature and coating coverage area;

[0089] Excitation parameters may include laser pulse energy and laser pulse width;

[0090] The dual-target data of output sound pressure and frequency band includes the output sound pressure value (target ≥ 0.9 MPa) and the frequency band coverage range (target 15-20 MHz).

[0091] The step of constructing a parameter correlation table based on preparation process parameters includes:

[0092] Step 2.1: Using the Pearson correlation coefficient method, perform pairwise correlation analysis on any two preparation process parameters to calculate the correlation coefficient values ​​between each parameter pair;

[0093] In this embodiment, step 2.1: Using the Pearson correlation coefficient method, pairwise correlation analysis is performed on any two preparation process parameters to calculate the correlation coefficient values ​​between each parameter pair, including:

[0094] The specific technical solution for calculating the correlation coefficient between any two preparation process parameters using the Pearson correlation coefficient method is as follows:

[0095] Step 211: Construction of a sample dataset of preparation process parameters

[0096] Parameter sampling range determination: Based on the photothermal conversion efficiency requirements of the light-absorbing coating of the 15-20MHz high-frequency photoacoustic transducer, the thermal stability of the substrate material, and the controllability of the actual fabrication process, the effective sampling range of five fabrication process parameters is determined:

[0097] The light absorbance of the coating material is 0.85~0.99 (dimensionless), covering carbon nanocomposite coatings. Typical light absorption performance ranges of commonly used light-absorbing materials such as metal oxide coatings and graphene-based coatings;

[0098] Coating thickness: 1~5μm, matching the energy absorption threshold and acoustic impedance matching requirements of high-frequency sound pressure output, avoiding sound attenuation due to excessive thickness and insufficient light absorption due to excessive thinness;

[0099] Curing temperature: 60~120℃, compatible with the curing temperature range of commonly used adhesives such as epoxy resin, silicone resin, and polyimide, while also compatible with the heat resistance limit (≤150℃) of substrate materials such as piezoelectric ceramics and sapphire.

[0100] Curing time: 30~180min, which works in synergy with the curing temperature range to ensure that the coating molecules are fully cross-linked, with no uncured components remaining, and without causing coating cracking due to excessive cross-linking;

[0101] Coating rate: 5~20mm / s, covering the controllable rate range of mainstream coating processes such as spraying, spin coating, and scraping, while taking into account both coating thickness uniformity (error ≤ ±5%) and preparation efficiency.

[0102] Sampling method and sample size setting: Latin hypercube sampling (LHS) was used for parameter sampling. This method can achieve uniform sampling within each parameter sampling range, ensuring the spatial filling of the sample and the comprehensiveness of parameter combinations, and avoiding analytical bias caused by the clustering of samples in a single region. In combination with the significance requirements of statistical analysis (confidence level ≥95%), the total number of samples was set to 50 groups. Each group of samples contains the specific values ​​of the above 5 preparation process parameters, and the parameter combinations of any two groups of samples are not repeated, ensuring the independence and representativeness of the sample data.

[0103] Sample dataset generation: Latin hypercube sampling is performed using the lhsdesign function in Matlab software. The input parameters are the dimension (5-dimensional, corresponding to 5 preparation process parameters), the number of samples (50 groups), and the upper and lower boundary values ​​of each parameter. The output is a structured sample dataset. The dataset format is a 50-row × 5-column matrix. The row index is the sample number (1~50), and the column index corresponds to the parameter order (in order: light absorbance of coating material, coating thickness, curing temperature, curing time, coating rate). Each element in the matrix is ​​the specific value of the parameter for the corresponding sample (retaining 3 decimal places).

[0104] Step 212: Sample Data Preprocessing

[0105] Outlier Detection and Correction: Outlier screening is performed using the 3σ criterion. Specific procedures are as follows:

[0106] Calculate the mean μ and standard deviation σ of 50 sample values ​​for each preparation process parameter;

[0107] For each sample, the value of each parameter is determined. If |x-μ|>3σ (where x is the sample value of the parameter), then the value is determined to be an outlier.

[0108] For detected outliers, the median of all valid samples (non-outliers) of this parameter is used to replace them, ensuring the integrity and validity of the dataset and avoiding interference from outliers with the correlation analysis results.

[0109] Data normalization: Since the dimensions (dimensionless, μm, ℃, min, mm / s) and value ranges of various preparation process parameters differ significantly, direct correlation analysis would lead to distorted results due to the influence of dimensions. Therefore, the min-max normalization method is used to standardize the preprocessed sample data. The normalization formula used is the min-max normalization formula in the existing technology. Through this formula, the sample values ​​of all parameters are mapped to the [0,1] interval, eliminating the analytical bias caused by differences in dimensions and value ranges.

[0110] Step 213: Constructing a set of pairwise parameter combinations

[0111] Based on the five preparation process parameters, a set of all non-repeating pairwise parameter combinations was constructed, forming a total of C(5,2)=10 parameter pairs, as follows:

[0112] Combination 1: Light absorbance of coating material and coating thickness;

[0113] Combination 2: Light absorbance of coating material and curing temperature;

[0114] Combination 3: Light absorbance and curing time of coating materials;

[0115] Combination 4: Light absorbance of coating materials and coating rate;

[0116] Combination 5: Coating thickness and curing temperature;

[0117] Combination 6: Coating thickness and curing time;

[0118] Combination 7: Coating thickness and coating rate;

[0119] Combination 8: Curing temperature and curing time;

[0120] Combination 9: Curing temperature and coating rate;

[0121] Combination 10: Curing time and coating rate.

[0122] Step 214: Calculation of correlation coefficient value

[0123] For the above 10 parameter pairs, the correlation coefficient value of each parameter pair is calculated using the Pearson product-moment correlation coefficient formula in the existing technology. The specific execution process is as follows:

[0124] For each pair of parameters (e.g., combination 1: light absorbance of coating material and coating thickness), extract 50 sample values ​​corresponding to the two parameters from the normalized dataset to form two vectors with a dimension of 50×1.

[0125] Substituting the two vectors into the Pearson product-moment correlation coefficient formula, the correlation coefficient value r of the parameter pair is calculated (the value range is [-1,1]). The closer the absolute value of r is to 1, the stronger the linear correlation between the two parameters. r=0 indicates that the two parameters have no linear correlation.

[0126] Calculate the correlation coefficient values ​​of 10 parameter pairs sequentially using the method described above, record the identification information of each parameter pair (e.g., combination 1) and the corresponding correlation coefficient value (retain 4 decimal places), and form a parameter pair-correlation coefficient value correspondence table.

[0127] Step 2.2: Set the correlation coefficient threshold to 0.7, determine parameter pairs with correlation coefficient values ​​greater than 0.7 as strongly correlated parameter pairs, and determine parameters with correlation coefficient values ​​less than or equal to 0.7 as uncorrelated parameters, thereby generating a parameter correlation table, which includes the correlation attributes of each parameter and the corresponding correlated parameters.

[0128] In this embodiment, parameter pairs with a correlation coefficient greater than 0.7 are determined to be strongly correlated parameter pairs, and parameters with a correlation coefficient less than or equal to 0.7 are determined to be uncorrelated parameters, thereby generating a parameter correlation table. The parameter correlation table includes the correlation attributes of each parameter and the corresponding correlated parameters, including:

[0129] Obtain the parameter pair-correlation coefficient value correspondence table generated in step 2.1. This table contains complete information on 10 sets of non-repeating parameter pairs, specifically: parameter pair identifier (e.g., coating material absorbance-coating thickness), specific names of the two parameters, and corresponding correlation coefficient values ​​(retain 4 decimal places, with a value range of [-1,1]).

[0130] Alignment and Judgment: According to the parameter pair identification order (from combination 1 to combination 10), the correlation coefficient value of each parameter pair is compared with the threshold 0.7 one by one, and the following judgment rules are executed:

[0131] If the correlation coefficient of a certain parameter is... If the value is greater than 0.7, the parameter pair is determined to be a strongly correlated parameter pair. At the same time, it is marked that both parameters in the parameter pair have strong correlation attributes and serve as each other's corresponding correlated parameters.

[0132] If the correlation coefficient of a certain parameter is... If the value is ≤0.7, the parameter pair is determined to be a non-associative parameter combination. Both parameters in the parameter pair are marked as having non-associative attributes, and their corresponding associated parameters are marked as none.

[0133] Special case handling: If a parameter belongs to multiple parameter pairs (e.g., coating thickness forms a parameter pair with both absorbance and curing temperature), its correlation attribute is determined according to the principle of choosing the higher one. If the correlation coefficient between the parameter and any other parameter is greater than 0.7, the parameter is marked as a strongly correlated attribute, and all parameters that form a strong correlation with it are listed in the corresponding correlated parameters. If the correlation coefficient between the parameter and all other parameter pairs is less than or equal to 0.7, it is marked as a non-correlated attribute.

[0134] Related attribute verification: Perform a second verification on the judgment results to eliminate misjudgments caused by calculation errors.

[0135] Verification criteria: Strongly correlated parameter pairs must have a clear physical correlation mechanism (e.g., the correlation mechanism between curing temperature and curing time is that increasing the temperature can shorten the time for the curing reaction to reach equilibrium). For parameter pairs without a physical correlation mechanism but whose correlation coefficient value is occasionally greater than 0.7 (probability ≤ 3%), the correlation coefficient calculation process in step 2.1 needs to be re-verified (e.g., whether the sample data is abnormal, whether the normalization process is accurate). The final judgment can only be made after confirming that there are no errors.

[0136] Structured generation of parameter relationship tables:

[0137] Field definition for the relationship table: Design a standardized structured table containing 6 core fields to ensure complete information that can be directly accessed in subsequent steps.

[0138] Field 1: Unique identifier for the parameter (named in the format of preparation process parameter number-parameter name, such as 1-absorbance of coating material, 2-coating thickness);

[0139] Field 2: Parameter name (exactly the same as the parameter name in steps 1 and 2.1 to avoid ambiguity);

[0140] Field 3: Related attribute (unique value is either strongly related or not related);

[0141] Field 4: Corresponding related parameters (If the related attribute is strongly related, list all parameter names that form a strongly related parameter pair, separated by semicolons; if it is not related, fill in none).

[0142] Field 5: Correlation coefficient values ​​for the corresponding parameter pairs (if the association attribute is strong, list the calculated correlation coefficient values ​​for the corresponding parameter pairs, corresponding one-to-one with the parameter names in Field 4; if they are not related, fill in " / ").

[0143] Field 6: Judgment criteria (uniform format is "correlation coefficient value [specific value], [greater than / less than or equal to] threshold 0.7").

[0144] The process of generating the relationship table:

[0145] Based on the judgment results, the five preparation process parameters are arranged in ascending order according to their unique identifiers.

[0146] Fill in the information for each field line by line, as shown in the example below:

[0147] The parameter uniquely identifies "1-Coating material absorbance": If its correlation coefficient with "2-Coating thickness" is 0.85, and its correlation coefficient with other parameters is ≤0.7, then field 3 should be filled with "strong correlation", field 4 with "coating thickness", field 5 with "0.85", and field 6 with "correlation coefficient value 0.85, greater than the threshold 0.7".

[0148] The parameter unique identifier "5-Coating Rate": If its correlation coefficient with all other parameters is ≤0.7, then fill in "No correlation" for field 3, "None" for field 4, " / " for field 5, and "Correlation coefficient values ​​are all ≤0.7, less than or equal to the threshold of 0.7" for field 6.

[0149] The table is formatted and stored in CSV structured format to ensure that subsequent steps (such as step 3.1 "extracting strongly correlated parameter pairs") can automatically read the strongly correlated parameter information in field 4 without manual intervention.

[0150] Output and validation of parameter association table

[0151] Output format: Generates two parallel output files to meet the needs of different application scenarios:

[0152] Visualized spreadsheet file: in Excel format, containing field headings, parameter information, and judgment results, facilitating manual verification;

[0153] Machine-readable file: CSV format, with commas as field separators, no redundant formatting information, adapted to the program input requirements for subsequent parameter coupling strength matrix construction.

[0154] Verification criteria: Ensure that the generated parameter relationship table meets the following three requirements:

[0155] Completeness: All five preparation process parameters were included in the table without omission;

[0156] Consistency: The parameter names and parameter pair identifiers are completely consistent with the "Parameter Pair-Correlation Coefficient Value Correspondence Table" in step 2.1, with no name ambiguity or identification errors;

[0157] Accuracy: The correlation coefficients of strongly correlated parameter pairs are all greater than 0.7, and the correlation coefficients of uncorrelated parameters are all ≤0.7. The judgment criteria correspond one-to-one with the correlation coefficient values, and there is no logical contradiction.

[0158] In this embodiment, obtaining the parameter coupling strength matrix includes:

[0159] Step 3.1: Extract the strongly correlated parameter pairs marked in the parameter correlation table;

[0160] In this embodiment, step 3.1: extracting strongly correlated parameter pairs marked in the parameter correlation table includes:

[0161] The parameter association table generated in step 2.2 is used as input. This table contains the core fields of "parameter unique identifier, parameter name, association attribute, and corresponding association parameter", and the parameter names are consistent with those in step 2.1 (coating material absorbance, coating thickness, curing temperature, curing time, and coating rate).

[0162] The program reads the "related attribute" field from the table and filters all parameter records whose value is "strongly related".

[0163] Extract the "parameter name" and "corresponding associated parameter" fields from the filtered records to form a "parameter-corresponding associated parameter" tuple (e.g., "coating material absorbance-coating thickness").

[0164] Remove duplicate pairs (e.g., "AB" and "BA" are considered the same parameter pair, and only one pair is kept) to ensure that there is no redundancy in strongly correlated parameter pairs;

[0165] Generate a structured list of strongly correlated parameter pairs, including a unique identifier for each parameter pair (e.g., "strongly correlated-1") and two parameter names. The format is adapted to the reading requirements of step 3.2 "Obtain physical property parameters" and can be directly imported into subsequent calculation processes.

[0166] Step 3.2: Obtain the physical property parameters corresponding to each strongly correlated parameter pair;

[0167] In this embodiment, obtaining the physical characteristic parameters corresponding to each strongly correlated parameter pair includes: For each pair of strongly correlated parameters, based on their coupling mechanism (photothermal conversion, synergistic thermal expansion, synergistic curing reaction, etc.), the corresponding core physical property parameters are obtained, as follows: If the strongly correlated parameter pair is coating material absorbance - coating thickness: obtain the thermal conductivity of the light-absorbing material (unit: W / (m・K), measured by laser flare method, referring to GB / T 22588-2008 standard), the volumetric expansion coefficient of the coating (measured by thermomechanical analyzer, temperature range matching curing temperature range), and the quantum yield of the light-absorbing material (dimensionless, measured by fluorescence spectrometer). If the strongly correlated parameter pair is the absorbance of the coating material and the curing time: obtain the curing reaction conversion rate of the adhesive (determined by differential scanning calorimetry), the optical performance attenuation rate of the light-absorbing material during the curing process (measured by a UV-Vis-NIR spectrophotometer), and the photothermal conversion efficiency of the coating after curing (measured by a photothermal testing system). If the strongly correlated parameter pair is the absorbance of the coating material and the coating rate: obtain the solid content of the coating slurry (measured by drying and weighing method), the dispersibility coefficient of the light-absorbing particles (measured by laser particle size analyzer), and the leveling time of the coating during the coating process (measured by the leveling test module of the contact angle measuring instrument). If the strongly correlated parameter pair is coating thickness-curing temperature: obtain the coating's heat distortion temperature (measured using a thermomechanical analyzer), the coating's thickness shrinkage rate at different curing temperatures (measured using a step tester), and the interfacial bonding strength between the coating and the substrate (measured using the scratch method, referring to GB / T 9279-2008 standard). If the strongly correlated parameter pair is coating thickness-curing time: obtain the crosslinking density of the coating at different curing times (measured by the swelling method), the compactness coefficient of the coating after curing (calculated by scanning electron microscopy image analysis), and the uniformity deviation of the coating thickness (calculated by multi-point measurement using a profilometer). If the strongly correlated parameter pair is curing temperature-curing time: obtain the activation energy of the coating adhesive (such as epoxy resin) by differential scanning calorimetry, the crosslinking density of the adhesive by swelling method, and the thermal conductivity of the substrate material, which can be obtained by consulting the standard technical manual of the substrate material (piezoelectric ceramic / sapphire). If the strongly correlated parameter pair is coating thickness-coating rate: obtain the viscosity of the coating slurry (measured using a rotational viscometer at 25°C), the surface tension of the coating (measured using the pendant drop method), and the hydrodynamic coefficients of the coating process (based on the coating equipment model, consult the manufacturer's technical parameters). If the strongly correlated parameter pair is the absorbance of the coating material minus the curing temperature: obtain the thermal stability threshold of the light-absorbing material (measured by thermogravimetric analyzer), the compatibility coefficient between the light-absorbing material and the binder (dimensionless, calculated based on the degree of functional group reaction determined by infrared spectroscopy), and the heat release rate of the curing process (measured by differential scanning calorimetry). If the strongly correlated parameter pair is curing temperature-coating rate: obtain the viscosity change rate of the slurry at different curing temperatures (measured using a rotational viscometer in temperature-varying mode), the surface drying time of the coating after coating (measured by the finger method, referring to GB / T1728-1979 standard), and the heat flux density of the coating during curing (measured by differential scanning calorimetry). If the strongly correlated parameter pair is curing time-coating rate: obtain the curing degree growth rate of the adhesive (determined by differential scanning calorimetry), the drying rate of the coating at different coating rates (measured by weight loss method), and the surface roughness of the coating after curing (measured by white light interferometer). Other strongly correlated parameter pairs (such as curing time-coating rate): Based on their physical action mechanism, the corresponding core physical characteristic parameters such as the curing rate growth rate of the adhesive and the drying rate of the coating are obtained, and the measurement methods all comply with the corresponding national standards or industry specifications.

[0168] Methods for determining physical property parameters based on strongly correlated parameters: For any parameter pair determined to be strongly correlated, the general rule for determining its physical characteristic parameters is as follows. Based on this rule, those skilled in the art can determine the core physical characteristic parameters corresponding to any strongly correlated parameter pair: Coupling mechanism identification principle: First, clarify the physical mechanism of the core coupling effect of the strongly correlated parameter pair, which is divided into 4 types of core mechanisms: ① photothermal conversion coupling mechanism, ② thermal expansion-structural deformation coupling mechanism, ③ curing reaction kinetics coupling mechanism, ④ coating molding fluid dynamics coupling mechanism; Parameter classification matching rules: Based on the core coupling mechanism of identification, the corresponding physical characteristic parameter categories are matched. The specific matching rules are as follows: Photothermal conversion coupling mechanism: matching photothermal performance parameters, including absorbance, thermal conductivity, quantum yield, photothermal conversion efficiency, and heat release rate; Thermal expansion-structural deformation coupling mechanism: matching thermal and mechanical performance parameters, including volume expansion coefficient, heat deformation temperature, interfacial bonding strength, thickness shrinkage rate, and compaction coefficient; Curing reaction kinetic coupling mechanism: matching curing reaction parameters, including reaction activation energy, crosslinking density, curing conversion rate, and degree of cure growth rate; Coating molding fluid dynamic coupling mechanism: matching fluid characteristic parameters, including slurry viscosity, surface tension, leveling time, drying rate, and fluid dynamic coefficients; Parameter acquisition guidelines: All physical property parameters should be acquired using national standards, industry specifications, or internationally accepted measurement methods, clearly defining the measuring instruments, test conditions, and data processing methods to ensure the reproducibility and accuracy of the parameters. Parameter simplification principle: The number of core physical characteristic parameters selected for each strongly correlated parameter pair should be 3-5. Priority should be given to parameters that play a dominant role in the coupling mechanism, and redundant parameters with low impact should be eliminated.

[0169] This method can cover any strongly correlated parameter pairs, and the acquisition methods are all existing technologies. It can determine the corresponding physical characteristic parameters of all parameter pairs.

[0170] Step 3.3: Based on the theory of thermal expansion, construct a mathematical framework for the coupling strength calculation model. The mathematical framework uses physical property parameters as input variables and coupling strength coefficient as output variables, and introduces a correlation function between the thermal expansion coefficient and the parameter interaction term.

[0171] In this embodiment, step 3.3: Based on the theory of thermal expansion, a mathematical framework for calculating the coupling strength is constructed. This mathematical framework uses physical property parameters as input variables and the coupling strength coefficient as the output variable. It introduces a correlation function between the thermal expansion coefficient and the parameter interaction term, including:

[0172] Objective function definition: Let the coupling strength coefficient be... (Output variable, value range [0,1], the closer the value is to 1, the stronger the coupling), the objective function of the mathematical framework is: ,in Let be the set of physical property parameters for strongly correlated parameter pairs (i,j), where α is the coefficient of thermal expansion. This is a parameter interaction item.

[0173] Input variable set: The acquired physical characteristic parameters are categorized by function and included in the input variable set. Including thermal parameters (Thermal conductivity, thermal stability threshold, and heat release rate are weighted at a fixed rate of 40%), material parameters (Parameters including volume expansion coefficient, quantum yield, crosslinking density, and compatibility coefficient, with a fixed weighting of 35%), process parameters. (Coating slurry viscosity, surface tension, hydrodynamic coefficient, cure rate increase, and drying rate parameters, with a fixed weight of 25%). All parameters are standardized to dimensionless values ​​(through min-max normalization).

[0174] Correlation function construction: Introducing a correlation function between the coefficient of thermal expansion and the parameter interaction term. , where β is the interaction coefficient (initially 0.3~0.5, calibrated in subsequent step 3.4). The standardized values ​​of the two parameters in the strongly correlated parameter pair are used to characterize the strength of their synergistic effect; the coupling relationship between the correlation function and the coefficient of thermal expansion is as follows: ,in For the effective coefficient of thermal expansion, γ is the basic thermal expansion coefficient of the parameter pair (taken from the physical property parameter set), and γ is the thermal expansion-interaction term coupling coefficient (initially taken as 0.2~0.4).

[0175] Core calculation formula: Integrating the coupling relationship between input variables, correlation functions, and thermal expansion coefficients to form the core calculation formula framework: ,in The weights of the physical property parameters are set according to their influence on thermal expansion, and the sum is 1. Let be the k-th physical characteristic parameter of the i,j parameter pair, and n be the number of physical characteristic parameters in the parameter pair.

[0176] In this embodiment, The acquisition method is as follows: Obtaining raw measured values: According to the measurement methods and national standards specified above, obtain the measured values ​​of all physical characteristic parameters under this category, calculate the arithmetic mean of the parameters in this category, and use it as the raw measured value for this category. ; Normalization: The min-max normalization method is used to normalize the data. Mapping to the [0,1] interval yields standardized values. The calculation formula is: ; in, This represents the industry standard upper limit for the physical property parameters of this category. This is the lower limit of the industry standard. Value constraints: The final value is strictly limited to [0,1]. When the normalization result exceeds the range, the corresponding boundary value is taken (0 if less than 0, 1 if greater than 1).

[0177] Core formula for calculating coupling strength coefficient: ; The coupling strength coefficient for the strongly correlated parameter pair (i,j) (output variable, value range [0,1], the closer the value is to 1, the stronger the coupling effect). The weight coefficient for the k-th category is... The classification weights correspond one-to-one, i.e., W1=0.4, W2=0.35, W3=0.25, and the sum is 1; The standardized dimensionless value for the k-th category is calculated using the method described above. The effective coefficient of thermal expansion is calculated from the correlation function between the coefficient of thermal expansion and the parameter interaction term; is the threshold value for the thermal expansion coefficient of the substrate material, and is a fixed constant.

[0178] Constraints: ① Coupling strength coefficient (Physically, the coupling strength has no negative value and has an upper limit); ② Effective thermal expansion coefficient ( (The threshold value for the thermal expansion coefficient of the substrate material is used to avoid coating cracking); ③ Parameter interaction terms (The value of the parameter is determined after standardization).

[0179] Step 3.4: Substitute the physical property parameters corresponding to each strongly correlated parameter into the mathematical framework of the coupling strength calculation model, determine the coefficient constants and constraints in the model, and form the coupling strength calculation model;

[0180] In this embodiment, step 3.4: Substituting the physical characteristic parameters corresponding to each strongly correlated parameter pair into the mathematical framework of the coupling strength calculation model, determining the coefficient constants and constraints in the model, and forming the coupling strength calculation model includes:

[0181] Determining constant coefficients: Three typical strongly correlated parameter pairs (coating thickness-absorbance, curing temperature-curing time, coating material absorbance-curing temperature) were selected. Five different combinations of physical property parameters were set for each parameter pair, forming a total of 15 independent experimental samples. For each sample, a corresponding photoacoustic transducer light-absorbing coating sample was prepared. The sample substrate, material formulation, and preparation process were completely consistent with the target coating of this application to ensure the validity of the experimental data.

[0182] Measurement of basic physical quantities: For each group of experimental samples, the following basic physical quantities were measured simultaneously: ① Coating thermal expansion ΔL: A laser interferometer (measurement accuracy ±1nm) was used to measure the thermal expansion displacement of the coating after heating within a temperature range that matches the curing process. The sampling frequency was 100Hz, and each sample was measured three times. The average value was taken as the final ΔL. ② Actual coating thickness d: The actual thickness of the coating was measured using a step meter (measurement accuracy ±0.01μm). Nine measurement points were evenly selected on the coating surface for each sample group, and the average value was taken after removing outliers. ③ Optical-acoustic conversion output sound pressure amplitude Using a standard high-frequency hydrophone (calibrated to 15-20MHz band), the output sound pressure amplitude of the sample under standard laser excitation was measured in an anechoic water tank. Each group of samples was measured 10 times, and the average value was taken. ④ Uncoupled reference sound pressure The sound pressure amplitude measured under the same laser excitation conditions using a blank substrate of the same thickness as the sample and without a light-absorbing coating was used as the reference value without coupling effect. ⑤ Theoretical limit sound pressure Using classical photoacoustic conversion formulas, the limiting output sound pressure of this set of parameters under the theoretically optimal coupling state is calculated.

[0183] Based on the theory of thermal expansion and the law of photoacoustic conversion, the measured coupling strength coefficient was determined. The calculation formula is: ; in, The measured coupling strength coefficient of this set of parameters to the sample is dimensionless and ranges from [0,1]. The thermal expansion strain of the coating characterizes the relative deformation of the coating after heating, and is directly related to the coupling effect of the parameter pair. The increase in sound pressure caused by the coupling effect characterizes the actual contribution of the parameter to the sound pressure output due to the coupling effect. The maximum sound pressure increment under the theoretically optimal coupling state is used as the normalized reference value.

[0184] For the 15 experimental samples, the measured values ​​of each sample were calculated according to the above formula. At the same time, the measured values ​​of the physical characteristic parameters corresponding to each sample were recorded to form a physical characteristic parameter set - measured calibration dataset. The dataset contains 15 independent calibration data sets, and each set of data contains complete parameter information and measured coupling strength coefficient.

[0185] Solving for model coefficient constants: Using the least squares method, the calibration dataset is substituted into the core calculation formula of the mathematical framework to construct the error objective function. The coefficient constants obtained by solving are: interaction coefficient β = 0.42, thermal expansion-interaction term coupling coefficient γ = 0.31; The weights of each parameter are determined according to their respective weights in relation to thermal expansion (thermal parameters 40%, material parameters 35%, process parameters 25%). (e.g., thermal conductivity weight 0.15, volume expansion coefficient weight 0.12, etc.), the total is 1.

[0186] Clearly define the constraints:

[0187] Coupling strength coefficient (When the value exceeds the limit, the boundary value is used);

[0188] Effective thermal expansion coefficient ℃ (to match the thermal expansion threshold of the piezoelectric ceramic substrate and prevent coating cracking).

[0189] Parameter interaction items (Standardized parameter value limits);

[0190] The values ​​of physical property parameters must be within the allowable error range of their measurement standards (e.g., thermal conductivity measurement error ≤ ±3%).

[0191] Model Formation: Integrating Determined Coefficient Constants ( With explicit constraints, and by substituting them into the mathematical framework of step 3.3, a complete and directly solvable coupling strength calculation model is formed. The model output is the coupling strength coefficient of strongly correlated parameter pairs. The format is adapted to meet the numerical calculation requirements of step 3.5.

[0192] Step 3.5: Solve the coupling strength calculation model through numerical calculation to obtain the coupling strength coefficients of each strongly correlated parameter pair;

[0193] In this embodiment, step 3.5: Solving the coupling strength calculation model through numerical calculation to obtain the coupling strength coefficients of each strongly correlated parameter pair includes:

[0194] Numerical calculation method selection and initialization: The Newton-Raphson numerical solution method is selected, the iteration accuracy threshold is set to 1e-6, the maximum number of iterations is 500, and the initial iteration value is 0.5 (initial estimated value of coupling strength coefficient).

[0195] Solution execution flow:

[0196] Based on the unique identifiers of strongly correlated parameter pairs, the physical characteristic parameters (already standardized) of each parameter pair are substituted into the coupling strength calculation model.

[0197] Initiate the Newton-Raphson iterative solution, calculate the model residual by successive approximations, and stop the iteration when the residual is less than the iteration accuracy threshold or the maximum number of iterations is reached. Output the current calculation result as a candidate value for the coupling strength coefficient of the parameter pair.

[0198] If the candidate value exceeds the [0,1] constraint range, it is corrected according to the constraint condition (0 for values ​​less than 0, 1 for values ​​greater than 1) to obtain the final coupling strength coefficient (4 decimal places).

[0199] Verify that the coupling strength coefficients of all strongly correlated parameter pairs satisfy the constraints of [0,1] and effective thermal expansion coefficient, and generate a table of correspondence between "strongly correlated parameter pairs - coupling strength coefficients", which includes parameter pair identifiers, dual parameter names, and coupling strength coefficients.

[0200] Step 3.6: Set the default coupling strength value of the non-associated parameters to 0.1. According to the classification order of preparation process parameters, structural parameters, and excitation parameters, arrange the coupling strength coefficients of each strongly correlated parameter pair with the default coupling strength values ​​of the non-associated parameters in sequence to construct a parameter coupling strength matrix corresponding to the dimension and the total number of parameters.

[0201] In this embodiment, step 3.6: Set the default coupling strength value of the non-associated parameters to 0.1. Following the classification order of fabrication process parameters, structural parameters, and excitation parameters, arrange the coupling strength coefficients of each strongly correlated parameter pair with the default coupling strength values ​​of the non-associated parameters in sequence. Construct a parameter coupling strength matrix corresponding to the dimension and the total number of parameters, including:

[0202] Following a fixed classification order of "preparation process parameters → structural parameters → excitation parameters", the index of all parameters (a total of 9 parameters, indexed 1-9) is clearly defined, and the specific order is as follows:

[0203] Preparation process parameters (index 1-5): 1-Absorbance of coating material, 2-Coating thickness, 3-Curing temperature, 4-Curing time, 5-Coating rate;

[0204] Structural parameters (index 6-7): 6-Transducer curvature, 7-Coating coverage area;

[0205] Excitation parameters (index 8-9): 8-Laser pulse energy, 9-Laser pulse width.

[0206] Matrix initialization and filling:

[0207] Initialize a parameter coupling strength matrix of dimension 9×9 (row and column indices correspond to the parameter sorting above), matrix elements This represents the coupling strength coefficient between the p-th parameter and the q-th parameter;

[0208] Extract the "strongly correlated parameter pair - coupling strength coefficient" correspondence table, determine the row and column positions of the strongly correlated parameter pairs according to the parameter index (e.g., "coating material absorbance - coating thickness" corresponds to (1,2) and (2,1)), fill the corresponding coupling strength coefficient into the matrix, and (The coupling strength is symmetrical);

[0209] Other non-strongly correlated parameter pairs (including parameter self-coupling) For coupling between non-associated parameters, enter the default coupling strength value of 0.1.

[0210] Matrix verification and output: Verify the matrix dimension (9×9), element value range (0.1-1), and symmetry, and generate a structured matrix file (including parameter index-parameter name mapping table and matrix data table).

[0211] In this embodiment, the generation of a dynamic weight allocation scheme based on the parameter coupling strength matrix includes:

[0212] Step 4.1: Extract the coupling strength coefficients corresponding to each parameter and strongly correlated parameter pair in the parameter coupling strength matrix;

[0213] In this embodiment, step 4.1: extracting the coupling strength coefficients corresponding to each parameter and strongly correlated parameter pair in the parameter coupling strength matrix includes:

[0214] The generated 9×9 parameter coupling strength matrix (including a parameter index-name mapping table) is used as input, and the matrix elements... The coupling strength coefficients corresponding to the p-th and q-th parameters are consistent with those in step 3.6 (1-5 are fabrication process parameters, 6-7 are structural parameters, and 8-9 are excitation parameters).

[0215] Extraction process:

[0216] Extracting the coupling strength coefficient of a single parameter: truncating the diagonal elements of the matrix. (p=1-9), corresponding to the coupling strength of each parameter, where the strongly correlated parameters are... The value is calculated in step 3.5, and the non-associated parameter is the default value of 0.1 set in step 3.6;

[0217] Extracting the coupling strength coefficient of strongly correlated parameter pairs: Based on the list of strongly correlated parameter pairs from step 3.1, determine the off-diagonal positions of the matrix according to the parameter index (p≠q), and extract the corresponding... (Due to matrix symmetry) Extracted only once), ensuring that all coefficients are >0.1 (meeting the definition of strong association).

[0218] Verify the consistency between the extracted results and the coefficients in steps 3.5 and 3.6, and generate a structured extraction result table containing the extraction object identifier (single parameter / strongly correlated parameter pair), parameter / parameter pair name, parameter index, and coupling strength coefficient (retaining 4 decimal places).

[0219] Step 4.2: Classify the coupling level according to the coupling strength coefficient, which includes strong coupling, medium coupling and weak coupling;

[0220] In this embodiment, step 4.2: The coupling level is divided according to the coupling strength coefficient, and the coupling level includes strong coupling, medium coupling, and weak coupling.

[0221] The structured extraction result table generated in step 4.1 is used as input. This table contains the coupling strength coefficient of each parameter / strongly correlated parameter pair (the value ranges from 0.1 to 1, and is rounded to 4 decimal places), which corresponds one-to-one with the parameter identifier and name.

[0222] Coupling level threshold setting and basis:

[0223] Threshold settings: Strong coupling ≥ 0.7, medium coupling < 0.7, weak coupling is a coupling strength coefficient ≥ 0.1 and < 0.4;

[0224] Level Classification:

[0225] Extract the coupling strength coefficient from the results table row by row;

[0226] Compare the coefficients with the above thresholds to determine the corresponding coupling level (strong / medium / weak).

[0227] For strongly correlated parameter pairs, the overall level is determined based on their coupling strength coefficient (without breaking down individual parameters).

[0228] Output a structured hierarchy table, including parameter / parameter pair identifiers, names, coupling strength coefficients, and coupling levels.

[0229] Step 4.3: Design weight allocation rules for different coupling levels, and calculate the joint weight of each strongly correlated parameter pair and the independent weight of each uncorrelated parameter according to the weight allocation rules.

[0230] In this embodiment, step 4.3: Design weight allocation rules for different coupling levels, and calculate the joint weight of each strongly correlated parameter pair and the independent weight of each uncorrelated parameter according to the weight allocation rules, including:

[0231] The general principle for weight allocation is as follows: strongly correlated parameter pairs are assigned joint weights (weights that characterize the synergistic effect of the two parameters), and uncorrelated parameters are assigned independent weights (weights that characterize the independent effect of a single parameter). The weight values ​​are all in the range of [0.1, 0.8] to ensure that the weight discrimination is compatible with the subsequent sensitivity analysis correction requirements.

[0232] Coupling level weight allocation rules:

[0233] Strong coupling (K≥0.7): The weight baseline range is 0.6-0.8, and it is quantified using a linear mapping formula. The rule is that the closer the coupling strength coefficient is to 1, the closer the weight is to 0.8.

[0234] Medium coupling (0.4≤K<0.7): The weight benchmark range is 0.3-0.5, and it is quantified using a linear mapping formula. The rule is that the closer the coupling strength coefficient is to 0.7, the closer the weight is to 0.5.

[0235] Weak coupling (0.1≤K<0.4): The weight baseline range is 0.1-0.2, and it is quantified using a linear mapping formula. The rule is that the closer the coupling strength coefficient is to 0.4, the closer the weight is to 0.2. (Note: Non-correlated parameters are all weakly coupled and their independent weights are calculated according to the weak coupling rule).

[0236] Joint weight calculation (strongly correlated parameter pairs):

[0237] Extracting the coupling strength coefficient of strongly correlated parameter pairs and corresponding levels;

[0238] Substitute the corresponding level into the linear mapping formula:

[0239] Strong coupling: ;

[0240] In-between coupling: ;

[0241] The calculation results are rounded to four decimal places to ensure that the weights within the same level vary. Dynamic changes reflect differences in coupling strength.

[0242] Independent weight calculation (non-correlated parameters):

[0243] Extracting the coupling strength coefficient of non-correlated parameters (All are 0.1 or ≥0.1 to <0.4);

[0244] Substituting into the weakly coupled linear mapping formula: ;

[0245] like =0.1 (default value in step 3.6), then =0.1, to ensure matching with the weak effect characteristics of non-associated parameters.

[0246] Generate a weight calculation result table, including parameter / parameter pair identifier, name, coupling level, coupling strength coefficient, weight type (joint / independent), and weight value.

[0247] Step 4.4: Integrate all parameters and the weights of parameter pairs to generate a dynamic weight allocation scheme, which includes the weight attributes and specific weight values ​​of each parameter and parameter pair.

[0248] Structured integration process:

[0249] Classification and sorting: Sort by preparation process parameters (independent weights), structural parameters (independent weights), excitation parameters (independent weights), and strongly correlated parameter pairs (joint weights) for easy retrieval later;

[0250] Field Definition: The core field for designing a dynamic weight allocation scheme, ensuring full coverage:

[0251] Field 1: Assign object identifier (format: parameter-index-name or parameter pair-identifier-two-parameter name, such as parameter-1-coating material absorbance, parameter pair-strong correlation-1-coating thickness-absorbance).

[0252] Field 2: Parameter / parameter pair classification (preparation process / structure / excitation / strongly correlated parameter pairs);

[0253] Field 3: Weight attribute (including weight type: independent / joint; coupling level: strong / medium / weak coupling);

[0254] Field 4: Coupling strength coefficient (retain 4 decimal places);

[0255] Field 5: Weight value (retain 4 decimal places);

[0256] Field 6: Related parameters / parameter pairs (Enter "None" for independent weights, and enter the names of both parameters for joint weights).

[0257] Output two standardized files:

[0258] Excel format: Contains all the above fields, facilitating manual review and parameter traceability;

[0259] JSON format: Fields are consistent with the visualization file, using a key-value pair structure.

[0260] In this embodiment, the step of substituting the dynamic weight allocation scheme into the sensitivity analysis algorithm to calculate the contribution of each parameter and its influence on the dual targets of output sound pressure and frequency band, thereby obtaining the parameter contribution dataset, includes:

[0261] Step 5.1: Initialize the Sobol algorithm, determine the parameter sampling range, number of iterations, and convergence conditions;

[0262] In this embodiment, initializing the Sobol algorithm and determining the parameter sampling range, number of iterations, and convergence conditions includes:

[0263] Parameter sampling range determination: Based on the high-frequency (15-20MHz) operating requirements of the light-absorbing coating of the photoacoustic transducer, the controllability of the preparation process, and the limits of material properties, the effective sampling range of each parameter is determined to ensure coverage of actual working conditions and suitability for sensitivity analysis accuracy.

[0264] Preparation process parameters (index 1-5): consistent with the sampling range in step 2.1 (coating material absorbance 0.85~0.99, coating thickness 1~5μm, curing temperature 60~120℃, curing time 30~180min, coating rate 5~20mm / s);

[0265] Structural parameters (index 6-7): Transducer curvature 5~20mm -1 (Adapted to high-frequency sound beam focusing requirements), coating coverage area 10~50mm² (matching the effective working area of ​​the transducer).

[0266] Excitation parameters (index 8-9): laser pulse energy 1~5mJ (to meet the photothermal conversion energy threshold), laser pulse width 5~20ns (to adapt to 15-20MHz frequency band response characteristics).

[0267] Iteration count setting: Considering the parameter dimension (9 dimensions), the accuracy requirements of variance decomposition of the Sobol algorithm, and the balance between computational efficiency, the number of iterations is set to 1000~2000 times; the basis for setting is that when the number of iterations is ≥1000 times, the variance contribution calculation error is ≤±2%, which meets the quantitative accuracy requirements of sensitivity analysis and avoids the waste of computational resources caused by too many iterations.

[0268] Convergence condition definition: A dual convergence criterion is adopted to ensure that the result is stable and reliable when the algorithm terminates.

[0269] Absolute convergence condition: In 20 consecutive iterations, the change in the variance contribution of each parameter and parameter pair is ≤1e-5 (dimensionless).

[0270] Relative convergence condition: The relative error between the sum of variance contributions in the current iteration and the average variance contributions in the previous 50 iterations is ≤0.5%;

[0271] Termination logic: The algorithm stops iterating when any of the above conditions are met or when the maximum number of iterations (2000) is reached.

[0272] Algorithm initialization execution: The Sobol algorithm toolbox is called through Matlab software. The above parameters, sampling range, number of iterations and convergence conditions are input to complete the algorithm initialization configuration. After initialization, the algorithm configuration file is output, which includes parameter dimensions, sampling range boundaries, iteration and convergence parameters.

[0273] Step 5.2: Generate a structured sensitivity analysis input dataset based on the dynamic weight allocation scheme;

[0274] In this embodiment, step 5.2: generating a structured sensitivity analysis input dataset according to the dynamic weight allocation scheme includes:

[0275] Structured dataset field definition: Design structured fields to adapt to the input requirements of the Sobol algorithm, ensuring that the information is not redundant and can be directly accessed. The fields are as follows:

[0276] Field 1: Unique identifier of the input object (completely consistent with the identifier of the assigned object in the dynamic weight allocation scheme, such as parameter-1-coating material absorbance, parameter-strong correlation-1-coating thickness-absorbance).

[0277] Field 2: Object type (value can be a single parameter or a strongly related parameter pair);

[0278] Field 3: Parameter classification (preparation process / structure / excitation parameters, strongly correlated parameter pairs are classified according to the first parameter);

[0279] Field 4: Dynamic weight value (directly taken from the dynamic weight allocation scheme, retaining 4 decimal places);

[0280] Field 5: Sampling range (For a single parameter, enter its own sampling range, such as 0.85-0.99; for strongly correlated parameter pairs, enter the sampling range of both parameters, separated by semicolons, such as 1-5μm; 0.85-0.99).

[0281] Field 6: Parameter Index (For a single parameter, fill in its own index, such as 1; for a strongly related parameter pair, fill in the two-parameter index, separated by commas, such as 1,2);

[0282] Field 7: Data type (values ​​can be dimensionless, length, temperature, etc., consistent with the physical properties of the parameter, used for algorithm numerical calculation adaptation).

[0283] Dataset generation process:

[0284] Step 1: Data Parsing and Association. A Python script reads the JSON file of the dynamic weight allocation scheme, extracting the allocation object identifier, weight value, and parameter category for each record. Simultaneously, the parameter sampling range table from Step 5.1 is read, and the sampling range and data type are associated with the corresponding allocation object based on the parameter index.

[0285] Step 2: Complete the information for strongly correlated parameter pairs. For input objects of strongly correlated parameter pair type, extract their respective sampling ranges and data types based on the dual-parameter index, and fill them in using the format of Parameter 1 range; Parameter 2 range and Parameter 1 type; Parameter 2 type, ensuring the completeness of the dual-parameter information.

[0286] Step 3: Data Standardization and Validation. Standardize the sampling range of all input objects (unify it to "lower limit ~ upper limit"), retain 4 decimal places for weight values, and keep the parameter index consistent with step 3.6 to avoid format ambiguity that could cause the algorithm to fail to read data.

[0287] Step 4: Structured Organization. Sort all input objects in ascending order by parameter index to generate a two-dimensional structured dataset (rows correspond to input objects, and columns correspond to the 7 fields mentioned above). The dataset dimension is the total number of input objects × 7 (total number of input objects = 9 individual parameters + number of strongly related parameter pairs).

[0288] Step 5.3: Substitute the sensitivity analysis input dataset into the initialized Sobol algorithm, use the dynamic weight value as the correction coefficient for the variance contribution calculation, and solve for each parameter and the first contribution of the parameter to the output sound pressure target and the second contribution of the parameter to the output frequency band target respectively.

[0289] By calling the batch data interface of the Sobol algorithm through Matlab software, the algorithm initialization configuration file is imported and the core parameters such as iteration accuracy (1e-6) and maximum number of iterations are fixed.

[0290] The structured input dataset is converted to the format required by the algorithm (preserving parameter indexes, sampling ranges, and dynamic weight numerical fields), redundant format information is removed, and matrix format data that the algorithm can directly read is generated (rows correspond to input objects, and columns correspond to parameter attributes).

[0291] Establish an input object-target variable association mapping: clearly define the output sound pressure target variable as the sound pressure amplitude after photoacoustic conversion of the light-absorbing coating, and the output frequency band target variable as the frequency band coverage range of the sound pressure response, consistent with the dual-target definition in step 1.

[0292] The correlation mapping between dynamic weights and variance contribution:

[0293] For each input object (single parameter / strongly correlated parameter pair), extract its corresponding dynamic weight value W from the mapping table as a dedicated correction coefficient for calculating the variance contribution of that object;

[0294] Establish correction coefficient binding rules: associate dynamic weight values ​​with the parameter indices of input objects one by one, store them in the algorithm's internal cache, and ensure that the variance contribution of each input object adopts its corresponding correction coefficient during the calculation process to avoid cross-contamination.

[0295] Variance contribution correction calculation:

[0296] Basic variance contribution calculation: For the two targets of output sound pressure and output frequency band, the original variance contribution of each input object is calculated using the variance decomposition module of the Sobol algorithm. (i.e., the percentage of parameter influence without the introduction of dynamic weights);

[0297] Dynamic weight correction mechanism: The correction logic of "original variance contribution × dynamic weight" is used to construct the correction variance contribution calculation model, as shown in the following formula:

[0298] ;in, To correct the variance contribution (i.e. the final first / second contribution), W is the dynamic weight value (calculated in step 4.4), ensuring that the larger the dynamic weight, the more significant the contribution of the parameter / parameter pair, which fits the core logic that the higher the coupling strength, the greater the impact.

[0299] Target differentiation calculation:

[0300] For the output sound pressure target: the sound pressure amplitude is used as the output variable of the algorithm and substituted into the above correction model to calculate the correction variance contribution of each input object, which is defined as the first contribution (value range [0,1]).

[0301] For the output frequency band target: take the frequency band coverage as the algorithm output variable, repeat the above correction calculation process, and obtain the corrected variance contribution of each input object, which is defined as the second contribution (value range [0,1]).

[0302] Contribution calculation and convergence determination:

[0303] Initiate the Sobol algorithm for iterative solution, and monitor the iteration process according to the convergence conditions set in step 5.1:

[0304] If, in 20 consecutive iterations, the change in the first / second contribution of all input objects is ≤1e-5, or the relative error is ≤0.5%, then convergence is determined and the iteration is stopped.

[0305] If the convergence condition is not met but the maximum number of iterations (2000) is reached, the result of the last iteration will be used as the final contribution value, and the result will be marked "converged after the maximum number of iterations".

[0306] The correctness of the correction coefficients is verified in real time during the solution process: if the dynamic weight W of an input object is 0.1 (non-associated parameter), its contribution after correction must be significantly lower than that of strongly coupled parameter pairs (W≥0.6) to ensure that the correction logic is effective.

[0307] The final intermediate result table of contribution is generated, which includes the unique identifier of the input object, the name of the parameter / parameter pair, the dynamic weight value, the first contribution (sound pressure target), and the second contribution (frequency band target), and is retained to 4 decimal places.

[0308] Step 5.4: Set the dual-objective weighting coefficients, and calculate the comprehensive impact contribution of each parameter and parameter pair based on the dual-objective weighting coefficients;

[0309] In this embodiment, step 5.4: setting dual-objective weighting coefficients, and calculating the comprehensive influence contribution of each parameter and parameter pair based on the dual-objective weighting coefficients includes:

[0310] Dual-objective weighting coefficient settings:

[0311] Setting principle: Based on the core requirement of high-frequency metrological calibration of photoacoustic transducers in the 15-20MHz range, the dual-target weighting coefficients need to take into account both the sound pressure amplitude meeting the standard (≥0.9MPa) and the full frequency band coverage (15-20MHz). At the same time, it supports adjustment as needed to adapt to different optimization scenarios. The total weighting coefficients are 1 (ω1+ω2=1).

[0312] Value range and default value:

[0313] Sound pressure target weighting coefficient ω1: 0.3-0.7 (default value 0.5, to adapt to equalization optimization requirements);

[0314] Frequency band target weighting coefficient ω2: 0.3-0.7 (default value 0.5, complementary to ω1);

[0315] Adjustment rules: If it is necessary to prioritize sound pressure output, set ω1=0.7 and ω2=0.3; if it is necessary to prioritize frequency band coverage, set ω1=0.3 and ω2=0.7. After adjustment, the constraint that the total weight sum is 1 is still satisfied.

[0316] Calculation of overall impact contribution:

[0317] The calculation model uses a weighted summation method to quantify the combined impact of the two objectives.

[0318] Calculation process:

[0319] Extract S1 and S2 of each input object in the intermediate result table of contribution line by line;

[0320] Substitute into the weighted summation formula, according to the set... Calculate the corresponding The result should be rounded to 4 decimal places.

[0321] If the calculation result exceeds the range [0,1] (due to numerical error), take the boundary value (0 if less than 0, 1 if greater than 1).

[0322] Step 5.5: Integrate the parameter identifiers, first contribution, second contribution, and comprehensive impact contribution of each parameter and parameter pair to generate a structured parameter contribution dataset.

[0323] In this embodiment, the step of filtering parameters and parameter pairs with an impact contribution greater than a first preset threshold from the parameter contribution dataset to generate a subset of key process parameters includes:

[0324] Step 6.1: Extract the comprehensive impact contribution and parameter identification information of each parameter and parameter pair in the parameter contribution dataset;

[0325] Step 6.2: Compare the overall impact contribution of each parameter and parameter pair with the first preset threshold one by one, and select the parameters and parameter pairs whose overall impact contribution is greater than the first preset threshold.

[0326] In this embodiment, the first preset threshold is 0.3, and the comparison and screening process is as follows:

[0327] Traverse the mapping table in ascending order based on the parameter identifier, and extract each object row by row. With unique identifier;

[0328] Execution judgment rule: If The first preset threshold (default 0.3) marks objects as to be retained; if ≤0.3, marked as redundant objects and not retained;

[0329] Special case handling: If a single parameter in a strongly correlated parameter pair... ≤0.3, but the parameters are correct. >0.3, retain the whole according to the parameters (in line with the synergy optimization logic).

[0330] Validation and output of screening results:

[0331] Validation criteria: Retained objects All values ​​are strictly greater than the threshold, with no boundary values ​​misjudged.

[0332] Generate an intermediate table of screening results, which includes the unique identifier of the object to be retained, the parameter / parameter pair name, the overall impact contribution, and the screening criteria (e.g., 0.42>0.3, retain).

[0333] Step 6.3: Integrate the selected parameters and parameter pairs, supplement their corresponding correlation attributes, weight values ​​and physical characteristic parameters, and generate a structured subset of key process parameters. The subset includes the correlation priority of each parameter and parameter pair with the output sound pressure-frequency band dual target.

[0334] In this embodiment, step 6.3: Integrate the selected parameters and parameter pairs, supplement their corresponding correlation attributes, weight values, and physical characteristic parameters, and generate a structured subset of key process parameters. The subset includes the correlation priority of each parameter and parameter pair with the output sound pressure-frequency band dual target, including:

[0335] Data integration and supplementation process:

[0336] Step 1: Association and Matching. Associate the filtered results with the supplementary data based on the "Unique Identifier," and complete the information for each object to be retained:

[0337] Related attributes: Supplemental coupling level (strong / medium / weak), weight type (independent / joint) (taken from dynamic weight allocation scheme);

[0338] Weight values: Supplement the specific values ​​of the dynamic weights (retain 4 decimal places, taken from step 4.4).

[0339] Physical property parameters: Fill in "None" for single parameters, and supplement the parameter set according to step 3.2 (including parameter name, value, unit, and measurement method) for strongly correlated parameters.

[0340] Contribution data: Supplement the first contribution (sound pressure) and the second contribution (frequency band) (taken from step 5.3).

[0341] Step 2: Setting Priorities. Priorities are set based on the dual-objective impact characteristics, with clear and unambiguous rules:

[0342] Prioritization is primarily based on the overall impact contribution (S). 综合 The primary factor is the first / second contribution level, with the second-highest contribution level as secondary.

[0343] Priority level: S 综合 ≥0.7 is set as Level 1 priority (core impact); 0.5≤S<0.7 is set as Level 2 priority (significant impact); 0.3 综合 <0.5 is set as a level 3 priority (general impact);

[0344] Dual-target adaptation labeling: Add sound pressure level dominance, frequency band dominance, or equalization dominance after the priority (if the first contribution is greater than the second contribution, then label it as sound pressure level dominance).

[0345] Structured key process parameter subset field design:

[0346] Field 1: Unique identifier of the object (consistent with step 6.2, such as "parameter-1-coating material absorbance" or "parameter pair-strong correlation-1-coating thickness-absorbance").

[0347] Field 2: Parameter / parameter pair name (exactly the same as the parameter name in the previous steps);

[0348] Field 3: Association attribute (coupling level + weight type, such as "strong coupling + joint weight" or "weak coupling + independent weight");

[0349] Field 4: Weight value (retain 4 decimal places);

[0350] Field 5: Physical property parameters (enter "None" for a single parameter; for strongly correlated parameter pairs, enter in the format "Parameter 1: [Name-Value-Unit]; Parameter 2: [Name-Value-Unit]").

[0351] Field 6: Dual-objective contribution (first contribution / second contribution, rounded to 4 decimal places);

[0352] ​Field 7: Association Priority (including level + dominance type, such as Level 1 - Balanced Dominance);

[0353] Field 8: Filtering criteria (Format: Overall contribution [value] > first preset threshold 0.3, keep).

[0354] In this embodiment, after step 6: selecting parameters and parameter pairs with influence contributions greater than a first preset threshold from the parameter contribution dataset to generate a subset of key process parameters, the optimization method for the photoacoustic transducer light-absorbing coating preparation process parameters further includes:

[0355] Obtain a multi-field coupling gain correction model;

[0356] A subset of key process parameters is input into a multi-field coupled gain correction model to obtain a parameter correction set with gain coefficients.

[0357] The non-dominated sorting genetic algorithm is used to solve the bi-objective optimization model, obtaining a Pareto optimal parameter solution set covering different optimization priorities, including:

[0358] Based on the parameter correction set with gain coefficients, a non-dominated sorting genetic algorithm is used to solve the bi-objective optimization model, obtaining a Pareto optimal parameter solution set covering different optimization priorities.

[0359] In this embodiment, the multi-field coupling gain correction model is based on the optical-thermal-acoustic multi-field coupling mechanism. Combining the thermal expansion theory and the photoacoustic conversion law, it focuses on the synergistic gain effect of key process parameters on the dual targets of sound pressure and frequency band. It constructs a quantitative correction model with key process parameters as input and gain coefficient as output to realize the performance potential of parameter values.

[0360] Model input and output definitions:

[0361] Input variables: Core fields of the key process parameter subset in step 6.3 (parameter / parameter pair name, physical property parameter, association priority, weight value);

[0362] Output variable: Single-parameter independent gain coefficient (Value range [1.0, 1.5]), Strong correlation parameter on joint gain coefficient (Value range [1.2, 1.8]), a gain coefficient > 1 indicates that there is a positive gain in the parameters.

[0363] Single-parameter independent gain: ,in For independent weights of parameters, Contribution to overall impact;

[0364] Strong correlation parameters affect joint gain: ,in For joint weights, For the effective coefficient of thermal expansion, The threshold for thermal expansion of the substrate;

[0365] In this embodiment, a subset of key process parameters is input into a multi-field coupled gain correction model to obtain a parameter correction set with gain coefficients, including:

[0366] Step 1: Data Analysis. Extract the parameter / parameter pair names, original sampling ranges, weight values, and overall impact contribution of the key process parameter subset;

[0367] Step 2: Gain coefficient calculation. Substitute the parameter type (single parameter / strongly correlated parameter pair) into the corresponding gain formula to calculate. or (Keep 3 decimal places);

[0368] Step 3: Parameter value correction. The original sampling range is expanded based on the gain coefficient, with the rule: corrected value range = original range × gain coefficient (the upper limit does not exceed the material / process limit, such as coating thickness ≤ 8μm after correction);

[0369] Step 4: Structured Integration. Generate a parameter correction set, including fields: object unique identifier, parameter / parameter pair name, original range, gain coefficient, corrected range, and association priority, ensuring that the data can be directly imported into the algorithm.

[0370] In this embodiment, based on the parameter correction set with gain coefficients, a non-dominated sorting genetic algorithm is used to solve the bi-objective optimization model, obtaining a Pareto optimal parameter solution set covering different optimization priorities, including:

[0371] Algorithm adaptation and solution process:

[0372] Algorithm initialization optimization. The population size is 100-200, the number of iterations is 50-100, the initial crossover probability is 0.7-0.9, and the initial mutation probability is 0.01-0.05; the convergence condition is set to no change in the Pareto front for 15 consecutive iterations.

[0373] The initial population is generated based on the correction set. Real-number encoding is used, with the encoding length equal to the number of key process parameters. The encoding values ​​are randomly generated according to the corrected range to ensure that the population covers the gain optimization interval.

[0374] Design of a gain-adaptive fitness function. Embedded gain coefficient weights, the formula is: Where G is the gain coefficient and P is the calculated sound pressure level. =1.2MPa, B is the frequency band coverage area. =5MHz. Integrating multi-field coupling gain coefficient (G) with dual-target weights. The positive contribution of the synergistic gain of the quantified parameters to the dual objectives is achieved, avoiding the shortcomings of traditional functions that ignore the performance potential of parameters. P is the calculated sound pressure level, B is the frequency band coverage, and G is the gain coefficient.

[0375] Step 4: Improved genetic operations. Perform fast non-dominated sorting to divide Pareto levels, and combine crowding to preserve diversity; adopt an adaptive strategy: when the population convergence is >80%, the crossover probability is reduced to 0.6 and the mutation probability is increased to 0.08 to avoid premature convergence.

[0376] Step 5: Iteration and Solution Set Generation. Repeat fitness calculation, sorting, crossover and mutation until the convergence condition or the maximum number of iterations is met, and filter all non-dominated solutions.

[0377] Step 6: Priority Classification. Classified by dual-objective weighting coefficients: ① Sound Pressure Priority ② Frequency band priority ( ); ③ Balanced optimization ( This forms a Pareto optimal parameter solution set that covers different needs.

[0378] In this embodiment, the dual-objective optimization model is as follows:

[0379] Primary objective: Maximize sound pressure level (maxP)

[0380] The mathematical expression is:

[0381] ;

[0382] Where P is the output sound pressure amplitude, and the target value is ≥0.9MPa; GP∈[1.0,1.8] is the sound pressure gain coefficient (taken from the parameter correction set with its own gain coefficient), which is determined by the joint gain of strongly correlated parameters or the independent gain of a single parameter; β is the volume expansion coefficient of water (constant).

[0383] This represents the peak power density of the laser pulse (a constant, adapting to the range of excitation parameters). The coating coverage area (variable, taken from the parameter correction set, 10-50mm) 2 η is the photothermal conversion efficiency (determined by the absorbance and quantum yield of the coating material); ρ is the effective thermal expansion coefficient (variable, taken from the physical property parameter set, ℃); ρ is the density of water (constant); c is the underwater sound speed (constant). The laser pulse width is taken from the parameter correction set, 5-20ns.

[0384] For the thermal conductivity of the coating (variable, taken from the set of physical property parameters); Thermal conductivity of the substrate (constant).

[0385] Second objective: Maximize frequency band coverage integrity ( ):

[0386] Based on the coupling effect of acoustic propagation characteristics and parameters, the mathematical expression is:

[0387] ;

[0388] Where B is the frequency band coverage range (unit: MHz), and the target value is ≥4.5MHz (i.e., 15-20MHz coverage ≥90%). For the frequency band gain coefficient (taken from the parameter correction set with built-in gain coefficient), ∈[1.0,1.6]), which is of the same origin as the sound pressure gain coefficient; k is the coupling coefficient (constant, k=3.0); The strong correlation parameter corresponds to the coupling strength coefficient (variable, taken from step 3.5). ∈[0.7,1.0]); For the strong correlation parameters, the joint weights (variables, taken from step 4.3) are... ∈[0.6,0.8]); The base bandwidth is constant (5MHz, i.e., the full bandwidth of 15-20MHz).

[0389] Constraints (including parametric / physical / performance triple constraints)

[0390] 1. Parameter value constraints (based on a parameter correction set with gain coefficients):

[0391] Light absorbance of coating material: ( ∈[1.0,1.5]);

[0392] Coating thickness: ( ∈[1.2,1.8], and d≤8μm, process limit);

[0393] Curing temperature: (°C, material thermal stability threshold);

[0394] Curing time: (t≤240min, process efficiency limitation);

[0395] Coating rate: (v≤25mm / s, equipment limit);

[0396] Structural parameters:

[0397] Transducer curvature: (No gain correction, fixed range of structural parameters);

[0398] Coating coverage area: ( ∈[1.0,1.5]);

[0399] Excitation parameters:

[0400] Laser pulse energy: ( ∈[1.0,1.5], and E≤6mJ).

[0401] Laser pulse width: ( ∈[1.0,1.5]).

[0402] Physical constraints (based on thermal expansion theory and material properties):

[0403] Effective coefficient of thermal expansion: ℃ (to prevent coating cracking);

[0404] Coating crosslinking density: (To ensure structural stability);

[0405] Photothermal conversion efficiency: η≥0.6 (to avoid energy waste).

[0406] 3. Performance constraints (based on metrological calibration requirements):

[0407] Sound pressure amplitude: P≥0.9MPa (minimum measurement requirement);

[0408] Frequency band coverage: B≥4.0MHz (minimum coverage requirement).

[0409] In this embodiment, the step of solving the bi-objective optimization model using a non-dominated sorting genetic algorithm based on a subset of key process parameters to obtain a Pareto optimal parameter solution set covering different optimization priorities includes:

[0410] Step 8.1: Initialize the non-dominated sorting genetic algorithm, setting the population size to 100-200, the number of iterations to 50-100, the initial crossover probability to 0.7-0.9, and the initial mutation probability to 0.01-0.05. Determine the algorithm's convergence criteria; employ a dual convergence criterion, stopping iteration when either condition is met:

[0411] Absolute convergence: In 15 consecutive iterations, the change in fitness value of all individuals at the Pareto front is ≤1e-5 (dimensionless).

[0412] Relative convergence: The relative error between the average fitness value of individuals at the Pareto front in the current iteration and the average fitness value in the previous 50 iterations is ≤0.5%;

[0413] Forced termination: If the above conditions are not met but the maximum number of iterations (80) is reached, output the current population.

[0414] Step 8.2: Based on the parameter correction set with gain coefficients and combined with the constraints of the bi-objective optimization model, generate the initial population using real number encoding.

[0415] Step 8.3: Introduce a fitness function based on the gain coefficient, embedding the parameter gain coefficient as a weight in the fitness calculation to calculate the fitness value of each individual in the population; in this embodiment, the fitness function is as follows:

[0416] ;

[0417] Where F is the fitness value (range [1.0, 1.8]).

[0418] G is the gain coefficient of the parameter / parameter pair (taken from the parameter correction set with its own gain coefficient, single parameter). ∈[1.0,1.5], strongly correlated parameter pairs ∈[1.2,1.8]);

[0419] ω1 is the sound pressure target weighting coefficient (0.3-0.7), ω2 is the frequency band target weighting coefficient (0.3-0.7), and ω1+ω2=1;

[0420] P is the calculated sound pressure level for the individual (unit: MPa).

[0421] B represents the frequency band coverage area corresponding to the individual.

[0422] Step 8.4: Based on the results of the fitness quantification, select superior individuals, perform improved non-dominated sorting on the current population, divide Pareto levels through fast non-dominated sorting, retain population diversity by combining crowding degree calculation, and at the same time adopt an adaptive crossover and mutation strategy to dynamically adjust the crossover probability and mutation probability according to the population convergence degree, and output the new generation population after selection, sorting and genetic operations.

[0423] In this embodiment, the population convergence is calculated as follows: C = number of individuals at the current Pareto level 1 / population size (C∈[0,1], the closer C is to 1, the higher the convergence).

[0424] Adaptive crossover probability adjustment: The constraint range is [0.7, 0.9] (when C ≥ 0.8, P) c =0.7, to avoid premature maturity; when C<0.5, P c =0.9, accelerating gene fusion);

[0425] Adaptive mutation probability adjustment: The constraint range is [0.01, 0.08] (when C ≥ 0.8). =0.08, introducing a new gene; C<0.5 =0.01, stable and high-quality population);

[0426] Selection operation: The roulette wheel selection method is used. The probability of an individual being selected = the individual's fitness value / the total fitness value of the population.

[0427] Crossover operation: Analog binary crossover (SBX) is used, with a crossover factor of 2.0 (to adapt to the continuity of parameter values ​​in real number encoding).

[0428] Mutation operation: Use polynomial mutation with a mutation factor of 20 (to control the mutation amplitude and ensure that the parameters do not exceed the corrected range).

[0429] Step 8.5: Repeat steps 8.3-8.4 for fitness calculation, individual selection, non-dominated sorting, and crossover / mutation operations until the preset number of iterations is reached or the convergence condition is met, and output the final population after iterative convergence.

[0430] Step 8.6: Select all non-dominated solutions from the final population and classify them according to three priorities: sound pressure priority, frequency band priority, and equalization optimization, to form a Pareto optimal parameter solution set covering different optimization needs.

[0431] In this embodiment, the priority categories are as follows:

[0432] Non-dominated solution selection rule: If the sound pressure value of individual A is greater than or equal to that of individual B and the frequency band coverage is greater than or equal to that of individual B, then B is a dominated solution and only non-dominated solutions are retained;

[0433] Three priority determination criteria (quantification thresholds):

[0434] Sound pressure priority solution set: first contribution ≥ 0.6, and calculated sound pressure value ≥ 1.0 MPa, frequency band coverage ≥ 4.0 MHz;

[0435] Frequency band priority solution set: second contribution degree ≥ 0.6, frequency band coverage ≥ 4.8MHz, and calculated sound pressure value ≥ 0.9MPa;

[0436] Equalization optimization solution set: first contribution ≥ 0.5 and second contribution ≥ 0.5, calculated sound pressure ≥ 0.95MPa and frequency band coverage ≥ 4.5MHz.

[0437] In this embodiment, the step of setting interference conditions and performing anti-interference tests on the Pareto optimal parameter solution set to screen out parameter combinations with performance fluctuations less than a second preset threshold, and the parameter combinations with outputs less than the second preset threshold as the optimal combination of light-absorbing coating preparation process parameters, includes:

[0438] Step 9.1: Obtain ambient temperature fluctuation conditions, laser pulse energy fluctuation conditions, and coating rate fluctuation conditions;

[0439] In this embodiment, the ambient temperature fluctuation conditions are: a base temperature of 25°C and a fluctuation range of ±5°C (i.e., 20°C to 30°C). The setting is based on the normal fluctuation range of industrial production ambient temperature, covering the differences between laboratory and workshop operating conditions.

[0440] Laser pulse energy fluctuation conditions: The range of laser pulse energy values ​​(1-6mJ) based on the parameter correction set, with a fluctuation amplitude of ±10% (e.g., when the energy reference value is 3mJ, the fluctuation range is 2.7-3.3mJ). The setting is based on the typical instability error of the laser source output energy.

[0441] Coating rate fluctuation conditions: The coating rate range (5-25mm / s) is based on the parameter correction set, with a fluctuation range of ±15% (e.g., when the base rate value is 10mm / s, the fluctuation range is 8.5-11.5mm / s). The setting is based on the mechanical transmission accuracy error of the coating equipment.

[0442] Step 9.2: Obtain the preset multi-field coupling anti-interference test platform, import each parameter combination in the Pareto optimal parameter solution set into the preset multi-field coupling anti-interference test platform, simulate the entire process of light-absorbing coating preparation and photoacoustic conversion, and measure the output sound pressure value and frequency band coverage corresponding to each parameter combination under the interference-free reference state, and record it as the reference performance data.

[0443] In this embodiment, the simulation principle is as follows:

[0444] Based on the heat conduction equation With acoustic wave equation The process parameters of the coupled coating preparation process fluctuate, enabling full-process simulation from coating curing to photoacoustic conversion;

[0445] The baseline conditions are defined as follows: ambient temperature 25℃, laser pulse energy without fluctuation, coating rate without fluctuation, and other parameters are fixed according to the Pareto optimal parameter combination. Each parameter combination is measured three times, and the average value is taken as the baseline performance data (sound pressure P0, frequency band coverage B0).

[0446] Step 9.3: Apply ambient temperature fluctuation conditions, laser pulse energy fluctuation conditions, and coating rate fluctuation conditions one by one, keeping other parameters constant, measure the actual performance data under each interference condition, and obtain the comprehensive performance fluctuation amount of each parameter combination;

[0447] Test sequence: Apply interference one by one in the order of ambient temperature fluctuation → laser pulse energy fluctuation → coating rate fluctuation. After each type of interference test is completed, restore the baseline state before conducting the next type of interference test to avoid interference superposition.

[0448] Data recording rules: For each interference condition, each parameter combination should be measured three times, and the actual sound pressure level should be recorded. (i=1,2,3), actual frequency band coverage area (i=1,2,3), outliers exceeding the accuracy range of the measuring instrument (such as sound pressure error > ±0.01MPa) are removed, and the average value of the remaining data is taken as the actual performance data under this working condition. ).

[0449] Step 9.4: Obtain the overall performance fluctuation of each parameter combination based on the baseline performance data and the actual performance data;

[0450] In this embodiment, the fluctuation of a single indicator is calculated as follows:

[0451] Sound pressure fluctuation: (Dimensionless, representing the relative fluctuation amplitude of sound pressure).

[0452] Frequency band fluctuation: (Dimensionless, representing the relative fluctuation amplitude of the frequency band);

[0453] Calculation of overall performance fluctuation: A dual-objective weighted summation model is adopted, with the weights consistent with the dual-objective weight coefficients in step 5.4. The formula is as follows:

[0454] ; where ΔS is the overall performance fluctuation (value range [0,1]). If there is no corresponding index fluctuation under a certain interference condition (such as ambient temperature fluctuation does not affect the frequency band), then the index fluctuation is 0.

[0455] Step 9.5: Compare the overall performance fluctuation of each parameter combination with the second threshold, and select the parameter combination that is less than the second threshold as the optimal combination of light-absorbing coating preparation process parameters.

[0456] In this embodiment, the second preset threshold is set to 0.08 (i.e. 8%).

[0457] In this embodiment, the screening rule is as follows: if the overall performance fluctuation ΔS of the parameter combination under all three interference conditions is less than 0.08, it is judged as qualified for anti-interference; if only some interference conditions are qualified, the average fluctuation of all conditions needs to be calculated, and if the average fluctuation is less than 0.08, it is still judged as qualified.

[0458] Anomaly Handling: If the baseline performance data of a certain parameter combination does not meet the requirements of sound pressure ≥ 0.9MPa and frequency band ≥ 4.5MHz, it will be directly rejected and will not participate in the anti-interference test; if the calculation result of the comprehensive performance fluctuation is negative (due to numerical error), the absolute value will be taken and then the threshold comparison will be performed.

[0459] Finally, all qualified parameter combinations are integrated, sorted in ascending order of comprehensive performance fluctuation, and the top 3 parameter combinations are output as the optimal combination of light-absorbing coating preparation process parameters (if there are less than 3 qualified combinations, all are output), and the baseline performance data, fluctuation of each interference condition and average fluctuation of each combination are marked.

[0460] This application has the following advantages:

[0461] Existing techniques rely solely on simple correlation analysis or empirical judgments of parameter relationships, failing to quantify coupling strength and thus neglecting parameter synergy effects in optimization. This method first employs the Pearson correlation coefficient method (with a correlation coefficient threshold of 0.7) to accurately identify strongly correlated parameter pairs. Then, based on thermal expansion theory, it constructs a coupling strength calculation model, introducing a correlation function between the thermal expansion coefficient and the parameter interaction term. Numerical calculations yield quantified coupling strength coefficients, ultimately forming a parameter coupling strength matrix. This matrix clearly defines the coupling degree (strong / medium / weak) of each parameter / parameter pair, transforming ambiguous parameter relationships into calculable quantitative indicators. This ensures that subsequent optimization processes always revolve around parameter synergy effects, fundamentally improving the targeting of optimization.

[0462] Traditional sensitivity analysis uses fixed weights, which fails to highlight the influence of strongly coupled parameter pairs, leading to biases in the identification of key parameters. This method, based on the parameter coupling strength matrix, classifies parameters into strong, moderate, and weak coupling levels and designs differentiated weight allocation rules. It calculates the joint weight of strongly correlated parameter pairs and the independent weights of uncorrelated parameters, forming a dynamic weight allocation scheme. This scheme directly links weights to coupling strength and the dual-objective impact, and uses them as variance contribution correction coefficients for the Sobol algorithm. This makes the sensitivity analysis results more closely match the needs of sound pressure level-frequency band dual-objective optimization, accurately identifying core influencing parameters.

[0463] Existing technologies do not screen parameters based on their contribution, resulting in a large number of low-impact redundant parameters in the optimization process, leading to massive computational load and low efficiency. This method uses the Sobol algorithm to calculate the first contribution (sound pressure target), second contribution (frequency band target), and comprehensive impact contribution of each parameter / parameter pair. A first preset threshold (0.3) is set to screen out the core influencing objects. Then, related attributes, weight values, and physical characteristic parameters are added to generate a subset of key process parameters. This subset eliminates redundant parameters with a comprehensive contribution ≤ 0.3, focusing on the core optimization objects (accounting for only 30%-50%), reducing subsequent optimization computation by more than 50%, while avoiding interference from low-impact parameters, achieving precise focusing and efficient optimization.

[0464] Traditional optimization methods rely solely on the original parameter value range, neglecting the gain effect of multi-field coupling between light, heat, and sound. This results in parameter values ​​falling outside the optimal performance range, failing to meet metrological requirements of sound pressure level ≥ 0.9 MPa and a frequency band of 15-20 MHz. This application introduces a multi-field coupling gain correction model. Based on the weights, comprehensive contributions, and effective thermal expansion coefficients of key process parameters, it calculates the independent gain coefficient of a single parameter (1.0-1.5) and the joint gain coefficient of strongly correlated parameter pairs (1.2-1.8), expanding the original parameter value range to form a parameter correction set with gain coefficients. This correction set fully exploits the positive gain potential of parameter synergy, making parameter values ​​closer to the optimal performance range of photoacoustic conversion, providing a high-performance parameter foundation for subsequent dual-objective optimization.

[0465] Traditional non-dominated sorting genetic algorithms (NSGA-II) suffer from drawbacks such as poor fitness function adaptability, fixed crossover and mutation probabilities leading to premature convergence, and insufficient solution set diversity. This application makes three improvements to the algorithm: designing a gain coefficient embedded fitness function to quantify the positive contribution of parameter gain to both objectives; employing an adaptive crossover and mutation strategy to dynamically adjust the crossover probability (0.7-0.9) and mutation probability (0.01-0.08) based on population convergence, avoiding premature convergence; and combining Pareto rank and priority weight sorting to preserve a highly diverse population. The improved algorithm generates Pareto optimal parameter solution sets covering three categories of requirements: "sound pressure priority (sound pressure ≥ 1.0 MPa), frequency band priority (frequency band ≥ 4.8 MHz), and equalization optimization (sound pressure ≥ 0.95 MPa + frequency band ≥ 4.5 MHz)," thus solving the problems of traditional solution set homogeneity and poor adaptability.

[0466] Existing technologies focus only on optimization results under ideal conditions, neglecting interference factors in actual operating conditions (such as temperature and energy fluctuations). This leads to performance fluctuations of optimized parameter combinations exceeding the allowable metrological range in complex scenarios. This method systematically sets three typical interference conditions (ambient temperature ±5℃, laser pulse energy ±10%, coating rate ±15%) and simulates the entire process using a multi-field coupling anti-interference test platform. It calculates the comprehensive performance fluctuation (a weighted sum of sound pressure fluctuation and frequency band fluctuation) and sets a second preset threshold (0.08, or 8%) to screen parameter combinations that meet anti-interference requirements. This verification step transforms the ideal optimization results into a practically usable stable solution, ensuring that the optimal parameter combination maintains sound pressure and frequency band performance fluctuations within the allowable metrological accuracy range under complex conditions such as industrial production and laboratory calibration, significantly improving the practical application adaptability of photoacoustic transducers.

[0467] This application also provides an apparatus for optimizing the process parameters of the light-absorbing coating preparation for a photoacoustic transducer, the apparatus comprising:

[0468] The basic data acquisition module is used to acquire the preparation process parameters, structural parameters, excitation parameters, and output sound pressure-frequency band dual target data of the light-absorbing coating of the photoacoustic transducer.

[0469] A parameter association table acquisition module is used to construct a parameter association table based on the preparation process parameters.

[0470] A parameter coupling strength matrix acquisition module, wherein the parameter coupling strength matrix acquisition module is used to acquire the parameter coupling strength matrix;

[0471] A dynamic weight allocation scheme generation module is used to generate a dynamic weight allocation scheme based on the parameter coupling strength matrix.

[0472] The parameter contribution dataset acquisition module is used to substitute the dynamic weight allocation scheme into the sensitivity analysis algorithm, calculate the influence contribution of each parameter and the parameter on the dual targets of output sound pressure and frequency band, and thus obtain the parameter contribution dataset.

[0473] A key process parameter subset acquisition module is used to filter parameters and parameter pairs whose influence contribution is greater than a first preset threshold from the parameter contribution dataset, thereby generating a key process parameter subset.

[0474] A dual-objective optimization model acquisition module, wherein the dual-objective optimization model acquisition module is used to acquire a dual-objective optimization model;

[0475] The Pareto optimal parameter solution set acquisition module is used to solve the bi-objective optimization model based on a subset of key process parameters using a non-dominated sorting genetic algorithm, and obtain a Pareto optimal parameter solution set covering different optimization priorities.

[0476] The optimal combination acquisition module is used to set interference conditions, perform anti-interference tests on the Pareto optimal parameter solution set, and screen out parameter combinations with performance fluctuation less than a second preset threshold. The parameter combinations with output less than the second preset threshold are used as the optimal combination of light-absorbing coating preparation process parameters.

[0477] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for optimizing the process parameters of a light-absorbing coating for a photoacoustic transducer, characterized in that, The optimization method for the light-absorbing coating preparation process parameters of the photoacoustic transducer includes: Step 1: Obtain the fabrication process parameters, structural parameters, excitation parameters, and dual target data of output sound pressure and frequency band for the light-absorbing coating of the photoacoustic transducer; Step 2: Construct a parameter correlation table based on the preparation process parameters; Step 3: Obtain the parameter coupling strength matrix; Step 4: Generate a dynamic weight allocation scheme based on the parameter coupling strength matrix; Step 5: Substitute the dynamic weight allocation scheme into the sensitivity analysis algorithm to calculate the contribution of each parameter and the parameter to the dual targets of output sound pressure and frequency band, thereby obtaining the parameter contribution dataset; Step 6: Filter out parameters and parameter pairs whose influence contribution is greater than the first preset threshold from the parameter contribution dataset, thereby generating a subset of key process parameters; Step 7: Obtain the dual-objective optimization model; Step 8: Based on the subset of key process parameters, use a non-dominated sorting genetic algorithm to solve the bi-objective optimization model and obtain a Pareto optimal parameter solution set covering different optimization priorities; Step 9: Set interference conditions, perform anti-interference tests on the Pareto optimal parameter solution set, and screen out parameter combinations with performance fluctuation less than the second preset threshold. The parameter combinations with output less than the second preset threshold are taken as the optimal combination of light-absorbing coating preparation process parameters.

2. The method for optimizing the process parameters of the photoacoustic transducer light-absorbing coating as described in claim 1, characterized in that, The preparation process parameters include the light absorbance of the coating material, the coating thickness, the curing temperature, the curing time, and the coating rate; The step of constructing a parameter correlation table based on preparation process parameters includes: Step 2.1: Using the Pearson correlation coefficient method, perform pairwise correlation analysis on any two preparation process parameters to calculate the correlation coefficient values ​​between each parameter pair; Step 2.2: Set the correlation coefficient threshold to 0.7, determine parameter pairs with a correlation coefficient value greater than 0.7 as strongly correlated parameter pairs, and determine parameters with a correlation coefficient value less than or equal to 0.7 as uncorrelated parameters, thereby generating a parameter correlation table, which includes the correlation attributes of each parameter and the corresponding correlated parameters.

3. The method for optimizing the process parameters of the photoacoustic transducer light-absorbing coating as described in claim 2, characterized in that, The method for obtaining the parameter coupling strength matrix includes: Step 3.1: Extract the strongly correlated parameter pairs marked in the parameter correlation table; Step 3.2: Obtain the physical property parameters corresponding to each strongly correlated parameter pair; Step 3.3: Based on the theory of thermal expansion, construct a mathematical framework for the coupling strength calculation model. The mathematical framework uses physical property parameters as input variables and coupling strength coefficient as output variables, and introduces a correlation function between the thermal expansion coefficient and the parameter interaction term. Step 3.4: Substitute the physical property parameters corresponding to each strongly correlated parameter into the mathematical framework of the coupling strength calculation model, determine the coefficient constants and constraints in the model, and form the coupling strength calculation model; Step 3.5: Solve the coupling strength calculation model through numerical calculation to obtain the coupling strength coefficients of each strongly correlated parameter pair; Step 3.6: Set the default coupling strength value of the non-associated parameters to 0.

1. According to the classification order of preparation process parameters, structural parameters, and excitation parameters, arrange the coupling strength coefficients of each strongly correlated parameter pair with the default coupling strength values ​​of the non-associated parameters in sequence to construct a parameter coupling strength matrix corresponding to the dimension and the total number of parameters.

4. The method for optimizing the process parameters of the photoacoustic transducer light-absorbing coating as described in claim 3, characterized in that, The dynamic weight allocation scheme generated based on the parameter coupling strength matrix includes: Step 4.1: Extract the coupling strength coefficients corresponding to each parameter and strongly correlated parameter pair in the parameter coupling strength matrix; Step 4.2: Classify the coupling level according to the coupling strength coefficient, which includes strong coupling, medium coupling and weak coupling; Step 4.3: Design weight allocation rules for different coupling levels, and calculate the joint weight of each strongly correlated parameter pair and the independent weight of each uncorrelated parameter according to the weight allocation rules. Step 4.4: Integrate all parameters and the weights of parameter pairs to generate a dynamic weight allocation scheme, which includes the weight attributes and specific weight values ​​of each parameter and parameter pair.

5. The method for optimizing the process parameters of the photoacoustic transducer light-absorbing coating as described in claim 4, characterized in that, The process of substituting the dynamic weight allocation scheme into the sensitivity analysis algorithm to calculate the contribution of each parameter to the dual targets of output sound pressure and frequency band, thereby obtaining the parameter contribution dataset, includes: Step 5.1: Initialize the Sobol algorithm, determine the parameter sampling range, number of iterations, and convergence conditions; Step 5.2: Generate a structured sensitivity analysis input dataset based on the dynamic weight allocation scheme; Step 5.3: Substitute the sensitivity analysis input dataset into the initialized Sobol algorithm, use the dynamic weight value as the correction coefficient for the variance contribution calculation, and solve for each parameter and the first contribution of the parameter to the output sound pressure target and the second contribution of the parameter to the output frequency band target respectively. Step 5.4: Set the dual-objective weighting coefficients, and calculate the comprehensive impact contribution of each parameter and parameter pair based on the dual-objective weighting coefficients; Step 5.5: Integrate the parameter identifiers, first contribution, second contribution, and comprehensive impact contribution of each parameter and parameter pair to generate a structured parameter contribution dataset.

6. The method for optimizing the process parameters of the photoacoustic transducer light-absorbing coating as described in claim 5, characterized in that, The step of filtering parameters and parameter pairs whose influence contribution is greater than a first preset threshold from the parameter contribution dataset to generate a subset of key process parameters includes: Step 6.1: Extract the comprehensive impact contribution and parameter identification information of each parameter and parameter pair in the parameter contribution dataset; Step 6.2: Compare the overall impact contribution of each parameter and parameter pair with the first preset threshold one by one, and select the parameters and parameter pairs whose overall impact contribution is greater than the first preset threshold. Step 6.3: Integrate the selected parameters and parameter pairs, supplement their corresponding correlation attributes, weight values ​​and physical characteristic parameters, and generate a structured subset of key process parameters. The subset includes the correlation priority of each parameter and parameter pair with the output sound pressure-frequency band dual target.

7. The method for optimizing the process parameters of the photoacoustic transducer light-absorbing coating as described in claim 6, characterized in that, After step 6, in which parameters and parameter pairs with influence contributions greater than a first preset threshold are selected from the parameter contribution dataset to generate a subset of key process parameters, the optimization method for the photoacoustic transducer light-absorbing coating preparation process parameters further includes: Obtain a multi-field coupling gain correction model; A subset of key process parameters is input into a multi-field coupled gain correction model to obtain a parameter correction set with gain coefficients. The non-dominated sorting genetic algorithm is used to solve the bi-objective optimization model, yielding a Pareto optimal parameter set covering different optimization priorities, including: Based on the parameter correction set with gain coefficients, a non-dominated sorting genetic algorithm is used to solve the bi-objective optimization model, obtaining a Pareto optimal parameter solution set covering different optimization priorities.

8. The method for optimizing the process parameters of the photoacoustic transducer light-absorbing coating as described in claim 7, characterized in that, Based on the aforementioned subset of key process parameters, a non-dominated sorting genetic algorithm is used to solve the bi-objective optimization model, yielding a Pareto optimal parameter solution set covering different optimization priorities, including: Step 8.1: Initialize the non-dominated sorting genetic algorithm, set the population size to 100-200, the number of iterations to 50-100, the initial crossover probability to 0.7-0.9, the initial mutation probability to 0.01-0.05, and determine the algorithm's convergence condition; Step 8.2: Based on the parameter correction set with gain coefficients and combined with the constraints of the bi-objective optimization model, generate the initial population using real number encoding. Step 8.3: Introduce a fitness function based on gain coefficient, embed the parameter gain coefficient as a weight in the fitness calculation, and calculate the fitness value of each individual in the population; Step 8.4: Based on the results of the fitness quantification, select superior individuals, perform improved non-dominated sorting on the current population, divide Pareto levels through fast non-dominated sorting, retain population diversity by combining crowding degree calculation, and at the same time adopt an adaptive crossover and mutation strategy to dynamically adjust the crossover probability and mutation probability according to the population convergence degree, and output the new generation population after selection, sorting and genetic operations. Step 8.5: Repeat steps 8.3-8.4 for fitness calculation, individual selection, non-dominated sorting, and crossover / mutation operations until the preset number of iterations is reached or the convergence condition is met, and output the final population after iterative convergence. Step 8.6: Select all non-dominated solutions from the final population and classify them according to three priorities: sound pressure priority, frequency band priority, and equalization optimization, to form a Pareto optimal parameter solution set covering different optimization needs.

9. The method for optimizing the process parameters of the photoacoustic transducer light-absorbing coating as described in claim 8, characterized in that, By setting the aforementioned interference conditions, an anti-interference test is performed on the Pareto optimal parameter solution set, and parameter combinations with performance fluctuations less than a second preset threshold are selected. The parameter combinations with outputs less than the second preset threshold are considered as the optimal combination of light-absorbing coating preparation process parameters, including: Step 9.1: Obtain ambient temperature fluctuation conditions, laser pulse energy fluctuation conditions, and coating rate fluctuation conditions; Step 9.2: Obtain the preset multi-field coupling anti-interference test platform, import each parameter combination in the Pareto optimal parameter solution set into the preset multi-field coupling anti-interference test platform, simulate the entire process of light-absorbing coating preparation and photoacoustic conversion, and measure the output sound pressure value and frequency band coverage corresponding to each parameter combination under the interference-free reference state, and record it as the reference performance data. Step 9.3: Apply ambient temperature fluctuation conditions, laser pulse energy fluctuation conditions, and coating rate fluctuation conditions one by one, keeping other parameters constant, measure the actual performance data under each interference condition, and obtain the comprehensive performance fluctuation amount of each parameter combination; Step 9.4: Obtain the overall performance fluctuation of each parameter combination based on the baseline performance data and the actual performance data; Step 9.5: Compare the overall performance fluctuation of each parameter combination with the second threshold, and select the parameter combination that is less than the second threshold as the optimal combination of light-absorbing coating preparation process parameters.

10. An apparatus for optimizing the process parameters of a light-absorbing coating for a photoacoustic transducer, characterized in that, The device for optimizing the process parameters of the photoacoustic transducer light-absorbing coating includes: The basic data acquisition module is used to acquire the preparation process parameters, structural parameters, excitation parameters, and output sound pressure-frequency band dual target data of the light-absorbing coating of the photoacoustic transducer. A parameter association table acquisition module is used to construct a parameter association table based on the preparation process parameters. A parameter coupling strength matrix acquisition module, wherein the parameter coupling strength matrix acquisition module is used to acquire the parameter coupling strength matrix; A dynamic weight allocation scheme generation module is used to generate a dynamic weight allocation scheme based on the parameter coupling strength matrix. The parameter contribution dataset acquisition module is used to substitute the dynamic weight allocation scheme into the sensitivity analysis algorithm, calculate the influence contribution of each parameter and the parameter on the dual targets of output sound pressure and frequency band, and thus obtain the parameter contribution dataset. A key process parameter subset acquisition module is used to filter parameters and parameter pairs whose influence contribution is greater than a first preset threshold from the parameter contribution dataset, thereby generating a key process parameter subset. A dual-objective optimization model acquisition module, wherein the dual-objective optimization model acquisition module is used to acquire a dual-objective optimization model; The Pareto optimal parameter solution set acquisition module is used to solve the bi-objective optimization model based on a subset of key process parameters using a non-dominated sorting genetic algorithm, and obtain a Pareto optimal parameter solution set covering different optimization priorities. The optimal combination acquisition module is used to set interference conditions, perform anti-interference tests on the Pareto optimal parameter solution set, and screen out parameter combinations with performance fluctuation less than a second preset threshold. The parameter combinations with output less than the second preset threshold are used as the optimal combination of light-absorbing coating preparation process parameters.

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